Phytoplankton productivity in relation to light intensity: A simple equation

USGS Publications Warehouse

Peterson, D.H.; Perry, M.J.; Bencala, K.E.; Talbot, M.C.

1987-01-01

A simple exponential equation is used to describe photosynthetic rate as a function of light intensity for a variety of unicellular algae and higher plants where photosynthesis is proportional to (1-e-??1). The parameter ?? (=Ik-1) is derived by a simultaneous curve-fitting method, where I is incident quantum-flux density. The exponential equation is tested against a wide range of data and is found to adequately describe P vs. I curves. The errors associated with photosynthetic parameters are calculated. A simplified statistical model (Poisson) of photon capture provides a biophysical basis for the equation and for its ability to fit a range of light intensities. The exponential equation provides a non-subjective simultaneous curve fitting estimate for photosynthetic efficiency (a) which is less ambiguous than subjective methods: subjective methods assume that a linear region of the P vs. I curve is readily identifiable. Photosynthetic parameters ?? and a are used widely in aquatic studies to define photosynthesis at low quantum flux. These parameters are particularly important in estuarine environments where high suspended-material concentrations and high diffuse-light extinction coefficients are commonly encountered. ?? 1987.

Quasi-Maximum Likelihood Estimation of Structural Equation Models with Multiple Interaction and Quadratic Effects

ERIC Educational Resources Information Center

Klein, Andreas G.; Muthen, Bengt O.

2007-01-01

In this article, a nonlinear structural equation model is introduced and a quasi-maximum likelihood method for simultaneous estimation and testing of multiple nonlinear effects is developed. The focus of the new methodology lies on efficiency, robustness, and computational practicability. Monte-Carlo studies indicate that the method is highly…

Evaluating Simultaneous Integrals

ERIC Educational Resources Information Center

Kwong, Harris

2012-01-01

Many integrals require two successive applications of integration by parts. During the process, another integral of similar type is often invoked. We propose a method which can integrate these two integrals simultaneously. All we need is to solve a linear system of equations.

The method of lines in three dimensional fracture mechanics

NASA Technical Reports Server (NTRS)

Gyekenyesi, J.; Berke, L.

1980-01-01

A review of recent developments in the calculation of design parameters for fracture mechanics by the method of lines (MOL) is presented. Three dimensional elastic and elasto-plastic formulations are examined and results from previous and current research activities are reported. The application of MOL to the appropriate partial differential equations of equilibrium leads to coupled sets of simultaneous ordinary differential equations. Solutions of these equations are obtained by the Peano-Baker and by the recurrance relations methods. The advantages and limitations of both solution methods from the computational standpoint are summarized.

Neural network based online simultaneous policy update algorithm for solving the HJI equation in nonlinear H∞ control.

PubMed

Wu, Huai-Ning; Luo, Biao

2012-12-01

It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newton's method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.

Maximum Likelihood and Restricted Likelihood Solutions in Multiple-Method Studies

PubMed Central

Rukhin, Andrew L.

2011-01-01

A formulation of the problem of combining data from several sources is discussed in terms of random effects models. The unknown measurement precision is assumed not to be the same for all methods. We investigate maximum likelihood solutions in this model. By representing the likelihood equations as simultaneous polynomial equations, the exact form of the Groebner basis for their stationary points is derived when there are two methods. A parametrization of these solutions which allows their comparison is suggested. A numerical method for solving likelihood equations is outlined, and an alternative to the maximum likelihood method, the restricted maximum likelihood, is studied. In the situation when methods variances are considered to be known an upper bound on the between-method variance is obtained. The relationship between likelihood equations and moment-type equations is also discussed. PMID:26989583

Maximum Likelihood and Restricted Likelihood Solutions in Multiple-Method Studies.

PubMed

Rukhin, Andrew L

2011-01-01

A formulation of the problem of combining data from several sources is discussed in terms of random effects models. The unknown measurement precision is assumed not to be the same for all methods. We investigate maximum likelihood solutions in this model. By representing the likelihood equations as simultaneous polynomial equations, the exact form of the Groebner basis for their stationary points is derived when there are two methods. A parametrization of these solutions which allows their comparison is suggested. A numerical method for solving likelihood equations is outlined, and an alternative to the maximum likelihood method, the restricted maximum likelihood, is studied. In the situation when methods variances are considered to be known an upper bound on the between-method variance is obtained. The relationship between likelihood equations and moment-type equations is also discussed.

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.

Similarity-transformed equation-of-motion vibrational coupled-cluster theory.

PubMed

Faucheaux, Jacob A; Nooijen, Marcel; Hirata, So

2018-02-07

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

Similarity-transformed equation-of-motion vibrational coupled-cluster theory

NASA Astrophysics Data System (ADS)

Faucheaux, Jacob A.; Nooijen, Marcel; Hirata, So

2018-02-01

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

Fully coupled simulation of multiple hydraulic fractures to propagate simultaneously from a perforated horizontal wellbore

NASA Astrophysics Data System (ADS)

Zeng, Qinglei; Liu, Zhanli; Wang, Tao; Gao, Yue; Zhuang, Zhuo

2018-02-01

In hydraulic fracturing process in shale rock, multiple fractures perpendicular to a horizontal wellbore are usually driven to propagate simultaneously by the pumping operation. In this paper, a numerical method is developed for the propagation of multiple hydraulic fractures (HFs) by fully coupling the deformation and fracturing of solid formation, fluid flow in fractures, fluid partitioning through a horizontal wellbore and perforation entry loss effect. The extended finite element method (XFEM) is adopted to model arbitrary growth of the fractures. Newton's iteration is proposed to solve these fully coupled nonlinear equations, which is more efficient comparing to the widely adopted fixed-point iteration in the literatures and avoids the need to impose fluid pressure boundary condition when solving flow equations. A secant iterative method based on the stress intensity factor (SIF) is proposed to capture different propagation velocities of multiple fractures. The numerical results are compared with theoretical solutions in literatures to verify the accuracy of the method. The simultaneous propagation of multiple HFs is simulated by the newly proposed algorithm. The coupled influences of propagation regime, stress interaction, wellbore pressure loss and perforation entry loss on simultaneous propagation of multiple HFs are investigated.

Exact dark soliton solutions for a family of N coupled nonlinear Schrödinger equations in optical fiber media.

PubMed

Nakkeeran, K

2001-10-01

We consider a family of N coupled nonlinear Schrödinger equations which govern the simultaneous propagation of N fields in the normal dispersion regime of an optical fiber with various important physical effects. The linear eigenvalue problem associated with the integrable form of all the equations is constructed with the help of the Ablowitz-Kaup-Newell-Segur method. Using the Hirota bilinear method, exact dark soliton solutions are explicitly derived.

Actuation for simultaneous motions and constraining efforts: an open chain example

NASA Astrophysics Data System (ADS)

Perreira, N. Duke

1997-06-01

A brief discussion on systems where simultaneous control of forces and velocities are desirable is given and an example linkage with revolute and prismatic joint is selected for further analysis. The Newton-Euler approach for dynamic system analysis is applied to the example to provide a basis of comparison. Gauge invariant transformations are used to convert the dynamic equations into invariant form suitable for use in a new dynamic system analysis method known as the motion-effort approach. This approach uses constraint elimination techniques based on singular value decompositions to recast the invariant form of dynamic system equations into orthogonal sets of motion and effort equations. Desired motions and constraining efforts are partitioned into ideally obtainable and unobtainable portions which are then used to determine the required actuation. The method is applied to the example system and an analytic estimate to its success is made.

Adjustment technique without explicit formation of normal equations /conjugate gradient method/

NASA Technical Reports Server (NTRS)

Saxena, N. K.

1974-01-01

For a simultaneous adjustment of a large geodetic triangulation system, a semiiterative technique is modified and used successfully. In this semiiterative technique, known as the conjugate gradient (CG) method, original observation equations are used, and thus the explicit formation of normal equations is avoided, 'huge' computer storage space being saved in the case of triangulation systems. This method is suitable even for very poorly conditioned systems where solution is obtained only after more iterations. A detailed study of the CG method for its application to large geodetic triangulation systems was done that also considered constraint equations with observation equations. It was programmed and tested on systems as small as two unknowns and three equations up to those as large as 804 unknowns and 1397 equations. When real data (573 unknowns, 965 equations) from a 1858-km-long triangulation system were used, a solution vector accurate to four decimal places was obtained in 2.96 min after 1171 iterations (i.e., 2.0 times the number of unknowns).

A novel method for simultaneous measurement of doped optical fiber parameters

NASA Astrophysics Data System (ADS)

Karimi, M.; Seraji, F. E.

2010-05-01

Simultaneous measurement technique of evaluating the doped optical fibers (DOF) parameters is a suitable scheme for DOF production industries. In this paper, we introduce a novel technique to characterize simultaneously the main parameters of DOF such as absorption and emission cross-sections (ACS, ECS), background loss coefficient (BLC), and low dopant concentration using the gain equation of DOFs. We used this new method to determine the ACS, ECS, BLC in a standard sample of Al-P-Erbium doped optical fiber. The results have been analyzed and compared with other reports.

Plane elasto-plastic analysis of v-notched plate under bending by boundary integral equation method. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Rzasnicki, W.

1973-01-01

A method of solution is presented, which, when applied to the elasto-plastic analysis of plates having a v-notch on one edge and subjected to pure bending, will produce stress and strain fields in much greater detail than presently available. Application of the boundary integral equation method results in two coupled Fredholm-type integral equations, subject to prescribed boundary conditions. These equations are replaced by a system of simultaneous algebraic equations and solved by a successive approximation method employing Prandtl-Reuss incremental plasticity relations. The method is first applied to number of elasto-static problems and the results compared with available solutions. Good agreement is obtained in all cases. The elasto-plastic analysis provides detailed stress and strain distributions for several cases of plates with various notch angles and notch depths. A strain hardening material is assumed and both plane strain and plane stress conditions are considered.

Grid adaption for hypersonic flow

NASA Technical Reports Server (NTRS)

Abolhassani, Jamshid S.; Tiwari, Surendra N.; Smith, Robert E.

1987-01-01

The methods of grid adaption are reviewed and a method is developed with the capability of adaption to several flow variables. This method is based on a variational approach and is an algebraic method which does not require the solution of partial differential equations. Also the method has been formulated in such a way that there is no need for any matrix inversion. The method is used in conjunction with the calculation of hypersonic flow over a blunt nose body. The equations of motion are the compressible Navier-Stokes equations where all viscous terms are retained. They are solved by the MacCormack time-splitting method. A movie has been produced which shows simultaneously the transient behavior of the solution and the grid adaption.

Dynamic characteristics of a variable-mass flexible missile

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Bankovskis, J.

1970-01-01

The general motion of a variable mass flexible missile with internal flow and aerodynamic forces is considered. The resulting formulation comprises six ordinary differential equations for rigid body motion and three partial differential equations for elastic motion. The simultaneous differential equations are nonlinear and possess time-dependent coefficients. The differential equations are solved by a semi-analytical method leading to a set of purely ordinary differential equations which are then solved numerically. A computer program was developed for the numerical solution and results are presented for a given set of initial conditions.

SPECIATION OF ORGANICS IN WATER

EPA Science Inventory

We describe herein a method for determining constants for simultaneously occurring, site-specific "microequilibria" (as with tautomers) for organics in water. The method is based in part on modeling temperature-variant Raman spectra according to the van't Hoff equation....

Numerical solution of system of boundary value problems using B-spline with free parameter

NASA Astrophysics Data System (ADS)

Gupta, Yogesh

2017-01-01

This paper deals with method of B-spline solution for a system of boundary value problems. The differential equations are useful in various fields of science and engineering. Some interesting real life problems involve more than one unknown function. These result in system of simultaneous differential equations. Such systems have been applied to many problems in mathematics, physics, engineering etc. In present paper, B-spline and B-spline with free parameter methods for the solution of a linear system of second-order boundary value problems are presented. The methods utilize the values of cubic B-spline and its derivatives at nodal points together with the equations of the given system and boundary conditions, ensuing into the linear matrix equation.

Apparatus and method for determining solids circulation rate

DOEpatents

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

2012-02-14

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

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.

Investigation of the Wave Propagation of Vector Modes of Light in a Spherically Symmetric Refractive Index Profile

NASA Astrophysics Data System (ADS)

Pozderac, Preston; Leary, Cody

We investigated the solutions to the Helmholtz equation in the case of a spherically symmetric refractive index using three different methods. The first method involves solving the Helmholtz equation for a step index profile and applying further constraints contained in Maxwell's equations. Utilizing these equations, we can simultaneously solve for the electric and magnetic fields as well as the allowed energies of photons propagating in this system. The second method applies a perturbative correction to these energies, which surfaces when deriving a Helmholtz type equation in a medium with an inhomogeneous refractive index. Applying first order perturbation theory, we examine how the correction term affects the energy of the photon. In the third method, we investigate the effects of the above perturbation upon solutions to the scalar Helmholtz equation, which are separable with respect to its polarization and spatial degrees of freedom. This work provides insights into the vector field structure of a photon guided by a glass microsphere.

Closed-form solution of temperature and heat flux in embedded cooling channels

NASA Astrophysics Data System (ADS)

Griggs, Steven Craig

1997-11-01

An analytical method is discussed for predicting temperature in a layered composite material with embedded cooling channels. The cooling channels are embedded in the material to maintain its temperature at acceptable levels. Problems of this type are encountered in the aerospace industry and include high-temperature or high-heat-flux protection for advanced composite-material skins of high-speed air vehicles; thermal boundary-layer flow control on supersonic transports; or infrared signature suppression on military vehicles. A Green's function solution of the diffusion equation is used to simultaneously predict the global and localized effects of temperature in the material and in the embedded cooling channels. The integral method is used to solve the energy equation with fluid flow to find the solution of temperature and heat flux in the cooling fluid and material simultaneously. This method of calculation preserves the three-dimensional nature of this problem.

A Simultaneous Equation Demand Model for Block Rates

NASA Astrophysics Data System (ADS)

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

1986-01-01

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

Real time quantitative phase microscopy based on single-shot transport of intensity equation (ssTIE) method

NASA Astrophysics Data System (ADS)

Yu, Wei; Tian, Xiaolin; He, Xiaoliang; Song, Xiaojun; Xue, Liang; Liu, Cheng; Wang, Shouyu

2016-08-01

Microscopy based on transport of intensity equation provides quantitative phase distributions which opens another perspective for cellular observations. However, it requires multi-focal image capturing while mechanical and electrical scanning limits its real time capacity in sample detections. Here, in order to break through this restriction, real time quantitative phase microscopy based on single-shot transport of the intensity equation method is proposed. A programmed phase mask is designed to realize simultaneous multi-focal image recording without any scanning; thus, phase distributions can be quantitatively retrieved in real time. It is believed the proposed method can be potentially applied in various biological and medical applications, especially for live cell imaging.

Differential equation based method for accurate approximations in optimization

NASA Technical Reports Server (NTRS)

Pritchard, Jocelyn I.; Adelman, Howard M.

1990-01-01

This paper describes a method to efficiently and accurately approximate the effect of design changes on structural response. The key to this new method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in msot cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacement are used to approximate bending stresses.

Differential equation based method for accurate approximations in optimization

NASA Technical Reports Server (NTRS)

Pritchard, Jocelyn I.; Adelman, Howard M.

1990-01-01

A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses.

Examining the Differences of Linear Systems between Finnish and Taiwanese Textbooks

ERIC Educational Resources Information Center

Yang, Der-Ching; Lin, Yung-Chi

2015-01-01

The purpose of this study was to examine the differences between Finnish and Taiwanese textbooks for grades 7 to 9 on the topic of solving systems of linear equations (simultaneous equations). The specific textbooks examined were TK in Taiwan and FL in Finland. The content analysis method was used to examine (a) the teaching sequence, (b)…

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, Longxiao; Gu, Hanming

2018-03-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor series expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain the P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion doesn't need certain assumptions and can estimate more parameters simultaneously. It has a better applicability. Meanwhile, by using the generalized linear method, the inversion is easily implemented and its calculation cost is small. We use the theoretical model to generate synthetic seismic records to test and analyze the influence of random noise. The results can prove the availability and anti-noise-interference ability of our method. We also apply the inversion to actual field data and prove the feasibility of our method in actual situation.

OPTIMIZATION OF RAMAN SPECTROSCOPY FOR SPECIATION OF ORGANICS IN WATER

EPA Science Inventory

We describe herein a method for determining constants for simultaneously occurring, site-specific "microequilibria" (as with tautomers) for organics in water. The method is based in part on modeling temperature-variant Raman spectra according to the van't Hoff equation. Spectra a...

ELECTRONIC DIGITAL COMPUTER

DOEpatents

Stone, J.J. Jr.; Bettis, E.S.; Mann, E.R.

1957-10-01

The electronic digital computer is designed to solve systems involving a plurality of simultaneous linear equations. The computer can solve a system which converges rather rapidly when using Von Seidel's method of approximation and performs the summations required for solving for the unknown terms by a method of successive approximations.

Motions, efforts and actuations in constrained dynamic systems: a multi-link open-chain example

NASA Astrophysics Data System (ADS)

Duke Perreira, N.

1999-08-01

The effort-motion method, which describes the dynamics of open- and closed-chain topologies of rigid bodies interconnected with revolute and prismatic pairs, is interpreted geometrically. Systems are identified for which the simultaneous control of forces and velocities is desirable, and a representative open-chain system is selected for use in the ensuing analysis. Gauge invariant transformations are used to recast the commonly used kinetic and kinematic equations into a dimensional gauge invariant form. Constraint elimination techniques based on singular value decompositions then recast the invariant equations into orthogonal and reciprocal sets of motion and effort equations written in state variable form. The ideal actuation is found that simultaneously achieves the obtainable portions of the desired constraining efforts and motions. The performance is then evaluated of using the actuation closest to the ideal actuation.

Adaptive Elastic Net for Generalized Methods of Moments.

PubMed

Caner, Mehmet; Zhang, Hao Helen

2014-01-30

Model selection and estimation are crucial parts of econometrics. This paper introduces a new technique that can simultaneously estimate and select the model in generalized method of moments (GMM) context. The GMM is particularly powerful for analyzing complex data sets such as longitudinal and panel data, and it has wide applications in econometrics. This paper extends the least squares based adaptive elastic net estimator of Zou and Zhang (2009) to nonlinear equation systems with endogenous variables. The extension is not trivial and involves a new proof technique due to estimators lack of closed form solutions. Compared to Bridge-GMM of Caner (2009), we allow for the number of parameters to diverge to infinity as well as collinearity among a large number of variables, also the redundant parameters set to zero via a data dependent technique. This method has the oracle property, meaning that we can estimate nonzero parameters with their standard limit and the redundant parameters are dropped from the equations simultaneously. Numerical examples are used to illustrate the performance of the new method.

Robust estimation of partially linear models for longitudinal data with dropouts and measurement error.

PubMed

Qin, Guoyou; Zhang, Jiajia; Zhu, Zhongyi; Fung, Wing

2016-12-20

Outliers, measurement error, and missing data are commonly seen in longitudinal data because of its data collection process. However, no method can address all three of these issues simultaneously. This paper focuses on the robust estimation of partially linear models for longitudinal data with dropouts and measurement error. A new robust estimating equation, simultaneously tackling outliers, measurement error, and missingness, is proposed. The asymptotic properties of the proposed estimator are established under some regularity conditions. The proposed method is easy to implement in practice by utilizing the existing standard generalized estimating equations algorithms. The comprehensive simulation studies show the strength of the proposed method in dealing with longitudinal data with all three features. Finally, the proposed method is applied to data from the Lifestyle Education for Activity and Nutrition study and confirms the effectiveness of the intervention in producing weight loss at month 9. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Optical properties reconstruction using the adjoint method based on the radiative transfer equation

NASA Astrophysics Data System (ADS)

Addoum, Ahmad; Farges, Olivier; Asllanaj, Fatmir

2018-01-01

An efficient algorithm is proposed to reconstruct the spatial distribution of optical properties in heterogeneous media like biological tissues. The light transport through such media is accurately described by the radiative transfer equation in the frequency-domain. The adjoint method is used to efficiently compute the objective function gradient with respect to optical parameters. Numerical tests show that the algorithm is accurate and robust to retrieve simultaneously the absorption μa and scattering μs coefficients for lowly and highly absorbing medium. Moreover, the simultaneous reconstruction of μs and the anisotropy factor g of the Henyey-Greenstein phase function is achieved with a reasonable accuracy. The main novelty in this work is the reconstruction of g which might open the possibility to image this parameter in tissues as an additional contrast agent in optical tomography.

A Model for the Oxidation of Carbon Silicon Carbide Composite Structures

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2004-01-01

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of carbon silicon carbide (C/SiC) composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The numerical method is demonstrated by utilizing the method to model the carbon oxidation and weight loss behavior of C/SiC specimens during thermogravimetric experiments. The numerical method is used to study the physics of carbon oxidation in carbon silicon carbide composites.

Using Excel's Solver Function to Facilitate Reciprocal Service Department Cost Allocations

ERIC Educational Resources Information Center

Leese, Wallace R.

2013-01-01

The reciprocal method of service department cost allocation requires linear equations to be solved simultaneously. These computations are often so complex as to cause the abandonment of the reciprocal method in favor of the less sophisticated and theoretically incorrect direct or step-down methods. This article illustrates how Excel's Solver…

Using Excel's Matrix Operations to Facilitate Reciprocal Cost Allocations

ERIC Educational Resources Information Center

Leese, Wallace R.; Kizirian, Tim

2009-01-01

The reciprocal method of service department cost allocation requires linear equations to be solved simultaneously. These computations are often so complex as to cause the abandonment of the reciprocal method in favor of the less sophisticated direct or step-down methods. Here is a short example demonstrating how Excel's sometimes unknown matrix…

Duality Quantum Simulation of the Yang-Baxter Equation

NASA Astrophysics Data System (ADS)

Zheng, Chao; Wei, Shijie

2018-04-01

The Yang-Baxter equation has become a significant theoretical tool in a variety of areas of physics. It is desirable to investigate the quantum simulation of the Yang-Baxter equation itself, exploring the connections between quantum integrability and quantum information processing, in which the unity of both the Yang-Baxter equation system and its quantum entanglement should be kept as a whole. In this work, we propose a duality quantum simulation algorithm of the Yang-Baxter equation, which contains the Yang-Baxter system and an ancillary qubit. Contrasting to conventional methods in which the two hand sides of the equation are simulated separately, they are simulated simultaneously in this proposal. Consequently, it opens up a way to further investigate entanglements in a Yang-Baxter equation.

Duality Quantum Simulation of the Yang-Baxter Equation

NASA Astrophysics Data System (ADS)

Zheng, Chao; Wei, Shijie

2018-07-01

The Yang-Baxter equation has become a significant theoretical tool in a variety of areas of physics. It is desirable to investigate the quantum simulation of the Yang-Baxter equation itself, exploring the connections between quantum integrability and quantum information processing, in which the unity of both the Yang-Baxter equation system and its quantum entanglement should be kept as a whole. In this work, we propose a duality quantum simulation algorithm of the Yang-Baxter equation, which contains the Yang-Baxter system and an ancillary qubit. Contrasting to conventional methods in which the two hand sides of the equation are simulated separately, they are simulated simultaneously in this proposal. Consequently, it opens up a way to further investigate entanglements in a Yang-Baxter equation.

Strong coupling in electromechanical computation

NASA Astrophysics Data System (ADS)

Füzi, János

2000-06-01

A method is presented to carry out simultaneously electromagnetic field and force computation, electrical circuit analysis and mechanical computation to simulate the dynamic operation of electromagnetic actuators. The equation system is solved by a predictor-corrector scheme containing a Powell error minimization algorithm which ensures that every differential equation (coil current, field strength rate, flux rate, speed of the keeper) is fulfilled within the same time step.

Simultaneous spectrophotometric determination of paracetamol and salicylamide in human serum and pharmaceutical formulations by a differential kinetic method.

PubMed

Zarei, Ali Reza; Afkhami, Abbas; Sarlak, Nahid

2005-01-01

A rapid, simple, and sensitive differential kinetic method is presented for the determinations of acetaminophen (also known as paracetamol) and salicylamide. The method is based on their oxidation reaction by Fe3+ ion in the presence of 1, 10-phenanthroline as indicator. The reactions can be monitored spectrophotometrically by measuring the increase in the absorbance of the solution at 510 nm. Two times were selected one in which only paracetamol is oxidized by Fe3+ ion and the other in which both drugs are oxidized by Fe3+ ion. The data were evaluated by the proportional equations method. The method allowed the simultaneous determination of paracetamol and salicylamide at concentrations between 0.5-20 and 1-40 microg/mL with relative standard deviations of 3.47 and 2.58%, respectively. The method was applied to the simultaneous determination of paracetamol and salicylamide in human serum and pharmaceutical formulations.

Propagation characteristics of two-color laser pulses in homogeneous plasma

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

Hemlata,; Saroch, Akanksha; Jha, Pallavi

2015-11-15

An analytical and numerical study of the evolution of two-color, sinusoidal laser pulses in cold, underdense, and homogeneous plasma has been presented. The wave equations for the radiation fields driven by linear as well as nonlinear contributions due to the two-color laser pulses have been set up. A variational technique is used to obtain the simultaneous equations describing the evolution of the laser spot size, pulse length, and chirp parameter. Numerical methods are used to graphically analyze the simultaneous evolution of these parameters due to the combined effect of the two-color laser pulses. Further, the pulse parameters are compared withmore » those obtained for a single laser pulse. Significant focusing, compression, and enhanced positive chirp is obtained due to the combined effect of simultaneously propagating two-color pulses as compared to a single pulse propagating in plasma.« less

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.

The Schrodinger Eigenvalue March

ERIC Educational Resources Information Center

Tannous, C.; Langlois, J.

2011-01-01

A simple numerical method for the determination of Schrodinger equation eigenvalues is introduced. It is based on a marching process that starts from an arbitrary point, proceeds in two opposite directions simultaneously and stops after a tolerance criterion is met. The method is applied to solving several 1D potential problems including symmetric…

Unified method to integrate and blend several, potentially related, sources of information for genetic evaluation.

PubMed

Vandenplas, Jérémie; Colinet, Frederic G; Gengler, Nicolas

2014-09-30

A condition to predict unbiased estimated breeding values by best linear unbiased prediction is to use simultaneously all available data. However, this condition is not often fully met. For example, in dairy cattle, internal (i.e. local) populations lead to evaluations based only on internal records while widely used foreign sires have been selected using internally unavailable external records. In such cases, internal genetic evaluations may be less accurate and biased. Because external records are unavailable, methods were developed to combine external information that summarizes these records, i.e. external estimated breeding values and associated reliabilities, with internal records to improve accuracy of internal genetic evaluations. Two issues of these methods concern double-counting of contributions due to relationships and due to records. These issues could be worse if external information came from several evaluations, at least partially based on the same records, and combined into a single internal evaluation. Based on a Bayesian approach, the aim of this research was to develop a unified method to integrate and blend simultaneously several sources of information into an internal genetic evaluation by avoiding double-counting of contributions due to relationships and due to records. This research resulted in equations that integrate and blend simultaneously several sources of information and avoid double-counting of contributions due to relationships and due to records. The performance of the developed equations was evaluated using simulated and real datasets. The results showed that the developed equations integrated and blended several sources of information well into a genetic evaluation. The developed equations also avoided double-counting of contributions due to relationships and due to records. Furthermore, because all available external sources of information were correctly propagated, relatives of external animals benefited from the integrated information and, therefore, more reliable estimated breeding values were obtained. The proposed unified method integrated and blended several sources of information well into a genetic evaluation by avoiding double-counting of contributions due to relationships and due to records. The unified method can also be extended to other types of situations such as single-step genomic or multi-trait evaluations, combining information across different traits.

Prestack density inversion using the Fatti equation constrained by the P- and S-wave impedance and density

NASA Astrophysics Data System (ADS)

Liang, Li-Feng; Zhang, Hong-Bing; Dan, Zhi-Wei; Xu, Zi-Qiang; Liu, Xiu-Juan; Cao, Cheng-Hao

2017-03-01

Simultaneous prestack inversion is based on the modified Fatti equation and uses the ratio of the P- and S-wave velocity as constraints. We use the relation of P-wave impedance and density (PID) and S-wave impedance and density (SID) to replace the constant Vp/Vs constraint, and we propose the improved constrained Fatti equation to overcome the effect of P-wave impedance on density. We compare the sensitivity of both methods using numerical simulations and conclude that the density inversion sensitivity improves when using the proposed method. In addition, the random conjugate-gradient method is used in the inversion because it is fast and produces global solutions. The use of synthetic and field data suggests that the proposed inversion method is effective in conventional and nonconventional lithologies.

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, L.; Gu, H.

2017-12-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion has a better applicability. It doesn't need some assumptions and can estimate more parameters simultaneously. Meanwhile, by using the generalized linear method, the inversion is easily realized and its calculation amount is small. We use the Marmousi model to generate synthetic seismic records to test and analyze the influence of random noise. Without noise, all estimation results are relatively accurate. With the increase of noise, P-wave velocity change and oil saturation change are stable and less affected by noise. S-wave velocity change is most affected by noise. Finally we use the actual field data of time-lapse seismic prospecting to process and the results can prove the availability and feasibility of our method in actual situation.

Numerical Modeling of Saturated Boiling in a Heated Tube

NASA Technical Reports Server (NTRS)

Majumdar, Alok; LeClair, Andre; Hartwig, Jason

2017-01-01

This paper describes a mathematical formulation and numerical solution of boiling in a heated tube. The mathematical formulation involves a discretization of the tube into a flow network consisting of fluid nodes and branches and a thermal network consisting of solid nodes and conductors. In the fluid network, the mass, momentum and energy conservation equations are solved and in the thermal network, the energy conservation equation of solids is solved. A pressure-based, finite-volume formulation has been used to solve the equations in the fluid network. The system of equations is solved by a hybrid numerical scheme which solves the mass and momentum conservation equations by a simultaneous Newton-Raphson method and the energy conservation equation by a successive substitution method. The fluid network and thermal network are coupled through heat transfer between the solid and fluid nodes which is computed by Chen's correlation of saturated boiling heat transfer. The computer model is developed using the Generalized Fluid System Simulation Program and the numerical predictions are compared with test data.

A convex penalty for switching control of partial differential equations

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

Clason, Christian; Rund, Armin; Kunisch, Karl

2016-01-19

A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. In conclusion, the efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.

Aerothermodynamic shape optimization of hypersonic blunt bodies

NASA Astrophysics Data System (ADS)

Eyi, Sinan; Yumuşak, Mine

2015-07-01

The aim of this study is to develop a reliable and efficient design tool that can be used in hypersonic flows. The flow analysis is based on the axisymmetric Euler/Navier-Stokes and finite-rate chemical reaction equations. The equations are coupled simultaneously and solved implicitly using Newton's method. The Jacobian matrix is evaluated analytically. A gradient-based numerical optimization is used. The adjoint method is utilized for sensitivity calculations. The objective of the design is to generate a hypersonic blunt geometry that produces the minimum drag with low aerodynamic heating. Bezier curves are used for geometry parameterization. The performances of the design optimization method are demonstrated for different hypersonic flow conditions.

An improved method for nonlinear parameter estimation: a case study of the Rössler model

NASA Astrophysics Data System (ADS)

He, Wen-Ping; Wang, Liu; Jiang, Yun-Di; Wan, Shi-Quan

2016-08-01

Parameter estimation is an important research topic in nonlinear dynamics. Based on the evolutionary algorithm (EA), Wang et al. (2014) present a new scheme for nonlinear parameter estimation and numerical tests indicate that the estimation precision is satisfactory. However, the convergence rate of the EA is relatively slow when multiple unknown parameters in a multidimensional dynamical system are estimated simultaneously. To solve this problem, an improved method for parameter estimation of nonlinear dynamical equations is provided in the present paper. The main idea of the improved scheme is to use all of the known time series for all of the components in some dynamical equations to estimate the parameters in single component one by one, instead of estimating all of the parameters in all of the components simultaneously. Thus, we can estimate all of the parameters stage by stage. The performance of the improved method was tested using a classic chaotic system—Rössler model. The numerical tests show that the amended parameter estimation scheme can greatly improve the searching efficiency and that there is a significant increase in the convergence rate of the EA, particularly for multiparameter estimation in multidimensional dynamical equations. Moreover, the results indicate that the accuracy of parameter estimation and the CPU time consumed by the presented method have no obvious dependence on the sample size.

Computationally efficient finite-difference modal method for the solution of Maxwell's equations.

PubMed

Semenikhin, Igor; Zanuccoli, Mauro

2013-12-01

In this work, a new implementation of the finite-difference (FD) modal method (FDMM) based on an iterative approach to calculate the eigenvalues and corresponding eigenfunctions of the Helmholtz equation is presented. Two relevant enhancements that significantly increase the speed and accuracy of the method are introduced. First of all, the solution of the complete eigenvalue problem is avoided in favor of finding only the meaningful part of eigenmodes by using iterative methods. Second, a multigrid algorithm and Richardson extrapolation are implemented. Simultaneous use of these techniques leads to an enhancement in terms of accuracy, which allows a simple method such as the FDMM with a typical three-point difference scheme to be significantly competitive with an analytical modal method.

A simplified analytic form for generation of axisymmetric plasma boundaries

DOE PAGES

Luce, Timothy C.

2017-02-23

An improved method has been formulated for generating analytic boundary shapes as input for axisymmetric MHD equilibria. This method uses the family of superellipses as the basis function, as previously introduced. The improvements are a simplified notation, reduction of the number of simultaneous nonlinear equations to be solved, and the realization that not all combinations of input parameters admit a solution to the nonlinear constraint equations. The method tests for the existence of a self-consistent solution and, when no solution exists, it uses a deterministic method to find a nearby solution. As a result, examples of generation of boundaries, includingmore » tests with an equilibrium solver, are given.« less

A simplified analytic form for generation of axisymmetric plasma boundaries

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

Luce, Timothy C.

An improved method has been formulated for generating analytic boundary shapes as input for axisymmetric MHD equilibria. This method uses the family of superellipses as the basis function, as previously introduced. The improvements are a simplified notation, reduction of the number of simultaneous nonlinear equations to be solved, and the realization that not all combinations of input parameters admit a solution to the nonlinear constraint equations. The method tests for the existence of a self-consistent solution and, when no solution exists, it uses a deterministic method to find a nearby solution. As a result, examples of generation of boundaries, includingmore » tests with an equilibrium solver, are given.« less

Method of fan sound mode structure determination

NASA Technical Reports Server (NTRS)

Pickett, G. F.; Sofrin, T. G.; Wells, R. W.

1977-01-01

A method for the determination of fan sound mode structure in the Inlet of turbofan engines using in-duct acoustic pressure measurements is presented. The method is based on the simultaneous solution of a set of equations whose unknowns are modal amplitude and phase. A computer program for the solution of the equation set was developed. An additional computer program was developed which calculates microphone locations the use of which results in an equation set that does not give rise to numerical instabilities. In addition to the development of a method for determination of coherent modal structure, experimental and analytical approaches are developed for the determination of the amplitude frequency spectrum of randomly generated sound models for use in narrow annulus ducts. Two approaches are defined: one based on the use of cross-spectral techniques and the other based on the use of an array of microphones.

Recursive Deadbeat Controller Design

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Phan, Minh Q.

1997-01-01

This paper presents a recursive algorithm for a deadbeat predictive controller design. The method combines together the concepts of system identification and deadbeat controller designs. It starts with the multi-step output prediction equation and derives the control force in terms of past input and output time histories. The formulation thus derived satisfies simultaneously system identification and deadbeat controller design requirements. As soon as the coefficient matrices are identified satisfying the output prediction equation, no further work is required to compute the deadbeat control gain matrices. The method can be implemented recursively just as any typical recursive system identification techniques.

A network thermodynamic method for numerical solution of the Nernst-Planck and Poisson equation system with application to ionic transport through membranes.

PubMed

Horno, J; González-Caballero, F; González-Fernández, C F

1990-01-01

Simple techniques of network thermodynamics are used to obtain the numerical solution of the Nernst-Planck and Poisson equation system. A network model for a particular physical situation, namely ionic transport through a thin membrane with simultaneous diffusion, convection and electric current, is proposed. Concentration and electric field profiles across the membrane, as well as diffusion potential, have been simulated using the electric circuit simulation program, SPICE. The method is quite general and extremely efficient, permitting treatments of multi-ion systems whatever the boundary and experimental conditions may be.

A recursive approach to the equations of motion for the maneuvering and control of flexible multi-body systems

NASA Technical Reports Server (NTRS)

Kwak, Moon K.; Meirovitch, Leonard

1991-01-01

Interest lies in a mathematical formulation capable of accommodating the problem of maneuvering a space structure consisting of a chain of articulated flexible substructures. Simultaneously, any perturbations from the 'rigid body' maneuvering and any elastic vibration must be suppressed. The equations of motion for flexible bodies undergoing rigid body motions and elastic vibrations can be obtained conveniently by means of Lagrange's equations in terms of quasi-coordinates. The advantage of this approach is that it yields equations in terms of body axes, which are the same axes that are used to express the control forces and torques. The equations of motion are nonlinear hybrid differential quations. The partial differential equations can be discretized (in space) by means of the finite element method or the classical Rayleigh-Ritz method. The result is a set of nonlinear ordinary differential equations of high order. The nonlinearity can be traced to the rigid body motions and the high order to the elastic vibration. Elastic motions tend to be small when compared with rigid body motions.

Parallelized implicit propagators for the finite-difference Schrödinger equation

NASA Astrophysics Data System (ADS)

Parker, Jonathan; Taylor, K. T.

1995-08-01

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

Second-order variational equations for N-body simulations

NASA Astrophysics Data System (ADS)

Rein, Hanno; Tamayo, Daniel

2016-07-01

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

Development and validation of simple spectrophotometric and chemometric methods for simultaneous determination of empagliflozin and metformin: Applied to recently approved pharmaceutical formulation

NASA Astrophysics Data System (ADS)

Ayoub, Bassam M.

2016-11-01

New univariate spectrophotometric method and multivariate chemometric approach were developed and compared for simultaneous determination of empagliflozin and metformin manipulating their zero order absorption spectra with application on their pharmaceutical preparation. Sample enrichment technique was used to increase concentration of empagliflozin after extraction from tablets to allow its simultaneous determination with metformin without prior separation. Validation parameters according to ICH guidelines were satisfactory over the concentration range of 2-12 μg mL- 1 for both drugs using simultaneous equation with LOD values equal to 0.20 μg mL- 1 and 0.19 μg mL- 1, LOQ values equal to 0.59 μg mL- 1 and 0.58 μg mL- 1 for empagliflozin and metformin, respectively. While the optimum results for the chemometric approach using partial least squares method (PLS-2) were obtained using concentration range of 2-10 μg mL- 1. The optimized validated methods are suitable for quality control laboratories enable fast and economic determination of the recently approved pharmaceutical combination Synjardy® tablets.

A probabilistic approach to radiative energy loss calculations for optically thick atmospheres - Hydrogen lines and continua

NASA Technical Reports Server (NTRS)

Canfield, R. C.; Ricchiazzi, P. J.

1980-01-01

An approximate probabilistic radiative transfer equation and the statistical equilibrium equations are simultaneously solved for a model hydrogen atom consisting of three bound levels and ionization continuum. The transfer equation for L-alpha, L-beta, H-alpha, and the Lyman continuum is explicitly solved assuming complete redistribution. The accuracy of this approach is tested by comparing source functions and radiative loss rates to values obtained with a method that solves the exact transfer equation. Two recent model solar-flare chromospheres are used for this test. It is shown that for the test atmospheres the probabilistic method gives values of the radiative loss rate that are characteristically good to a factor of 2. The advantage of this probabilistic approach is that it retains a description of the dominant physical processes of radiative transfer in the complete redistribution case, yet it achieves a major reduction in computational requirements.

Multiple Frequency Contrast Source Inversion Method for Vertical Electromagnetic Profiling: 2D Simulation Results and Analyses

NASA Astrophysics Data System (ADS)

Li, Jinghe; Song, Linping; Liu, Qing Huo

2016-02-01

A simultaneous multiple frequency contrast source inversion (CSI) method is applied to reconstructing hydrocarbon reservoir targets in a complex multilayered medium in two dimensions. It simulates the effects of a salt dome sedimentary formation in the context of reservoir monitoring. In this method, the stabilized biconjugate-gradient fast Fourier transform (BCGS-FFT) algorithm is applied as a fast solver for the 2D volume integral equation for the forward computation. The inversion technique with CSI combines the efficient FFT algorithm to speed up the matrix-vector multiplication and the stable convergence of the simultaneous multiple frequency CSI in the iteration process. As a result, this method is capable of making quantitative conductivity image reconstruction effectively for large-scale electromagnetic oil exploration problems, including the vertical electromagnetic profiling (VEP) survey investigated here. A number of numerical examples have been demonstrated to validate the effectiveness and capacity of the simultaneous multiple frequency CSI method for a limited array view in VEP.

Two different spectrofluorimetric methods for simultaneous determination of gemfibrozil and rosiglitazone in human plasma.

PubMed

El-Din, Mohie M K Sharaf; Attia, Khalid A M; Nassar, Mohamed W I; Kaddah, Mohamed M Y

2010-10-15

Two accurate, reliable, and highly sensitive spectrofluorimetric methods were developed for simultaneous determination of binary mixture gemfibrozil and rosiglitazone in human plasma without prior separation steps. The first method is based on synchronous fluorescence spectrometry using double scans. At Δλ=27nm, gemfibrozil yields detectable signal that is independent of the presence of rosiglitazone. Similarly, at Δλ=120nm the signal of rosiglitazone is not influenced by the presence of gemfibrozil. Signals at two wavelengths, 301 (Δλ=27nm) and 368nm (Δλ=120nm) vary linearly with gemfibrozil and rosiglitazone concentrations over the range 100-700ngmL(-1) (for gemfibrozil) and 20-140ngmL(-1) (for rosiglitazone), respectively. The limits of detection (LOD) were 2.3 and 2.72ngmL(-1) for gemfibrozil and rosiglitazone, respectively. The second method is based on the technique of simultaneous equations (Vierodt's method), in which 258nm was selected as the excitation wavelength. Two equations are constructed based on the fact that at ( λ(EM)₂=302 nm of gemfibrozil) and (λ(EM)₂=369 nm of rosiglitazone) the fluorescence of the mixture is the sum of the individual fluorescence of gemfibrozil and rosiglitazone. The limits of detection (LOD) were 28.1 and 23.63ngmL(-1) for gemfibrozil and rosiglitazone, respectively. The proposed methods were successfully applied for the determination of the two compounds in synthetic mixtures and in human plasma with a good recovery. Copyright © 2010 Elsevier B.V. All rights reserved.

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

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

The Schrödinger–Langevin equation with linear dissipation is integrated by propagating an ensemble of Bohmian trajectories for the ground state of quantum systems. Substituting the wave function expressed in terms of the complex action into the Schrödinger–Langevin equation yields the complex quantum Hamilton–Jacobi equation with linear dissipation. We transform this equation into the arbitrary Lagrangian–Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation is simultaneously integrated with the trajectory guidance equation. Then, the computational method is applied to the harmonic oscillator, the double well potential, and the ground vibrational state of methyl iodide.more » The excellent agreement between the computational and the exact results for the ground state energies and wave functions shows that this study provides a synthetic trajectory approach to the ground state of quantum systems.« less

The thermodynamic properties of oxygen and nitrogen. Part 1: Thermodynamic properties of nitrogen from 115 R to 3500 R with pressures to 150000 psia

NASA Technical Reports Server (NTRS)

Stewart, R. B.; Jacobsen, R. T.; Myers, A. F.

1972-01-01

An equation of state is presented for liquid and gaseous nitrogen for temperatures from 115 R to 3500 R and pressures to 150,000 psia. All of the pressure-density-temperature data available from the published literature have been reviewed, and appropriate corrections have been identified and applied to bring experimental temperatures into accord with the International Practical Temperature Scale of 1968. Comparisons of property values calculated from the equation of state to measured values are included to illustrate the accuracy of the equation in representing the data. The coefficients of the equation of state were determined by a weighted least squares fit to selected published data and, simultaneously, to constant volume data determined by corresponding states analysis from oxygen data, and to data which define the phase equilibrium criteria for the saturated liquid and saturated vapor. The methods of weighting the various data for simultaneous fitting are presented and discussed. The equation of state is estimated to be accurate to within 0.5 percent in the liquid region, to within 0.1 percent for supercritical isotherms up to 15,000 psia, and to within 0.3 percent from 15,000 to 150,000 psia.

A note on the relations between thermodynamics, energy definitions and Friedmann equations

NASA Astrophysics Data System (ADS)

Moradpour, H.; Nunes, Rafael C.; Abreu, Everton M. C.; Neto, Jorge Ananias

2017-04-01

We investigate the relation between the Friedmann and thermodynamic pressure equations, through solving the Friedmann and thermodynamic pressure equations simultaneously. Our investigation shows that a perfect fluid, as a suitable solution for the Friedmann equations leading to the standard modeling of the universe expansion history, cannot simultaneously satisfy the thermodynamic pressure equation and those of Friedmann. Moreover, we consider various energy definitions, such as the Komar mass, and solve the Friedmann and thermodynamic pressure equations simultaneously to get some models for dark energy fluids. The cosmological consequences of obtained solutions are also addressed. Our results indicate that some of obtained solutions may unify the dominated fluid in both the primary inflationary and current accelerating eras into one model. In addition, by taking into account a cosmic fluid of a known equation of state (EoS), and combining it with the Friedmann and thermodynamic pressure equations, we obtain the corresponding energy of these cosmic fluids and face their limitations. Finally, we point out the cosmological features of this cosmic fluid and also study its observational constraints.

Scalable Parallel Computation for Extended MHD Modeling of Fusion Plasmas

NASA Astrophysics Data System (ADS)

Glasser, Alan H.

2008-11-01

Parallel solution of a linear system is scalable if simultaneously doubling the number of dependent variables and the number of processors results in little or no increase in the computation time to solution. Two approaches have this property for parabolic systems: multigrid and domain decomposition. Since extended MHD is primarily a hyperbolic rather than a parabolic system, additional steps must be taken to parabolize the linear system to be solved by such a method. Such physics-based preconditioning (PBP) methods have been pioneered by Chac'on, using finite volumes for spatial discretization, multigrid for solution of the preconditioning equations, and matrix-free Newton-Krylov methods for the accurate solution of the full nonlinear preconditioned equations. The work described here is an extension of these methods using high-order spectral element methods and FETI-DP domain decomposition. Application of PBP to a flux-source representation of the physics equations is discussed. The resulting scalability will be demonstrated for simple wave and for ideal and Hall MHD waves.

Numerical models analysis of energy conversion process in air-breathing laser propulsion

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

Hong Yanji; Song Junling; Cui Cunyan

Energy source was considered as a key essential in this paper to describe energy conversion process in air-breathing laser propulsion. Some secondary factors were ignored when three independent modules, ray transmission module, energy source term module and fluid dynamic module, were established by simultaneous laser radiation transportation equation and fluid mechanics equation. The incidence laser beam was simulated based on ray tracing method. The calculated results were in good agreement with those of theoretical analysis and experiments.

Modeling of flow systems for implementation under KATE

NASA Technical Reports Server (NTRS)

Whitlow, Jonathan E.

1990-01-01

The modeling of flow systems is a task currently being investigated at Kennedy Space Center in parallel with the development of the KATE artificial intelligence system used for monitoring diagnosis and control. Various aspects of the modeling issues are focussed on with particular emphasis on a water system scheduled for demonstration within the KATE environment in September of this year. LISP procedures were written to solve the continuity equations for three internal pressure nodes using Newton's method for simultaneous nonlinear equations.

Different Spectrophotometric Methods for Simultaneous Determination of Trelagliptin and Its Acid Degradation Product

PubMed Central

Hassan, Mostafa A.; Zaghary, Wafaa A.

2018-01-01

New spectrophotometric and chemometric methods were carried out for the simultaneous assay of trelagliptin (TRG) and its acid degradation product (TAD) and applied successfully as a stability indicating assay to recently approved Zafatek® tablets. TAD was monitored using TLC to ensure complete degradation. Furthermore, HPLC was used to confirm dealing with one major acid degradation product. The proposed methods were developed by manipulating zero-order, first-derivative, and ratio spectra of TRG and TAD using simultaneous equation, first-derivative, and mean-centering methods, respectively. Using Spectra Manager II and Minitab v.14 software, the absorbance at 274 nm–260.4 nm, amplitudes at 260.4 nm–274.0 nm, and mean-centered values at 287.6 nm–257.2 nm were measured against methanol as a blank for TRG and TAD, respectively. Linearity and the other validation parameters were acceptable at concentration ranges of 5–50 μg/mL and 2.5–25 μg/mL for TRG and TAD, respectively. Using one-way analysis of variance (ANOVA), the optimized methods were compared and proved to be accurate for the simultaneous assay of TRG and TAD. PMID:29629213

Different Spectrophotometric Methods for Simultaneous Determination of Trelagliptin and Its Acid Degradation Product.

PubMed

Mowaka, Shereen; Ayoub, Bassam M; Hassan, Mostafa A; Zaghary, Wafaa A

2018-01-01

New spectrophotometric and chemometric methods were carried out for the simultaneous assay of trelagliptin (TRG) and its acid degradation product (TAD) and applied successfully as a stability indicating assay to recently approved Zafatek® tablets. TAD was monitored using TLC to ensure complete degradation. Furthermore, HPLC was used to confirm dealing with one major acid degradation product. The proposed methods were developed by manipulating zero-order, first-derivative, and ratio spectra of TRG and TAD using simultaneous equation, first-derivative, and mean-centering methods, respectively. Using Spectra Manager II and Minitab v.14 software, the absorbance at 274 nm-260.4 nm, amplitudes at 260.4 nm-274.0 nm, and mean-centered values at 287.6 nm-257.2 nm were measured against methanol as a blank for TRG and TAD, respectively. Linearity and the other validation parameters were acceptable at concentration ranges of 5-50  μ g/mL and 2.5-25  μ g/mL for TRG and TAD, respectively. Using one-way analysis of variance (ANOVA), the optimized methods were compared and proved to be accurate for the simultaneous assay of TRG and TAD.

Analysis of rice policy based on presidential instruction on household food security: simultaneous equation model

NASA Astrophysics Data System (ADS)

Sembiring, S. A.

2018-02-01

The objective of this research is to analyze the impacts of rice policy on the household food security. The research used cross section data, were collected from 74 respondent as determined by purposive sampling in Sei Rejo villages, the Sub District of Sei Rampah, Serdang Bedagai District in the Province of North Sumatera. Rice policy model specification uses the simultaneous equations consisting of 6 structural equations and 6 identity equations which was estimated using Two Stages Least Squares (2SLS) method. The results show that the effectiveness of government purchase price of dried harvest paddy gave a positive impact on paddy planted area and lead to an increase paddy production and an increase of the rice production gave a positive impact on household rice availability and household rice surplus, and the increase of household rice surplus gave the quantity of Raskin decrease, whereas the increase of fertilizers gave a negative impact on paddy planted area and lead to decrease paddy production and to decrease in rice production was followed by an decrease in household rice availability and household rice surplus, and the decrease of household rice surplus gave the quantity of Raskin increase.

Novel spectrophotometric methods for simultaneous determination of timolol and dorzolamide in their binary mixture.

PubMed

Lotfy, Hayam Mahmoud; Hegazy, Maha A; Rezk, Mamdouh R; Omran, Yasmin Rostom

2014-05-21

Two smart and novel spectrophotometric methods namely; absorbance subtraction (AS) and amplitude modulation (AM) were developed and validated for the determination of a binary mixture of timolol maleate (TIM) and dorzolamide hydrochloride (DOR) in presence of benzalkonium chloride without prior separation, using unified regression equation. Additionally, simple, specific, accurate and precise spectrophotometric methods manipulating ratio spectra were developed and validated for simultaneous determination of the binary mixture namely; simultaneous ratio subtraction (SRS), ratio difference (RD), ratio subtraction (RS) coupled with extended ratio subtraction (EXRS), constant multiplication method (CM) and mean centering of ratio spectra (MCR). The proposed spectrophotometric procedures do not require any separation steps. Accuracy, precision and linearity ranges of the proposed methods were determined and the specificity was assessed by analyzing synthetic mixtures of both drugs. They were applied to their pharmaceutical formulation and the results obtained were statistically compared to that of a reported spectrophotometric method. The statistical comparison showed that there is no significant difference between the proposed methods and the reported one regarding both accuracy and precision. Copyright © 2014 Elsevier B.V. All rights reserved.

A nonperturbative light-front coupled-cluster method

NASA Astrophysics Data System (ADS)

Hiller, J. R.

2012-10-01

The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from standard coupled-cluster theory, to obtain form factors and other observables.

SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER

DOEpatents

Collier, D.M.; Meeks, L.A.; Palmer, J.P.

1960-05-10

A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.

Wave multiple scattering by a finite number of unclosed circular cylinders

NASA Technical Reports Server (NTRS)

Veliyev, E. I.; Veremey, V. V.

1984-01-01

The boundary value problem of plane H-polarized electromagnetic wave multiple scattering by a finite number of unclosed circular cylinders is solved. The solution is obtained by two different methods: the method of successive scattering and the method of partial matrix inversion for simultaneous dual equations. The advantages of the successive scattering method are shown. Computer calculations of the suface currents and the total cross section are presented for the structure of two screens.

Simultaneous stochastic inversion for geomagnetic main field and secular variation. I - A large-scale inverse problem

NASA Technical Reports Server (NTRS)

Bloxham, Jeremy

1987-01-01

The method of stochastic inversion is extended to the simultaneous inversion of both main field and secular variation. In the present method, the time dependency is represented by an expansion in Legendre polynomials, resulting in a simple diagonal form for the a priori covariance matrix. The efficient preconditioned Broyden-Fletcher-Goldfarb-Shanno algorithm is used to solve the large system of equations resulting from expansion of the field spatially to spherical harmonic degree 14 and temporally to degree 8. Application of the method to observatory data spanning the 1900-1980 period results in a data fit of better than 30 nT, while providing temporally and spatially smoothly varying models of the magnetic field at the core-mantle boundary.

Quantitative estimation of itopride hydrochloride and rabeprazole sodium from capsule formulation.

PubMed

Pillai, S; Singhvi, I

2008-09-01

Two simple, accurate, economical and reproducible UV spectrophotometric methods and one HPLC method for simultaneous estimation of two component drug mixture of itopride hydrochloride and rabeprazole sodium from combined capsule dosage form have been developed. First developed method involves formation and solving of simultaneous equations using 265.2 nm and 290.8 nm as two wavelengths. Second method is based on two wavelength calculation, wavelengths selected for estimation of itopride hydrochloride was 278.0 nm and 298.8 nm and for rabeprazole sodium 253.6 nm and 275.2 nm. Developed HPLC method is a reverse phase chromatographic method using phenomenex C(18) column and acetonitrile: phosphate buffer (35:65 v/v) pH 7.0 as mobile phase. All developed methods obey Beer's law in concentration range employed for respective methods. Results of analysis were validated statistically and by recovery studies.

Quantitative Estimation of Itopride Hydrochloride and Rabeprazole Sodium from Capsule Formulation

PubMed Central

Pillai, S.; Singhvi, I.

2008-01-01

Two simple, accurate, economical and reproducible UV spectrophotometric methods and one HPLC method for simultaneous estimation of two component drug mixture of itopride hydrochloride and rabeprazole sodium from combined capsule dosage form have been developed. First developed method involves formation and solving of simultaneous equations using 265.2 nm and 290.8 nm as two wavelengths. Second method is based on two wavelength calculation, wavelengths selected for estimation of itopride hydrochloride was 278.0 nm and 298.8 nm and for rabeprazole sodium 253.6 nm and 275.2 nm. Developed HPLC method is a reverse phase chromatographic method using phenomenex C18 column and acetonitrile: phosphate buffer (35:65 v/v) pH 7.0 as mobile phase. All developed methods obey Beer's law in concentration range employed for respective methods. Results of analysis were validated statistically and by recovery studies. PMID:21394269

Frequency-domain elastic full waveform inversion using encoded simultaneous sources

NASA Astrophysics Data System (ADS)

Jeong, W.; Son, W.; Pyun, S.; Min, D.

2011-12-01

Currently, numerous studies have endeavored to develop robust full waveform inversion and migration algorithms. These processes require enormous computational costs, because of the number of sources in the survey. To avoid this problem, the phase encoding technique for prestack migration was proposed by Romero (2000) and Krebs et al. (2009) proposed the encoded simultaneous-source inversion technique in the time domain. On the other hand, Ben-Hadj-Ali et al. (2011) demonstrated the robustness of the frequency-domain full waveform inversion with simultaneous sources for noisy data changing the source assembling. Although several studies on simultaneous-source inversion tried to estimate P- wave velocity based on the acoustic wave equation, seismic migration and waveform inversion based on the elastic wave equations are required to obtain more reliable subsurface information. In this study, we propose a 2-D frequency-domain elastic full waveform inversion technique using phase encoding methods. In our algorithm, the random phase encoding method is employed to calculate the gradients of the elastic parameters, source signature estimation and the diagonal entries of approximate Hessian matrix. The crosstalk for the estimated source signature and the diagonal entries of approximate Hessian matrix are suppressed with iteration as for the gradients. Our 2-D frequency-domain elastic waveform inversion algorithm is composed using the back-propagation technique and the conjugate-gradient method. Source signature is estimated using the full Newton method. We compare the simultaneous-source inversion with the conventional waveform inversion for synthetic data sets of the Marmousi-2 model. The inverted results obtained by simultaneous sources are comparable to those obtained by individual sources, and source signature is successfully estimated in simultaneous source technique. Comparing the inverted results using the pseudo Hessian matrix with previous inversion results provided by the approximate Hessian matrix, it is noted that the latter are better than the former for deeper parts of the model. This work was financially supported by the Brain Korea 21 project of Energy System Engineering, by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0006155), by the Energy Efficiency & Resources of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy (No. 2010T100200133).

Multidisciplinary optimization of controlled space structures with global sensitivity equations

NASA Technical Reports Server (NTRS)

Padula, Sharon L.; James, Benjamin B.; Graves, Philip C.; Woodard, Stanley E.

1991-01-01

A new method for the preliminary design of controlled space structures is presented. The method coordinates standard finite element structural analysis, multivariable controls, and nonlinear programming codes and allows simultaneous optimization of the structures and control systems of a spacecraft. Global sensitivity equations are a key feature of this method. The preliminary design of a generic geostationary platform is used to demonstrate the multidisciplinary optimization method. Fifteen design variables are used to optimize truss member sizes and feedback gain values. The goal is to reduce the total mass of the structure and the vibration control system while satisfying constraints on vibration decay rate. Incorporating the nonnegligible mass of actuators causes an essential coupling between structural design variables and control design variables. The solution of the demonstration problem is an important step toward a comprehensive preliminary design capability for structures and control systems. Use of global sensitivity equations helps solve optimization problems that have a large number of design variables and a high degree of coupling between disciplines.

Numerical solution of second order ODE directly by two point block backward differentiation formula

NASA Astrophysics Data System (ADS)

Zainuddin, Nooraini; Ibrahim, Zarina Bibi; Othman, Khairil Iskandar; Suleiman, Mohamed; Jamaludin, Noraini

2015-12-01

Direct Two Point Block Backward Differentiation Formula, (BBDF2) for solving second order ordinary differential equations (ODEs) will be presented throughout this paper. The method is derived by differentiating the interpolating polynomial using three back values. In BBDF2, two approximate solutions are produced simultaneously at each step of integration. The method derived is implemented by using fixed step size and the numerical results that follow demonstrate the advantage of the direct method as compared to the reduction method.

Explicit accounting of electronic effects on the Hugoniot of porous materials

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

Nayak, Bishnupriya; Menon, S. V. G., E-mail: menon.svg98@gmail.com

2016-03-28

A generalized enthalpy based equation of state, which includes thermal electron excitations explicitly, is formulated from simple considerations. Its application to obtain Hugoniot of materials needs simultaneous evaluation of pressure-volume curve and temperature, the latter requiring solution of a differential equation. The errors involved in two recent papers [Huayun et al., J. Appl. Phys. 92, 5917 (2002); 92, 5924 (2002)], which employed this approach, are brought out and discussed. In addition to developing the correct set of equations, the present work also provides a numerical method to implement this approach. Constant pressure specific heat of ions and electrons and ionicmore » enthalpy parameter, needed for applications, are calculated using a three component equation of state. The method is applied to porous Cu with different initial porosities. Comparison of results with experimental data shows good agreement. It is found that temperatures along the Hugoniot of porous materials are significantly modified due to electronic effects.« less

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

NASA Astrophysics Data System (ADS)

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

2010-03-01

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

Analytical treatment of gas flows through multilayer insulation, project 1

NASA Technical Reports Server (NTRS)

Lin, J. T.

1972-01-01

A theoretical investigation of gas flow inside a multilayer insulation system was made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was also investigated. It was shown that when the relaxation time is less than the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given and comparisons with experimental data were made.

The International Market for MBA Qualifications: The Relationship between Tuition Fees and Applications

ERIC Educational Resources Information Center

Elliott, Caroline; Soo, Kwok Tong

2013-01-01

This paper explores the relationship between tuition fees charged by MBA programmes and the number of applications to these programmes, using a panel dataset comprising universities from countries across the world. Using Three-Stage-Least-Squares methods for simultaneous equations, we find a two-way relationship between tuition fees and…

Quantitative phase microscopy for cellular dynamics based on transport of intensity equation.

PubMed

Li, Ying; Di, Jianglei; Ma, Chaojie; Zhang, Jiwei; Zhong, Jinzhan; Wang, Kaiqiang; Xi, Teli; Zhao, Jianlin

2018-01-08

We demonstrate a simple method for quantitative phase imaging of tiny transparent objects such as living cells based on the transport of intensity equation. The experiments are performed using an inverted bright field microscope upgraded with a flipping imaging module, which enables to simultaneously create two laterally separated images with unequal defocus distances. This add-on module does not include any lenses or gratings and is cost-effective and easy-to-alignment. The validity of this method is confirmed by the measurement of microlens array and human osteoblastic cells in culture, indicating its potential in the applications of dynamically measuring living cells and other transparent specimens in a quantitative, non-invasive and label-free manner.

Simultaneous Constraints on the Mass and Radius of Aql X–1 from Quiescence and X-Ray Burst Observations

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

Li, Zhaosheng; Falanga, Maurizio; Chen, Li

The measurement of neutron star mass and radius is one of the most direct ways to distinguish between various dense matter equations of state. The mass and radius of accreting neutron stars hosted in low-mass X-ray binaries can be constrained by several methods, including photospheric radius expansion from type I X-ray bursts and from quiescent spectra. In this paper, we apply for the first time these two methods simultaneously to constrain the mass and radius of Aql X–1. The quiescent spectra from Chandra and XMM-Newton , and photospheric radius expansion bursts from RXTE are used. The determination of the massmore » and radius of Aql X–1 is also used to verify the consistency between the two methods and to narrow down the uncertainties of the neutron star mass and radius. It is found that the distance to Aql X–1 should be in the range of 4.0–5.75 kpc, based on the overlapping confidence regions between photospheric radius expansion burst and quiescent spectra methods. In addition, we show that the mass and radius determined for the compact star in Aql X–1 are compatible with strange star equations of state and conventional neutron star models.« less

Differences between Presentation Methods in Working Memory Procedures: A Matter of Working Memory Consolidation

PubMed Central

Ricker, Timothy J.; Cowan, Nelson

2014-01-01

Understanding forgetting from working memory, the memory used in ongoing cognitive processing, is critical to understanding human cognition. In the last decade a number of conflicting findings have been reported regarding the role of time in forgetting from working memory. This has led to a debate concerning whether longer retention intervals necessarily result in more forgetting. An obstacle to directly comparing conflicting reports is a divergence in methodology across studies. Studies which find no forgetting as a function of retention-interval duration tend to use sequential presentation of memory items, while studies which find forgetting as a function of retention-interval duration tend to use simultaneous presentation of memory items. Here, we manipulate the duration of retention and the presentation method of memory items, presenting items either sequentially or simultaneously. We find that these differing presentation methods can lead to different rates of forgetting because they tend to differ in the time available for consolidation into working memory. The experiments detailed here show that equating the time available for working memory consolidation equates the rates of forgetting across presentation methods. We discuss the meaning of this finding in the interpretation of previous forgetting studies and in the construction of working memory models. PMID:24059859

Deducing multiple interfacial dynamics during polymeric foaming.

PubMed

Chandan, Mohammed Rehaan; Naskar, Nilanjon; Das, Anuja; Mukherjee, Rabibrata; Harikrishnan, Gopalakrishna Pillai

2018-06-15

Several interfacial phenomena are active during polymeric foaming, the dynamics of which significantly influence terminal stability, cell structure and in turn the thermo-mechanical properties of temporally evolved foam. Understanding these dynamics is important in achieving desired foam properties. Here, we introduce a method to simultaneously portray the time evolution of bubble growth, lamella thinning and Plateau border drainage, occurring during reactive polymeric foaming. In this method, we initially conduct bulk and surface shear rheology under polymerizing and non-foaming conditions. In a subsequent step, foaming experiments were conducted in a rheometer. The microscopic structural dimensions pertaining to the terminal values of the dynamics of each interfacial phenomena are then measured using a combination of scanning electron microscopy, optical microscopy and imaging ellipsometry, after the foaming is over. The measured surface and bulk rheological parameters are incorporated in time evolution equations that are derived from mass and momentum transport occurring when a model viscoelastic fluid is foamed by gas dispersion. Analytical and numerical solutions to these equations portray the dynamics. We demonstrate this method for a series of reactive polyurethane foams generated from different chemical sources. The effectiveness of our method is in simultaneously obtaining these dynamics that are difficult to directly monitor due to short active durations over multiple length scales.

Simultaneous measurement of liposome extravasation and content release in tumors.

PubMed

Wu, N Z; Braun, R D; Gaber, M H; Lin, G M; Ong, E T; Shan, S; Papahadjopoulos, D; Dewhirst, M W

1997-03-01

The success of liposome-based drug delivery systems for tumor targeting relies on maximum extravasation of liposomes into tumor interstitium, as well as optimal release of contents from the liposomes once within the tumor Liposome extravasation and content release are two separate processes that can be individually or jointly manipulated so a method is needed to monitor these two processes independently and simultaneously. In this report, we describe a method to measure liposome extravasation and content release in tumor tissues growing in a rat skinfold window chamber preparation. Mixtures of liposomes containing either doxorubicin or calcein, both of which are fluorescent, and liposomes surface-labeled with rhodamine were injected intravenously. Fluorescent, light intensities in a tumor region in two fluorescent channels were measured using an image-processing system. Light intensities of plasma from blood samples were also measured using this system. These measurements were used to calculate the amounts of liposomes and released contents in both plasma and tumor interstitium. The calculations were based on the fact that the liposome surface labels and contents emit fluorescent light at different wavelengths and when encapsulated, the contents fluorescence is self-quenched. The model included equations to account for fluorescent light "cross-contamination" by the two fluorochromes as well as equations relating the measured fluorescent light intensities to the amounts of liposomes and released contents. This method was applied to three situations in which liposome extravasation and content release were manipulated in different, predictable ways. Our results indicate that this method can perform simultaneous independent and quantitative measurements of liposome extravasation and content release. This method can potentially be used to study drug delivery of other carrier systems in vivo.

Simultaneous determination of atorvastatin calcium and olmesartan medoxomil in a pharmaceutical formulation by reversed phase high-performance liquid chromatography, high-performance thin-layer chromatography, and UV spectrophotometric methods.

PubMed

Soni, Hiral; Kothari, Charmy; Khatri, Deepak; Mehta, Priti

2014-01-01

Validated RP-HPLC, HPTLC, and UV spectrophotometric methods have been developed for the simultaneous determination of atorvastatin calcium (ATV) and olmesartan medoxomil (OLM) in a pharmaceutical formulation. The RP-HPLC separation was achieved on a Kromasil C18 column (250 x 4.6 mm, 5 microm particle size) using 0.01 M potassium dihydrogen o-phosphate (pH 4 adjusted with o-phosphoric acid)-acetonitrile (50 + 50, v/v) as the mobile phase at a flow rate of 1.5 mL/min. Quantification was achieved by UV detection at 276 nm. The HPTLC separation was achieved on precoated silica gel 60F254 plates using chloroform-methanol-acetonitrile (4 + 2+ 4, v/v/v) mobile phase. Quantification was achieved with UV detection at 276 nm. The UV-Vis spectrophotometric method was based on the simultaneous equation method that involves measurement of absorbance at two wavelengths, i.e., 255 nm (lambda max of OLM) and 246.2 nm (lambda max of ATV) in methanol. All three methods were validated as per International Conference on Harmonization guidelines. The proposed methods were simple, precise, accurate, and applicable for the simultaneous determination of ATV and OLM in a marketed formulation. The results obtained by applying the proposed methods were statistically analyzed and were found satisfactory.

Spatiotemporal motion boundary detection and motion boundary velocity estimation for tracking moving objects with a moving camera: a level sets PDEs approach with concurrent camera motion compensation.

PubMed

Feghali, Rosario; Mitiche, Amar

2004-11-01

The purpose of this study is to investigate a method of tracking moving objects with a moving camera. This method estimates simultaneously the motion induced by camera movement. The problem is formulated as a Bayesian motion-based partitioning problem in the spatiotemporal domain of the image quence. An energy functional is derived from the Bayesian formulation. The Euler-Lagrange descent equations determine imultaneously an estimate of the image motion field induced by camera motion and an estimate of the spatiotemporal motion undary surface. The Euler-Lagrange equation corresponding to the surface is expressed as a level-set partial differential equation for topology independence and numerically stable implementation. The method can be initialized simply and can track multiple objects with nonsimultaneous motions. Velocities on motion boundaries can be estimated from geometrical properties of the motion boundary. Several examples of experimental verification are given using synthetic and real-image sequences.

How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students' mathematical performance

NASA Astrophysics Data System (ADS)

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-12-01

We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students' mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students' simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students' formulation and combination of equations. Several reasons may explain this difference, including the students' different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

Aerodynamic optimization by simultaneously updating flow variables and design parameters with application to advanced propeller designs

NASA Technical Reports Server (NTRS)

Rizk, Magdi H.

1988-01-01

A scheme is developed for solving constrained optimization problems in which the objective function and the constraint function are dependent on the solution of the nonlinear flow equations. The scheme updates the design parameter iterative solutions and the flow variable iterative solutions simultaneously. It is applied to an advanced propeller design problem with the Euler equations used as the flow governing equations. The scheme's accuracy, efficiency and sensitivity to the computational parameters are tested.

Oxidation Behavior of Carbon Fiber-Reinforced Composites

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2008-01-01

OXIMAP is a numerical (FEA-based) solution tool capable of calculating the carbon fiber and fiber coating oxidation patterns within any arbitrarily shaped carbon silicon carbide composite structure as a function of time, temperature, and the environmental oxygen partial pressure. The mathematical formulation is derived from the mechanics of the flow of ideal gases through a chemically reacting, porous solid. The result of the formulation is a set of two coupled, non-linear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined at each time step using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The non-linear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual finite element method, allowing for the solution of the differential equations numerically.

The method of lines in analyzing solids containing cracks

NASA Technical Reports Server (NTRS)

Gyekenyesi, John P.

1990-01-01

A semi-numerical method is reviewed for solving a set of coupled partial differential equations subject to mixed and possibly coupled boundary conditions. The line method of analysis is applied to the Navier-Cauchy equations of elastic and elastoplastic equilibrium to calculate the displacement distributions in various, simple geometry bodies containing cracks. The application of this method to the appropriate field equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. When decoupling of the equations and their boundary conditions is not possible, the use of a successive approximation procedure permits the analytical solution of the resulting ordinary differential equations. The use of this method is illustrated by reviewing and presenting selected solutions of mixed boundary value problems in three dimensional fracture mechanics. These solutions are of great importance in fracture toughness testing, where accurate stress and displacement distributions are required for the calculation of certain fracture parameters. Computations obtained for typical flawed specimens include that for elastic as well as elastoplastic response. Problems in both Cartesian and cylindrical coordinate systems are included. Results are summarized for a finite geometry rectangular bar with a central through-the-thickness or rectangular surface crack under remote uniaxial tension. In addition, stress and displacement distributions are reviewed for finite circular bars with embedded penny-shaped cracks, and rods with external annular or ring cracks under opening mode tension. The results obtained show that the method of lines presents a systematic approach to the solution of some three-dimensional mechanics problems with arbitrary boundary conditions. The advantage of this method over other numerical solutions is that good results are obtained even from the use of a relatively coarse grid.

Study of stability of the difference scheme for the model problem of the gaslift process

NASA Astrophysics Data System (ADS)

Temirbekov, Nurlan; Turarov, Amankeldy

2017-09-01

The paper studies a model of the gaslift process where the motion in a gas-lift well is described by partial differential equations. The system describing the studied process consists of equations of motion, continuity, equations of thermodynamic state, and hydraulic resistance. A two-layer finite-difference Lax-Vendroff scheme is constructed for the numerical solution of the problem. The stability of the difference scheme for the model problem is investigated using the method of a priori estimates, the order of approximation is investigated, the algorithm for numerical implementation of the gaslift process model is given, and the graphs are presented. The development and investigation of difference schemes for the numerical solution of systems of equations of gas dynamics makes it possible to obtain simultaneously exact and monotonic solutions.

A numerical method for measuring capacitive soft sensors through one channel

NASA Astrophysics Data System (ADS)

Tairych, Andreas; Anderson, Iain A.

2018-03-01

Soft capacitive stretch sensors are well suited for unobtrusive wearable body motion capture. Conventional sensing methods measure sensor capacitances through separate channels. In sensing garments with many sensors, this results in high wiring complexity, and a large footprint of rigid sensing circuit boards. We have developed a more efficient sensing method that detects multiple sensors through only one channel, and one set of wires. It is based on a R-C transmission line assembled from capacitive conductive fabric stretch sensors, and external resistors. The unknown capacitances are identified by solving a system of nonlinear equations. These equations are established by modelling and continuously measuring transmission line reactances at different frequencies. Solving these equations numerically with a Newton-Raphson solver for the unknown capacitances enables real time reading of all sensors. The method was verified with a prototype comprising three sensors that is capable of detecting both individually and simultaneously stretched sensors. Instead of using three channels and six wires to detect the sensors, the task was achieved with only one channel and two wires.

The thermodynamic properties of nitrogen from 65 to 2000 K with pressures to 10,000 atmospheres. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Jacobsen, R. T.

1972-01-01

An equation of state is presented for liquid and gaseous nitrogen for temperatures from 65 degrees K to 2000 degrees K and pressures to 10,000 atmospheres. All the pressure-density-temperature data available from published literature have been corrected and applied to bring experimental temperatures into accord with the International Practical Temperature Scale of 1968. The coefficients of the equation of state were determined by a weighted least squares fit to selected published pressure-density-temperature data. The methods of weighting the various data for simultaneous fitting are presented and discussed.

Correcting magnetic probe perturbations on current density measurements of current carrying plasmas.

PubMed

Knoblauch, P; Raspa, V; Di Lorenzo, F; Lazarte, A; Clausse, A; Moreno, C

2010-09-01

A method to infer the current density distribution in the current sheath of a plasma focus discharge from a magnetic probe is formulated and then applied to experimental data obtained in a 1.1 kJ device. Distortions on the magnetic probe signal caused by current redistribution and by a time-dependent total discharge current are considered simultaneously, leading to an integral equation for the current density. Two distinct, easy to implement, numerical procedures are given to solve such equation. Experimental results show the coexistence of at least two maxima in the current density structure of a nitrogen sheath.

Application of augmented-Lagrangian methods in meteorology: Comparison of different conjugate-gradient codes for large-scale minimization

NASA Technical Reports Server (NTRS)

Navon, I. M.

1984-01-01

A Lagrange multiplier method using techniques developed by Bertsekas (1982) was applied to solving the problem of enforcing simultaneous conservation of the nonlinear integral invariants of the shallow water equations on a limited area domain. This application of nonlinear constrained optimization is of the large dimensional type and the conjugate gradient method was found to be the only computationally viable method for the unconstrained minimization. Several conjugate-gradient codes were tested and compared for increasing accuracy requirements. Robustness and computational efficiency were the principal criteria.

A current-excited triple-time-voltage oversampling method for bio-impedance model for cost-efficient circuit system.

PubMed

Yan Hong; Yong Wang; Wang Ling Goh; Yuan Gao; Lei Yao

2015-08-01

This paper presents a mathematic method and a cost-efficient circuit to measure the value of each component of the bio-impedance model at electrode-electrolyte interface. The proposed current excited triple-time-voltage oversampling (TTVO) method deduces the component values by solving triple simultaneous electric equation (TSEE) at different time nodes during a current excitation, which are the voltage functions of time. The proposed triple simultaneous electric equations (TSEEs) allows random selections of the time nodes, hence numerous solutions can be obtained during a single current excitation. Following that, the oversampling approach is engaged by averaging all solutions of multiple TSEEs acquired after a single current excitation, which increases the practical measurement accuracy through the improvement of the signal-to-noise ratio (SNR). In addition, a print circuit board (PCB) that consists a switched current exciter and an analog-to-digital converter (ADC) is designed for signal acquisition. This presents a great cost reduction when compared against other instrument-based measurement data reported [1]. Through testing, the measured values of this work is proven to be in superb agreements on the true component values of the electrode-electrolyte interface model. This work is most suited and also useful for biological and biomedical applications, to perform tasks such as stimulations, recordings, impedance characterizations, etc.

A Two-moment Radiation Hydrodynamics Module in ATHENA Using a Godunov Method

NASA Astrophysics Data System (ADS)

Skinner, M. A.; Ostriker, E. C.

2013-04-01

We describe a module for the Athena code that solves the grey equations of radiation hydrodynamics (RHD) using a local variable Eddington tensor (VET) based on the M1 closure of the two-moment hierarchy of the transfer equation. The variables are updated via a combination of explicit Godunov methods to advance the gas and radiation variables including the non-stiff source terms, and a local implicit method to integrate the stiff source terms. We employ the reduced speed of light approximation (RSLA) with subcycling of the radiation variables in order to reduce computational costs. The streaming and diffusion limits are well-described by the M1 closure model, and our implementation shows excellent behavior for problems containing both regimes simultaneously. Our operator-split method is ideally suited for problems with a slowly-varying radiation field and dynamical gas flows, in which the effect of the RSLA is minimal.

Auxiliary variables for numerically solving nonlinear equations with softly broken symmetries.

PubMed

Olum, Ken D; Masoumi, Ali

2017-06-01

General methods for solving simultaneous nonlinear equations work by generating a sequence of approximate solutions that successively improve a measure of the total error. However, if the total error function has a narrow curved valley, the available techniques tend to find the solution after a very large number of steps, if ever. The solver first converges rapidly to the valley, but once there it converges extremely slowly to the solution. In this paper we show that in the specific physically important case where these valleys are the result of a softly broken symmetry, the solution can often be found much more quickly by adding the generators of the softly broken symmetry as auxiliary variables. This makes the number of variables more than the equations and hence there will be a family of solutions, any one of which would be acceptable. We present a procedure for finding solutions in this case and apply it to several simple examples and an important problem in the physics of false vacuum decay. We also provide a Mathematica package that implements Powell's hybrid method with the generalization to allow more variables than equations.

From Nonradiating Sources to Directionally Invisible Objects

NASA Astrophysics Data System (ADS)

Hurwitz, Elisa

The goal of this dissertation is to extend the understanding of invisible objects, in particular nonradiating sources and directional nonscattering scatterers. First, variations of null-field nonradiating sources are derived from Maxwell's equations. Next, it is shown how to design a nonscattering scatterer by applying the boundary conditions for nonradiating sources to the scalar wave equation, referred to here as the "field cloak method". This technique is used to demonstrate directionally invisible scatterers for an incident field with one direction of incidence, and the influence of symmetry on the directionality is explored. This technique, when applied to the scalar wave equation, is extended to show that a directionally invisible object may be invisible for multiple directions of incidence simultaneously. This opens the door to the creation of optically switchable, directionally invisible objects which could be implemented in couplers and other novel optical devices. Next, a version of the "field cloak method" is extended to the Maxwell's electro-magnetic vector equations, allowing more flexibility in the variety of directionally invisible objects that can be designed. This thesis concludes with examples of such objects and future applications.

Nonparametric estimates of drift and diffusion profiles via Fokker-Planck algebra.

PubMed

Lund, Steven P; Hubbard, Joseph B; Halter, Michael

2014-11-06

Diffusion processes superimposed upon deterministic motion play a key role in understanding and controlling the transport of matter, energy, momentum, and even information in physics, chemistry, material science, biology, and communications technology. Given functions defining these random and deterministic components, the Fokker-Planck (FP) equation is often used to model these diffusive systems. Many methods exist for estimating the drift and diffusion profiles from one or more identifiable diffusive trajectories; however, when many identical entities diffuse simultaneously, it may not be possible to identify individual trajectories. Here we present a method capable of simultaneously providing nonparametric estimates for both drift and diffusion profiles from evolving density profiles, requiring only the validity of Langevin/FP dynamics. This algebraic FP manipulation provides a flexible and robust framework for estimating stationary drift and diffusion coefficient profiles, is not based on fluctuation theory or solved diffusion equations, and may facilitate predictions for many experimental systems. We illustrate this approach on experimental data obtained from a model lipid bilayer system exhibiting free diffusion and electric field induced drift. The wide range over which this approach provides accurate estimates for drift and diffusion profiles is demonstrated through simulation.

Lean body mass correction of standardized uptake value in simultaneous whole-body positron emission tomography and magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Jochimsen, Thies H.; Schulz, Jessica; Busse, Harald; Werner, Peter; Schaudinn, Alexander; Zeisig, Vilia; Kurch, Lars; Seese, Anita; Barthel, Henryk; Sattler, Bernhard; Sabri, Osama

2015-06-01

This study explores the possibility of using simultaneous positron emission tomography—magnetic resonance imaging (PET-MRI) to estimate the lean body mass (LBM) in order to obtain a standardized uptake value (SUV) which is less dependent on the patients' adiposity. This approach is compared to (1) the commonly-used method based on a predictive equation for LBM, and (2) to using an LBM derived from PET-CT data. It is hypothesized that an MRI-based correction of SUV provides a robust method due to the high soft-tissue contrast of MRI. A straightforward approach to calculate an MRI-derived LBM is presented. It is based on the fat and water images computed from the two-point Dixon MRI primarily used for attenuation correction in PET-MRI. From these images, a water fraction was obtained for each voxel. Averaging over the whole body yielded the weight-normalized LBM. Performance of the new approach in terms of reducing variations of 18F-Fludeoxyglucose SUVs in brain and liver across 19 subjects was compared with results using predictive methods and PET-CT data to estimate the LBM. The MRI-based method reduced the coefficient of variation of SUVs in the brain by 41  ± 10% which is comparable to the reduction by the PET-CT method (35  ± 10%). The reduction of the predictive LBM method was 29  ± 8%. In the liver, the reduction was less clear, presumably due to other sources of variation. In conclusion, employing the Dixon data in simultaneous PET-MRI for calculation of lean body mass provides a brain SUV which is less dependent on patient adiposity. The reduced dependency is comparable to that obtained by CT and predictive equations. Therefore, it is more comparable across patients. The technique does not impose an overhead in measurement time and is straightforward to implement.

Lean body mass correction of standardized uptake value in simultaneous whole-body positron emission tomography and magnetic resonance imaging.

PubMed

Jochimsen, Thies H; Schulz, Jessica; Busse, Harald; Werner, Peter; Schaudinn, Alexander; Zeisig, Vilia; Kurch, Lars; Seese, Anita; Barthel, Henryk; Sattler, Bernhard; Sabri, Osama

2015-06-21

This study explores the possibility of using simultaneous positron emission tomography--magnetic resonance imaging (PET-MRI) to estimate the lean body mass (LBM) in order to obtain a standardized uptake value (SUV) which is less dependent on the patients' adiposity. This approach is compared to (1) the commonly-used method based on a predictive equation for LBM, and (2) to using an LBM derived from PET-CT data. It is hypothesized that an MRI-based correction of SUV provides a robust method due to the high soft-tissue contrast of MRI. A straightforward approach to calculate an MRI-derived LBM is presented. It is based on the fat and water images computed from the two-point Dixon MRI primarily used for attenuation correction in PET-MRI. From these images, a water fraction was obtained for each voxel. Averaging over the whole body yielded the weight-normalized LBM. Performance of the new approach in terms of reducing variations of (18)F-Fludeoxyglucose SUVs in brain and liver across 19 subjects was compared with results using predictive methods and PET-CT data to estimate the LBM. The MRI-based method reduced the coefficient of variation of SUVs in the brain by 41 ± 10% which is comparable to the reduction by the PET-CT method (35 ± 10%). The reduction of the predictive LBM method was 29 ± 8%. In the liver, the reduction was less clear, presumably due to other sources of variation. In conclusion, employing the Dixon data in simultaneous PET-MRI for calculation of lean body mass provides a brain SUV which is less dependent on patient adiposity. The reduced dependency is comparable to that obtained by CT and predictive equations. Therefore, it is more comparable across patients. The technique does not impose an overhead in measurement time and is straightforward to implement.

Calculation of reinforced-concrete frame strength under a simultaneous static cross section load and a column lateral impact

NASA Astrophysics Data System (ADS)

Belov, Nikolay; Yugov, Nikolay; Kopanitsa, Dmitry; Kopanitsa, Georgy; Yugov, Alexey; Kaparulin, Sergey; Plyaskin, Andrey; Kalichkina, Anna; Ustinov, Artyom

2016-01-01

When designing buildings with reinforced concrete that are planned to resist dynamic loads it is necessary to calculate this structural behavior under operational static and emergency impact and blast loads. Calculations of the structures under shock-wave loads can be performed by solving dynamic equations that do not consider static loads. Due to this fact the calculation of reinforced concrete frame under a simultaneous static and dynamic load in full 3d settings becomes a very non trivial and resource consuming problem. This problem can be split into two tasks. The first one is a shock-wave problem that can be solved using software package RANET-3, which allows solving the problem using finite elements method adapted for dynamic task. This method calculates strain-stress state of the material and its dynamic destruction, which is considered as growth and consolidation of micro defects under loading. On the second step the results of the first step are taken as input parameters for quasi static calculation of simultaneous static and dynamic load using finite elements method in AMP Civil Engineering-11.

Computation of the stability derivatives via CFD and the sensitivity equations

NASA Astrophysics Data System (ADS)

Lei, Guo-Dong; Ren, Yu-Xin

2011-04-01

The method to calculate the aerodynamic stability derivates of aircrafts by using the sensitivity equations is extended to flows with shock waves in this paper. Using the newly developed second-order cell-centered finite volume scheme on the unstructured-grid, the unsteady Euler equations and sensitivity equations are solved simultaneously in a non-inertial frame of reference, so that the aerodynamic stability derivatives can be calculated for aircrafts with complex geometries. Based on the numerical results, behavior of the aerodynamic sensitivity parameters near the shock wave is discussed. Furthermore, the stability derivatives are analyzed for supersonic and hypersonic flows. The numerical results of the stability derivatives are found in good agreement with theoretical results for supersonic flows, and variations of the aerodynamic force and moment predicted by the stability derivatives are very close to those obtained by CFD simulation for both supersonic and hypersonic flows.

Generalized constitutive equations for piezo-actuated compliant mechanism

NASA Astrophysics Data System (ADS)

Cao, Junyi; Ling, Mingxiang; Inman, Daniel J.; Lin, Jin

2016-09-01

This paper formulates analytical models to describe the static displacement and force interactions between generic serial-parallel compliant mechanisms and their loads by employing the matrix method. In keeping with the familiar piezoelectric constitutive equations, the generalized constitutive equations of compliant mechanism represent the input-output displacement and force relations in the form of a generalized Hooke’s law and as analytical functions of physical parameters. Also significantly, a new model of output displacement for compliant mechanism interacting with piezo-stacks and elastic loads is deduced based on the generalized constitutive equations. Some original findings differing from the well-known constitutive performance of piezo-stacks are also given. The feasibility of the proposed models is confirmed by finite element analysis and by experiments under various elastic loads. The analytical models can be an insightful tool for predicting and optimizing the performance of a wide class of compliant mechanisms that simultaneously consider the influence of loads and piezo-stacks.

A comparison of critical heat flux in tubes and bilaterally heated annuli

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

Doerffer, S.; Groeneveld, D.C.; Cheng, S.C.

1995-09-01

This paper examines the critical heat flux (CHF) behaviour for annular flow in bilaterally heated annuli and compares it to that in tubes and unilaterally heated annuli. It was found that the differences in CHF between bilaterally and unilaterally heated annuli or tubes strongly depend on pressure and quality. the CHF in bilaterally heated annuli can be predicted by tube CHF prediction methods for the simultaneous CHF occurrence at both surfaces, and the following flow conditions: pressure 7-10 MPa, mass flux 0.5-4.0 Mg/m{sup 2}s and critical quality 0.23-0.9. The effect on CHF of the outer-to-inner surface heat flux ratio, wasmore » also examined. The prediction of CHF for bilaterally heated annuli was based on the droplet-diffusion model proposed by Kirillov and Smogalev. While their model refers only to CHF occurrence at the inner surface, we extended it to cases where CHF occurs at the outer surface, and simultaneously at both surfaces, thus covering all cases of CHF occurrence in bilaterally heated annuli. From the annuli CHF data of Becker and Letzter, we derived empirical functions required by the model. the proposed equations provide good accuracy for the CHF data used in this study. Moreover, the equations can predict conditions at which CHF occurs simultaneously at both surfaces. Also, this method can be used for cases with only one heated surface.« less

Quantitative Estimation of Seismic Velocity Changes Using Time-Lapse Seismic Data and Elastic-Wave Sensitivity Approach

NASA Astrophysics Data System (ADS)

Denli, H.; Huang, L.

2008-12-01

Quantitative monitoring of reservoir property changes is essential for safe geologic carbon sequestration. Time-lapse seismic surveys have the potential to effectively monitor fluid migration in the reservoir that causes geophysical property changes such as density, and P- and S-wave velocities. We introduce a novel method for quantitative estimation of seismic velocity changes using time-lapse seismic data. The method employs elastic sensitivity wavefields, which are the derivatives of elastic wavefield with respect to density, P- and S-wave velocities of a target region. We derive the elastic sensitivity equations from analytical differentiations of the elastic-wave equations with respect to seismic-wave velocities. The sensitivity equations are coupled with the wave equations in a way that elastic waves arriving in a target reservoir behave as a secondary source to sensitivity fields. We use a staggered-grid finite-difference scheme with perfectly-matched layers absorbing boundary conditions to simultaneously solve the elastic-wave equations and the elastic sensitivity equations. By elastic-wave sensitivities, a linear relationship between relative seismic velocity changes in the reservoir and time-lapse seismic data at receiver locations can be derived, which leads to an over-determined system of equations. We solve this system of equations using a least- square method for each receiver to obtain P- and S-wave velocity changes. We validate the method using both surface and VSP synthetic time-lapse seismic data for a multi-layered model and the elastic Marmousi model. Then we apply it to the time-lapse field VSP data acquired at the Aneth oil field in Utah. A total of 10.5K tons of CO2 was injected into the oil reservoir between the two VSP surveys for enhanced oil recovery. The synthetic and field data studies show that our new method can quantitatively estimate changes in seismic velocities within a reservoir due to CO2 injection/migration.

MHD Modeling of the Solar Wind with Turbulence Transport and Heating

NASA Technical Reports Server (NTRS)

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

2009-01-01

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

Two-dimensional computer simulation of EMVJ and grating solar cells under AMO illumination

NASA Technical Reports Server (NTRS)

Gray, J. L.; Schwartz, R. J.

1984-01-01

A computer program, SCAP2D (Solar Cell Analysis Program in 2-Dimensions), is used to evaluate the Etched Multiple Vertical Junction (EMVJ) and grating solar cells. The aim is to demonstrate how SCAP2D can be used to evaluate cell designs. The cell designs studied are by no means optimal designs. The SCAP2D program solves the three coupled, nonlinear partial differential equations, Poisson's Equation and the hole and electron continuity equations, simultaneously in two-dimensions using finite differences to discretize the equations and Newton's Method to linearize them. The variables solved for are the electrostatic potential and the hole and electron concentrations. Each linear system of equations is solved directly by Gaussian Elimination. Convergence of the Newton Iteration is assumed when the largest correction to the electrostatic potential or hole or electron quasi-potential is less than some predetermined error. A typical problem involves 2000 nodes with a Jacobi matrix of order 6000 and a bandwidth of 243.

Thermal engineering research. [Runge-Kutta investigation of gas flow inside multilayer insulation system for rocket booster fuel tanks

NASA Technical Reports Server (NTRS)

Shih, C. C.

1973-01-01

A theoretical investigation of gas flow inside a multilayer insulation system has been made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas mixture was obtained by considering the diffusion mechanism of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was investigated. It has been shown that when the relaxation time is small compared with the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given, and comparisons with experimental data were made.

Unsteady MHD free convection flow of casson fluid over an inclined vertical plate embedded in a porous media

NASA Astrophysics Data System (ADS)

Manideep, P.; Raju, R. Srinivasa; Rao, T. Siva Nageswar; Reddy, G. Jithender

2018-05-01

This paper deals, an unsteady magnetohydrodynamic heat transfer natural convection flow of non-Newtonian Casson fluid over an inclined vertical plate embedded in a porous media with the presence of boundary conditions such as oscillating velocity, constant wall temperature. The governing dimensionless boundary layer partial differential equations are reduced to simultaneous algebraic linear equation for velocity, temperature of Casson fluid through finite element method. Those equations are solved by Thomas algorithm after imposing the boundary conditions through MATLAB for analyzing the behavior of Casson fluid velocity and temperature with various physical parameters. Also analyzed the local skin-friction and rate of heat transfer. Compared the present results with earlier reported studies, the results are comprehensively authenticated and robust FEM.

Solution of system of multidimensional differential equations in X for identification of gold nanoparticles on fibers with elimination of uncertainty

NASA Astrophysics Data System (ADS)

Dobrovolskaya, T. A.; Emelyanov, V. M.; Emelyanov, V. V.

2018-05-01

There are the results of the compilation and solution of a system of multidimensional differential correlation equations of distribution ellipses in the identification of colloidal gold nanoparticles on polyester fibers with multi-dimensional correlation components of Raman polarization spectra. A proposed method is to increase the accuracy and speed of identification of silver nanoparticles on polyester fibers, taking into account the longitudinal and transverse polarization of laser radiation over the entire spectral range, analyzing in sequence and in order simultaneously two peaks along the X-transverse and along the Y-along the fibers. During a solution of the system using a nonlinear quadratic and differential equation with respect to X, an uncertainty arises, the elimination of which is numerical addition Δ = + 0.02985

High Order Accurate Finite Difference Modeling of Seismo-Acoustic Wave Propagation in a Moving Atmosphere and a Heterogeneous Earth Model Coupled Across a Realistic Topography

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

Petersson, N. Anders; Sjogreen, Bjorn

Here, we develop a numerical method for simultaneously simulating acoustic waves in a realistic moving atmosphere and seismic waves in a heterogeneous earth model, where the motions are coupled across a realistic topography. We model acoustic wave propagation by solving the linearized Euler equations of compressible fluid mechanics. The seismic waves are modeled by the elastic wave equation in a heterogeneous anisotropic material. The motion is coupled by imposing continuity of normal velocity and normal stresses across the topographic interface. Realistic topography is resolved on a curvilinear grid that follows the interface. The governing equations are discretized using high ordermore » accurate finite difference methods that satisfy the principle of summation by parts. We apply the energy method to derive the discrete interface conditions and to show that the coupled discretization is stable. The implementation is verified by numerical experiments, and we demonstrate a simulation of coupled wave propagation in a windy atmosphere and a realistic earth model with non-planar topography.« less

High Order Accurate Finite Difference Modeling of Seismo-Acoustic Wave Propagation in a Moving Atmosphere and a Heterogeneous Earth Model Coupled Across a Realistic Topography

DOE PAGES

Petersson, N. Anders; Sjogreen, Bjorn

2017-04-18

Here, we develop a numerical method for simultaneously simulating acoustic waves in a realistic moving atmosphere and seismic waves in a heterogeneous earth model, where the motions are coupled across a realistic topography. We model acoustic wave propagation by solving the linearized Euler equations of compressible fluid mechanics. The seismic waves are modeled by the elastic wave equation in a heterogeneous anisotropic material. The motion is coupled by imposing continuity of normal velocity and normal stresses across the topographic interface. Realistic topography is resolved on a curvilinear grid that follows the interface. The governing equations are discretized using high ordermore » accurate finite difference methods that satisfy the principle of summation by parts. We apply the energy method to derive the discrete interface conditions and to show that the coupled discretization is stable. The implementation is verified by numerical experiments, and we demonstrate a simulation of coupled wave propagation in a windy atmosphere and a realistic earth model with non-planar topography.« less

Determination of alloy content from plume spectral measurements

NASA Technical Reports Server (NTRS)

Madzsar, George C.

1991-01-01

The mathematical derivation for a method to determine the identities and amounts of alloys present in a flame where numerous alloys may be present is described. This method is applicable if the total number of elemental species from all alloys that may be in the flame is greater than or equal to the total number of alloys. Arranging the atomic spectral line emission equations for the elemental species as a series of simultaneous equations enables solution for identity and amount of the alloy present in the flame. This technique is intended for identification and quantification of alloy content in the plume of a rocket engine. Spectroscopic measurements reveal the atomic species entrained in the plume. Identification of eroding alloys may lead to the identification of the eroding component.

Simultaneous computation of jet turbulence and noise

NASA Technical Reports Server (NTRS)

Berman, C. H.; Ramos, J. I.

1989-01-01

The existing flow computation methods, wave computation techniques, and theories based on noise source models are reviewed in order to assess the capabilities of numerical techniques to compute jet turbulence noise and understand the physical mechanisms governing it over a range of subsonic and supersonic nozzle exit conditions. In particular, attention is given to (1) methods for extrapolating near field information, obtained from flow computations, to the acoustic far field and (2) the numerical solution of the time-dependent Lilley equation.

Combined effects of nonparaxiality, optical activity, and walk-off on rogue wave propagation in optical fibers filled with chiral materials.

PubMed

Temgoua, D D Estelle; Tchokonte, M B Tchoula; Kofane, T C

2018-04-01

The generalized nonparaxial nonlinear Schrödinger (NLS) equation in optical fibers filled with chiral materials is reduced to the higher-order integrable Hirota equation. Based on the modified Darboux transformation method, the nonparaxial chiral optical rogue waves are constructed from the scalar model with modulated coefficients. We show that the parameters of nonparaxiality, third-order dispersion, and differential gain or loss term are the main keys to control the amplitude, linear, and nonlinear effects in the model. Moreover, the influence of nonparaxiality, optical activity, and walk-off effect are also evidenced under the defocusing and focusing regimes of the vector nonparaxial NLS equations with constant and modulated coefficients. Through an algorithm scheme of wider applicability on nonparaxial beam propagation methods, the most influential effect and the simultaneous controllability of combined effects are underlined, showing their properties and their potential applications in optical fibers and in a variety of complex dynamical systems.

Combined effects of nonparaxiality, optical activity, and walk-off on rogue wave propagation in optical fibers filled with chiral materials

NASA Astrophysics Data System (ADS)

Temgoua, D. D. Estelle; Tchokonte, M. B. Tchoula; Kofane, T. C.

2018-04-01

The generalized nonparaxial nonlinear Schrödinger (NLS) equation in optical fibers filled with chiral materials is reduced to the higher-order integrable Hirota equation. Based on the modified Darboux transformation method, the nonparaxial chiral optical rogue waves are constructed from the scalar model with modulated coefficients. We show that the parameters of nonparaxiality, third-order dispersion, and differential gain or loss term are the main keys to control the amplitude, linear, and nonlinear effects in the model. Moreover, the influence of nonparaxiality, optical activity, and walk-off effect are also evidenced under the defocusing and focusing regimes of the vector nonparaxial NLS equations with constant and modulated coefficients. Through an algorithm scheme of wider applicability on nonparaxial beam propagation methods, the most influential effect and the simultaneous controllability of combined effects are underlined, showing their properties and their potential applications in optical fibers and in a variety of complex dynamical systems.

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

Garifullin, R. N., E-mail: rustem@matem.anrb.ru; Suleimanov, B. I., E-mail: bisul@mail.r

An analysis is presented of the effect of weak dispersion on transitions from weak to strong discontinuities in inviscid fluid dynamics. In the neighborhoods of transition points, this effect is described by simultaneous solutions to the Korteweg-de Vries equation u{sub t}'+ uu{sub x}' + u{sub xxx}' = 0 and fifth-order nonautonomous ordinary differential equations. As x{sup 2} + t{sup 2} {yields}{infinity}, the asymptotic behavior of these simultaneous solutions in the zone of undamped oscillations is given by quasi-simple wave solutions to Whitham equations of the form r{sub i}(t, x) = tl{sub i} x/t{sup 2}.

Computational method for multi-modal microscopy based on transport of intensity equation

NASA Astrophysics Data System (ADS)

Li, Jiaji; Chen, Qian; Sun, Jiasong; Zhang, Jialin; Zuo, Chao

2017-02-01

In this paper, we develop the requisite theory to describe a hybrid virtual-physical multi-modal imaging system which yields quantitative phase, Zernike phase contrast, differential interference contrast (DIC), and light field moment imaging simultaneously based on transport of intensity equation(TIE). We then give the experimental demonstration of these ideas by time-lapse imaging of live HeLa cell mitosis. Experimental results verify that a tunable lens based TIE system, combined with the appropriate post-processing algorithm, can achieve a variety of promising imaging modalities in parallel with the quantitative phase images for the dynamic study of cellular processes.

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

NASA Technical Reports Server (NTRS)

Lee, Kam-Pui; Gupta, Roop N.

1992-01-01

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

Simultaneous analysis of large INTEGRAL/SPI1 datasets: Optimizing the computation of the solution and its variance using sparse matrix algorithms

NASA Astrophysics Data System (ADS)

Bouchet, L.; Amestoy, P.; Buttari, A.; Rouet, F.-H.; Chauvin, M.

2013-02-01

Nowadays, analyzing and reducing the ever larger astronomical datasets is becoming a crucial challenge, especially for long cumulated observation times. The INTEGRAL/SPI X/γ-ray spectrometer is an instrument for which it is essential to process many exposures at the same time in order to increase the low signal-to-noise ratio of the weakest sources. In this context, the conventional methods for data reduction are inefficient and sometimes not feasible at all. Processing several years of data simultaneously requires computing not only the solution of a large system of equations, but also the associated uncertainties. We aim at reducing the computation time and the memory usage. Since the SPI transfer function is sparse, we have used some popular methods for the solution of large sparse linear systems; we briefly review these methods. We use the Multifrontal Massively Parallel Solver (MUMPS) to compute the solution of the system of equations. We also need to compute the variance of the solution, which amounts to computing selected entries of the inverse of the sparse matrix corresponding to our linear system. This can be achieved through one of the latest features of the MUMPS software that has been partly motivated by this work. In this paper we provide a brief presentation of this feature and evaluate its effectiveness on astrophysical problems requiring the processing of large datasets simultaneously, such as the study of the entire emission of the Galaxy. We used these algorithms to solve the large sparse systems arising from SPI data processing and to obtain both their solutions and the associated variances. In conclusion, thanks to these newly developed tools, processing large datasets arising from SPI is now feasible with both a reasonable execution time and a low memory usage.

Demand for antenatal care in South Africa.

PubMed

Kirigia, J M; Lambo, E; Sambo, L G

2000-01-01

On May,24 1994, the then South African president, Mr. Nelson Mandela, declared that all health care for children under the age of 6 years, and pregnant women would be free. Unfortunately, there has been no significant decrease in maternal, perinatal and infant mortality. Thus, there is a need of research into the factors that influence the demand for antenatal services. The objectives of this paper are to (a) establish the determinants of individual pregnant women's choice to seek antenatal care; and (b) deal with potential endogeneity bias in the relationship between the decision to seek pre-natal care and perceived health status. The joint determination of consumption of antenatal care and pregnant woman's health status requires estimation of a simultaneous system. To help mitigate the simultaneity bias and avoid the inconsistency inherent in the application of Ordinary least Squares (OLS) method to simultaneous equations systems, we used Two-Stage Probit Maximum Likelihood Estimator Method. In the antenatal structural-form equation, the coefficients for TOILET, AGE, OCCUPATION, EMPLOYMENT, SMOKER, METHODS and QUALITY were statistically significant at P

Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions.

PubMed

Salis, Howard; Kaznessis, Yiannis

2005-02-01

The dynamical solution of a well-mixed, nonlinear stochastic chemical kinetic system, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more "fast" reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the "Next Reaction" variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a large-scale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations.

Accelerating molecular property calculations with nonorthonormal Krylov space methods

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

Furche, Filipp; Krull, Brandon T.; Nguyen, Brian D.

Here, we formulate Krylov space methods for large eigenvalue problems and linear equation systems that take advantage of decreasing residual norms to reduce the cost of matrix-vector multiplication. The residuals are used as subspace basis without prior orthonormalization, which leads to generalized eigenvalue problems or linear equation systems on the Krylov space. These nonorthonormal Krylov space (nKs) algorithms are favorable for large matrices with irregular sparsity patterns whose elements are computed on the fly, because fewer operations are necessary as the residual norm decreases as compared to the conventional method, while errors in the desired eigenpairs and solution vectors remainmore » small. We consider real symmetric and symplectic eigenvalue problems as well as linear equation systems and Sylvester equations as they appear in configuration interaction and response theory. The nKs method can be implemented in existing electronic structure codes with minor modifications and yields speed-ups of 1.2-1.8 in typical time-dependent Hartree-Fock and density functional applications without accuracy loss. The algorithm can compute entire linear subspaces simultaneously which benefits electronic spectra and force constant calculations requiring many eigenpairs or solution vectors. The nKs approach is related to difference density methods in electronic ground state calculations, and particularly efficient for integral direct computations of exchange-type contractions. By combination with resolution-of-the-identity methods for Coulomb contractions, three- to fivefold speed-ups of hybrid time-dependent density functional excited state and response calculations are achieved.« less

Accelerating molecular property calculations with nonorthonormal Krylov space methods

DOE PAGES

Furche, Filipp; Krull, Brandon T.; Nguyen, Brian D.; ...

2016-05-03

Here, we formulate Krylov space methods for large eigenvalue problems and linear equation systems that take advantage of decreasing residual norms to reduce the cost of matrix-vector multiplication. The residuals are used as subspace basis without prior orthonormalization, which leads to generalized eigenvalue problems or linear equation systems on the Krylov space. These nonorthonormal Krylov space (nKs) algorithms are favorable for large matrices with irregular sparsity patterns whose elements are computed on the fly, because fewer operations are necessary as the residual norm decreases as compared to the conventional method, while errors in the desired eigenpairs and solution vectors remainmore » small. We consider real symmetric and symplectic eigenvalue problems as well as linear equation systems and Sylvester equations as they appear in configuration interaction and response theory. The nKs method can be implemented in existing electronic structure codes with minor modifications and yields speed-ups of 1.2-1.8 in typical time-dependent Hartree-Fock and density functional applications without accuracy loss. The algorithm can compute entire linear subspaces simultaneously which benefits electronic spectra and force constant calculations requiring many eigenpairs or solution vectors. The nKs approach is related to difference density methods in electronic ground state calculations, and particularly efficient for integral direct computations of exchange-type contractions. By combination with resolution-of-the-identity methods for Coulomb contractions, three- to fivefold speed-ups of hybrid time-dependent density functional excited state and response calculations are achieved.« less

GIZMO: Multi-method magneto-hydrodynamics+gravity code

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2014-10-01

GIZMO is a flexible, multi-method magneto-hydrodynamics+gravity code that solves the hydrodynamic equations using a variety of different methods. It introduces new Lagrangian Godunov-type methods that allow solving the fluid equations with a moving particle distribution that is automatically adaptive in resolution and avoids the advection errors, angular momentum conservation errors, and excessive diffusion problems that seriously limit the applicability of “adaptive mesh” (AMR) codes, while simultaneously avoiding the low-order errors inherent to simpler methods like smoothed-particle hydrodynamics (SPH). GIZMO also allows the use of SPH either in “traditional” form or “modern” (more accurate) forms, or use of a mesh. Self-gravity is solved quickly with a BH-Tree (optionally a hybrid PM-Tree for periodic boundaries) and on-the-fly adaptive gravitational softenings. The code is descended from P-GADGET, itself descended from GADGET-2 (ascl:0003.001), and many of the naming conventions remain (for the sake of compatibility with the large library of GADGET work and analysis software).

Multidisciplinary optimization of a controlled space structure using 150 design variables

NASA Technical Reports Server (NTRS)

James, Benjamin B.

1993-01-01

A controls-structures interaction design method is presented. The method coordinates standard finite-element structural analysis, multivariable controls, and nonlinear programming codes and allows simultaneous optimization of the structure and control system of a spacecraft. Global sensitivity equations are used to account for coupling between the disciplines. Use of global sensitivity equations helps solve optimization problems that have a large number of design variables and a high degree of coupling between disciplines. The preliminary design of a generic geostationary platform is used to demonstrate the multidisciplinary optimization method. Design problems using 15, 63, and 150 design variables to optimize truss member sizes and feedback gain values are solved and the results are presented. The goal is to reduce the total mass of the structure and the vibration control system while satisfying constraints on vibration decay rate. Incorporation of the nonnegligible mass of actuators causes an essential coupling between structural design variables and control design variables.

Analysis of the possibilities and limits of the Moldflow method

NASA Astrophysics Data System (ADS)

Brierre, M.

1982-01-01

The Moldflow information and computation service is presented. Moldflow is a computer program and data bank available as a computer aid to dimensioning thermoplastic injection molding equipment and processes. It is based on the simultaneous solution of thermal and rheological equations and is intended to completely simulate the injection process. The Moldflow system is described and algorithms are discussed, based on Moldflow listings.

Model verification of large structural systems

NASA Technical Reports Server (NTRS)

Lee, L. T.; Hasselman, T. K.

1977-01-01

A methodology was formulated, and a general computer code implemented for processing sinusoidal vibration test data to simultaneously make adjustments to a prior mathematical model of a large structural system, and resolve measured response data to obtain a set of orthogonal modes representative of the test model. The derivation of estimator equations is shown along with example problems. A method for improving the prior analytic model is included.

Laser pyrometry

NASA Technical Reports Server (NTRS)

Stein, Alexander

1988-01-01

A method of determining the emissivity of a hot target from a laser-based reflectance measurement which is conducted simultaneously with a measurement of the target radiance is described. Once the correct radiance and emissivity are determined, one calculates the true target temperature from these parameters via the Planck equations. The design and performance of a laser pyrometer is described. The accuracy of laser pyrometry and the effect of ambient radiance are addressed.

A Practical, Robust and Fast Method for Location Localization in Range-Based Systems.

PubMed

Huang, Shiping; Wu, Zhifeng; Misra, Anil

2017-12-11

Location localization technology is used in a number of industrial and civil applications. Real time location localization accuracy is highly dependent on the quality of the distance measurements and efficiency of solving the localization equations. In this paper, we provide a novel approach to solve the nonlinear localization equations efficiently and simultaneously eliminate the bad measurement data in range-based systems. A geometric intersection model was developed to narrow the target search area, where Newton's Method and the Direct Search Method are used to search for the unknown position. Not only does the geometric intersection model offer a small bounded search domain for Newton's Method and the Direct Search Method, but also it can self-correct bad measurement data. The Direct Search Method is useful for the coarse localization or small target search domain, while the Newton's Method can be used for accurate localization. For accurate localization, by utilizing the proposed Modified Newton's Method (MNM), challenges of avoiding the local extrema, singularities, and initial value choice are addressed. The applicability and robustness of the developed method has been demonstrated by experiments with an indoor system.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Chacon, Luis

2005-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. A crucial element is the development of an effective multilevel treatment of the grid equation.ootnotetextL. Chac'on, G. Lapenta, A fully implicit, nonlinear adaptive grid strategy, J. Comput. Phys., accepted (2005) We will show that such an approach is competitive vs. uniform grids both from the accuracy (due to adaptivity) and the efficiency standpoints. Results for a variety of models 1D and 2D geometries, including nonlinear diffusion, radiation-diffusion, Burgers equation, and gas dynamics will be presented.

Dynamic coupling of subsurface and seepage flows solved within a regularized partition formulation

NASA Astrophysics Data System (ADS)

Marçais, J.; de Dreuzy, J.-R.; Erhel, J.

2017-11-01

Hillslope response to precipitations is characterized by sharp transitions from purely subsurface flow dynamics to simultaneous surface and subsurface flows. Locally, the transition between these two regimes is triggered by soil saturation. Here we develop an integrative approach to simultaneously solve the subsurface flow, locate the potential fully saturated areas and deduce the generated saturation excess overland flow. This approach combines the different dynamics and transitions in a single partition formulation using discontinuous functions. We propose to regularize the system of partial differential equations and to use classic spatial and temporal discretization schemes. We illustrate our methodology on the 1D hillslope storage Boussinesq equations (Troch et al., 2003). We first validate the numerical scheme on previous numerical experiments without saturation excess overland flow. Then we apply our model to a test case with dynamic transitions from purely subsurface flow dynamics to simultaneous surface and subsurface flows. Our results show that discretization respects mass balance both locally and globally, converges when the mesh or time step are refined. Moreover the regularization parameter can be taken small enough to ensure accuracy without suffering of numerical artefacts. Applied to some hundreds of realistic hillslope cases taken from Western side of France (Brittany), the developed method appears to be robust and efficient.

Algebraic aspects of the driven dynamics in the density operator and correlation functions calculation for multi-level open quantum systems

NASA Astrophysics Data System (ADS)

Bogolubov, Nikolai N.; Soldatov, Andrey V.

2017-12-01

Exact and approximate master equations were derived by the projection operator method for the reduced statistical operator of a multi-level quantum system with finite number N of quantum eigenstates interacting with arbitrary external classical fields and dissipative environment simultaneously. It was shown that the structure of these equations can be simplified significantly if the free Hamiltonian driven dynamics of an arbitrary quantum multi-level system under the influence of the external driving fields as well as its Markovian and non-Markovian evolution, stipulated by the interaction with the environment, are described in terms of the SU(N) algebra representation. As a consequence, efficient numerical methods can be developed and employed to analyze these master equations for real problems in various fields of theoretical and applied physics. It was also shown that literally the same master equations hold not only for the reduced density operator but also for arbitrary nonequilibrium multi-time correlation functions as well under the only assumption that the system and the environment are uncorrelated at some initial moment of time. A calculational scheme was proposed to account for these lost correlations in a regular perturbative way, thus providing additional computable terms to the correspondent master equations for the correlation functions.

Measuring the neutron star tidal deformability with equation-of-state-independent relations and gravitational waves

NASA Astrophysics Data System (ADS)

Chatziioannou, Katerina; Haster, Carl-Johan; Zimmerman, Aaron

2018-05-01

Gravitational wave measurements of binary neutron star coalescences offer information about the properties of the extreme matter that comprises the stars. Despite our expectation that all neutron stars in the Universe obey the same equation of state, i.e. the properties of the matter that forms them are universal, current tidal inference analyses treat the two bodies as independent. We present a method to measure the effect of tidal interactions in the gravitational wave signal—and hence constrain the equation of state—that assumes that the two binary components obey the same equation of state. Our method makes use of a relation between the tidal deformabilities of the two stars given the ratio of their masses, a relation that has been shown to only have a weak dependence on the equation of state. We use this to link the tidal deformabilities of the two stars in a realistic parameter inference study while simultaneously marginalizing over the error in the relation. This approach incorporates more physical information into our analysis, thus leading to a better measurement of tidal effects in gravitational wave signals. Through simulated signals we estimate that uncertainties in the measured tidal parameters are reduced by a factor of at least 2—and in some cases up to 10—depending on the equation of state and mass ratio of the system.

Implicit time-integration method for simultaneous solution of a coupled non-linear system

NASA Astrophysics Data System (ADS)

Watson, Justin Kyle

Historically large physical problems have been divided into smaller problems based on the physics involved. This is no different in reactor safety analysis. The problem of analyzing a nuclear reactor for design basis accidents is performed by a handful of computer codes each solving a portion of the problem. The reactor thermal hydraulic response to an event is determined using a system code like TRAC RELAP Advanced Computational Engine (TRACE). The core power response to the same accident scenario is determined using a core physics code like Purdue Advanced Core Simulator (PARCS). Containment response to the reactor depressurization in a Loss Of Coolant Accident (LOCA) type event is calculated by a separate code. Sub-channel analysis is performed with yet another computer code. This is just a sample of the computer codes used to solve the overall problems of nuclear reactor design basis accidents. Traditionally each of these codes operates independently from each other using only the global results from one calculation as boundary conditions to another. Industry's drive to uprate power for reactors has motivated analysts to move from a conservative approach to design basis accident towards a best estimate method. To achieve a best estimate calculation efforts have been aimed at coupling the individual physics models to improve the accuracy of the analysis and reduce margins. The current coupling techniques are sequential in nature. During a calculation time-step data is passed between the two codes. The individual codes solve their portion of the calculation and converge to a solution before the calculation is allowed to proceed to the next time-step. This thesis presents a fully implicit method of simultaneous solving the neutron balance equations, heat conduction equations and the constitutive fluid dynamics equations. It discusses the problems involved in coupling different physics phenomena within multi-physics codes and presents a solution to these problems. The thesis also outlines the basic concepts behind the nodal balance equations, heat transfer equations and the thermal hydraulic equations, which will be coupled to form a fully implicit nonlinear system of equations. The coupling of separate physics models to solve a larger problem and improve accuracy and efficiency of a calculation is not a new idea, however implementing them in an implicit manner and solving the system simultaneously is. Also the application to reactor safety codes is new and has not be done with thermal hydraulics and neutronics codes on realistic applications in the past. The coupling technique described in this thesis is applicable to other similar coupled thermal hydraulic and core physics reactor safety codes. This technique is demonstrated using coupled input decks to show that the system is solved correctly and then verified by using two derivative test problems based on international benchmark problems the OECD/NRC Three mile Island (TMI) Main Steam Line Break (MSLB) problem (representative of pressurized water reactor analysis) and the OECD/NRC Peach Bottom (PB) Turbine Trip (TT) benchmark (representative of boiling water reactor analysis).

Discontinuous Galerkin finite element method for the nonlinear hyperbolic problems with entropy-based artificial viscosity stabilization

NASA Astrophysics Data System (ADS)

Zingan, Valentin Nikolaevich

This work develops a discontinuous Galerkin finite element discretization of non- linear hyperbolic conservation equations with efficient and robust high order stabilization built on an entropy-based artificial viscosity approximation. The solutions of equations are represented by elementwise polynomials of an arbitrary degree p > 0 which are continuous within each element but discontinuous on the boundaries. The discretization of equations in time is done by means of high order explicit Runge-Kutta methods identified with respective Butcher tableaux. To stabilize a numerical solution in the vicinity of shock waves and simultaneously preserve the smooth parts from smearing, we add some reasonable amount of artificial viscosity in accordance with the physical principle of entropy production in the interior of shock waves. The viscosity coefficient is proportional to the local size of the residual of an entropy equation and is bounded from above by the first-order artificial viscosity defined by a local wave speed. Since the residual of an entropy equation is supposed to be vanishingly small in smooth regions (of the order of the Local Truncation Error) and arbitrarily large in shocks, the entropy viscosity is almost zero everywhere except the shocks, where it reaches the first-order upper bound. One- and two-dimensional benchmark test cases are presented for nonlinear hyperbolic scalar conservation laws and the system of compressible Euler equations. These tests demonstrate the satisfactory stability properties of the method and optimal convergence rates as well. All numerical solutions to the test problems agree well with the reference solutions found in the literature. We conclude that the new method developed in the present work is a valuable alternative to currently existing techniques of viscous stabilization.

Supply Rate and Equilibrium Inventory of Air Force Enlisted Personnel: A Simultaneous Model of the Accession and Retention Markets Incorporating Force Level Constraints. Final Report for Period July 1969-June 1976.

ERIC Educational Resources Information Center

DeVany, Arthur S.; And Others

This research was designed to develop and test a model of the Air Force manpower market. The study indicates that previous manpower supply studies failed to account for simultaneous determination of enlistments and retentions and misinterpreted regressions as supply equations. They are, instead, reduced form equations resulting from joint…

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.

Spectrophotometric and HPLC Methods for Simultaneous Estimation of Amlodipine Besilate, Losartan Potassium and Hydrochlorothiazide in Tablets

PubMed Central

Wankhede, S. B.; Raka, K. C.; Wadkar, S. B.; Chitlange, S. S.

2010-01-01

Two UV-spectrophotometric and one reverse phase high performance liquid chromatography methods have been developed for the simultaneous estimation of amlodipine besilate, losartan potassium and hydrochlorothiazide in tablet dosage form. The first UV spectrophotometric method was a determination using the simultaneous equation method at 236.5, 254 and 271 nm over the concentration range 5-25, 10-50 and 5-25 μg/ml for amlodipine besilate, losartan potassium and hydrochlorothiazide, respectively. The second UV method was a determination using the area under curve method at 231.5-241.5, 249-259 and 266-276 nm over the concentration range of 5-25, 5-25 and 10-50 μg/ml for amlodipine besilate, hydrochlorothiazide and losartan potassium, respectively. In reverse phase high performance liquid chromatography analysis is carried out using 0.025 M phosphate buffer (pH 3.7):acetonitrile (57:43 v/v) as the mobile phase and Kromasil C18 (4.6 mm i.d×250 mm) column as stationery phase with detection wavelength of 232 nm linearity was obtained in the concentration range of 2-14, 20-140 and 5-40 μg/ml for amlodipine besilate, losartan potassium and hydrochlorothiazide, respectively. Both UV-spectrophotometric and reverse phase high performance liquid chromatography methods were statistically validated and can be used for analysis of combined dose tablet formulation containing amlodipine besilate, losartan potassium and hydrochlorothiazide. PMID:20582208

Kinetic theory of oxygen isotopic exchange between minerals and water

USGS Publications Warehouse

Criss, R.E.; Gregory, R.T.; Taylor, H.P.

1987-01-01

Kinetic and mass conservation equations are used to describe oxygen isotopic exchange between minerals and water in "closed" and open hydrothermal systems. In cases where n coexisting mineral phases having different reaction rates are present, the exchange process is described by a system of n + 1 simultaneous differential equations consisting of n pseudo first-order rate equations and a conservation of mass equation. The simultaneous solutions to these equations generate curved exchange trajectories on ??-?? plots. Families of such trajectories generated under conditions allowing for different fluid mole fractions, different fluid isotopic compositions, or different fluid flow rates are connected by positive-sloped isochronous lines. These isochrons reproduce the effects observed in hydrothermally exchanged mineral pairs including 1) steep positive slopes, 2) common reversals in the measured fractionation factors (??), and 3) measured fractionations that are highly variable over short distances where no thermal gradient can be geologically demonstrated. ?? 1987.

A hybrid numerical technique for predicting the aerodynamic and acoustic fields of advanced turboprops

NASA Technical Reports Server (NTRS)

Homicz, G. F.; Moselle, J. R.

1985-01-01

A hybrid numerical procedure is presented for the prediction of the aerodynamic and acoustic performance of advanced turboprops. A hybrid scheme is proposed which in principle leads to a consistent simultaneous prediction of both fields. In the inner flow a finite difference method, the Approximate-Factorization Alternating-Direction-Implicit (ADI) scheme, is used to solve the nonlinear Euler equations. In the outer flow the linearized acoustic equations are solved via a Boundary-Integral Equation (BIE) method. The two solutions are iteratively matched across a fictitious interface in the flow so as to maintain continuity. At convergence the resulting aerodynamic load prediction will automatically satisfy the appropriate free-field boundary conditions at the edge of the finite difference grid, while the acoustic predictions will reflect the back-reaction of the radiated field on the magnitude of the loading source terms, as well as refractive effects in the inner flow. The equations and logic needed to match the two solutions are developed and the computer program implementing the procedure is described. Unfortunately, no converged solutions were obtained, due to unexpectedly large running times. The reasons for this are discussed and several means to alleviate the situation are suggested.

Hot QCD equations of state and relativistic heavy ion collisions

NASA Astrophysics Data System (ADS)

Chandra, Vinod; Kumar, Ravindra; Ravishankar, V.

2007-11-01

We study two recently proposed equations of state obtained from high-temperature QCD and show how they can be adapted to use them for making predictions for relativistic heavy ion collisions. The method involves extracting equilibrium distribution functions for quarks and gluons from the equation of state (EOS), which in turn will allow a determination of the transport and other bulk properties of the quark gluon-plasma. Simultaneously, the method also yields a quasiparticle description of interacting quarks and gluons. The first EOS is perturbative in the QCD coupling constant and has contributions of O(g5). The second EOS is an improvement over the first, with contributions up to O[g6ln(1/g)]; it incorporates the nonperturbative hard thermal contributions. The interaction effects are shown to be captured entirely by the effective chemical potentials for the gluons and the quarks, in both cases. The chemical potential is seen to be highly sensitive to the EOS. As an application, we determine the screening lengths, which are, indeed, the most important diagnostics for QGP. The screening lengths are seen to behave drastically differently depending on the EOS considered and therefore yield a way to distinguish the two equations of state in heavy ion collisions.

Determination of orbit chaoticity indicators with analytically normalized tangent vector. (Russian Title: Определение показателей хаотичности орбит с аналитически нормированным касательным вектором )

NASA Astrophysics Data System (ADS)

Shefer, V. A.

2011-07-01

Transformations of differential equations of the methods for determining the Lyapunov Characteristic Indicator and MEGNO indicators are suggested. The transformations improve the behavior of the differential equations by their simultaneous numerical integration. The use of the transformed equations is especially efficient for the investigation of orbits in stochastic regimes.

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.

Practical approximation method for firing-rate models of coupled neural networks with correlated inputs

NASA Astrophysics Data System (ADS)

Barreiro, Andrea K.; Ly, Cheng

2017-08-01

Rapid experimental advances now enable simultaneous electrophysiological recording of neural activity at single-cell resolution across large regions of the nervous system. Models of this neural network activity will necessarily increase in size and complexity, thus increasing the computational cost of simulating them and the challenge of analyzing them. Here we present a method to approximate the activity and firing statistics of a general firing rate network model (of the Wilson-Cowan type) subject to noisy correlated background inputs. The method requires solving a system of transcendental equations and is fast compared to Monte Carlo simulations of coupled stochastic differential equations. We implement the method with several examples of coupled neural networks and show that the results are quantitatively accurate even with moderate coupling strengths and an appreciable amount of heterogeneity in many parameters. This work should be useful for investigating how various neural attributes qualitatively affect the spiking statistics of coupled neural networks.

Cosmological constraints from strong gravitational lensing in clusters of galaxies.

PubMed

Jullo, Eric; Natarajan, Priyamvada; Kneib, Jean-Paul; D'Aloisio, Anson; Limousin, Marceau; Richard, Johan; Schimd, Carlo

2010-08-20

Current efforts in observational cosmology are focused on characterizing the mass-energy content of the universe. We present results from a geometric test based on strong lensing in galaxy clusters. Based on Hubble Space Telescope images and extensive ground-based spectroscopic follow-up of the massive galaxy cluster Abell 1689, we used a parametric model to simultaneously constrain the cluster mass distribution and dark energy equation of state. Combining our cosmological constraints with those from x-ray clusters and the Wilkinson Microwave Anisotropy Probe 5-year data gives Omega(m) = 0.25 +/- 0.05 and w(x) = -0.97 +/- 0.07, which are consistent with results from other methods. Inclusion of our method with all other available techniques brings down the current 2sigma contours on the dark energy equation-of-state parameter w(x) by approximately 30%.

On multiple crack identification by ultrasonic scanning

NASA Astrophysics Data System (ADS)

Brigante, M.; Sumbatyan, M. A.

2018-04-01

The present work develops an approach which reduces operator equations arising in the engineering problems to the problem of minimizing the discrepancy functional. For this minimization, an algorithm of random global search is proposed, which is allied to some genetic algorithms. The efficiency of the method is demonstrated by the solving problem of simultaneous identification of several linear cracks forming an array in an elastic medium by using the circular Ultrasonic scanning.

Calculation of reinforced-concrete frame strength under a simultaneous static cross section load and a column lateral impact

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

Belov, Nikolay, E-mail: n.n.belov@mail.ru; Kopanitsa, Dmitry, E-mail: kopanitsa@mail.ru; Yugov, Alexey, E-mail: yugalex@mail.ru

When designing buildings with reinforced concrete that are planned to resist dynamic loads it is necessary to calculate this structural behavior under operational static and emergency impact and blast loads. Calculations of the structures under shock-wave loads can be performed by solving dynamic equations that do not consider static loads. Due to this fact the calculation of reinforced concrete frame under a simultaneous static and dynamic load in full 3d settings becomes a very non trivial and resource consuming problem. This problem can be split into two tasks. The first one is a shock-wave problem that can be solved usingmore » software package RANET-3, which allows solving the problem using finite elements method adapted for dynamic task. This method calculates strain-stress state of the material and its dynamic destruction, which is considered as growth and consolidation of micro defects under loading. On the second step the results of the first step are taken as input parameters for quasi static calculation of simultaneous static and dynamic load using finite elements method in AMP Civil Engineering-11.« less

Simultaneous Localization and Mapping with Iterative Sparse Extended Information Filter for Autonomous Vehicles.

PubMed

He, Bo; Liu, Yang; Dong, Diya; Shen, Yue; Yan, Tianhong; Nian, Rui

2015-08-13

In this paper, a novel iterative sparse extended information filter (ISEIF) was proposed to solve the simultaneous localization and mapping problem (SLAM), which is very crucial for autonomous vehicles. The proposed algorithm solves the measurement update equations with iterative methods adaptively to reduce linearization errors. With the scalability advantage being kept, the consistency and accuracy of SEIF is improved. Simulations and practical experiments were carried out with both a land car benchmark and an autonomous underwater vehicle. Comparisons between iterative SEIF (ISEIF), standard EKF and SEIF are presented. All of the results convincingly show that ISEIF yields more consistent and accurate estimates compared to SEIF and preserves the scalability advantage over EKF, as well.

Computation of steady and unsteady quasi-one-dimensional viscous/inviscid interacting internal flows at subsonic, transonic, and supersonic Mach numbers

NASA Technical Reports Server (NTRS)

Swafford, Timothy W.; Huddleston, David H.; Busby, Judy A.; Chesser, B. Lawrence

1992-01-01

Computations of viscous-inviscid interacting internal flowfields are presented for steady and unsteady quasi-one-dimensional (Q1D) test cases. The unsteady Q1D Euler equations are coupled with integral boundary-layer equations for unsteady, two-dimensional (planar or axisymmetric), turbulent flow over impermeable, adiabatic walls. The coupling methodology differs from that used in most techniques reported previously in that the above mentioned equation sets are written as a complete system and solved simultaneously; that is, the coupling is carried out directly through the equations as opposed to coupling the solutions of the different equation sets. Solutions to the coupled system of equations are obtained using both explicit and implicit numerical schemes for steady subsonic, steady transonic, and both steady and unsteady supersonic internal flowfields. Computed solutions are compared with measurements as well as Navier-Stokes and inverse boundary-layer methods. An analysis of the eigenvalues of the coefficient matrix associated with the quasi-linear form of the coupled system of equations indicates the presence of complex eigenvalues for certain flow conditions. It is concluded that although reasonable solutions can be obtained numerically, these complex eigenvalues contribute to the overall difficulty in obtaining numerical solutions to the coupled system of equations.

Profiles of electrified drops and bubbles

NASA Technical Reports Server (NTRS)

Basaran, O. A.; Scriven, L. E.

1982-01-01

Axisymmetric equilibrium shapes of conducting drops and bubbles, (1) pendant or sessile on one face of a circular parallel-plate capacitor or (2) free and surface-charged, are found by solving simultaneously the free boundary problem consisting of the augmented Young-Laplace equation for surface shape and the Laplace equation for electrostatic field, given the surface potential. The problem is nonlinear and the method is a finite element algorithm employing Newton iteration, a modified frontal solver, and triangular as well as quadrilateral tessellations of the domain exterior to the drop in order to facilitate refined analysis of sharply curved drop tips seen in experiments. The stability limit predicted by this computer-aided theoretical analysis agrees well with experiments.

Substructure method in high-speed monorail dynamic problems

NASA Astrophysics Data System (ADS)

Ivanchenko, I. I.

2008-12-01

The study of actions of high-speed moving loads on bridges and elevated tracks remains a topical problem for transport. In the present study, we propose a new method for moving load analysis of elevated tracks (monorail structures or bridges), which permits studying the interaction between two strained objects consisting of rod systems and rigid bodies with viscoelastic links; one of these objects is the moving load (monorail rolling stock), and the other is the carrying structure (monorail elevated track or bridge). The methods for moving load analysis of structures were developed in numerous papers [1-15]. At the first stage, when solving the problem about a beam under the action of the simplest moving load such as a moving weight, two fundamental methods can be used; the same methods are realized for other structures and loads. The first method is based on the use of a generalized coordinate in the expansion of the deflection in the natural shapes of the beam, and the problem is reduced to solving a system of ordinary differential equations with variable coefficients [1-3]. In the second method, after the "beam-weight" system is decomposed, just as in the problem with the weight impact on the beam [4], solving the problem is reduced to solving an integral equation for the dynamic weight reaction [6, 7]. In [1-3], an increase in the number of retained forms leads to an increase in the order of the system of equations; in [6, 7], difficulties arise when solving the integral equations related to the conditional stability of the step procedures. The method proposed in [9, 14] for beams and rod systems combines the above approaches and eliminates their drawbacks, because it permits retaining any necessary number of shapes in the deflection expansion and has a resolving system of equations with an unconditionally stable integration scheme and with a minimum number of unknowns, just as in the method of integral equations [6, 7]. This method is further developed for combined schemes modeling a strained elastic compound moving structure and a monorail elevated track. The problems of development of methods for dynamic analysis of monorails are very topical, especially because of increasing speeds of the rolling stock motion. These structures are studied in [16-18]. In the present paper, the above problem is solved by using the method for the moving load analysis and a step procedure of integration with respect to time, which were proposed in [9, 19], respectively. Further, these components are used to enlarge the possibilities of the substructure method in problems of dynamics. In the approach proposed for moving load analysis of structures, for a substructure (having the shape of a boundary element or a superelement) we choose an object moving at a constant speed (a monorail rolling stock); in this case, we use rod boundary elements of large length, which are gathered in a system modeling these objects. In particular, sets of such elements form a model of a monorail rolling stock, namely, carriage hulls, wheeled carts, elements of the wheel spring suspension, models of continuous beams of monorail ways and piers with foundations admitting emergency subsidence and unilateral links. These specialized rigid finite elements with linear and nonlinear links, included into the set of earlier proposed finite elements [14, 19], permit studying unsteady vibrations in the "monorail train-elevated track" (MTET) system taking into account various irregularities on the beam-rail, the pier emergency subsidence, and their elastic support by the basement. In this case, a high degree of the structure spatial digitization is obtained by using rods with distributed parameters in the analysis. The displacements are approximated by linear functions and trigonometric Fourier series, which, as was already noted, permits increasing the number of degrees of freedom of the system under study simultaneously preserving the order of the resolving system of equations. This approach permits studying the stress-strain state in the MTET system and determining accelerations at the desired points of the rolling stock. The proposed numerical procedure permits uniquely solving linear and nonlinear differential equations describing the operation of the model, which replaces the system by a monorail rolling stock consisting of several specialized mutually connected cars and a system of continuous beams on elastic inertial supports. This approach (based on the use of a moving substructure, which is also modeled by a system of boundary rod elements) permits maximally reducing the number of unknowns in the resolving system of equations at each step of its solution [11]. The authors of the preceding investigations of this problem, when studying the simultaneous vibrations of bridges and moving loads, considered only the case in which the rolling stock was represented by sufficiently complicated systems of rigid bodies connected by viscoelastic links [3-18] and the rolling stock motion was described by systems of ordinary differential equations. A specific characteristic of the proposed method is that it is convenient to derive the equations of motion of both the rolling stock and the bridge structure. The method [9, 14] permits obtaining the equations of interaction between the structures as two separate finite-element structures. Hence the researcher need not traditionally write out the system of equations of motion, for example, for the rolling stock (of cars) with finitely many degrees of freedom [3-18].We note several papers where simultaneous vibrations of an elastic moving load and an elastic carrying structure are considered in a rather narrow region and have a specific character. For example, the motion of an elastic rod along an elastic infinite rod on an elastic foundation is studied in [20], and the body of a car moving along a beam is considered as a rod with ten concentrated masses in [21].

Inter-Slice Blood Flow and Magnetization Transfer Effects as A New Simultaneous Imaging Strategy.

PubMed

Han, Paul Kyu; Barker, Jeffrey W; Kim, Ki Hwan; Choi, Seung Hong; Bae, Kyongtae Ty; Park, Sung-Hong

2015-01-01

The recent blood flow and magnetization transfer (MT) technique termed alternate ascending/descending directional navigation (ALADDIN) achieves the contrast using interslice blood flow and MT effects with no separate preparation RF pulse, thereby potentially overcoming limitations of conventional methods. In this study, we examined the signal characteristics of ALADDIN as a simultaneous blood flow and MT imaging strategy, by comparing it with pseudo-continuous ASL (pCASL) and conventional MT asymmetry (MTA) methods, all of which had the same bSSFP readout. Bloch-equation simulations and experiments showed ALADDIN perfusion signals increased with flip angle, whereas MTA signals peaked at flip angle around 45°-60°. ALADDIN provided signals comparable to those of pCASL and conventional MTA methods emulating the first, second, and third prior slices of ALADDIN under the same scan conditions, suggesting ALADDIN signals to be superposition of signals from multiple labeling planes. The quantitative cerebral blood flow signals from a modified continuous ASL model overestimated the perfusion signals compared to those measured with a pulsed ASL method. Simultaneous mapping of blood flow, MTA, and MT ratio in the whole brain is feasible with ALADDIN within a clinically reasonable time, which can potentially help diagnosis of various diseases.

Numerical analysis method for linear induction machines.

NASA Technical Reports Server (NTRS)

Elliott, D. G.

1972-01-01

A numerical analysis method has been developed for linear induction machines such as liquid metal MHD pumps and generators and linear motors. Arbitrary phase currents or voltages can be specified and the moving conductor can have arbitrary velocity and conductivity variations from point to point. The moving conductor is divided into a mesh and coefficients are calculated for the voltage induced at each mesh point by unit current at every other mesh point. Combining the coefficients with the mesh resistances yields a set of simultaneous equations which are solved for the unknown currents.

A PDE approach for quantifying and visualizing tumor progression and regression

NASA Astrophysics Data System (ADS)

Sintay, Benjamin J.; Bourland, J. Daniel

2009-02-01

Quantification of changes in tumor shape and size allows physicians the ability to determine the effectiveness of various treatment options, adapt treatment, predict outcome, and map potential problem sites. Conventional methods are often based on metrics such as volume, diameter, or maximum cross sectional area. This work seeks to improve the visualization and analysis of tumor changes by simultaneously analyzing changes in the entire tumor volume. This method utilizes an elliptic partial differential equation (PDE) to provide a roadmap of boundary displacement that does not suffer from the discontinuities associated with other measures such as Euclidean distance. Streamline pathways defined by Laplace's equation (a commonly used PDE) are used to track tumor progression and regression at the tumor boundary. Laplace's equation is particularly useful because it provides a smooth, continuous solution that can be evaluated with sub-pixel precision on variable grid sizes. Several metrics are demonstrated including maximum, average, and total regression and progression. This method provides many advantages over conventional means of quantifying change in tumor shape because it is observer independent, stable for highly unusual geometries, and provides an analysis of the entire three-dimensional tumor volume.

New nonlinear control algorithms for multiple robot arms

NASA Technical Reports Server (NTRS)

Tarn, T. J.; Bejczy, A. K.; Yun, X.

1988-01-01

Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space.

High-Order Implicit-Explicit Multi-Block Time-stepping Method for Hyperbolic PDEs

NASA Technical Reports Server (NTRS)

Nielsen, Tanner B.; Carpenter, Mark H.; Fisher, Travis C.; Frankel, Steven H.

2014-01-01

This work seeks to explore and improve the current time-stepping schemes used in computational fluid dynamics (CFD) in order to reduce overall computational time. A high-order scheme has been developed using a combination of implicit and explicit (IMEX) time-stepping Runge-Kutta (RK) schemes which increases numerical stability with respect to the time step size, resulting in decreased computational time. The IMEX scheme alone does not yield the desired increase in numerical stability, but when used in conjunction with an overlapping partitioned (multi-block) domain significant increase in stability is observed. To show this, the Overlapping-Partition IMEX (OP IMEX) scheme is applied to both one-dimensional (1D) and two-dimensional (2D) problems, the nonlinear viscous Burger's equation and 2D advection equation, respectively. The method uses two different summation by parts (SBP) derivative approximations, second-order and fourth-order accurate. The Dirichlet boundary conditions are imposed using the Simultaneous Approximation Term (SAT) penalty method. The 6-stage additive Runge-Kutta IMEX time integration schemes are fourth-order accurate in time. An increase in numerical stability 65 times greater than the fully explicit scheme is demonstrated to be achievable with the OP IMEX method applied to 1D Burger's equation. Results from the 2D, purely convective, advection equation show stability increases on the order of 10 times the explicit scheme using the OP IMEX method. Also, the domain partitioning method in this work shows potential for breaking the computational domain into manageable sizes such that implicit solutions for full three-dimensional CFD simulations can be computed using direct solving methods rather than the standard iterative methods currently used.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Serazio, C.; Chacon, L.; Lapenta, G.

2006-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. Crucial elements are the development of an effective multilevel treatment of the grid equation, and a robust, rigorous error estimator. For the latter, we explore the effectiveness of a coarse grid correction error estimator, which faithfully reproduces spatial truncation errors for conservative equations. We will show that the moving mesh approach is competitive vs. uniform grids both in accuracy (due to adaptivity) and efficiency. Results for a variety of models 1D and 2D geometries will be presented. L. Chac'on, G. Lapenta, J. Comput. Phys., 212 (2), 703 (2006) G. Lapenta, L. Chac'on, J. Comput. Phys., accepted (2006)

Scilab software as an alternative low-cost computing in solving the linear equations problem

NASA Astrophysics Data System (ADS)

Agus, Fahrul; Haviluddin

2017-02-01

Numerical computation packages are widely used both in teaching and research. These packages consist of license (proprietary) and open source software (non-proprietary). One of the reasons to use the package is a complexity of mathematics function (i.e., linear problems). Also, number of variables in a linear or non-linear function has been increased. The aim of this paper was to reflect on key aspects related to the method, didactics and creative praxis in the teaching of linear equations in higher education. If implemented, it could be contribute to a better learning in mathematics area (i.e., solving simultaneous linear equations) that essential for future engineers. The focus of this study was to introduce an additional numerical computation package of Scilab as an alternative low-cost computing programming. In this paper, Scilab software was proposed some activities that related to the mathematical models. In this experiment, four numerical methods such as Gaussian Elimination, Gauss-Jordan, Inverse Matrix, and Lower-Upper Decomposition (LU) have been implemented. The results of this study showed that a routine or procedure in numerical methods have been created and explored by using Scilab procedures. Then, the routine of numerical method that could be as a teaching material course has exploited.

Sequential-Simultaneous Analysis of Japanese Children's Performance on the Japanese McCarthy.

ERIC Educational Resources Information Center

Ishikuma, Toshinori; And Others

This study explored the hypothesis that Japanese children perform significantly better on simultaneous processing than on sequential processing. The Kaufman Assessment Battery for Children (K-ABC) served as the criterion of the two types of mental processing. Regression equations to predict Sequential and Simultaneous processing from McCarthy…

Unleashing Empirical Equations with "Nonlinear Fitting" and "GUM Tree Calculator"

NASA Astrophysics Data System (ADS)

Lovell-Smith, J. W.; Saunders, P.; Feistel, R.

2017-10-01

Empirical equations having large numbers of fitted parameters, such as the international standard reference equations published by the International Association for the Properties of Water and Steam (IAPWS), which form the basis of the "Thermodynamic Equation of Seawater—2010" (TEOS-10), provide the means to calculate many quantities very accurately. The parameters of these equations are found by least-squares fitting to large bodies of measurement data. However, the usefulness of these equations is limited since uncertainties are not readily available for most of the quantities able to be calculated, the covariance of the measurement data is not considered, and further propagation of the uncertainty in the calculated result is restricted since the covariance of calculated quantities is unknown. In this paper, we present two tools developed at MSL that are particularly useful in unleashing the full power of such empirical equations. "Nonlinear Fitting" enables propagation of the covariance of the measurement data into the parameters using generalized least-squares methods. The parameter covariance then may be published along with the equations. Then, when using these large, complex equations, "GUM Tree Calculator" enables the simultaneous calculation of any derived quantity and its uncertainty, by automatic propagation of the parameter covariance into the calculated quantity. We demonstrate these tools in exploratory work to determine and propagate uncertainties associated with the IAPWS-95 parameters.

Equation of state of paramagnetic CrN from ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

Steneteg, Peter; Alling, Björn; Abrikosov, Igor A.

2012-04-01

The equation of state for chromium nitride has been debated in the literature in connection with a proposed collapse of its bulk modulus following the pressure-induced transition from the paramagnetic cubic phase to the antiferromagnetic orthorhombic phase [F. Rivadulla , Nature Mater.1476-112210.1038/nmat2549 8, 947 (2009); B. Alling , Nature Mater.1476-112210.1038/nmat2722 9, 283 (2010)]. Experimentally the measurements are complicated due to the low transition pressure, while theoretically the simulation of magnetic disorder represents a major challenge. Here a first-principles method is suggested for the calculation of thermodynamic properties of magnetic materials in their high-temperature paramagnetic phase. It is based on ab initio molecular dynamics and simultaneous redistributions of the disordered but finite local magnetic moments. We apply this disordered local moments molecular dynamics method to the case of CrN and simulate its equation of state. In particular the debated bulk modulus is calculated in the paramagnetic cubic phase and is shown to be very similar to that of the antiferromagnetic orthorhombic CrN phase for all considered temperatures.

A new look at the simultaneous analysis and design of structures

NASA Technical Reports Server (NTRS)

Striz, Alfred G.

1994-01-01

The minimum weight optimization of structural systems, subject to strength and displacement constraints as well as size side constraints, was investigated by the Simultaneous ANalysis and Design (SAND) approach. As an optimizer, the code NPSOL was used which is based on a sequential quadratic programming (SQP) algorithm. The structures were modeled by the finite element method. The finite element related input to NPSOL was automatically generated from the input decks of such standard FEM/optimization codes as NASTRAN or ASTROS, with the stiffness matrices, at present, extracted from the FEM code ANALYZE. In order to avoid ill-conditioned matrices that can be encountered when the global stiffness equations are used as additional nonlinear equality constraints in the SAND approach (with the displacements as additional variables), the matrix displacement method was applied. In this approach, the element stiffness equations are used as constraints instead of the global stiffness equations, in conjunction with the nodal force equilibrium equations. This approach adds the element forces as variables to the system. Since, for complex structures and the associated large and very sparce matrices, the execution times of the optimization code became excessive due to the large number of required constraint gradient evaluations, the Kreisselmeier-Steinhauser function approach was used to decrease the computational effort by reducing the nonlinear equality constraint system to essentially a single combined constraint equation. As the linear equality and inequality constraints require much less computational effort to evaluate, they were kept in their previous form to limit the complexity of the KS function evaluation. To date, the standard three-bar, ten-bar, and 72-bar trusses have been tested. For the standard SAND approach, correct results were obtained for all three trusses although convergence became slower for the 72-bar truss. When the matrix displacement method was used, correct results were still obtained, but the execution times became excessive due to the large number of constraint gradient evaluations required. Using the KS function, the computational effort dropped, but the optimization seemed to become less robust. The investigation of this phenomenon is continuing. As an alternate approach, the code MINOS for the optimization of sparse matrices can be applied to the problem in lieu of the Kreisselmeier-Steinhauser function. This investigation is underway.

An analytic method to account for drag in the Vinti Satellite theory

NASA Technical Reports Server (NTRS)

Watson, J. S.; Mistretta, G. D.; Bonavito, N. L.

1974-01-01

To retain separability in the Vinti theory of earth satellite motion when a nonconservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In this approach, the Hamiltonian is preserved in form, and remains the total energy, but the initial or boundary conditions and hence the Jacobi constants of the motion advance with time through the variational equations. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabular data at all altitudes and simultaneously reduced the variational equations to indefinite integrals with closed form evaluations. The values of the limits for any arbitrary time interval are obtained from the Vinti program.

Fokker-Planck-Based Acceleration for SN Equations with Highly Forward Peaked Scattering in Slab Geometry

NASA Astrophysics Data System (ADS)

Patel, Japan

Short mean free paths are characteristic of charged particles. High energy charged particles often have highly forward peaked scattering cross sections. Transport problems involving such charged particles are also highly optically thick. When problems simultaneously have forward peaked scattering and high optical thickness, their solution, using standard iterative methods, becomes very inefficient. In this dissertation, we explore Fokker-Planck-based acceleration for solving such problems.

Simultaneous reconstruction of 3D refractive index, temperature, and intensity distribution of combustion flame by double computed tomography technologies based on spatial phase-shifting method

NASA Astrophysics Data System (ADS)

Guo, Zhenyan; Song, Yang; Yuan, Qun; Wulan, Tuya; Chen, Lei

2017-06-01

In this paper, a transient multi-parameter three-dimensional (3D) reconstruction method is proposed to diagnose and visualize a combustion flow field. Emission and transmission tomography based on spatial phase-shifted technology are combined to reconstruct, simultaneously, the various physical parameter distributions of a propane flame. Two cameras triggered by the internal trigger mode capture the projection information of the emission and moiré tomography, respectively. A two-step spatial phase-shifting method is applied to extract the phase distribution in the moiré fringes. By using the filtered back-projection algorithm, we reconstruct the 3D refractive-index distribution of the combustion flow field. Finally, the 3D temperature distribution of the flame is obtained from the refractive index distribution using the Gladstone-Dale equation. Meanwhile, the 3D intensity distribution is reconstructed based on the radiation projections from the emission tomography. Therefore, the structure and edge information of the propane flame are well visualized.

Optimal cure cycle design of a resin-fiber composite laminate

NASA Technical Reports Server (NTRS)

Hou, Jean W.; Sheen, Jeenson

1987-01-01

A unified computed aided design method was studied for the cure cycle design that incorporates an optimal design technique with the analytical model of a composite cure process. The preliminary results of using this proposed method for optimal cure cycle design are reported and discussed. The cure process of interest is the compression molding of a polyester which is described by a diffusion reaction system. The finite element method is employed to convert the initial boundary value problem into a set of first order differential equations which are solved simultaneously by the DE program. The equations for thermal design sensitivities are derived by using the direct differentiation method and are solved by the DE program. A recursive quadratic programming algorithm with an active set strategy called a linearization method is used to optimally design the cure cycle, subjected to the given design performance requirements. The difficulty of casting the cure cycle design process into a proper mathematical form is recognized. Various optimal design problems are formulated to address theses aspects. The optimal solutions of these formulations are compared and discussed.

Students' conceptual performance on synthesis physics problems with varying mathematical complexity

NASA Astrophysics Data System (ADS)

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-06-01

A body of research on physics problem solving has focused on single-concept problems. In this study we use "synthesis problems" that involve multiple concepts typically taught in different chapters. We use two types of synthesis problems, sequential and simultaneous synthesis tasks. Sequential problems require a consecutive application of fundamental principles, and simultaneous problems require a concurrent application of pertinent concepts. We explore students' conceptual performance when they solve quantitative synthesis problems with varying mathematical complexity. Conceptual performance refers to the identification, follow-up, and correct application of the pertinent concepts. Mathematical complexity is determined by the type and the number of equations to be manipulated concurrently due to the number of unknowns in each equation. Data were collected from written tasks and individual interviews administered to physics major students (N =179 ) enrolled in a second year mechanics course. The results indicate that mathematical complexity does not impact students' conceptual performance on the sequential tasks. In contrast, for the simultaneous problems, mathematical complexity negatively influences the students' conceptual performance. This difference may be explained by the students' familiarity with and confidence in particular concepts coupled with cognitive load associated with manipulating complex quantitative equations. Another explanation pertains to the type of synthesis problems, either sequential or simultaneous task. The students split the situation presented in the sequential synthesis tasks into segments but treated the situation in the simultaneous synthesis tasks as a single event.

Equations for the Filled Inelastic Membrane: A More General Derivation

ERIC Educational Resources Information Center

Deakin, Michael A. B.

2011-01-01

An earlier paper discussed the case of a flexible but inextensible membrane filled to capacity with incompressible fluid. It was found that the resulting shape satisfies a set of three simultaneous partial differential equations. This article gives a more general derivation of these equations and shows their form in an interesting special case.

Hybrid numerical method for solution of the radiative transfer equation in one, two, or three dimensions.

PubMed

Reinersman, Phillip N; Carder, Kendall L

2004-05-01

A hybrid method is presented by which Monte Carlo (MC) techniques are combined with an iterative relaxation algorithm to solve the radiative transfer equation in arbitrary one-, two-, or three-dimensional optical environments. The optical environments are first divided into contiguous subregions, or elements. MC techniques are employed to determine the optical response function of each type of element. The elements are combined, and relaxation techniques are used to determine simultaneously the radiance field on the boundary and throughout the interior of the modeled environment. One-dimensional results compare well with a standard radiative transfer model. The light field beneath and adjacent to a long barge is modeled in two dimensions and displayed. Ramifications for underwater video imaging are discussed. The hybrid model is currently capable of providing estimates of the underwater light field needed to expedite inspection of ship hulls and port facilities.

Communication on SWIPT and EH Using Electromagnetic Behaviour for Power Allocation in Wireless Networks

NASA Astrophysics Data System (ADS)

Khan, Sohel Rana; Ajij, Sayyad

2017-12-01

This review paper focuses on the basic relations between wireless power transfer, wireless information transfer and combined phenomenon of simultaneous wireless information and power transfer. The authors reviewed and discussed electromagnetic fields behaviour (EMB) for enhancing the power allocation strategies (PAS) in energy harvesting (EH) wireless communication systems. Further, this paper presents relations between Friis transmission equation and Maxwell's equations to be used in propagation models for reduction in specific absorption rate (SAR). This paper provides a review of various methods and concepts reported in earlier works. This paper also reviews Poynting vector and power densities along with boundary conditions for antennas and human body. Finally, this paper explores the usage of electromagnetic behaviour for the possible enhancement in power saving methods for electromagnetic behaviour centered-wireless energy harvesting (EMBC-WEH). At the same time, possibilities of PAS for reduction in SAR are discussed.

Stress analysis of rotating propellers subject to forced excitations

NASA Astrophysics Data System (ADS)

Akgun, Ulas

Turbine blades experience vibrations due to the flow disturbances. These vibrations are the leading cause for fatigue failure in turbine blades. This thesis presents the finite element analysis methods to estimate the maximum vibrational stresses of rotating structures under forced excitation. The presentation included starts with the derived equations of motion for vibration of rotating beams using energy methods under the Euler Bernoulli beam assumptions. The nonlinear large displacement formulation captures the centrifugal stiffening and gyroscopic effects. The weak form of the equations and their finite element discretization are shown. The methods implemented were used for normal modes analyses and forced vibration analyses of rotating beam structures. The prediction of peak stresses under simultaneous multi-mode excitation show that the maximum vibrational stresses estimated using the linear superposition of the stresses can greatly overestimate the stresses if the phase information due to damping (physical and gyroscopic effects) are neglected. The last section of this thesis also presents the results of a practical study that involves finite element analysis and redesign of a composite propeller.

Double density dynamics: realizing a joint distribution of a physical system and a parameter system

NASA Astrophysics Data System (ADS)

Fukuda, Ikuo; Moritsugu, Kei

2015-11-01

To perform a variety of types of molecular dynamics simulations, we created a deterministic method termed ‘double density dynamics’ (DDD), which realizes an arbitrary distribution for both physical variables and their associated parameters simultaneously. Specifically, we constructed an ordinary differential equation that has an invariant density relating to a joint distribution of the physical system and the parameter system. A generalized density function leads to a physical system that develops under nonequilibrium environment-describing superstatistics. The joint distribution density of the physical system and the parameter system appears as the Radon-Nikodym derivative of a distribution that is created by a scaled long-time average, generated from the flow of the differential equation under an ergodic assumption. The general mathematical framework is fully discussed to address the theoretical possibility of our method, and a numerical example representing a 1D harmonic oscillator is provided to validate the method being applied to the temperature parameters.

Simultaneous Localization and Mapping with Iterative Sparse Extended Information Filter for Autonomous Vehicles

PubMed Central

He, Bo; Liu, Yang; Dong, Diya; Shen, Yue; Yan, Tianhong; Nian, Rui

2015-01-01

In this paper, a novel iterative sparse extended information filter (ISEIF) was proposed to solve the simultaneous localization and mapping problem (SLAM), which is very crucial for autonomous vehicles. The proposed algorithm solves the measurement update equations with iterative methods adaptively to reduce linearization errors. With the scalability advantage being kept, the consistency and accuracy of SEIF is improved. Simulations and practical experiments were carried out with both a land car benchmark and an autonomous underwater vehicle. Comparisons between iterative SEIF (ISEIF), standard EKF and SEIF are presented. All of the results convincingly show that ISEIF yields more consistent and accurate estimates compared to SEIF and preserves the scalability advantage over EKF, as well. PMID:26287194

Simultaneous Determination of Ofloxacin and Flavoxate Hydrochloride by Absorption Ratio and Second Derivative UV Spectrophotometry

PubMed Central

Attimarad, Mahesh

2010-01-01

The objective of this study was to develop simple, precise, accurate and sensitive UV spectrophotometric methods for the simultaneous determination of ofloxacin (OFX) and flavoxate HCl (FLX) in pharmaceutical formulations. The first method is based on absorption ratio method, by formation of Q absorbance equation at 289 nm (λmax of OFX) and 322.4 nm (isoabsorptive point). The linearity range was found to be 1 to 30 μg/ml for FLX and OFX. In the method-II second derivative absorption at 311.4 nm for OFX (zero crossing for FLX) and at 246.2 nm for FLX (zero crossing for OFX) was used for the determination of the drugs and the linearity range was found to be 2 to 30 μg/ml for OFX and 2-75 μg /ml for FLX. The accuracy and precision of the methods were determined and validated statistically. Both the methods showed good reproducibility and recovery with % RSD less than 1.5%. Both the methods were found to be rapid, specific, precise and accurate and can be successfully applied for the routine analysis of OFX and FLX in combined dosage form PMID:24826003

Numerical simulation code for self-gravitating Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Madarassy, Enikő J. M.; Toth, Viktor T.

2013-04-01

We completed the development of simulation code that is designed to study the behavior of a conjectured dark matter galactic halo that is in the form of a Bose-Einstein Condensate (BEC). The BEC is described by the Gross-Pitaevskii equation, which can be solved numerically using the Crank-Nicholson method. The gravitational potential, in turn, is described by Poisson’s equation, that can be solved using the relaxation method. Our code combines these two methods to study the time evolution of a self-gravitating BEC. The inefficiency of the relaxation method is balanced by the fact that in subsequent time iterations, previously computed values of the gravitational field serve as very good initial estimates. The code is robust (as evidenced by its stability on coarse grids) and efficient enough to simulate the evolution of a system over the course of 109 years using a finer (100×100×100) spatial grid, in less than a day of processor time on a contemporary desktop computer. Catalogue identifier: AEOR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOR_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5248 No. of bytes in distributed program, including test data, etc.: 715402 Distribution format: tar.gz Programming language: C++ or FORTRAN. Computer: PCs or workstations. Operating system: Linux or Windows. Classification: 1.5. Nature of problem: Simulation of a self-gravitating Bose-Einstein condensate by simultaneous solution of the Gross-Pitaevskii and Poisson equations in three dimensions. Solution method: The Gross-Pitaevskii equation is solved numerically using the Crank-Nicholson method; Poisson’s equation is solved using the relaxation method. The time evolution of the system is governed by the Gross-Pitaevskii equation; the solution of Poisson’s equation at each time step is used as an initial estimate for the next time step, which dramatically increases the efficiency of the relaxation method. Running time: Depends on the chosen size of the problem. On a typical personal computer, a 100×100×100 grid can be solved with a time span of 10 Gyr in approx. a day of running time.

Inversion of solar extinction data from the Apollo-Soyuz Test Project Stratospheric Aerosol Measurement (ASTP/SAM) experiment

NASA Technical Reports Server (NTRS)

Pepin, T. J.

1977-01-01

The inversion methods are reported that have been used to determine the vertical profile of the extinction coefficient due to the stratospheric aerosols from data measured during the ASTP/SAM solar occultation experiment. Inversion methods include the onion skin peel technique and methods of solving the Fredholm equation for the problem subject to smoothing constraints. The latter of these approaches involves a double inversion scheme. Comparisons are made between the inverted results from the SAM experiment and near simultaneous measurements made by lidar and balloon born dustsonde. The results are used to demonstrate the assumptions required to perform the inversions for aerosols.

Describing the dynamics of processes consisting simultaneously of Poissonian and non-Poissonian kinetics

NASA Astrophysics Data System (ADS)

Eule, S.; Friedrich, R.

2013-03-01

Dynamical processes exhibiting non-Poissonian kinetics with nonexponential waiting times are frequently encountered in nature. Examples are biochemical processes like gene transcription which are known to involve multiple intermediate steps. However, often a second process, obeying Poissonian statistics, affects the first one simultaneously, such as the degradation of mRNA in the above example. The aim of the present article is to provide a concise treatment of such random systems which are affected by regular and non-Poissonian kinetics at the same time. We derive the governing master equation and provide a controlled approximation scheme for this equation. The simplest approximation leads to generalized reaction rate equations. For a simple model of gene transcription we solve the resulting equation and show how the time evolution is influenced significantly by the type of waiting time distribution assumed for the non-Poissonian process.

Predicting chemical degradation during storage from two successive concentration ratios: Theoretical investigation.

PubMed

Peleg, Micha; Normand, Mark D

2015-09-01

When a vitamin's, pigment's or other food component's chemical degradation follows a known fixed order kinetics, and its rate constant's temperature-dependence follows a two parameter model, then, at least theoretically, it is possible to extract these two parameters from two successive experimental concentration ratios determined during the food's non-isothermal storage. This requires numerical solution of two simultaneous equations, themselves the numerical solutions of two differential rate equations, with a program especially developed for the purpose. Once calculated, these parameters can be used to reconstruct the entire degradation curve for the particular temperature history and predict the degradation curves for other temperature histories. The concept and computation method were tested with simulated degradation under rising and/or falling oscillating temperature conditions, employing the exponential model to characterize the rate constant's temperature-dependence. In computer simulations, the method's predictions were robust against minor errors in the two concentration ratios. The program to do the calculations was posted as freeware on the Internet. The temperature profile can be entered as an algebraic expression that can include 'If' statements, or as an imported digitized time-temperature data file, to be converted into an Interpolating Function by the program. The numerical solution of the two simultaneous equations requires close initial guesses of the exponential model's parameters. Programs were devised to obtain these initial values by matching the two experimental concentration ratios with a generated degradation curve whose parameters can be varied manually with sliders on the screen. These programs too were made available as freeware on the Internet and were tested with published data on vitamin A. Copyright © 2015 Elsevier Ltd. All rights reserved.

Computers and Mathematics

DTIC Science & Technology

1989-01-01

Signs of Algebraic Numbers T. Sakkalis, New Mexico State University, Las Cruces ................................. 130 Efficient Reduction of Quadratic...equations. These equations are solved for dl,.. , d. and el ’.. e,, and a basis of minimal non-zero simultaneous solutions in which if d1 # 0, then ei = 0 and...and < el ,..,- emm d, dm > need to be considered because of the symmetric nature of the diophantine equations. These equations can be solved using

Geometric multigrid for an implicit-time immersed boundary method

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

Guy, Robert D.; Philip, Bobby; Griffith, Boyce E.

2014-10-12

The immersed boundary (IB) method is an approach to fluid-structure interaction that uses Lagrangian variables to describe the deformations and resulting forces of the structure and Eulerian variables to describe the motion and forces of the fluid. Explicit time stepping schemes for the IB method require solvers only for Eulerian equations, for which fast Cartesian grid solution methods are available. Such methods are relatively straightforward to develop and are widely used in practice but often require very small time steps to maintain stability. Implicit-time IB methods permit the stable use of large time steps, but efficient implementations of such methodsmore » require significantly more complex solvers that effectively treat both Lagrangian and Eulerian variables simultaneously. Moreover, several different approaches to solving the coupled Lagrangian-Eulerian equations have been proposed, but a complete understanding of this problem is still emerging. This paper presents a geometric multigrid method for an implicit-time discretization of the IB equations. This multigrid scheme uses a generalization of box relaxation that is shown to handle problems in which the physical stiffness of the structure is very large. Numerical examples are provided to illustrate the effectiveness and efficiency of the algorithms described herein. Finally, these tests show that using multigrid as a preconditioner for a Krylov method yields improvements in both robustness and efficiency as compared to using multigrid as a solver. They also demonstrate that with a time step 100–1000 times larger than that permitted by an explicit IB method, the multigrid-preconditioned implicit IB method is approximately 50–200 times more efficient than the explicit method.« less

The Elasto-Plastic Stability of Plates

NASA Technical Reports Server (NTRS)

Ilyushin, A. A.

1947-01-01

This article explains results developed from the following research: 'The Stability of Plates and Shells beyond the Elastic Limit.' A significant improvement is found in the derivation of the relations between the stress factors and the strains resulting from the instability of plates and shells. In a strict analysis, the problem reduces to the solution of two simultaneous nonlinear partial differential equations of the fourth order in the deflection and stress function, and in the approximate analysis to a single linear equation of the Bryan type. Solutions are given for the special cases of a rectangular plate buckling into a cylindrical form, and of an arbitrarily shaped plate under uniform compression. These solutions indicate that the accuracy obtained by the approximate method is satisfactory.

Elastic effects on vibration of bilayer graphene sheets incorporating integrated VdWs interactions

NASA Astrophysics Data System (ADS)

Kamali, Kamran; Nazemnezhad, Reza; Zare, Mojtaba

2018-03-01

The following study addresses the free vibration analysis of a bilayer graphene sheet (BLGS) embedded in an elastic medium in the presence of shear and tensile-compressive effects of van der Waals (vdWs) interactions. To ascertain the contribution of each force, the effects are considered separately and simultaneously. To model the geometry of the BLGS, the sandwich plate theory and the Hamilton’s principle are considered to derive the governing equations of motion. The Harmonic differential quadrature method is applied to solve the coupled equations and obtain the natural frequencies and related mode shapes. The results reveal that the contribution of tensile-compressive modulus of elastic medium is the most in changing the frequency of BLGSs.

A level set-based topology optimization method for simultaneous design of elastic structure and coupled acoustic cavity using a two-phase material model

NASA Astrophysics Data System (ADS)

Noguchi, Yuki; Yamamoto, Takashi; Yamada, Takayuki; Izui, Kazuhiro; Nishiwaki, Shinji

2017-09-01

This papers proposes a level set-based topology optimization method for the simultaneous design of acoustic and structural material distributions. In this study, we develop a two-phase material model that is a mixture of an elastic material and acoustic medium, to represent an elastic structure and an acoustic cavity by controlling a volume fraction parameter. In the proposed model, boundary conditions at the two-phase material boundaries are satisfied naturally, avoiding the need to express these boundaries explicitly. We formulate a topology optimization problem to minimize the sound pressure level using this two-phase material model and a level set-based method that obtains topologies free from grayscales. The topological derivative of the objective functional is approximately derived using a variational approach and the adjoint variable method and is utilized to update the level set function via a time evolutionary reaction-diffusion equation. Several numerical examples present optimal acoustic and structural topologies that minimize the sound pressure generated from a vibrating elastic structure.

Transient Torque Method: A Fast and Nonintrusive Technique to Simultaneously Determine Viscosity and Electrical Conductivity of Semiconducting and Metallic Melts

NASA Technical Reports Server (NTRS)

Li, C.; Ban, H.; Lin, B.; Scripa, R. N.; Su, C.-H.; Lehoczky, S. L.; Zhu, S.

2004-01-01

A transient torque method was developed to rapidly and simultaneously determine the viscosity and electrical conductivity of liquid metals and molten semiconductors. The experimental setup of the transient torque method is similar to that of the oscillation cup method. The melt sample is sealed inside a fused silica ampoule, and the ampoule is suspended by a long quartz fiber to form a torsional oscillation system. A rotating magnetic field is used to induce a rotating flow in the conductive melt, which causes the ampoule to rotate around its vertical axis. A sensitive angular detector is used to measure the deflection angle of the ampoule. Based on the transient behavior of the deflection angle as the rotating magnetic field is applied, the electrical conductivity and viscosity of the melt can be obtained simultaneously by numerically fitting the data to a set of governing equations. The transient torque viscometer was applied successfully to measure the viscosity and electrical conductivity of high purity mercury at 53.4 C. The results were in excellent agreement with published data. The method is nonintrusive; capable of rapid measurement of the viscosity of toxic, high vapor pressure melts at elevated temperatures. In addition, the transient torque viscometer can also be operated as an oscillation cup viscometer to measure just the viscosity of the melt or as a rotating magnetic field method to determine the electrical conductivity of a melt or a solid if desired.

Asymptotic properties of blow-up solutions in reaction-diffusion equations with nonlocal boundary flux

NASA Astrophysics Data System (ADS)

Liu, Bingchen; Dong, Mengzhen; Li, Fengjie

2018-04-01

This paper deals with a reaction-diffusion problem with coupled nonlinear inner sources and nonlocal boundary flux. Firstly, we propose the critical exponents on nonsimultaneous blow-up under some conditions on the initial data. Secondly, we combine the scaling technique and the Green's identity method to determine four kinds of simultaneous blow-up rates. Thirdly, the lower and the upper bounds of blow-up time are derived by using Sobolev-type differential inequalities.

A Numerical Model of Unsteady, Subsonic Aeroelastic Behavior. Ph.D Thesis

NASA Technical Reports Server (NTRS)

Strganac, Thomas W.

1987-01-01

A method for predicting unsteady, subsonic aeroelastic responses was developed. The technique accounts for aerodynamic nonlinearities associated with angles of attack, vortex-dominated flow, static deformations, and unsteady behavior. The fluid and the wing together are treated as a single dynamical system, and the equations of motion for the structure and flow field are integrated simultaneously and interactively in the time domain. The method employs an iterative scheme based on a predictor-corrector technique. The aerodynamic loads are computed by the general unsteady vortex-lattice method and are determined simultaneously with the motion of the wing. Because the unsteady vortex-lattice method predicts the wake as part of the solution, the history of the motion is taken into account; hysteresis is predicted. Two models are used to demonstrate the technique: a rigid wing on an elastic support experiencing plunge and pitch about the elastic axis, and an elastic wing rigidly supported at the root chord experiencing spanwise bending and twisting. The method can be readily extended to account for structural nonlinearities and/or substitute aerodynamic load models. The time domain solution coupled with the unsteady vortex-lattice method provides the capability of graphically depicting wing and wake motion.

Efficient quantum state transfer in an engineered chain of quantum bits

NASA Astrophysics Data System (ADS)

Sandberg, Martin; Knill, Emanuel; Kapit, Eliot; Vissers, Michael R.; Pappas, David P.

2016-03-01

We present a method of performing quantum state transfer in a chain of superconducting quantum bits. Our protocol is based on engineering the energy levels of the qubits in the chain and tuning them all simultaneously with an external flux bias. The system is designed to allow sequential adiabatic state transfers, resulting in on-demand quantum state transfer from one end of the chain to the other. Numerical simulations of the master equation using realistic parameters for capacitive nearest-neighbor coupling, energy relaxation, and dephasing show that fast, high-fidelity state transfer should be feasible using this method.

A NURBS-enhanced finite volume solver for steady Euler equations

NASA Astrophysics Data System (ADS)

Meng, Xucheng; Hu, Guanghui

2018-04-01

In Hu and Yi (2016) [20], a non-oscillatory k-exact reconstruction method was proposed towards the high-order finite volume methods for steady Euler equations, which successfully demonstrated the high-order behavior in the simulations. However, the degeneracy of the numerical accuracy of the approximate solutions to problems with curved boundary can be observed obviously. In this paper, the issue is resolved by introducing the Non-Uniform Rational B-splines (NURBS) method, i.e., with given discrete description of the computational domain, an approximate NURBS curve is reconstructed to provide quality quadrature information along the curved boundary. The advantages of using NURBS include i). both the numerical accuracy of the approximate solutions and convergence rate of the numerical methods are improved simultaneously, and ii). the NURBS curve generation is independent of other modules of the numerical framework, which makes its application very flexible. It is also shown in the paper that by introducing more elements along the normal direction for the reconstruction patch of the boundary element, significant improvement in the convergence to steady state can be achieved. The numerical examples confirm the above features very well.

Signal inference with unknown response: calibration-uncertainty renormalized estimator.

PubMed

Dorn, Sebastian; Enßlin, Torsten A; Greiner, Maksim; Selig, Marco; Boehm, Vanessa

2015-01-01

The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration-uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calibration, but its covariance structure. The idea of the CURE method, developed in the framework of information field theory, is to start with an assumed calibration to successively include more and more portions of calibration uncertainty into the signal inference equations and to absorb the resulting corrections into renormalized signal (and calibration) solutions. Thereby, the signal inference and calibration problem turns into a problem of solving a single system of ordinary differential equations and can be identified with common resummation techniques used in field theories. We verify the CURE method by applying it to a simplistic toy example and compare it against existent self-calibration schemes, Wiener filter solutions, and Markov chain Monte Carlo sampling. We conclude that the method is able to keep up in accuracy with the best self-calibration methods and serves as a noniterative alternative to them.

Numerical evaluation of the intensity transport equation for well-known wavefronts and intensity distributions

NASA Astrophysics Data System (ADS)

Campos-García, Manuel; Granados-Agustín, Fermín.; Cornejo-Rodríguez, Alejandro; Estrada-Molina, Amilcar; Avendaño-Alejo, Maximino; Moreno-Oliva, Víctor Iván.

2013-11-01

In order to obtain a clearer interpretation of the Intensity Transport Equation (ITE), in this work, we propose an algorithm to solve it for some particular wavefronts and its corresponding intensity distributions. By simulating intensity distributions in some planes, the ITE is turns into a Poisson equation with Neumann boundary conditions. The Poisson equation is solved by means of the iterative algorithm SOR (Simultaneous Over-Relaxation).

Mathematical Analysis of the Solidification Behavior of Plain Steel Based on Solute- and Heat-Transfer Equations in the Liquid-Solid Zone

NASA Astrophysics Data System (ADS)

Fujimura, Toshio; Takeshita, Kunimasa; Suzuki, Ryosuke O.

2018-04-01

An analytical approximate solution to non-linear solute- and heat-transfer equations in the unsteady-state mushy zone of Fe-C plain steel has been obtained, assuming a linear relationship between the solid fraction and the temperature of the mushy zone. The heat transfer equations for both the solid and liquid zone along with the boundary conditions have been linked with the equations to solve the whole equations. The model predictions ( e.g., the solidification constants and the effective partition ratio) agree with the generally accepted values and with a separately performed numerical analysis. The solidus temperature predicted by the model is in the intermediate range of the reported formulas. The model and Neuman's solution are consistent in the low carbon range. A conventional numerical heat analysis ( i.e., an equivalent specific heat method using the solidus temperature predicted by the model) is consistent with the model predictions for Fe-C plain steels. The model presented herein simplifies the computations to solve the solute- and heat-transfer simultaneous equations while searching for a solidus temperature as a part of the solution. Thus, this model can reduce the complexity of analyses considering the heat- and solute-transfer phenomena in the mushy zone.

Estimation of true serum thyroglobulin concentration using simultaneous measurement of serum antithyroglobulin antibody.

PubMed

Ahn, Byeong-Cheol; Lee, Won Kee; Jeong, Shin Young; Lee, Sang-Woo; Lee, Jaetae

2013-01-01

We investigated the analytical interference of antithyroglobulin antibody (TgAb) to thyroglobulin (Tg) measurement and tried to convert measured Tg concentration to true Tg concentration using a mathematical equation which includes a concentration of TgAb. Methods. Tg was measured by immunoradiometric assay and TgAb by radioimmunoassy. Experimental samples were produced by mixing Tg and TgAb standard solutions or mixing patients' serum with high Tg or high TgAb. Mathematical equations for prediction of expected Tg concentration with measured Tg and TgAb concentrations were deduced. The Tg concentration calculated using the equations was compared with the expected Tg concentration. Results. Measured Tg concentrations of samples having high TgAb were significantly lower than their expected Tg concentration. Magnitude of TgAb interference with the Tg assay showed a positive correlation with concentration of TgAb. Mathematical equations for estimation of expected Tg concentration using measured Tg and TgAb concentrations were successfully deduced and the calculated Tg concentration showed excellent correlation with expected Tg concentration. Conclusions. A mathematic equation for estimation of true Tg concentration using measured Tg and TgAb concentration was deduced. Tg concentration calculated by use of the equation might be more valuable than measured Tg concentration in patients with differentiated thyroid cancer.

Numerical simulation of advective-dispersive multisolute transport with sorption, ion exchange and equilibrium chemistry

USGS Publications Warehouse

Lewis, F.M.; Voss, C.I.; Rubin, Jacob

1986-01-01

A model was developed that can simulate the effect of certain chemical and sorption reactions simultaneously among solutes involved in advective-dispersive transport through porous media. The model is based on a methodology that utilizes physical-chemical relationships in the development of the basic solute mass-balance equations; however, the form of these equations allows their solution to be obtained by methods that do not depend on the chemical processes. The chemical environment is governed by the condition of local chemical equilibrium, and may be defined either by the linear sorption of a single species and two soluble complexation reactions which also involve that species, or binary ion exchange and one complexation reaction involving a common ion. Partial differential equations that describe solute mass balance entirely in the liquid phase are developed for each tenad (a chemical entity whose total mass is independent of the reaction process) in terms of their total dissolved concentration. These equations are solved numerically in two dimensions through the modification of an existing groundwater flow/transport computer code. (Author 's abstract)

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

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Protection Relaying Scheme Based on Fault Reactance Operation Type

NASA Astrophysics Data System (ADS)

Tsuji, Kouichi

The theories of operation of existing relays are roughly divided into two types: one is the current differential types based on Kirchhoff's first law and the other is impedance types based on second law. We can apply the Kirchhoff's laws to strictly formulate fault phenomena, so the circuit equations are represented non linear simultaneous equations with variables fault point k and fault resistance Rf. This method has next two defect. 1) heavy computational burden for the iterative calculation on N-R method, 2) relay operator can not easily understand principle of numerical matrix operation. The new protection relay principles we proposed this paper focuses on the fact that the reactance component on fault point is almost zero. Two reactance Xf(S), Xf(R) on branch both ends are calculated by operation of solving linear equations. If signs of Xf(S) and Xf(R) are not same, it can be judged that the fault point exist in the branch. This reactance Xf corresponds to difference of branch reactance between actual fault point and imaginaly fault point. And so relay engineer can to understand fault location by concept of “distance". The simulation results using this new method indicates the highly precise estimation of fault locations compared with the inspected fault locations on operating transmission lines.

Fluid-structure interaction with pipe-wall viscoelasticity during water hammer

NASA Astrophysics Data System (ADS)

Keramat, A.; Tijsseling, A. S.; Hou, Q.; Ahmadi, A.

2012-01-01

Fluid-structure interaction (FSI) due to water hammer in a pipeline which has viscoelastic wall behaviour is studied. Appropriate governing equations are derived and numerically solved. In the numerical implementation of the hydraulic and structural equations, viscoelasticity is incorporated using the Kelvin-Voigt mechanical model. The equations are solved by two different approaches, namely the Method of Characteristics-Finite Element Method (MOC-FEM) and full MOC. In both approaches two important effects of FSI in fluid-filled pipes, namely Poisson and junction coupling, are taken into account. The study proposes a more comprehensive model for studying fluid transients in pipelines as compared to previous works, which take into account either FSI or viscoelasticity. To verify the proposed mathematical model and its numerical solutions, the following problems are investigated: axial vibration of a viscoelastic bar subjected to a step uniaxial loading, FSI in an elastic pipe, and hydraulic transients in a pressurised polyethylene pipe without FSI. The results of each case are checked with available exact and experimental results. Then, to study the simultaneous effects of FSI and viscoelasticity, which is the new element of the present research, one problem is solved by the two different numerical approaches. Both numerical methods give the same results, thus confirming the correctness of the solutions.

Constant pressure and temperature discrete-time Langevin molecular dynamics

NASA Astrophysics Data System (ADS)

Grønbech-Jensen, Niels; Farago, Oded

2014-11-01

We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems—a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.

Implicit Plasma Kinetic Simulation Using The Jacobian-Free Newton-Krylov Method

NASA Astrophysics Data System (ADS)

Taitano, William; Knoll, Dana; Chacon, Luis

2009-11-01

The use of fully implicit time integration methods in kinetic simulation is still area of algorithmic research. A brute-force approach to simultaneously including the field equations and the particle distribution function would result in an intractable linear algebra problem. A number of algorithms have been put forward which rely on an extrapolation in time. They can be thought of as linearly implicit methods or one-step Newton methods. However, issues related to time accuracy of these methods still remain. We are pursuing a route to implicit plasma kinetic simulation which eliminates extrapolation, eliminates phase-space from the linear algebra problem, and converges the entire nonlinear system within a time step. We accomplish all this using the Jacobian-Free Newton-Krylov algorithm. The original research along these lines considered particle methods to advance the distribution function [1]. In the current research we are advancing the Vlasov equations on a grid. Results will be presented which highlight algorithmic details for single species electrostatic problems and coupled ion-electron electrostatic problems. [4pt] [1] H. J. Kim, L. Chac'on, G. Lapenta, ``Fully implicit particle in cell algorithm,'' 47th Annual Meeting of the Division of Plasma Physics, Oct. 24-28, 2005, Denver, CO

Technical note: Evaluation of the simultaneous measurements of mesospheric OH, HO2, and O3 under a photochemical equilibrium assumption - a statistical approach

NASA Astrophysics Data System (ADS)

Kulikov, Mikhail Y.; Nechaev, Anton A.; Belikovich, Mikhail V.; Ermakova, Tatiana S.; Feigin, Alexander M.

2018-05-01

This Technical Note presents a statistical approach to evaluating simultaneous measurements of several atmospheric components under the assumption of photochemical equilibrium. We consider simultaneous measurements of OH, HO2, and O3 at the altitudes of the mesosphere as a specific example and their daytime photochemical equilibrium as an evaluating relationship. A simplified algebraic equation relating local concentrations of these components in the 50-100 km altitude range has been derived. The parameters of the equation are temperature, neutral density, local zenith angle, and the rates of eight reactions. We have performed a one-year simulation of the mesosphere and lower thermosphere using a 3-D chemical-transport model. The simulation shows that the discrepancy between the calculated evolution of the components and the equilibrium value given by the equation does not exceed 3-4 % in the full range of altitudes independent of season or latitude. We have developed a statistical Bayesian evaluation technique for simultaneous measurements of OH, HO2, and O3 based on the equilibrium equation taking into account the measurement error. The first results of the application of the technique to MLS/Aura data (Microwave Limb Sounder) are presented in this Technical Note. It has been found that the satellite data of the HO2 distribution regularly demonstrate lower altitudes of this component's mesospheric maximum. This has also been confirmed by model HO2 distributions and comparison with offline retrieval of HO2 from the daily zonal means MLS radiance.

Equation solvers for distributed-memory computers

NASA Technical Reports Server (NTRS)

Storaasli, Olaf O.

1994-01-01

A large number of scientific and engineering problems require the rapid solution of large systems of simultaneous equations. The performance of parallel computers in this area now dwarfs traditional vector computers by nearly an order of magnitude. This talk describes the major issues involved in parallel equation solvers with particular emphasis on the Intel Paragon, IBM SP-1 and SP-2 processors.

A Case of Inconsistent Equatings: How the Man with Four Watches Decides What Time It Is

ERIC Educational Resources Information Center

Livingston, Samuel A.; Antal, Judit

2010-01-01

A simultaneous equating of four new test forms to each other and to one previous form was accomplished through a complex design incorporating seven separate equating links. Each new form was linked to the reference form by four different paths, and each path produced a different score conversion. The procedure used to resolve these inconsistencies…

Mechanisms Inducing Jet Rotation in Shear-Formed Shaped-Charge Liners.

DTIC Science & Technology

1990-03-01

of deviatoric strain, and compressibility affects only the equation of state , not the deviatoric stress /strain relation. An anisotropic formulation is...strains, a more accurate scalar equation of state should simultaneously be employed to account for non-linear compressibility effects . A4 A.3 Elastic... obtainable knowing the previous and present cycles’ average stress . However, many non-linear equations

An Improved Computational Method for the Calculation of Mixture Liquid-Vapor Critical Points

NASA Astrophysics Data System (ADS)

Dimitrakopoulos, Panagiotis; Jia, Wenlong; Li, Changjun

2014-05-01

Knowledge of critical points is important to determine the phase behavior of a mixture. This work proposes a reliable and accurate method in order to locate the liquid-vapor critical point of a given mixture. The theoretical model is developed from the rigorous definition of critical points, based on the SRK equation of state (SRK EoS) or alternatively, on the PR EoS. In order to solve the resulting system of nonlinear equations, an improved method is introduced into an existing Newton-Raphson algorithm, which can calculate all the variables simultaneously in each iteration step. The improvements mainly focus on the derivatives of the Jacobian matrix, on the convergence criteria, and on the damping coefficient. As a result, all equations and related conditions required for the computation of the scheme are illustrated in this paper. Finally, experimental data for the critical points of 44 mixtures are adopted in order to validate the method. For the SRK EoS, average absolute errors of the predicted critical-pressure and critical-temperature values are 123.82 kPa and 3.11 K, respectively, whereas the commercial software package Calsep PVTSIM's prediction errors are 131.02 kPa and 3.24 K. For the PR EoS, the two above mentioned average absolute errors are 129.32 kPa and 2.45 K, while the PVTSIM's errors are 137.24 kPa and 2.55 K, respectively.

A systematic linear space approach to solving partially described inverse eigenvalue problems

NASA Astrophysics Data System (ADS)

Hu, Sau-Lon James; Li, Haujun

2008-06-01

Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

Actor-critic-based optimal tracking for partially unknown nonlinear discrete-time systems.

PubMed

Kiumarsi, Bahare; Lewis, Frank L

2015-01-01

This paper presents a partially model-free adaptive optimal control solution to the deterministic nonlinear discrete-time (DT) tracking control problem in the presence of input constraints. The tracking error dynamics and reference trajectory dynamics are first combined to form an augmented system. Then, a new discounted performance function based on the augmented system is presented for the optimal nonlinear tracking problem. In contrast to the standard solution, which finds the feedforward and feedback terms of the control input separately, the minimization of the proposed discounted performance function gives both feedback and feedforward parts of the control input simultaneously. This enables us to encode the input constraints into the optimization problem using a nonquadratic performance function. The DT tracking Bellman equation and tracking Hamilton-Jacobi-Bellman (HJB) are derived. An actor-critic-based reinforcement learning algorithm is used to learn the solution to the tracking HJB equation online without requiring knowledge of the system drift dynamics. That is, two neural networks (NNs), namely, actor NN and critic NN, are tuned online and simultaneously to generate the optimal bounded control policy. A simulation example is given to show the effectiveness of the proposed method.

Distortion of liquid film discharging from twin-fluid atomizer

NASA Astrophysics Data System (ADS)

Mehring, C.; Sirignano, W. A.

2001-11-01

The nonlinear distortion and disintegration of a thin liquid film exiting from a two-dimensional twin-fluid atomizer is analyzed numerically. Pulsed gas jets impacting on both sides of the discharging liquid film at the atomizer exit generate dilational and/or sinuous deformations of the film. Both liquid phase and gas phase are inviscid and incompressible. For the liquid phase the so-called long-wavelength approximation is employed yielding a system of unsteady one-dimensional equations for the planar film. Solution of Laplace's equation for the velocity potential yields the gas-phase velocity field on both sides of the liquid stream. Coupling between both phases is described through kinematic and dynamic boundary conditions at the phase interfaces, and includes the solution of the unsteady Bernoulli equation to determine the gas-phase pressure along the interfaces. Both gas- and liquid-phase equations are solved simultaneously. Solution of Laplace's equation for the gas streams is obtained by means of a boundary-element method. Numerical solutions for the liquid phase use the Lax-Wendroff method with Richtmyer splitting. Sheet distortion resulting from the stagnation pressure of the impacting gas jets and subsequent disturbance amplification due to Kelvin-Helmholtz effects are studied for various combinations of gas-pulse timing, gas-jet impact angles, gas-to-liquid-density ratio, liquid-phase Weber number and gas-jet-to-liquid-jet-momentum ratio. Dilational and sinuous oscillations of the liquid are examined and film pinch-off is predicted.

Simultaneous gas chromatographic determination of chlorpyrifos and its impurity sulfotep in liquid pesticide formulations.

PubMed

Płonka, Marlena; Walorczyk, Stanisław; Miszczyk, Marek; Kronenbach-Dylong, Dorota

2016-11-01

An analytical method for simultaneous determination of the active substance (chlorpyrifos) and its relevant impurity (sulfotep) in commercial pesticide formulations has been developed and validated. The proposed method entails extraction of the analytes from samples by sonication with acetone and analysis by gas chromatography-flame ionization detection (GC-FID). The proposed method was characterized by satisfactory accuracy and precision. The repeatability expressed as relative standard deviation (RSD) was lower than the acceptable values calculated from the modified Horwitz equation whereas individual recoveries were in the range of 98-102% and 80-120% for chlorpyrifos and sulfotep, respectively. The limit of quantification (LOQ) for the impurity (sulfotep) was 0.003 mg mL(-1) corresponding to the maximum permitted level according to Food and Agricultural Organization of the United Nations (FAO) specifications for the active substance (chlorpyrifos) being 3 g kg(-1) of the chlorpyrifos content found. The main advantage of the proposed method was a considerable reduction in the analysis time since both analytes were determined based on a single injection into the GC-FID. Analysis of real samples of commercial pesticide formulations confirmed fitness-for-purpose of the proposed method.

Helicopter Control Energy Reduction Using Moving Horizontal Tail

PubMed Central

Oktay, Tugrul; Sal, Firat

2015-01-01

Helicopter moving horizontal tail (i.e., MHT) strategy is applied in order to save helicopter flight control system (i.e., FCS) energy. For this intention complex, physics-based, control-oriented nonlinear helicopter models are used. Equations of MHT are integrated into these models and they are together linearized around straight level flight condition. A specific variance constrained control strategy, namely, output variance constrained Control (i.e., OVC) is utilized for helicopter FCS. Control energy savings due to this MHT idea with respect to a conventional helicopter are calculated. Parameters of helicopter FCS and dimensions of MHT are simultaneously optimized using a stochastic optimization method, namely, simultaneous perturbation stochastic approximation (i.e., SPSA). In order to observe improvement in behaviors of classical controls closed loop analyses are done. PMID:26180841

Probing interactions of thermal Sr Rydberg atoms using simultaneous optical and ion detection

NASA Astrophysics Data System (ADS)

Hanley, Ryan K.; Bounds, Alistair D.; Huillery, Paul; Keegan, Niamh C.; Faoro, Riccardo; Bridge, Elizabeth M.; Weatherill, Kevin J.; Jones, Matthew P. A.

2017-06-01

We demonstrate a method for probing interaction effects in a thermal beam of strontium atoms using simultaneous measurements of Rydberg EIT and spontaneously created ions or electrons. We present a Doppler-averaged optical Bloch equation model that reproduces the optical signals and allows us to connect the optical coherences and the populations. We use this to determine that the spontaneous ionization process in our system occurs due to collisions between Rydberg and ground state atoms in the EIT regime. We measure the cross section of this process to be 0.6+/- 0.2 {σ }{geo}, where {σ }{geo} is the geometrical cross section of the Rydberg atom. This result adds complementary insight to a range of recent studies of interacting thermal Rydberg ensembles.

Recursive formulas for the partial fraction expansion of a rational function with multiple poles.

NASA Technical Reports Server (NTRS)

Chang, F.-C.

1973-01-01

The coefficients in the partial fraction expansion considered are given by Heaviside's formula. The evaluation of the coefficients involves the differential of a quotient of two polynomials. A simplified approach for the evaluation of the coefficients is discussed. Leibniz rule is applied and a recurrence formula is derived. A coefficient can also be determined from a system of simultaneous equations. Practical methods for the performance of the computational operations involved in both approaches are considered.

Practical calculation of laminar and turbulent bled-off boundary layers

NASA Technical Reports Server (NTRS)

Eppler, R.

1978-01-01

Bleed-off of boundary layer material is shown to be an effective means for reducing drag by conserving the laminar boundary layer and preventing separation of the turbulent boundary layer. The case in which the two effects of bleed-off overlap is examined. Empirical methods are extended to the case of bleed-off. Laminar and turbulent boundary layers are treated simultaneously and the approximation differential equations are solved without an uncertain error. The case without bleed-off is also treated.

Plane wave diffraction by a finite plate with impedance boundary conditions.

PubMed

Nawaz, Rab; Ayub, Muhammad; Javaid, Akmal

2014-01-01

In this study we have examined a plane wave diffraction problem by a finite plate having different impedance boundaries. The Fourier transforms were used to reduce the governing problem into simultaneous Wiener-Hopf equations which are then solved using the standard Wiener-Hopf procedure. Afterwards the separated and interacted fields were developed asymptotically by using inverse Fourier transform and the modified stationary phase method. Detailed graphical analysis was also made for various physical parameters we were interested in.

Numerical Problem Solving Using Mathcad in Undergraduate Reaction Engineering

ERIC Educational Resources Information Center

Parulekar, Satish J.

2006-01-01

Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

A Nonlinear, Multiinput, Multioutput Process Control Laboratory Experiment

ERIC Educational Resources Information Center

Young, Brent R.; van der Lee, James H.; Svrcek, William Y.

2006-01-01

Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

MIMO nonlinear ultrasonic tomography by propagation and backpropagation method.

PubMed

Dong, Chengdong; Jin, Yuanwei

2013-03-01

This paper develops a fast ultrasonic tomographic imaging method in a multiple-input multiple-output (MIMO) configuration using the propagation and backpropagation (PBP) method. By this method, ultrasonic excitation signals from multiple sources are transmitted simultaneously to probe the objects immersed in the medium. The scattering signals are recorded by multiple receivers. Utilizing the nonlinear ultrasonic wave propagation equation and the received time domain scattered signals, the objects are to be reconstructed iteratively in three steps. First, the propagation step calculates the predicted acoustic potential data at the receivers using an initial guess. Second, the difference signal between the predicted value and the measured data is calculated. Third, the backpropagation step computes updated acoustical potential data by backpropagating the difference signal to the same medium computationally. Unlike the conventional PBP method for tomographic imaging where each source takes turns to excite the acoustical field until all the sources are used, the developed MIMO-PBP method achieves faster image reconstruction by utilizing multiple source simultaneous excitation. Furthermore, we develop an orthogonal waveform signaling method using a waveform delay scheme to reduce the impact of speckle patterns in the reconstructed images. By numerical experiments we demonstrate that the proposed MIMO-PBP tomographic imaging method results in faster convergence and achieves superior imaging quality.

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

PubMed Central

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

2017-01-01

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

Assessing Spurious Interaction Effects in Structural Equation Modeling

ERIC Educational Resources Information Center

Harring, Jeffrey R.; Weiss, Brandi A.; Li, Ming

2015-01-01

Several studies have stressed the importance of simultaneously estimating interaction and quadratic effects in multiple regression analyses, even if theory only suggests an interaction effect should be present. Specifically, past studies suggested that failing to simultaneously include quadratic effects when testing for interaction effects could…

New displacement-based methods for optimal truss topology design

NASA Technical Reports Server (NTRS)

Bendsoe, Martin P.; Ben-Tal, Aharon; Haftka, Raphael T.

1991-01-01

Two alternate methods for maximum stiffness truss topology design are presented. The ground structure approach is used, and the problem is formulated in terms of displacements and bar areas. This large, nonconvex optimization problem can be solved by a simultaneous analysis and design approach. Alternatively, an equivalent, unconstrained, and convex problem in the displacements only can be formulated, and this problem can be solved by a nonsmooth, steepest descent algorithm. In both methods, the explicit solving of the equilibrium equations and the assembly of the global stiffness matrix are circumvented. A large number of examples have been studied, showing the attractive features of topology design as well as exposing interesting features of optimal topologies.

Improved Multi-Axial, Temperature and Time Dependent (MATT) Failure Model

NASA Technical Reports Server (NTRS)

Richardson, D. E.; Anderson, G. L.; Macon, D. J.

2002-01-01

An extensive effort has recently been completed by the Space Shuttle's Reusable Solid Rocket Motor (RSRM) nozzle program to completely characterize the effects of multi-axial loading, temperature and time on the failure characteristics of three filled epoxy adhesives (TIGA 321, EA913NA, EA946). As part of this effort, a single general failure criterion was developed that accounted for these effects simultaneously. This model was named the Multi- Axial, Temperature, and Time Dependent or MATT failure criterion. Due to the intricate nature of the failure criterion, some parameters were required to be calculated using complex equations or numerical methods. This paper documents some simple but accurate modifications to the failure criterion to allow for calculations of failure conditions without complex equations or numerical techniques.

Optimal preconditioning of lattice Boltzmann methods

NASA Astrophysics Data System (ADS)

Izquierdo, Salvador; Fueyo, Norberto

2009-09-01

A preconditioning technique to accelerate the simulation of steady-state problems using the single-relaxation-time (SRT) lattice Boltzmann (LB) method was first proposed by Guo et al. [Z. Guo, T. Zhao, Y. Shi, Preconditioned lattice-Boltzmann method for steady flows, Phys. Rev. E 70 (2004) 066706-1]. The key idea in this preconditioner is to modify the equilibrium distribution function in such a way that, by means of a Chapman-Enskog expansion, a time-derivative preconditioner of the Navier-Stokes (NS) equations is obtained. In the present contribution, the optimal values for the free parameter γ of this preconditioner are searched both numerically and theoretically; the later with the aid of linear-stability analysis and with the condition number of the system of NS equations. The influence of the collision operator, single- versus multiple-relaxation-times (MRT), is also studied. Three steady-state laminar test cases are used for validation, namely: the two-dimensional lid-driven cavity, a two-dimensional microchannel and the three-dimensional backward-facing step. Finally, guidelines are suggested for an a priori definition of optimal preconditioning parameters as a function of the Reynolds and Mach numbers. The new optimally preconditioned MRT method derived is shown to improve, simultaneously, the rate of convergence, the stability and the accuracy of the lattice Boltzmann simulations, when compared to the non-preconditioned methods and to the optimally preconditioned SRT one. Additionally, direct time-derivative preconditioning of the LB equation is also studied.

On the Convenience of Using the Complete Linearization Method in Modelling the BLR of AGN

NASA Astrophysics Data System (ADS)

Patriarchi, P.; Perinotto, M.

The Complete Linearization Method (Mihalas, 1978) consists in the determination of the radiation field (at a set of frequency points), atomic level populations, temperature, electron density etc., by resolving the system of radiative transfer, thermal equilibrium, statistical equilibrium equations simultaneously and self-consistently. Since the system is not linear, it must be solved by iteration after linearization, using a perturbative method, starting from an initial guess solution. Of course the Complete Linearization Method is more time consuming than the previous one. But how great can this disadvantage be in the age of supercomputers? It is possible to approximately evaluate the CPU time needed to run a model by computing the number of multiplications necessary to solve the system.

Structural equation modeling and natural systems

USGS Publications Warehouse

Grace, James B.

2006-01-01

This book, first published in 2006, presents an introduction to the methodology of structural equation modeling, illustrates its use, and goes on to argue that it has revolutionary implications for the study of natural systems. A major theme of this book is that we have, up to this point, attempted to study systems primarily using methods (such as the univariate model) that were designed only for considering individual processes. Understanding systems requires the capacity to examine simultaneous influences and responses. Structural equation modeling (SEM) has such capabilities. It also possesses many other traits that add strength to its utility as a means of making scientific progress. In light of the capabilities of SEM, it can be argued that much of ecological theory is currently locked in an immature state that impairs its relevance. It is further argued that the principles of SEM are capable of leading to the development and evaluation of multivariate theories of the sort vitally needed for the conservation of natural systems.

A New Method for Determining the Equation of State of Aluminized Explosive

NASA Astrophysics Data System (ADS)

Zhou, Zheng-Qing; Nie, Jian-Xin; Guo, Xue-Yong; Wang, Qiu-Shi; Ou, Zhuo-Cheng; Jiao, Qing-Jie

2015-01-01

The time-dependent Jones—Wilkins—Lee equation of state (JWL-EOS) is applied to describe detonation state products for aluminized explosives. To obtain the time-dependent JWL-EOS parameters, cylinder tests and underwater explosion experiments are performed. According to the result of the wall radial velocity in cylinder tests and the shock wave pressures in underwater explosion experiments, the time-dependent JWL-EOS parameters are determined by iterating these variables in AUTODYN hydrocode simulations until the experimental values are reproduced. In addition, to verify the reliability of the derived JWL-EOS parameters, the aluminized explosive experiment is conducted in concrete. The shock wave pressures in the affected concrete bodies are measured by using manganin pressure sensors, and the rod velocity is obtained by using a high-speed camera. Simultaneously, the shock wave pressure and the rod velocity are calculated by using the derived time-dependent JWL equation of state. The calculated results are in good agreement with the experimental data.

Modeling and Simulation of Radiative Compressible Flows in Aerodynamic Heating Arc-Jet Facility

NASA Technical Reports Server (NTRS)

Bensassi, Khalil; Laguna, Alejandro A.; Lani, Andrea; Mansour, Nagi N.

2016-01-01

Numerical simulations of an arc heated flow inside NASA's 20 [MW] Aerodynamics heating facility (AHF) are performed in order to investigate the three-dimensional swirling flow and the current distribution inside the wind tunnel. The plasma is considered in Local Thermodynamics Equilibrium(LTE) and is composed of Air-Argon gas mixture. The governing equations are the Navier-Stokes equations that include source terms corresponding to Joule heating and radiative cooling. The former is obtained by solving an electric potential equation, while the latter is calculated using an innovative massively parallel ray-tracing algorithm. The fully coupled system is closed by the thermodynamics relations and transport properties which are obtained from Chapman-Enskog method. A novel strategy was developed in order to enable the flow solver and the radiation calculation to be preformed independently and simultaneously using a different number of processors. Drastic reduction in the computational cost was achieved using this strategy. Details on the numerical methods used for space discretization, time integration and ray-tracing algorithm will be presented. The effect of the radiative cooling on the dynamics of the flow will be investigated. The complete set of equations were implemented within the COOLFluiD Framework. Fig. 1 shows the geometry of the Anode and part of the constrictor of the Aerodynamics heating facility (AHF). Fig. 2 shows the velocity field distribution along (x-y) plane and the streamline in (z-y) plane.

A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.

PubMed

Pau, George S H; Almgren, Ann S; Bell, John B; Lijewski, Michael J

2009-11-28

In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method.

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

Simultaneous Estimation of Amlodipine Besilate and Olmesartan Medoxomil in Pharmaceutical Dosage Form

PubMed Central

Wankhede, S. B.; Wadkar, S. B.; Raka, K. C.; Chitlange, S. S.

2009-01-01

Two UV Spectrophotometric and one reverse phase high performance liquid chromatography methods have been developed for the simultaneous estimation of amlodipine besilate and olmesartan medoxomil in tablet dosage form. First UV spectrophotometric method was a determination using the simultaneous equation method at 237.5 nm and 255.5 nm over the concentration range 10-50 μg/ml and 10-50 μg/ml, for amlodipine besilate and olmesartan medoxomil with accuracy 100.09%, and 100.22% respectively. Second UV spectrophotometric method was a determination using the area under curve method at 242.5-232.5 nm and 260.5-250.5 nm over the concentration range of 10-50 μg/ml and 10-50 μg/ml, for amlodipine besilate and olmesartan medoxomil with accuracy 100.10%, and 100.48%, respectively. In reverse phase high performance liquid chromatography analysis carried out using 0.05M potassuim dihydrogen phosphate buffer:acetonitrile (50:50 v/v) as the mobile phase and Kromasil C18 (4.6 mm i.d.×250 mm) column as the stationery phase with detection wavelength of 238 nm. Flow rate was 1.0 ml/min. Retention time for amlodipine besilate and olmesartan medoxomil were 3.69 and 5.36 min, respectively. Linearity was obtained in the concentration range of 4-20 μg/ml and 10-50 μg/ml for amlodipine besilate and olmesartan medoxomil, respectively. Proposed methods can be used for the estimation of amlodipine besilate and olmesartan medoxomil in tablet dosage form provided all the validation parameters are met. PMID:20502580

Complex double-mass dynamic model of rotor on thrust foil gas dynamic bearings

NASA Astrophysics Data System (ADS)

Sytin, A.; Babin, A.; Vasin, S.

2017-08-01

The present paper considers simulation of a rotor’s dynamics behaviour on thrust foil gas dynamic bearings based on simultaneous solution of gas dynamics differential equations, equations of theory of elasticity, motion equations and some additional equations. A double-mass dynamic system was considered during the rotor’s motion simulation which allows not only evaluation of rotor’s dynamic behaviour, but also to evaluate the influence of operational and load parameters on the dynamics of the rotor-bearing system.

Unified Framework for Deriving Simultaneous Equation Algorithms for Water Distribution Networks

EPA Science Inventory

The known formulations for steady state hydraulics within looped water distribution networks are re-derived in terms of linear and non-linear transformations of the original set of partly linear and partly non-linear equations that express conservation of mass and energy. All of ...

Robust variable selection method for nonparametric differential equation models with application to nonlinear dynamic gene regulatory network analysis.

PubMed

Lu, Tao

2016-01-01

The gene regulation network (GRN) evaluates the interactions between genes and look for models to describe the gene expression behavior. These models have many applications; for instance, by characterizing the gene expression mechanisms that cause certain disorders, it would be possible to target those genes to block the progress of the disease. Many biological processes are driven by nonlinear dynamic GRN. In this article, we propose a nonparametric differential equation (ODE) to model the nonlinear dynamic GRN. Specially, we address following questions simultaneously: (i) extract information from noisy time course gene expression data; (ii) model the nonlinear ODE through a nonparametric smoothing function; (iii) identify the important regulatory gene(s) through a group smoothly clipped absolute deviation (SCAD) approach; (iv) test the robustness of the model against possible shortening of experimental duration. We illustrate the usefulness of the model and associated statistical methods through a simulation and a real application examples.

Mesoscopic Modeling of Blood Clotting: Coagulation Cascade and Platelets Adhesion

NASA Astrophysics Data System (ADS)

Yazdani, Alireza; Li, Zhen; Karniadakis, George

2015-11-01

The process of clot formation and growth at a site on a blood vessel wall involve a number of multi-scale simultaneous processes including: multiple chemical reactions in the coagulation cascade, species transport and flow. To model these processes we have incorporated advection-diffusion-reaction (ADR) of multiple species into an extended version of Dissipative Particle Dynamics (DPD) method which is considered as a coarse-grained Molecular Dynamics method. At the continuum level this is equivalent to the Navier-Stokes equation plus one advection-diffusion equation for each specie. The chemistry of clot formation is now understood to be determined by mechanisms involving reactions among many species in dilute solution, where reaction rate constants and species diffusion coefficients in plasma are known. The role of blood particulates, i.e. red cells and platelets, in the clotting process is studied by including them separately and together in the simulations. An agonist-induced platelet activation mechanism is presented, while platelets adhesive dynamics based on a stochastic bond formation/dissociation process is included in the model.

ATTITUDE FILTERING ON SO(3)

NASA Technical Reports Server (NTRS)

Markley, F. Landis

2005-01-01

A new method is presented for the simultaneous estimation of the attitude of a spacecraft and an N-vector of bias parameters. This method uses a probability distribution function defined on the Cartesian product of SO(3), the group of rotation matrices, and the Euclidean space W N .The Fokker-Planck equation propagates the probability distribution function between measurements, and Bayes s formula incorporates measurement update information. This approach avoids all the issues of singular attitude representations or singular covariance matrices encountered in extended Kalman filters. In addition, the filter has a consistent initialization for a completely unknown initial attitude, owing to the fact that SO(3) is a compact space.

Mathematical modeling of sample stacking methods in microfluidic systems

NASA Astrophysics Data System (ADS)

Horek, Jon

Gradient focusing methods are a general class of experimental techniques used to simultaneously separate and increase the cross-sectionally averaged concentration of charged particle mixtures. In comparison, Field Amplified Sample Stacking (FASS) techniques first concentrate the collection of molecules before separating them. Together, we denote gradient focusing and FASS methods "sample stacking" and study the dynamics of a specific method, Temperature Gradient Focusing (TGF), in which an axial temperature gradient is applied along a channel filled with weak buffer. Gradients in electroosmotic fluid flow and electrophoretic species velocity create the simultaneous separating and concentrating mechanism mentioned above. In this thesis, we begin with the observation that very little has been done to model the dynamics of gradient focusing, and proceed to solve the fundamental equations of fluid mechanics and scalar transport, assuming the existence of slow axial variations and the Taylor-Aris dispersion coefficient. In doing so, asymptotic methods reduce the equations from 3D to 1D, and we arrive at a simple 1D model which can be used to predict the transient evolution of the cross-sectionally averaged analyte concentration. In the second half of this thesis, we run several numerical focusing experiments with a 3D finite volume code. Comparison of the 1D theory and 3D simulations illustrates not only that the asymptotic theory converges as a certain parameter tends to zero, but also that fairly large axial slip velocity gradients lead to quite small errors in predicted steady variance. Additionally, we observe that the axial asymmetry of the electrophoretic velocity model leads to asymmetric peak shapes, a violation of the symmetric Gaussians predicted by the 1D theory. We conclude with some observations on the effect of Peclet number and gradient strength on the performance of focusing experiments, and describe a method for experimental optimization. Such knowledge is useful for design of lab-on-a-chip devices.

Simultaneous estimation of aquifer thickness, conductivity, and BC using borehole and hydrodynamic data with geostatistical inverse direct method

NASA Astrophysics Data System (ADS)

Gao, F.; Zhang, Y.

2017-12-01

A new inverse method is developed to simultaneously estimate aquifer thickness and boundary conditions using borehole and hydrodynamic measurements from a homogeneous confined aquifer under steady-state ambient flow. This method extends a previous groundwater inversion technique which had assumed known aquifer geometry and thickness. In this research, thickness inversion was successfully demonstrated when hydrodynamic data were supplemented with measured thicknesses from boreholes. Based on a set of hybrid formulations which describe approximate solutions to the groundwater flow equation, the new inversion technique can incorporate noisy observed data (i.e., thicknesses, hydraulic heads, Darcy fluxes or flow rates) at measurement locations as a set of conditioning constraints. Given sufficient quantity and quality of the measurements, the inverse method yields a single well-posed system of equations that can be solved efficiently with nonlinear optimization. The method is successfully tested on two-dimensional synthetic aquifer problems with regular geometries. The solution is stable when measurement errors are increased, with error magnitude reaching up to +/- 10% of the range of the respective measurement. When error-free observed data are used to condition the inversion, the estimated thickness is within a +/- 5% error envelope surrounding the true value; when data contain increasing errors, the estimated thickness become less accurate, as expected. Different combinations of measurement types are then investigated to evaluate data worth. Thickness can be inverted with the combination of observed heads and at least one of the other types of observations such as thickness, Darcy fluxes, or flow rates. Data requirement of the new inversion method is thus not much different from that of interpreting classic well tests. Future work will improve upon this research by developing an estimation strategy for heterogeneous aquifers while drawdown data from hydraulic tests will also be incorporated as conditioning measurements.

Effect of tumor shape, size, and tissue transport properties on drug delivery to solid tumors

PubMed Central

2014-01-01

Background The computational methods provide condition for investigation related to the process of drug delivery, such as convection and diffusion of drug in extracellular matrices, drug extravasation from microvessels or to lymphatic vessels. The information of this process clarifies the mechanisms of drug delivery from the injection site to absorption by a solid tumor. In this study, an advanced numerical method is used to solve fluid flow and solute transport equations simultaneously to investigate the effect of tumor shape and size on drug delivery to solid tumor. Methods The advanced mathematical model used in our previous work is further developed by adding solute transport equation to the governing equations. After applying appropriate boundary and initial conditions on tumor and surrounding tissue geometry, the element-based finite volume method is used for solving governing equations of drug delivery in solid tumor. Also, the effects of size and shape of tumor and some of tissue transport parameters such as effective pressure and hydraulic conductivity on interstitial fluid flow and drug delivery are investigated. Results Sensitivity analysis shows that drug delivery in prolate shape is significantly better than other tumor shapes. Considering size effect, increasing tumor size decreases drug concentration in interstitial fluid. This study shows that dependency of drug concentration in interstitial fluid to osmotic and intravascular pressure is negligible. Conclusions This study shows that among diffusion and convection mechanisms of drug transport, diffusion is dominant in most different tumor shapes and sizes. In tumors in which the convection has considerable effect, the drug concentration is larger than that of other tumors at the same time post injection. PMID:24987457

Chaotic dynamics and diffusion in a piecewise linear equation

NASA Astrophysics Data System (ADS)

Shahrear, Pabel; Glass, Leon; Edwards, Rod

2015-03-01

Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.

A Model for the Oxidation of C/SiC Composite Structures

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2003-01-01

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of C/SiC composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. Within the mathematical formulation, two diffusion mechanisms are possible: (1) the relative diffusion of one species with respect to the mixture, which is concentration gradient driven and (2) the diffusion associated with the average velocity of the gas mixture, which is total gas pressure gradient driven. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations must be solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of space and time. The local rate of carbon oxidation is determined as a function of space and time using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The end result is a numerical scheme capable of determining the variation of the local carbon oxidation rates as a function of space and time for any arbitrary C/SiC composite structures.

Higher symmetries and exact solutions of linear and nonlinear Schr{umlt o}dinger equation

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

Fushchych, W.I.; Nikitin, A.G.

1997-11-01

A new approach for the analysis of partial differential equations is developed which is characterized by a simultaneous use of higher and conditional symmetries. Higher symmetries of the Schr{umlt o}dinger equation with an arbitrary potential are investigated. Nonlinear determining equations for potentials are solved using reductions to Weierstrass, Painlev{acute e}, and Riccati forms. Algebraic properties of higher order symmetry operators are analyzed. Combinations of higher and conditional symmetries are used to generate families of exact solutions of linear and nonlinear Schr{umlt o}dinger equations. {copyright} {ital 1997 American Institute of Physics.}

Gradients and Non-Adiabatic Derivative Coupling Terms for Spin-Orbit Wavefunctions

DTIC Science & Technology

2011-06-01

derivative, symmetric to the first time derivative. Solutions to the Dirac equation simultaneously satisfy the simple relativistic wave equation, the...For Pooki vi Acknowledgments I would like to thank the members of my committee for their time and...Theorem..............................................................................191 Appendix J. The Symmetric Group

Will Learning to Solve One-Step Equations Pose a Challenge to 8th Grade Students?

ERIC Educational Resources Information Center

Ngu, Bing Hiong; Phan, Huy P.

2017-01-01

Assimilating multiple interactive elements simultaneously in working memory to allow understanding to occur, while solving an equation, would impose a high cognitive load. "Element interactivity" arises from the interaction between elements within and across operational and relational lines. Moreover, operating with special features…

Study of a two-dimension transient heat propagation in cylindrical coordinates by means of two finite difference methods

NASA Astrophysics Data System (ADS)

Dumencu, A.; Horbaniuc, B.; Dumitraşcu, G.

2016-08-01

The analytical approach of unsteady conduction heat transfer under actual conditions represent a very difficult (if not insurmountable) problem due to the issues related to finding analytical solutions for the conduction heat transfer equation. Various techniques have been developed in order to overcome these difficulties, among which the alternate directions method and the decomposition method. Both of them are particularly suited for two-dimension heat propagation. The paper deals with both techniques in order to verify whether the results provided are in good accordance. The studied case consists of a long hollow cylinder, and considers that the time-dependent temperature field varies both in the radial and the axial directions. The implicit technique is used in both methods and involves the simultaneous solving of a set of equations for all of the nodes for each time step successively for each of the two directions. Gauss elimination is used to obtain the solution of the set, representing the nodal temperatures. After using the two techniques the results show a very good agreement, and since the decomposition is easier to use in terms of computer code and running time, this technique seems to be more recommendable.

[Compatible biomass models of natural spruce (Picea asperata)].

PubMed

Wang, Jin Chi; Deng, Hua Feng; Huang, Guo Sheng; Wang, Xue Jun; Zhang, Lu

2017-10-01

By using nonlinear measurement error method, the compatible tree volume and above ground biomass equations were established based on the volume and biomass data of 150 sampling trees of natural spruce (Picea asperata). Two approaches, controlling directly under total aboveground biomass and controlling jointly from level to level, were used to design the compatible system for the total aboveground biomass and the biomass of four components (stem, bark, branch and foliage), and the total ground biomass could be estimated independently or estimated simultaneously in the system. The results showed that the R 2 of the one variable and bivariate compatible tree volume and aboveground biomass equations were all above 0.85, and the maximum value reached 0.99. The prediction effect of the volume equations could be improved significantly when tree height was included as predictor, while it was not significant in biomass estimation. For the compatible biomass systems, the one variable model based on controlling jointly from level to level was better than the model using controlling directly under total above ground biomass, but the bivariate models of the two methods were similar. Comparing the imitative effects of the one variable and bivariate compatible biomass models, the results showed that the increase of explainable variables could significantly improve the fitness of branch and foliage biomass, but had little effect on other components. Besides, there was almost no difference between the two methods of estimation based on the comparison.

Finite-sample corrected generalized estimating equation of population average treatment effects in stepped wedge cluster randomized trials.

PubMed

Scott, JoAnna M; deCamp, Allan; Juraska, Michal; Fay, Michael P; Gilbert, Peter B

2017-04-01

Stepped wedge designs are increasingly commonplace and advantageous for cluster randomized trials when it is both unethical to assign placebo, and it is logistically difficult to allocate an intervention simultaneously to many clusters. We study marginal mean models fit with generalized estimating equations for assessing treatment effectiveness in stepped wedge cluster randomized trials. This approach has advantages over the more commonly used mixed models that (1) the population-average parameters have an important interpretation for public health applications and (2) they avoid untestable assumptions on latent variable distributions and avoid parametric assumptions about error distributions, therefore, providing more robust evidence on treatment effects. However, cluster randomized trials typically have a small number of clusters, rendering the standard generalized estimating equation sandwich variance estimator biased and highly variable and hence yielding incorrect inferences. We study the usual asymptotic generalized estimating equation inferences (i.e., using sandwich variance estimators and asymptotic normality) and four small-sample corrections to generalized estimating equation for stepped wedge cluster randomized trials and for parallel cluster randomized trials as a comparison. We show by simulation that the small-sample corrections provide improvement, with one correction appearing to provide at least nominal coverage even with only 10 clusters per group. These results demonstrate the viability of the marginal mean approach for both stepped wedge and parallel cluster randomized trials. We also study the comparative performance of the corrected methods for stepped wedge and parallel designs, and describe how the methods can accommodate interval censoring of individual failure times and incorporate semiparametric efficient estimators.

Multiscale modeling and computation of optically manipulated nano devices

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

Bao, Gang, E-mail: baog@zju.edu.cn; Liu, Di, E-mail: richardl@math.msu.edu; Luo, Songting, E-mail: luos@iastate.edu

2016-07-01

We present a multiscale modeling and computational scheme for optical-mechanical responses of nanostructures. The multi-physical nature of the problem is a result of the interaction between the electromagnetic (EM) field, the molecular motion, and the electronic excitation. To balance accuracy and complexity, we adopt the semi-classical approach that the EM field is described classically by the Maxwell equations, and the charged particles follow the Schrödinger equations quantum mechanically. To overcome the numerical challenge of solving the high dimensional multi-component many-body Schrödinger equations, we further simplify the model with the Ehrenfest molecular dynamics to determine the motion of the nuclei, andmore » use the Time-Dependent Current Density Functional Theory (TD-CDFT) to calculate the excitation of the electrons. This leads to a system of coupled equations that computes the electromagnetic field, the nuclear positions, and the electronic current and charge densities simultaneously. In the regime of linear responses, the resonant frequencies initiating the out-of-equilibrium optical-mechanical responses can be formulated as an eigenvalue problem. A self-consistent multiscale method is designed to deal with the well separated space scales. The isomerization of azobenzene is presented as a numerical example.« less

Scattering of electromagnetic plane wave from a perfect electric conducting strip placed at interface of topological insulator-chiral medium

NASA Astrophysics Data System (ADS)

Shoukat, Sobia; Naqvi, Qaisar A.

2016-12-01

In this manuscript, scattering from a perfect electric conducting strip located at planar interface of topological insulator (TI)-chiral medium is investigated using the Kobayashi Potential method. Longitudinal components of electric and magnetic vector potential in terms of unknown weighting function are considered. Use of related set of boundary conditions yields two algebraic equations and four dual integral equations (DIEs). Integrand of two DIEs are expanded in terms of the characteristic functions with expansion coefficients which must satisfy, simultaneously, the discontinuous property of the Weber-Schafheitlin integrals, required edge and boundary conditions. The resulting expressions are then combined with algebraic equations to express the weighting function in terms of expansion coefficients, these expansion coefficients are then substituted in remaining DIEs. The projection is applied using the Jacobi polynomials. This treatment yields matrix equation for expansion coefficients which is solved numerically. These unknown expansion coefficients are used to find the scattered field. The far zone scattering width is investigated with respect to different parameters of the geometry, i.e, chirality of chiral medium, angle of incidence, size of the strip. Significant effects of different parameters including TI parameter on the scattering width are noted.

A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study.

PubMed

Kaplan, David; Chen, Jianshen

2012-07-01

A two-step Bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous Bayesian propensity score approaches. The corresponding variance estimators are also provided. The two-step Bayesian propensity score is provided for three methods of implementation: propensity score stratification, weighting, and optimal full matching. Three simulation studies and one case study are presented to elaborate the proposed two-step Bayesian propensity score approach. Results of the simulation studies reveal that greater precision in the propensity score equation yields better recovery of the frequentist-based treatment effect. A slight advantage is shown for the Bayesian approach in small samples. Results also reveal that greater precision around the wrong treatment effect can lead to seriously distorted results. However, greater precision around the correct treatment effect parameter yields quite good results, with slight improvement seen with greater precision in the propensity score equation. A comparison of coverage rates for the conventional frequentist approach and proposed Bayesian approach is also provided. The case study reveals that credible intervals are wider than frequentist confidence intervals when priors are non-informative.

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.

Numerical procedures for the calculation of the stresses in monocoques III : calculation of the bending moments in fuselage frames

NASA Technical Reports Server (NTRS)

Hoff, N J; Libby, Paul A; Klein, Bertran

1946-01-01

This report deals with the calculation of the bending moments in and the distortions of fuselage rings upon which known concentrated and distributed loads are acting. In the procedure suggested, the ring is divided into a number of beams each having a constant radius of curvature. The forces and moments caused in the end sections of the beams by individual unit displacements of the end sections are listed in a table designated as the operations table in conformity with Southwell's nomenclature. The operations table and the external loads are equivalent to a set of linear equations. For their solution the following three procedures are presented: 1) Southwell's method of systematic relaxations. This is a step-by-step approximation procedure guided by the physical interpretation of the changes in the values of the unknown. 2) The growing unit procedure in which the individual beams are combined successively into beams of increasing length until finally the entire ring becomes a single beam. In each step of the procedure a set of not more than three simultaneous linear equations is solved. 3) Solution of the entire set of simultaneous equations by the methods of the matrix calculus. In order to demonstrate the manner in which the calculations may be carried out, the following numerical examples are worked out: 1) Curved beam with both its end sections rigidly fixed. The load is a concentrated force. 2) Egg-shape ring with symmetric concentrated loads. 3) Circular ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 4) Same with V-braces incorporated in the ring. 5) Egg-shape ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 6) Same with V-braces incorporated in the ring. The results of these calculations are checked, whenever possible, by calculations carried out according to known methods of analysis. The agreement is found to be good. The amount of work necessary for the solution of ring problems by the methods described in the present report is practically independent of the degree of redundancy of the structure. For this reason the methods are recommended for use particularly in problems of rings having one or more internal bracing elements.

Robust adaptive antiswing control of underactuated crane systems with two parallel payloads and rail length constraint.

PubMed

Zhang, Zhongcai; Wu, Yuqiang; Huang, Jinming

2016-11-01

The antiswing control and accurate positioning are simultaneously investigated for underactuated crane systems in the presence of two parallel payloads on the trolley and rail length limitation. The equations of motion for the crane system in question are established via the Euler-Lagrange equation. An adaptive control strategy is proposed with the help of system energy function and energy shaping technique. Stability analysis shows that under the designed adaptive controller, the payload swings can be suppressed ultimately and the trolley can be regulated to the destination while not exceeding the pre-specified boundaries. Simulation results are provided to show the satisfactory control performances of the presented control method in terms of working efficiency as well as robustness with respect to external disturbances. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Are the dressed gluon and ghost propagators in the Landau gauge presently determined in the confinement regime of QCD?

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

Pennington, M. R.; Wilson, D. J.

2011-11-01

The gluon and ghost propagators in Landau gauge QCD are investigated using the Schwinger-Dyson equation approach. Working in Euclidean spacetime, we solve for these propagators using a selection of vertex inputs, initially for the ghost equation alone and then for both propagators simultaneously. The results are shown to be highly sensitive to the choices of vertices. We favor the infrared finite ghost solution from studying the ghost equation alone where we argue for a specific unique solution. In order to solve this simultaneously with the gluon using a dressed-one-loop truncation, we find that a nontrivial full ghost-gluon vertex is requiredmore » in the vanishing gluon momentum limit. The self-consistent solutions we obtain correspond to having a masslike term in the gluon propagator dressing, in agreement with similar studies supporting the long-held proposal of Cornwall.« less

Solubility correlations. Part 1. Simultaneous fitting of both solute and solvent properties.

PubMed

Battino, Rubin; Seybold, Paul G

2007-11-01

A method is described for estimating solubility by fitting both solute and solvent properties in a single equation. The method is illustrated by examining the solubilities of five rare gases (He, Ne, Ar, Kr, Xe) and five 'permanent' gases (O(2), N(2), CH(4), CF(4), SF(6)) in either n-alkane (C(5)H(12) to C(16)H(34)) or alkan-1-ol (CH(3)OH to C(11)H(23)OH) solvents. Generally, the correlation (R(2)) values of the fits achieved were significantly better than 0.9. It is suggested that similar methods can be used for estimating other physico-chemical properties such as excess molar volumes and enthalpies of solution.

Design Manual for Microgravity Two-Phase Flow and Heat Transfer

DTIC Science & Technology

1989-10-01

simultaneous solution of two equations. One equation is a dimensionless two-.nhase momentum equation for a separated flow and the other is a dimensionless...created by the flow of the gas over a wave (the Bernoulli effect) is sufficient to lift the waves in a stratified flow to the top of the pipe. A... momentum equation to determine a dimensionless parameter related to the liquid flow rate: 14 [(Ug*Dg*)1(1J*) 2[ [ [ + - 4Y X 2 =9 k (1-16) [U *D1*] -n

Analysis with electron microscope of multielement samples using pure element standards

DOEpatents

King, Wayne E.

1987-01-01

A method and modified analytical electron microscope for determining the concentration of elements in a multielement sample by exposing samples with differing thicknesses for each element to a beam of electrons, simultaneously measuring the electron dosage and x-ray intensities for each sample of element to determine a "K.sub.AB " value to be used in the equation ##EQU1## where I is intensity and C is concentration for elements A and B, and exposing the multielement sample to determine the concentrations of the elements in the sample.

Full design of fuzzy controllers using genetic algorithms

NASA Technical Reports Server (NTRS)

Homaifar, Abdollah; Mccormick, ED

1992-01-01

This paper examines the applicability of genetic algorithms (GA) in the complete design of fuzzy logic controllers. While GA has been used before in the development of rule sets or high performance membership functions, the interdependence between these two components dictates that they should be designed together simultaneously. GA is fully capable of creating complete fuzzy controllers given the equations of motion of the system, eliminating the need for human input in the design loop. We show the application of this new method to the development of a cart controller.

Full design of fuzzy controllers using genetic algorithms

NASA Technical Reports Server (NTRS)

Homaifar, Abdollah; Mccormick, ED

1992-01-01

This paper examines the applicability of genetic algorithms in the complete design of fuzzy logic controllers. While GA has been used before in the development of rule sets or high performance membership functions, the interdependence between these two components dictates that they should be designed together simultaneously. GA is fully capable of creating complete fuzzy controllers given the equations of motion of the system, eliminating the need for human input in the design loop. We show the application of this new method to the development of a cart controller.

Testing for Structural Change by D-Methods in Switching Simultaneous Equations Models.

DTIC Science & Technology

1982-02-01

on ’Oaening Strate Raquiremets wad PP 225 Mili1tary Posture"). Chicago. il.. Septmer 2, 1976). Mengel . Marc. ’bciletons, Fluctuations, and tile Hopt...Telephocne Laoratories, Inc. Journal of tile Amrican Societ for Inforeeatlon Science, Vol. 3 N&. 6, pp. 366-370, Novowbr 1977). AD A04 425 PP 227 Mengel , Marc...Journal of Chemical Physics, Mengel , Marc S. end Thomas, Jons A., Jr., "Anelytical Vol. 69, ft. 8, Oct 1S, 1918). AD AD03 787 Methads In Search The"r," 86

Field Dislocation Mechanics for heterogeneous elastic materials: A numerical spectral approach

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

Djaka, Komlan Senam; Villani, Aurelien; Taupin, Vincent

Spectral methods using Fast Fourier Transform (FFT) algorithms have recently seen a surge in interest in the mechanics of materials community. The present work addresses the critical question of determining accurate local mechanical fields using FFT methods without artificial fluctuations arising from materials and defects induced discontinuities. Precisely, this work introduces a numerical approach based on intrinsic discrete Fourier transforms for the simultaneous treatment of material discontinuities arising from the presence of dislocations and from elastic stiffness heterogeneities. To this end, the elasto-static equations of the field dislocation mechanics theory for periodic heterogeneous materials are numerically solved with FFT inmore » the case of dislocations in proximity of inclusions of varying stiffness. An optimal intrinsic discrete Fourier transform method is sought based on two distinct schemes. A centered finite difference scheme for differential rules are used for numerically solving the Poisson-type equation in the Fourier space, while centered finite differences on a rotated grid is chosen for the computation of the modified Fourier–Green’s operator associated with the Lippmann–Schwinger-type equation. By comparing different methods with analytical solutions for an edge dislocation in a composite material, it is found that the present spectral method is accurate, devoid of any numerical oscillation, and efficient even for an infinite phase elastic contrast like a hole embedded in a matrix containing a dislocation. The present FFT method is then used to simulate physical cases such as the elastic fields of dislocation dipoles located near the matrix/inclusion interface in a 2D composite material and the ones due to dislocation loop distributions surrounding cubic inclusions in 3D composite material. In these configurations, the spectral method allows investigating accurately the elastic interactions and image stresses due to dislocation fields in the presence of elastic inhomogeneities.« less

Field Dislocation Mechanics for heterogeneous elastic materials: A numerical spectral approach

DOE PAGES

Djaka, Komlan Senam; Villani, Aurelien; Taupin, Vincent; ...

2017-03-01

Spectral methods using Fast Fourier Transform (FFT) algorithms have recently seen a surge in interest in the mechanics of materials community. The present work addresses the critical question of determining accurate local mechanical fields using FFT methods without artificial fluctuations arising from materials and defects induced discontinuities. Precisely, this work introduces a numerical approach based on intrinsic discrete Fourier transforms for the simultaneous treatment of material discontinuities arising from the presence of dislocations and from elastic stiffness heterogeneities. To this end, the elasto-static equations of the field dislocation mechanics theory for periodic heterogeneous materials are numerically solved with FFT inmore » the case of dislocations in proximity of inclusions of varying stiffness. An optimal intrinsic discrete Fourier transform method is sought based on two distinct schemes. A centered finite difference scheme for differential rules are used for numerically solving the Poisson-type equation in the Fourier space, while centered finite differences on a rotated grid is chosen for the computation of the modified Fourier–Green’s operator associated with the Lippmann–Schwinger-type equation. By comparing different methods with analytical solutions for an edge dislocation in a composite material, it is found that the present spectral method is accurate, devoid of any numerical oscillation, and efficient even for an infinite phase elastic contrast like a hole embedded in a matrix containing a dislocation. The present FFT method is then used to simulate physical cases such as the elastic fields of dislocation dipoles located near the matrix/inclusion interface in a 2D composite material and the ones due to dislocation loop distributions surrounding cubic inclusions in 3D composite material. In these configurations, the spectral method allows investigating accurately the elastic interactions and image stresses due to dislocation fields in the presence of elastic inhomogeneities.« less

SDF technology in location and navigation procedures: a survey of applications

NASA Astrophysics Data System (ADS)

Kelner, Jan M.; Ziółkowski, Cezary

2017-04-01

The basis for development the Doppler location method, also called the signal Doppler frequency (SDF) method or technology is the analytical solution of the wave equation for a mobile source. This paper presents an overview of the simulations, numerical analysis and empirical studies of the possibilities and the range of SDF method applications. In the paper, the various applications from numerous publications are collected and described. They mainly focus on the use of SDF method in: emitter positioning, electronic warfare, crisis management, search and rescue, navigation. The developed method is characterized by an innovative, unique property among other location methods, because it allows the simultaneous location of the many radio emitters. Moreover, this is the first method based on the Doppler effect, which allows positioning of transmitters, using a single mobile platform. In the paper, the results of the using SDF method by the other teams are also presented.

Program For Finite-Element Analyses Of Phase-Change Fluids

NASA Technical Reports Server (NTRS)

Viterna, L. A.

1995-01-01

PHASTRAN analyzes heat-transfer and flow behaviors of materials undergoing phase changes. Many phase changes operate over range of accelerations or effective gravitational fields. To analyze such thermal systems, it is necessary to obtain simultaneous solutions for equations of conservation of energy, momentum, and mass, and for equation of state. Written in APL2.

A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study

ERIC Educational Resources Information Center

Kaplan, David; Chen, Jianshen

2012-01-01

A two-step Bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous Bayesian propensity score approaches. The corresponding variance estimators are also provided. The two-step Bayesian propensity score is provided for…

Quantification of multiple simultaneously occurring nitrogen flows in the euphotic ocean

NASA Astrophysics Data System (ADS)

Xu, Min Nina; Wu, Yanhua; Zheng, Li Wei; Zheng, Zhenzhen; Zhao, Huade; Laws, Edward A.; Kao, Shuh-Ji

2017-03-01

The general features of the N cycle in the sunlit region of the ocean are well known, but methodological difficulties have previously confounded simultaneous quantification of transformation rates among the many different forms of N, e.g., ammonium (NH4+), nitrite (NO2-), nitrate (NO3-), and particulate/dissolved organic nitrogen (PN/DON). However, recent advances in analytical methodology have made it possible to employ a convenient isotope labeling technique to quantify in situ fluxes among oft-measured nitrogen species within the euphotic zone. Addition of a single 15N-labeled NH4+ tracer and monitoring of the changes in the concentrations and isotopic compositions of the total dissolved nitrogen (TDN), PN, NH4+, NO2-, and NO3- pools allowed us to quantify the 15N and 14N fluxes simultaneously. Constraints expressing the balance of 15N and 14N fluxes between the different N pools were expressed in the form of simultaneous equations, the unique solution of which via matrix inversion yielded the relevant N fluxes, including rates of NH4+, NO2-, and NO3- uptake; ammonia oxidation; nitrite oxidation; DON release; and NH4+ uptake by bacteria. The matrix inversion methodology that we used was designed specifically to analyze the results of incubations under simulated in situ conditions in the euphotic zone. By taking into consideration simultaneous fluxes among multiple N pools, we minimized potential artifacts caused by non-targeted processes in traditional source-product methods. The proposed isotope matrix method facilitates post hoc analysis of data from on-deck incubation experiments and can be used to probe effects of environmental factors (e.g., pH, temperature, and light) on multiple processes under controlled conditions.

Using Plate Finite Elements for Modeling Fillets in Design, Optimization, and Dynamic Analysis

NASA Technical Reports Server (NTRS)

Brown, A. M.; Seugling, R. M.

2003-01-01

A methodology has been developed that allows the use of plate elements instead of numerically inefficient solid elements for modeling structures with 90 degree fillets. The technique uses plate bridges with pseudo Young's modulus (Eb) and thickness (tb) values placed between the tangent points of the fillets. These parameters are obtained by solving two nonlinear simultaneous equations in terms of the independent variables rlt and twallt. These equations are generated by equating the rotation at the tangent point of a bridge system with that of a fillet, where both rotations are derived using beam theory. Accurate surface fits of the solutions are also presented to provide the user with closed-form equations for the parameters. The methodology was verified on the subcomponent level and with a representative filleted structure, where the technique yielded a plate model exhibiting a level of accuracy better than or equal to a high-fidelity solid model and with a 90-percent reduction in the number of DOFs. The application of this method for parametric design studies, optimization, and dynamic analysis should prove extremely beneficial for the finite element practitioner. Although the method does not attempt to produce accurate stresses in the filleted region, it can also be used to obtain stresses elsewhere in the structure for preliminary analysis. A future avenue of study is to extend the theory developed here to other fillet geometries, including fillet angles other than 90 and multifaceted intersections.

Brute force meets Bruno force in parameter optimisation: introduction of novel constraints for parameter accuracy improvement by symbolic computation.

PubMed

Nakatsui, M; Horimoto, K; Lemaire, F; Ürgüplü, A; Sedoglavic, A; Boulier, F

2011-09-01

Recent remarkable advances in computer performance have enabled us to estimate parameter values by the huge power of numerical computation, the so-called 'Brute force', resulting in the high-speed simultaneous estimation of a large number of parameter values. However, these advancements have not been fully utilised to improve the accuracy of parameter estimation. Here the authors review a novel method for parameter estimation using symbolic computation power, 'Bruno force', named after Bruno Buchberger, who found the Gröbner base. In the method, the objective functions combining the symbolic computation techniques are formulated. First, the authors utilise a symbolic computation technique, differential elimination, which symbolically reduces an equivalent system of differential equations to a system in a given model. Second, since its equivalent system is frequently composed of large equations, the system is further simplified by another symbolic computation. The performance of the authors' method for parameter accuracy improvement is illustrated by two representative models in biology, a simple cascade model and a negative feedback model in comparison with the previous numerical methods. Finally, the limits and extensions of the authors' method are discussed, in terms of the possible power of 'Bruno force' for the development of a new horizon in parameter estimation.

On iterative algorithms for quantitative photoacoustic tomography in the radiative transport regime

NASA Astrophysics Data System (ADS)

Wang, Chao; Zhou, Tie

2017-11-01

In this paper, we present a numerical reconstruction method for quantitative photoacoustic tomography (QPAT), based on the radiative transfer equation (RTE), which models light propagation more accurately than diffusion approximation (DA). We investigate the reconstruction of absorption coefficient and scattering coefficient of biological tissues. An improved fixed-point iterative method to retrieve the absorption coefficient, given the scattering coefficient, is proposed for its cheap computational cost; the convergence of this method is also proved. The Barzilai-Borwein (BB) method is applied to retrieve two coefficients simultaneously. Since the reconstruction of optical coefficients involves the solutions of original and adjoint RTEs in the framework of optimization, an efficient solver with high accuracy is developed from Gao and Zhao (2009 Transp. Theory Stat. Phys. 38 149-92). Simulation experiments illustrate that the improved fixed-point iterative method and the BB method are competitive methods for QPAT in the relevant cases.

A New Method to Comprehensively Diagnose Shock Waves in the Solar Atmosphere Based on Simultaneous Spectroscopic and Imaging Observations

NASA Astrophysics Data System (ADS)

Ruan, Wenzhi; Yan, Limei; He, Jiansen; Zhang, Lei; Wang, Linghua; Wei, Yong

2018-06-01

Shock waves are believed to play an important role in plasma heating. The shock-like temporal jumps in radiation intensity and Doppler shift have been identified in the solar atmosphere. However, a quantitative diagnosis of the shocks in the solar atmosphere is still lacking, seriously hindering the understanding of shock dissipative heating of the solar atmosphere. Here, we propose a new method to realize the goal of the shock quantitative diagnosis, based on Rankine–Hugoniot equations and taking the advantages of simultaneous imaging and spectroscopic observations from, e.g., IRIS (Interface Region Imaging Spectrograph). Because of this method, the key parameters of shock candidates can be derived, such as the bulk velocity and temperature of the plasma in the upstream and downstream, the propagation speed and direction. The method is applied to the shock candidates observed by IRIS, and the overall characteristics of the shocks are revealed quantitatively for the first time. This method is also tested with the help of forward modeling, i.e., virtual observations of simulated shocks. The parameters obtained from the method are consistent with the parameters of the shock formed in the model and are independent of the viewing direction. Therefore, the method we proposed here is applicable to the quantitative and comprehensive diagnosis of the observed shocks in the solar atmosphere.

Inverting x,y grid coordinates to obtain latitude and longitude in the vanderGrinten projection

NASA Technical Reports Server (NTRS)

Rubincam, D. P.

1980-01-01

The latitude and longitude of a point on the Earth's surface are found from its x,y grid coordinates in the vanderGrinten projection. The latitude is a solution of a cubic equation and the longitude a solution of a quadratic equation. Also, the x,y grid coordinates of a point on the Earth's surface can be found if its latitude and longitude are known by solving two simultaneous quadratic equations.

Parallel computation using boundary elements in solid mechanics

NASA Technical Reports Server (NTRS)

Chien, L. S.; Sun, C. T.

1990-01-01

The inherent parallelism of the boundary element method is shown. The boundary element is formulated by assuming the linear variation of displacements and tractions within a line element. Moreover, MACSYMA symbolic program is employed to obtain the analytical results for influence coefficients. Three computational components are parallelized in this method to show the speedup and efficiency in computation. The global coefficient matrix is first formed concurrently. Then, the parallel Gaussian elimination solution scheme is applied to solve the resulting system of equations. Finally, and more importantly, the domain solutions of a given boundary value problem are calculated simultaneously. The linear speedups and high efficiencies are shown for solving a demonstrated problem on Sequent Symmetry S81 parallel computing system.

Algorithms for solving large sparse systems of simultaneous linear equations on vector processors

NASA Technical Reports Server (NTRS)

David, R. E.

1984-01-01

Very efficient algorithms for solving large sparse systems of simultaneous linear equations have been developed for serial processing computers. These involve a reordering of matrix rows and columns in order to obtain a near triangular pattern of nonzero elements. Then an LU factorization is developed to represent the matrix inverse in terms of a sequence of elementary Gaussian eliminations, or pivots. In this paper it is shown how these algorithms are adapted for efficient implementation on vector processors. Results obtained on the CYBER 200 Model 205 are presented for a series of large test problems which show the comparative advantages of the triangularization and vector processing algorithms.

Transient Torque Method: A Fast and Non-Intrusive Technique to Simultaneously Determine Viscosity and Electrical Conductivity of Semiconducting and Metallic Melts

NASA Technical Reports Server (NTRS)

Li, C.; Ban, H.; Lin, B.; Scripa, R. N.; Su, C.; Lehoczky, S. L.; Zhu, S.

2003-01-01

A transient torque method was developed to rapidly and simultaneously determine the viscosity and electrical conductivity of semiconducting or metallic melts. The experimental setup is similar to that for the oscillation cup technique. The melt sample is sealed inside a fused silica ampoule, and the ampoule is suspended by a long quartz fiber to form a torsional oscillation system. A rotating magnetic field is used to induce a rotating flow in the conductive melt, which causes the ampoule to rotate along its axis. A sensitive angular detector is used to measure the deflection angle of the ampoule. Based on the transient behavior of the deflection angle as the rotating magnetic field is applied, the electrical conductivity and viscosity of the melt can be obtained simultaneously by numerically fitting the data to a set of governing equations. The transient torque viscometer was applied successfully to measure the viscosity and electrical conductivity of high purity mercury at 53.4 C. The results were in excellent agreement with the published data. The main advantage of the technique is that the measurement can be completed in one or two minutes, as opposed to the one or two-hour measurement time required by the oscillation cup technique. The method is non-intrusive; capable of rapid measurement of the viscosity of toxic, high vapor pressure melts at elevated temperatures. In addition, the transient torque viscometer can also be operated as an oscillation cup viscometer if desired.

System Simulation by Recursive Feedback: Coupling a Set of Stand-Alone Subsystem Simulations

NASA Technical Reports Server (NTRS)

Nixon, D. D.

2001-01-01

Conventional construction of digital dynamic system simulations often involves collecting differential equations that model each subsystem, arran g them to a standard form, and obtaining their numerical gin solution as a single coupled, total-system simultaneous set. Simulation by numerical coupling of independent stand-alone subsimulations is a fundamentally different approach that is attractive because, among other things, the architecture naturally facilitates high fidelity, broad scope, and discipline independence. Recursive feedback is defined and discussed as a candidate approach to multidiscipline dynamic system simulation by numerical coupling of self-contained, single-discipline subsystem simulations. A satellite motion example containing three subsystems (orbit dynamics, attitude dynamics, and aerodynamics) has been defined and constructed using this approach. Conventional solution methods are used in the subsystem simulations. Distributed and centralized implementations of coupling have been considered. Numerical results are evaluated by direct comparison with a standard total-system, simultaneous-solution approach.

Transonic aeroelastic analysis of launch vehicle configurations. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Filgueirasdeazevedo, Joao Luiz

1988-01-01

A numerical study of the aeroelastic stability of typical launch vehicle configurations in transonic flight is performed. Recent computational fluid dynamics techniques are used to simulate the transonic aerodynamic flow fields, as opposed to relying on experimental data for the unsteady aerodynamic pressures. The flow solver is coupled to an appropriate structural representation of the vehicle. The aerodynamic formulation is based on the thin layer approximation to the Reynolds-Averaged Navier-Stokes equations, where the account for turbulent mixing is done by the two-layer Baldwin and Lomax algebraic eddy viscosity model. The structural-dynamic equations are developed considering free-free flexural vibration of an elongated beam with variable properties and are cast in modal form. Aeroelastic analyses are performed by integrating simultaneously in the two sets of equations. By tracing the growth or decay of a perturbed oscillation, the aeroelastic stability of a given constant configuration can be ascertained. The method is described in detail, and results that indicate its application are presented. Applications include some validation cases for the algorithm developed, as well as the study of configurations known to have presented flutter programs in the past.

Econometric Model of Rice Policy Based On Presidential Instruction

NASA Astrophysics Data System (ADS)

Abadi Sembiring, Surya; Hutauruk, Julia

2018-01-01

The objective of research is to build an econometric model based on Presidential Instruction rice policy. The data was monthly time series from March 2005 to September 2009. Rice policy model specification using simultaneous equation, consisting of 14 structural equations and four identity equation, which was estimated using Two Stages Least Squares (2SLS) method. The results show that: (1) an increase of government purchasing price of dried harvest paddy has a positive impact on to increase in total rice production and community rice stock, (2) an increase community rice stock lead to decrease the rice imports, (3) an increase of the realization of the distribution of subsidized ZA fertilizers and the realization of the distribution of subsidized NPK fertilizers has a positive impact on to increase in total rice production and community rice stock and to reduce rice imports, (4) the price of the dried harvest paddy is highly responsive to the water content of dried harvest paddy both the short run and long run, (5) the quantity of rice imported is highly responsive to the imported rice price, both short run and long run.

Simultaneous determination of selegiline and desmethylselegiline in human body fluids by headspace solid-phase microextraction and gas chromatography-mass spectrometry.

PubMed

Kuriki, Ayako; Kumazawa, Takeshi; Lee, Xiao-Pen; Hasegawa, Chika; Kawamura, Mitsuru; Suzuki, Osamu; Sato, Keizo

2006-12-05

A method for the simultaneous determination of selegiline and its metabolite, desmethylselegiline, in human whole blood and urine is presented. The method, which combines a fiber-based headspace solid-phase microextraction (SPME) technique with gas chromatography-mass spectrometry (GC-MS), required optimization of various parameters (e.g., salt additives, extraction temperatures, extraction times and the extraction properties of the SPME fiber coatings). Pargyline was used as the internal standard. Extraction efficiencies for both selegiline and desmethylselegiline were 2.0-3.4% for whole blood, and 8.0-13.2% for urine. The regression equations for selegiline and desmethylselegiline extracted from whole blood were linear (r(2)=0.996 and 0.995) within the concentration ranges 0.1-10 and 0.2-20 ng/ml, respectively. For urine, the regression equations for selegiline and desmethylselegiline were linear (r(2)=0.999 and 0.998) within the concentration ranges 0.05-5.0 and 0.1-10 ng/ml, respectively. The limit of detection for selegiline and desmethylselegiline was 0.01-0.05 ng/ml for both samples. The lower and upper limits of quantification for each compound were 0.05-0.2 and 5-20 ng/ml, respectively. Intra- and inter-day coefficients of variation for selegiline and desmethylselegiline in both samples were not greater than 8.7 and 11.7%, respectively. The determination of selegiline and desmethylselegiline concentrations in Parkinson's disease patients undergoing continuous selegiline treatment is presented and is shown to validate the present methodology.

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...

Estimation of Bid Curves in Power Exchanges using Time-varying Simultaneous-Equations Models

NASA Astrophysics Data System (ADS)

Ofuji, Kenta; Yamaguchi, Nobuyuki

Simultaneous-equations model (SEM) is generally used in economics to estimate interdependent endogenous variables such as price and quantity in a competitive, equilibrium market. In this paper, we have attempted to apply SEM to JEPX (Japan Electric Power eXchange) spot market, a single-price auction market, using the publicly available data of selling and buying bid volumes, system price and traded quantity. The aim of this analysis is to understand the magnitude of influences to the auctioned prices and quantity from the selling and buying bids, than to forecast prices and quantity for risk management purposes. In comparison with the Ordinary Least Squares (OLS) estimation where the estimation results represent average values that are independent of time, we employ a time-varying simultaneous-equations model (TV-SEM) to capture structural changes inherent in those influences, using State Space models with Kalman filter stepwise estimation. The results showed that the buying bid volumes has that highest magnitude of influences among the factors considered, exhibiting time-dependent changes, ranging as broad as about 240% of its average. The slope of the supply curve also varies across time, implying the elastic property of the supply commodity, while the demand curve remains comparatively inelastic and stable over time.

Prediction of light aircraft interior sound pressure level from the measured sound power flowing in to the cabin

NASA Technical Reports Server (NTRS)

Atwal, Mahabir S.; Heitman, Karen E.; Crocker, Malcolm J.

1986-01-01

The validity of the room equation of Crocker and Price (1982) for predicting the cabin interior sound pressure level was experimentally tested using a specially constructed setup for simultaneous measurements of transmitted sound intensity and interior sound pressure levels. Using measured values of the reverberation time and transmitted intensities, the equation was used to predict the space-averaged interior sound pressure level for three different fuselage conditions. The general agreement between the room equation and experimental test data is considered good enough for this equation to be used for preliminary design studies.

Rocket/launcher structural dynamics

NASA Technical Reports Server (NTRS)

Ferragut, N. J.

1976-01-01

The equations of motion describing the interactions between a rocket and a launcher were derived using Lagrange's Equation. A rocket launching was simulated. The motions of both the rocket and the launcher can be considered in detail. The model contains flexible elements and rigid elements. The rigid elements (masses) were judiciously utilized to simplify the derivation of the equations. The advantages of simultaneous shoe release were illustrated. Also, the loading history of the interstage structure of a boosted configuration was determined. The equations shown in this analysis could be used as a design tool during the modification of old launchers and the design of new launchers.

Finite temperature dynamics of a Holstein polaron: The thermo-field dynamics approach

NASA Astrophysics Data System (ADS)

Chen, Lipeng; Zhao, Yang

2017-12-01

Combining the multiple Davydov D2 Ansatz with the method of thermo-field dynamics, we study finite temperature dynamics of a Holstein polaron on a lattice. It has been demonstrated, using the hierarchy equations of motion method as a benchmark, that our approach provides an efficient, robust description of finite temperature dynamics of the Holstein polaron in the simultaneous presence of diagonal and off-diagonal exciton-phonon coupling. The method of thermo-field dynamics handles temperature effects in the Hilbert space with key numerical advantages over other treatments of finite-temperature dynamics based on quantum master equations in the Liouville space or wave function propagation with Monte Carlo importance sampling. While for weak to moderate diagonal coupling temperature increases inhibit polaron mobility, it is found that off-diagonal coupling induces phonon-assisted transport that dominates at high temperatures. Results on the mean square displacements show that band-like transport features dominate the diagonal coupling cases, and there exists a crossover from band-like to hopping transport with increasing temperature when including off-diagonal coupling. As a proof of concept, our theory provides a unified treatment of coherent and incoherent transport in molecular crystals and is applicable to any temperature.

The reservoir model: a differential equation model of psychological regulation.

PubMed

Deboeck, Pascal R; Bergeman, C S

2013-06-01

Differential equation models can be used to describe the relationships between the current state of a system of constructs (e.g., stress) and how those constructs are changing (e.g., based on variable-like experiences). The following article describes a differential equation model based on the concept of a reservoir. With a physical reservoir, such as one for water, the level of the liquid in the reservoir at any time depends on the contributions to the reservoir (inputs) and the amount of liquid removed from the reservoir (outputs). This reservoir model might be useful for constructs such as stress, where events might "add up" over time (e.g., life stressors, inputs), but individuals simultaneously take action to "blow off steam" (e.g., engage coping resources, outputs). The reservoir model can provide descriptive statistics of the inputs that contribute to the "height" (level) of a construct and a parameter that describes a person's ability to dissipate the construct. After discussing the model, we describe a method of fitting the model as a structural equation model using latent differential equation modeling and latent distribution modeling. A simulation study is presented to examine recovery of the input distribution and output parameter. The model is then applied to the daily self-reports of negative affect and stress from a sample of older adults from the Notre Dame Longitudinal Study on Aging. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

The Reservoir Model: A Differential Equation Model of Psychological Regulation

PubMed Central

Deboeck, Pascal R.; Bergeman, C. S.

2017-01-01

Differential equation models can be used to describe the relationships between the current state of a system of constructs (e.g., stress) and how those constructs are changing (e.g., based on variable-like experiences). The following article describes a differential equation model based on the concept of a reservoir. With a physical reservoir, such as one for water, the level of the liquid in the reservoir at any time depends on the contributions to the reservoir (inputs) and the amount of liquid removed from the reservoir (outputs). This reservoir model might be useful for constructs such as stress, where events might “add up” over time (e.g., life stressors, inputs), but individuals simultaneously take action to “blow off steam” (e.g., engage coping resources, outputs). The reservoir model can provide descriptive statistics of the inputs that contribute to the “height” (level) of a construct and a parameter that describes a person's ability to dissipate the construct. After discussing the model, we describe a method of fitting the model as a structural equation model using latent differential equation modeling and latent distribution modeling. A simulation study is presented to examine recovery of the input distribution and output parameter. The model is then applied to the daily self-reports of negative affect and stress from a sample of older adults from the Notre Dame Longitudinal Study on Aging. PMID:23527605

Prediction Equation for Calculating Fat Mass in Young Indian Adults

PubMed Central

Sandhu, Jaspal Singh; Gupta, Giniya; Shenoy, Shweta

2010-01-01

Purpose Accurate measurement or prediction of fat mass is useful in physiology, nutrition and clinical medicine. Most predictive equations currently used to assess percentage of body fat or fat mass, using simple anthropometric measurements were derived from people in western societies and they may not be appropriate for individuals with other genotypic and phenotypic characteristics. We developed equations to predict fat mass from anthropometric measurements in young Indian adults. Methods Fat mass was measured in 60 females and 58 males, aged 20 to 29 yrs by using hydrostatic weighing and by simultaneous measurement of residual lung volume. Anthropometric measure included weight (kg), height (m) and 4 skinfold thickness [STs (mm)]. Sex specific linear regression model was developed with fat mass as the dependent variable and all anthropometric measures as independent variables. Results The prediction equation obtained for fat mass (kg) for males was 8.46+0.32 (weight) − 15.16 (height) + 9.54 (log of sum of 4 STs) (R2= 0. 53, SEE=3.42 kg) and − 20.22 + 0.33 (weight) + 3.44 (height) + 7.66 (log of sum of 4 STs) (R2=0.72, SEE=3.01kg) for females. Conclusion A new prediction equation for the measurement of fat mass was derived and internally validated in young Indian adults using simple anthropometric measurements. PMID:22375197

A fully vectorized numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Patel, N.

1983-01-01

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

Two-Dimensional Mathematical Modeling of the Pack Carburizing Process

NASA Astrophysics Data System (ADS)

Sarkar, S.; Gupta, G. S.

2008-10-01

Pack carburization is the oldest method among the case-hardening treatments, and sufficient attempts have not been made to understand this process in terms of heat and mass transfer, effect of alloying elements, dimensions of the sample, etc. Thus, a two-dimensional mathematical model in cylindrical coordinate is developed for simulating the pack carburization process for chromium-bearing steel in this study. Heat and mass balance equations are solved simultaneously, where the surface temperature of the sample varies with time, but the carbon potential at the surface during the process remains constant. The fully implicit finite volume technique is used to solve the governing equations. Good agreement has been found between the predicted and published data. The effect of temperature, carburizing time, dimensions of the sample, etc. on the pack carburizing process shows some interesting results. It is found that the two-dimensional model gives better insight into understanding the carburizing process.

Solitonlike pulses along a modified Noguchi nonlinear electrical network with second-neighbor interactions: Analytical studies

NASA Astrophysics Data System (ADS)

Kengne, E.; Liu, W. M.

2018-05-01

A modified lossless nonlinear Noguchi transmission network with second-neighbor interactions is considered. In the semidiscrete limit, we apply the reductive perturbation method and show that the dynamics of modulated waves propagating through the network are governed by an NLS equation with linear external potential. Classes of exact solitonic solutions of this network equation are derived, proving possible transmission of both bright and dark solitonlike pulses through the network. The effects of both the coupling second-neighbor parameter L3 and the strength λ of the linear potential on the dynamics of modulated waves through the network are investigated. One of the main results of our work is that with the introduction of the second neighbors in the network, two solitary signals, either two bright solitary signals or one bright and one dark solitary signal, may simultaneously propagate at the same frequency through the network.

Autonomous orbital navigation using Kepler's equation

NASA Technical Reports Server (NTRS)

Boltz, F. W.

1974-01-01

A simple method of determining the six elements of elliptic satellite orbits has been developed for use aboard manned and unmanned spacecraft orbiting the earth, moon, or any planet. The system requires the use of a horizon sensor or other device for determining the local vertical, a precision clock or timing device, and Apollo-type navigation equipment including an inertial measurement unit (IMU), a digital computer, and a coupling data unit. The three elements defining the in-plane motion are obtained from simultaneous measurements of central angle traversed around the planet and elapsed flight time using a linearization of Kepler's equation about a reference orbit. It is shown how Kalman filter theory may also be used to determine the in-plane orbital elements. The three elements defining the orbit orientation are obtained from position angles in celestial coordinates derived from the IMU with the spacecraft vertically oriented after alignment of the IMU to a known inertial coordinate frame.

Automatic measurements and computations for radiochemical analyses

USGS Publications Warehouse

Rosholt, J.N.; Dooley, J.R.

1960-01-01

In natural radioactive sources the most important radioactive daughter products useful for geochemical studies are protactinium-231, the alpha-emitting thorium isotopes, and the radium isotopes. To resolve the abundances of these thorium and radium isotopes by their characteristic decay and growth patterns, a large number of repeated alpha activity measurements on the two chemically separated elements were made over extended periods of time. Alpha scintillation counting with automatic measurements and sample changing is used to obtain the basic count data. Generation of the required theoretical decay and growth functions, varying with time, and the least squares solution of the overdetermined simultaneous count rate equations are done with a digital computer. Examples of the complex count rate equations which may be solved and results of a natural sample containing four ??-emitting isotopes of thorium are illustrated. These methods facilitate the determination of the radioactive sources on the large scale required for many geochemical investigations.

Numerical Simulations of Buoyancy Effects in low Density Gas Jets

NASA Technical Reports Server (NTRS)

Satti, R. P.; Pasumarthi, K. S.; Agrawal, A. K.

2004-01-01

This paper deals with the computational analysis of buoyancy effects in the near field of an isothermal helium jet injected into quiescent ambient air environment. The transport equations of helium mass fraction coupled with the conservation equations of mixture mass and momentum were solved using a staggered grid finite volume method. Laminar, axisymmetric, unsteady flow conditions were considered for the analysis. An orthogonal system with non-uniform grids was used to capture the instability phenomena. Computations were performed for Earth gravity and during transition from Earth to different gravitational levels. The flow physics was described by simultaneous visualizations of velocity and concentration fields at Earth and microgravity conditions. Computed results were validated by comparing with experimental data substantiating that buoyancy induced global flow oscillations present in Earth gravity are absent in microgravity. The dependence of oscillation frequency and amplitude on gravitational forcing was presented to further quantify the buoyancy effects.

The development of comparative bias index

NASA Astrophysics Data System (ADS)

Aimran, Ahmad Nazim; Ahmad, Sabri; Afthanorhan, Asyraf; Awang, Zainudin

2017-08-01

Structural Equation Modeling (SEM) is a second generation statistical analysis techniques developed for analyzing the inter-relationships among multiple variables in a model simultaneously. There are two most common used methods in SEM namely Covariance-Based Structural Equation Modeling (CB-SEM) and Partial Least Square Path Modeling (PLS-PM). There have been continuous debates among researchers in the use of PLS-PM over CB-SEM. While there is few studies were conducted to test the performance of CB-SEM and PLS-PM bias in estimating simulation data. This study intends to patch this problem by a) developing the Comparative Bias Index and b) testing the performance of CB-SEM and PLS-PM using developed index. Based on balanced experimental design, two multivariate normal simulation data with of distinct specifications of size 50, 100, 200 and 500 are generated and analyzed using CB-SEM and PLS-PM.

Nonadditivity of forward and simultaneous maskinga

PubMed Central

Svec, Adam; Joshi, Suyash N.; Jesteadt, Walt

2013-01-01

The current study measured the additional masking obtained for combinations of forward and simultaneous maskers as a function of forward masker bandwidth, signal delay, and simultaneous masker level. The effects of the two individual maskers were equated in all conditions. Additional masking increased with increasing masker level, increasing signal delay, and decreasing masker bandwidth. The portion of the simultaneous masker that made the greater contribution to additional masking was the part that overlapped with the signal, not with the forward masker. The changes in additional masking observed as a function of forward masker bandwidth and the interaction between the effects of forward and simultaneous maskers call into question the use of additional masking as a measure of basilar membrane compression and present problems for the use of simultaneous noise to simulate hearing loss. PMID:24116423

Nonlinear Ion Harmonics in the Paul Trap with Added Octopole Field: Theoretical Characterization and New Insight into Nonlinear Resonance Effect.

PubMed

Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu

2016-02-01

The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition.

Fully adaptive propagation of the quantum-classical Liouville equation

NASA Astrophysics Data System (ADS)

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-01

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Fully adaptive propagation of the quantum-classical Liouville equation.

PubMed

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-15

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Iohexol clearance is superior to creatinine-based renal function estimating equations in detecting short-term renal function decline in chronic heart failure

PubMed Central

Cvan Trobec, Katja; Kerec Kos, Mojca; von Haehling, Stephan; Anker, Stefan D.; Macdougall, Iain C.; Ponikowski, Piotr; Lainscak, Mitja

2015-01-01

Aim To compare the performance of iohexol plasma clearance and creatinine-based renal function estimating equations in monitoring longitudinal renal function changes in chronic heart failure (CHF) patients, and to assess the effects of body composition on the equation performance. Methods Iohexol plasma clearance was measured in 43 CHF patients at baseline and after at least 6 months. Simultaneously, renal function was estimated with five creatinine-based equations (four- and six-variable Modification of Diet in Renal Disease, Cockcroft-Gault, Cockcroft-Gault adjusted for lean body mass, Chronic Kidney Disease Epidemiology Collaboration equation) and body composition was assessed using bioimpedance and dual-energy x-ray absorptiometry. Results Over a median follow-up of 7.5 months (range 6-17 months), iohexol clearance significantly declined (52.8 vs 44.4 mL/[min ×1.73 m2], P = 0.001). This decline was significantly higher in patients receiving mineralocorticoid receptor antagonists at baseline (mean decline -22% of baseline value vs -3%, P = 0.037). Mean serum creatinine concentration did not change significantly during follow-up and no creatinine-based renal function estimating equation was able to detect the significant longitudinal decline of renal function determined by iohexol clearance. After accounting for body composition, the accuracy of the equations improved, but not their ability to detect renal function decline. Conclusions Renal function measured with iohexol plasma clearance showed relevant decline in CHF patients, particularly in those treated with mineralocorticoid receptor antagonists. None of the equations for renal function estimation was able to detect these changes. ClinicalTrials.gov registration number NCT01829880 PMID:26718759

New Approaches to Coding Information using Inverse Scattering Transform

NASA Astrophysics Data System (ADS)

Frumin, L. L.; Gelash, A. A.; Turitsyn, S. K.

2017-06-01

Remarkable mathematical properties of the integrable nonlinear Schrödinger equation (NLSE) can offer advanced solutions for the mitigation of nonlinear signal distortions in optical fiber links. Fundamental optical soliton, continuous, and discrete eigenvalues of the nonlinear spectrum have already been considered for the transmission of information in fiber-optic channels. Here, we propose to apply signal modulation to the kernel of the Gelfand-Levitan-Marchenko equations that offers the advantage of a relatively simple decoder design. First, we describe an approach based on exploiting the general N -soliton solution of the NLSE for simultaneous coding of N symbols involving 4 ×N coding parameters. As a specific elegant subclass of the general schemes, we introduce a soliton orthogonal frequency division multiplexing (SOFDM) method. This method is based on the choice of identical imaginary parts of the N -soliton solution eigenvalues, corresponding to equidistant soliton frequencies, making it similar to the conventional OFDM scheme, thus, allowing for the use of the efficient fast Fourier transform algorithm to recover the data. Then, we demonstrate how to use this new approach to control signal parameters in the case of the continuous spectrum.

A semi-analytical method for near-trapped mode and fictitious frequencies of multiple scattering by an array of elliptical cylinders in water waves

NASA Astrophysics Data System (ADS)

Chen, Jeng-Tzong; Lee, Jia-Wei

2013-09-01

In this paper, we focus on the water wave scattering by an array of four elliptical cylinders. The null-field boundary integral equation method (BIEM) is used in conjunction with degenerate kernels and eigenfunctions expansion. The closed-form fundamental solution is expressed in terms of the degenerate kernel containing the Mathieu and the modified Mathieu functions in the elliptical coordinates. Boundary densities are represented by using the eigenfunction expansion. To avoid using the addition theorem to translate the Mathieu functions, the present approach can solve the water wave problem containing multiple elliptical cylinders in a semi-analytical manner by introducing the adaptive observer system. Regarding water wave problems, the phenomena of numerical instability of fictitious frequencies may appear when the BIEM/boundary element method (BEM) is used. Besides, the near-trapped mode for an array of four identical elliptical cylinders is observed in a special layout. Both physical (near-trapped mode) and mathematical (fictitious frequency) resonances simultaneously appear in the present paper for a water wave problem by an array of four identical elliptical cylinders. Two regularization techniques, the combined Helmholtz interior integral equation formulation (CHIEF) method and the Burton and Miller approach, are adopted to alleviate the numerical resonance due to fictitious frequency.

Modelling Evolutionary Algorithms with Stochastic Differential Equations.

PubMed

Heredia, Jorge Pérez

2017-11-20

There has been renewed interest in modelling the behaviour of evolutionary algorithms (EAs) by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogues of the additive and multiplicative drift theorems from runtime analysis. In addition, we derive a new more general multiplicative drift theorem that also covers non-elitist EAs. This theorem simultaneously allows for positive and negative results, providing information on the algorithm's progress even when the problem cannot be optimised efficiently. Finally, we provide results for some well-known heuristics namely Random Walk (RW), Random Local Search (RLS), the (1+1) EA, the Metropolis Algorithm (MA), and the Strong Selection Weak Mutation (SSWM) algorithm.

Recent Advances in the Method of Forces: Integrated Force Method of Structural Analysis

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.

1998-01-01

Stress that can be induced in an elastic continuum can be determined directly through the simultaneous application of the equilibrium equations and the compatibility conditions. In the literature, this direct stress formulation is referred to as the integrated force method. This method, which uses forces as the primary unknowns, complements the popular equilibrium-based stiffness method, which considers displacements as the unknowns. The integrated force method produces accurate stress, displacement, and frequency results even for modest finite element models. This version of the force method should be developed as an alternative to the stiffness method because the latter method, which has been researched for the past several decades, may have entered its developmental plateau. Stress plays a primary role in the development of aerospace and other products, and its analysis is difficult. Therefore, it is advisable to use both methods to calculate stress and eliminate errors through comparison. This paper examines the role of the integrated force method in analysis, animation and design.

Simultaneous determination of nortriptyline hydrochloride and fluphenazine hydrochloride in microgram quantities from low dosage forms by liquid chromatography-UV detection.

PubMed

Ashour, Safwan; Kattan, Nuha

2012-12-01

A novel method for the simultaneous high-performance liquid chromatographic determination of nortriptyline hydrochloride and fluphenazine hydrochloride was developed and validated. Fluvastatin sodium was used as internal standard. The determination was performed on a Hypersil Gold C 8 column (250 mm × 4.6 mm i.d., 5 μm particle size) at 25 °C; the mobile phase, consisting of a mixture of formic acid (0.1 M, pH 2.16)-methanol (33:67, v / v), was delivered at a flow rate of 1.1 mL/min and detector wavelength at 251 nm. The retention time of nortriptyline, fluphenazine and fluvastatin was found to be 5.11, 8.05 and 11.38 min, respectively. Linearity ranges were 5.0-1350.0 and 10.0-1350.0 μg/mL with limit of detection values of 0.72 and 0.31 μg/mL, for nortriptyline and fluphenazine, respectively. Results of assay and recovery studies were statistically evaluated for its accuracy and precision. Correlation coefficients ( r 2 ) of the regression equations were greater than 0.999 in all cases. According to the validation results, the proposed method was found to be specific, accurate, precise and could be applied to the simultaneous quantitative analysis of nortriptyline and fluphenazine.

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

PubMed Central

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

2013-01-01

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

PDEMOD: Software for control/structures optimization

NASA Technical Reports Server (NTRS)

Taylor, Lawrence W., Jr.; Zimmerman, David

1991-01-01

Because of the possibility of adverse interaction between the control system and the structural dynamics of large, flexible spacecraft, great care must be taken to ensure stability and system performance. Because of the high cost of insertion of mass into low earth orbit, it is prudent to optimize the roles of structure and control systems simultaneously. Because of the difficulty and the computational burden in modeling and analyzing the control structure system dynamics, the total problem is often split and treated iteratively. It would aid design if the control structure system dynamics could be represented in a single system of equations. With the use of the software PDEMOD (Partial Differential Equation Model), it is now possible to optimize structure and control systems simultaneously. The distributed parameter modeling approach enables embedding the control system dynamics into the same equations for the structural dynamics model. By doing this, the current difficulties involved in model order reduction are avoided. The NASA Mini-MAST truss is used an an example for studying integrated control structure design.

A Chebyshev Collocation Method for Moving Boundaries, Heat Transfer, and Convection During Directional Solidification

NASA Technical Reports Server (NTRS)

Zhang, Yiqiang; Alexander, J. I. D.; Ouazzani, J.

1994-01-01

Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid-fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and name propagation. The directional solidification of semi-conductor crystals by the Bridgman-Stockbarger method is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt-solid interface. In this work, a Chebyshev pseudospectra collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, finite-difference preconditioned conjugate minimum residual method and a Picard type iterative scheme.

Finding Equations of Tangents to Conics

ERIC Educational Resources Information Center

Baloglou, George; Helfgott, Michel

2004-01-01

A calculus-free approach is offered for determining the equation of lines tangent to conics. Four types of problems are discussed: line tangent to a conic at a given point, line tangent to a conic passing through a given point outside the conic, line of a given slope tangent to a conic, and line tangent to two conics simultaneously; in each case,…

Sensitivity analysis for aeroacoustic and aeroelastic design of turbomachinery blades

NASA Technical Reports Server (NTRS)

Lorence, Christopher B.; Hall, Kenneth C.

1995-01-01

A new method for computing the effect that small changes in the airfoil shape and cascade geometry have on the aeroacoustic and aeroelastic behavior of turbomachinery cascades is presented. The nonlinear unsteady flow is assumed to be composed of a nonlinear steady flow plus a small perturbation unsteady flow that is harmonic in time. First, the full potential equation is used to describe the behavior of the nonlinear mean (steady) flow through a two-dimensional cascade. The small disturbance unsteady flow through the cascade is described by the linearized Euler equations. Using rapid distortion theory, the unsteady velocity is split into a rotational part that contains the vorticity and an irrotational part described by a scalar potential. The unsteady vorticity transport is described analytically in terms of the drift and stream functions computed from the steady flow. Hence, the solution of the linearized Euler equations may be reduced to a single inhomogeneous equation for the unsteady potential. The steady flow and small disturbance unsteady flow equations are discretized using bilinear quadrilateral isoparametric finite elements. The nonlinear mean flow solution and streamline computational grid are computed simultaneously using Newton iteration. At each step of the Newton iteration, LU decomposition is used to solve the resulting set of linear equations. The unsteady flow problem is linear, and is also solved using LU decomposition. Next, a sensitivity analysis is performed to determine the effect small changes in cascade and airfoil geometry have on the mean and unsteady flow fields. The sensitivity analysis makes use of the nominal steady and unsteady flow LU decompositions so that no additional matrices need to be factored. Hence, the present method is computationally very efficient. To demonstrate how the sensitivity analysis may be used to redesign cascades, a compressor is redesigned for improved aeroelastic stability and two different fan exit guide vanes are redesigned for reduced downstream radiated noise. In addition, a framework detailing how the two-dimensional version of the method may be used to redesign three-dimensional geometries is presented.

Simulation of chemical-vapor-deposited silicon carbide for a cold wall vertical reactor

NASA Astrophysics Data System (ADS)

Lee, Y. L.; Sanchez, J. M.

1997-07-01

The growth rate of silicon carbide obtained by low-pressure chemical vapor deposition from tetramethylsilane is numerically simulated for a cold wall vertical reactor. The transport equations for momentum, heat, and mass transfer are simultaneously solved by employing the finite volume method. A model for reaction rate is also proposed in order to predict the measured growth rates [A. Figueras, S. Garelik, J. Santiso, R. Rodroguez-Clemente, B. Armas, C. Combescure, R. Berjoan, J.M. Saurel and R. Caplain, Mater. Sci. Eng. B 11 (1992) 83]. Finally, the effects of thermal diffusion on the growth rate are investigated.

Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2

NASA Technical Reports Server (NTRS)

Karki, K. C.; Patankar, S. V.; Runchal, A. K.; Mongia, H. C.

1988-01-01

The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially.

Simultaneous PET and Multispectral 3-Dimensional Fluorescence Optical Tomography Imaging System

PubMed Central

Li, Changqing; Yang, Yongfeng; Mitchell, Gregory S.; Cherry, Simon R.

2015-01-01

Integrated PET and 3-dimensional (3D) fluorescence optical tomography (FOT) imaging has unique and attractive features for in vivo molecular imaging applications. We have designed, built, and evaluated a simultaneous PET and 3D FOT system. The design of the FOT system is compatible with many existing small-animal PET scanners. Methods The 3D FOT system comprises a novel conical mirror that is used to view the whole-body surface of a mouse with an electron-multiplying charge-coupled device camera when a collimated laser beam is projected on the mouse to stimulate fluorescence. The diffusion equation was used to model the propagation of optical photons inside the mouse body, and 3D fluorescence images were reconstructed iteratively from the fluorescence intensity measurements measured from the surface of the mouse. Insertion of the conical mirror into the gantry of a small-animal PET scanner allowed simultaneous PET and 3D FOT imaging. Results The mutual interactions between PET and 3D FOT were evaluated experimentally. PET has negligible effects on 3D FOT performance. The inserted conical mirror introduces a reduction in the sensitivity and noise-equivalent count rate of the PET system and increases the scatter fraction. PET–FOT phantom experiments were performed. An in vivo experiment using both PET and FOT was also performed. Conclusion Phantom and in vivo experiments demonstrate the feasibility of simultaneous PET and 3D FOT imaging. The first in vivo simultaneous PET–FOT results are reported. PMID:21810591

On the equivalence of dynamically orthogonal and bi-orthogonal methods: Theory and numerical simulations

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

Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em, E-mail: george_karniadakis@brown.edu

2014-08-01

The Karhunen–Lòeve (KL) decomposition provides a low-dimensional representation for random fields as it is optimal in the mean square sense. Although for many stochastic systems of practical interest, described by stochastic partial differential equations (SPDEs), solutions possess this low-dimensional character, they also have a strongly time-dependent form and to this end a fixed-in-time basis may not describe the solution in an efficient way. Motivated by this limitation of standard KL expansion, Sapsis and Lermusiaux (2009) [26] developed the dynamically orthogonal (DO) field equations which allow for the simultaneous evolution of both the spatial basis where uncertainty ‘lives’ but also themore » stochastic characteristics of uncertainty. Recently, Cheng et al. (2013) [28] introduced an alternative approach, the bi-orthogonal (BO) method, which performs the exact same tasks, i.e. it evolves the spatial basis and the stochastic characteristics of uncertainty. In the current work we examine the relation of the two approaches and we prove theoretically and illustrate numerically their equivalence, in the sense that one method is an exact reformulation of the other. We show this by deriving a linear and invertible transformation matrix described by a matrix differential equation that connects the BO and the DO solutions. We also examine a pathology of the BO equations that occurs when two eigenvalues of the solution cross, resulting in an instantaneous, infinite-speed, internal rotation of the computed spatial basis. We demonstrate that despite the instantaneous duration of the singularity this has important implications on the numerical performance of the BO approach. On the other hand, it is observed that the BO is more stable in nonlinear problems involving a relatively large number of modes. Several examples, linear and nonlinear, are presented to illustrate the DO and BO methods as well as their equivalence.« less

Quasi solution of radiation transport equation

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

Pogosbekyan, L.R.; Lysov, D.A.

There is uncertainty with experimental data as well as with input data of theoretical calculations. The neutron distribution from the variational principle, which takes into account both theoretical and experimental data, is obtained to increase the accuracy and speed of neutronic calculations. The neutron imbalance in mesh cells and the discrepancy between experimentally measured and calculated functional of the neutron distribution are simultaneously minimized. A fast-working and simple-programming iteration method is developed to minimize the objective functional. The method can be used in the core monitoring and control system for (a) power distribution calculations, (b) in- and ex-core detector calibration,more » (c) macro-cross sections or isotope distribution correction by experimental data, and (d) core and detector diagnostics.« less

A joint analysis of the Drake equation and the Fermi paradox

NASA Astrophysics Data System (ADS)

Prantzos, Nikos

2013-07-01

I propose a unified framework for a joint analysis of the Drake equation and the Fermi paradox, which enables a simultaneous, quantitative study of both of them. The analysis is based on a simplified form of the Drake equation and on a fairly simple scheme for the colonization of the Milky Way. It appears that for sufficiently long-lived civilizations, colonization of the Galaxy is the only reasonable option to gain knowledge about other life forms. This argument allows one to define a region in the parameter space of the Drake equation, where the Fermi paradox definitely holds (`Strong Fermi paradox').

Identification and control of structures in space

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Quinn, R. D.; Norris, M. A.

1984-01-01

The derivation of the equations of motion for the Spacecraft Control Laboratory Experiment (SCOLE) is reported and the equations of motion of a similar structure orbiting the earth are also derived. The structure is assumed to undergo large rigid-body maneuvers and small elastic deformations. A perturbation approach is proposed whereby the quantities defining the rigid-body maneuver are assumed to be relatively large, with the elastic deformations and deviations from the rigid-body maneuver being relatively small. The perturbation equations have the form of linear equations with time-dependent coefficients. An active control technique can then be formulated to permit maneuvering of the spacecraft and simultaneously suppressing the elastic vibration.

Analysis of hysteresis effect on the vibration motion of a bimodal non-uniform micro-cantilever using MCS theory

NASA Astrophysics Data System (ADS)

Korayem, M. H.; Korayem, A. H.; Hosseini Hashemi, Sh.

2016-02-01

Nowadays, to enhance the performance of atomic force microscopy (AFM) micro-cantilevers (MCs) during imaging, reduce costs and increase the surface topography precision, advanced MCs equipped with piezoelectric layers are utilized. Using the modified couple stress (MCS) theory not only makes the modeling more exhaustive, but also increases the accuracy of prediction of the vibration behavior of the system. In this paper, Hamilton's principle by consideration of the MCS theory has been used to extract the equations. In addition, to discretize the equations, differential quadrature method has been adopted. Analysis of the hysteresis effect on the vibration behavior of the AFM MC is of significant importance. Thus, to model the hysteresis effect, Bouc-Wen method, which is solved simultaneously with the vibration equations of non-uniform Timoshenko beam, has been utilized. Furthermore, a bimodal excitation of the MC has been considered. The results reveal that the hysteresis effect appears as a phase difference in the time response. Finally, the effect of the geometric parameters on the vibration frequency of the system which is excited by combination of the first two vibration modes of the non-uniform piezoelectric MC has been examined. The results indicate the considerable effect of the MC length in comparison with other geometric parameters such as the MC width and thickness.

Investigation of obstacle effect to improve conjugate heat transfer in backward facing step channel using fast simulation of incompressible flow

NASA Astrophysics Data System (ADS)

Nouri-Borujerdi, Ali; Moazezi, Arash

2018-01-01

The current study investigates the conjugate heat transfer characteristics for laminar flow in backward facing step channel. All of the channel walls are insulated except the lower thick wall under a constant temperature. The upper wall includes a insulated obstacle perpendicular to flow direction. The effect of obstacle height and location on the fluid flow and heat transfer are numerically explored for the Reynolds number in the range of 10 ≤ Re ≤ 300. Incompressible Navier-Stokes and thermal energy equations are solved simultaneously in fluid region by the upwind compact finite difference scheme based on flux-difference splitting in conjunction with artificial compressibility method. In the thick wall, the energy equation is obtained by Laplace equation. A multi-block approach is used to perform parallel computing to reduce the CPU time. Each block is modeled separately by sharing boundary conditions with neighbors. The developed program for modeling was written in FORTRAN language with OpenMP API. The obtained results showed that using of the multi-block parallel computing method is a simple robust scheme with high performance and high-order accurate. Moreover, the obtained results demonstrated that the increment of Reynolds number and obstacle height as well as decrement of horizontal distance between the obstacle and the step improve the heat transfer.

A high-fidelity method to analyze perturbation evolution in turbulent flows

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

Unnikrishnan, S., E-mail: sasidharannair.1@osu.edu; Gaitonde, Datta V., E-mail: gaitonde.3@osu.edu

2016-04-01

Small perturbation propagation in fluid flows is usually examined by linearizing the governing equations about a steady basic state. It is often useful, however, to study perturbation evolution in the unsteady evolving turbulent environment. Such analyses can elucidate the role of perturbations in the generation of coherent structures or the production of noise from jet turbulence. The appropriate equations are still the linearized Navier–Stokes equations, except that the linearization must be performed about the instantaneous evolving turbulent state, which forms the coefficients of the linearized equations. This is a far more difficult problem since in addition to the turbulent state,more » its rate of change and the perturbation field are all required at each instant. In this paper, we develop and use a novel technique for this problem by using a pair (denoted “baseline” and “twin”) of simultaneous synchronized Large-Eddy Simulations (LES). At each time-step, small disturbances whose propagation characteristics are to be studied, are introduced into the twin through a forcing term. At subsequent time steps, the difference between the two simulations is shown to be equivalent to solving the forced Navier–Stokes equations, linearized about the instantaneous turbulent state. The technique does not put constraints on the forcing, which could be arbitrary, e.g., white noise or other stochastic variants. We consider, however, “native” forcing having properties of disturbances that exist naturally in the turbulent environment. The method then isolates the effect of turbulence in a particular region on the rest of the field, which is useful in the study of noise source localization. The synchronized technique is relatively simple to implement into existing codes. In addition to minimizing the storage and retrieval of large time-varying datasets, it avoids the need to explicitly linearize the governing equations, which can be a very complicated task for viscous terms or turbulence closures. The method is illustrated by application to a well-validated Mach 1.3 jet. Specifically, the effects of turbulence on the jet lipline and core collapse regions on the near-acoustic field are isolated. The properties of the method, including linearity and effect of initial transients, are discussed. The results provide insight into how turbulence from different parts of the jet contribute to the observed dominance of low and high frequency content at shallow and sideline angles, respectively.« less

A high-fidelity method to analyze perturbation evolution in turbulent flows

NASA Astrophysics Data System (ADS)

Unnikrishnan, S.; Gaitonde, Datta V.

2016-04-01

Small perturbation propagation in fluid flows is usually examined by linearizing the governing equations about a steady basic state. It is often useful, however, to study perturbation evolution in the unsteady evolving turbulent environment. Such analyses can elucidate the role of perturbations in the generation of coherent structures or the production of noise from jet turbulence. The appropriate equations are still the linearized Navier-Stokes equations, except that the linearization must be performed about the instantaneous evolving turbulent state, which forms the coefficients of the linearized equations. This is a far more difficult problem since in addition to the turbulent state, its rate of change and the perturbation field are all required at each instant. In this paper, we develop and use a novel technique for this problem by using a pair (denoted "baseline" and "twin") of simultaneous synchronized Large-Eddy Simulations (LES). At each time-step, small disturbances whose propagation characteristics are to be studied, are introduced into the twin through a forcing term. At subsequent time steps, the difference between the two simulations is shown to be equivalent to solving the forced Navier-Stokes equations, linearized about the instantaneous turbulent state. The technique does not put constraints on the forcing, which could be arbitrary, e.g., white noise or other stochastic variants. We consider, however, "native" forcing having properties of disturbances that exist naturally in the turbulent environment. The method then isolates the effect of turbulence in a particular region on the rest of the field, which is useful in the study of noise source localization. The synchronized technique is relatively simple to implement into existing codes. In addition to minimizing the storage and retrieval of large time-varying datasets, it avoids the need to explicitly linearize the governing equations, which can be a very complicated task for viscous terms or turbulence closures. The method is illustrated by application to a well-validated Mach 1.3 jet. Specifically, the effects of turbulence on the jet lipline and core collapse regions on the near-acoustic field are isolated. The properties of the method, including linearity and effect of initial transients, are discussed. The results provide insight into how turbulence from different parts of the jet contribute to the observed dominance of low and high frequency content at shallow and sideline angles, respectively.

A theory of post-stall transients in axial compression systems. I - Development of equations

NASA Technical Reports Server (NTRS)

Moore, F. K.; Greitzer, E. M.

1985-01-01

An approximate theory is presented for post-stall transients in multistage axial compression systems. The theory leads to a set of three simultaneous nonlinear third-order partial differential equations for pressure rise, and average and disturbed values of flow coefficient, as functions of time and angle around the compressor. By a Galerkin procedure, angular dependence is averaged, and the equations become first order in time. These final equations are capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. It is shown how rotating-stall-like and surgelike motions are coupled through these equations, and also how the instantaneous compressor pumping characteristic changes during the transient stall process.

Physical properties of asteroids derived from a novel approach to modeling of optical lightcurves and WISE thermalinfrared data

NASA Astrophysics Data System (ADS)

Durech, Josef; Hanus, Josef; Delbo, Marco; Ali-Lagoa, Victor; Carry, Benoit

2014-11-01

Convex shape models and spin vectors of asteroids are now routinely derived from their disk-integrated lightcurves by the lightcurve inversion method of Kaasalainen et al. (2001, Icarus 153, 37). These shape models can be then used in combination with thermal infrared data and a thermophysical model to derive other physical parameters - size, albedo, macroscopic roughness and thermal inertia of the surface. In this classical two-step approach, the shape and spin parameters are kept fixed during the thermophysical modeling when the emitted thermal flux is computed from the surface temperature, which is computed by solving a 1-D heat diffusion equation in sub-surface layers. A novel method of simultaneous inversion of optical and infrared data was presented by Durech et al. (2012, LPI Contribution No. 1667, id.6118). The new algorithm uses the same convex shape representation as the lightcurve inversion but optimizes all relevant physical parameters simultaneously (including the shape, size, rotation vector, thermal inertia, albedo, surface roughness, etc.), which leads to a better fit to the thermal data and a reliable estimation of model uncertainties. We applied this method to selected asteroids using their optical lightcurves from archives and thermal infrared data observed by the Wide-field Infrared Survey Explorer (WISE) satellite. We will (i) show several examples of how well our model fits both optical and infrared data, (ii) discuss the uncertainty of derived parameters (namely the thermal inertia), (iii) compare results obtained with the two-step approach with those obtained by our method, (iv) discuss the advantages of this simultaneous approach with respect to the classical two-step approach, and (v) advertise the possibility to use this approach to tens of thousands asteroids for which enough WISE and optical data exist.

Sqeezing generated by a nonlinear master equation and by amplifying-dissipative Hamiltonians

NASA Technical Reports Server (NTRS)

Dodonov, V. V.; Marchiolli, M. A.; Mizrahi, Solomon S.; Moussa, M. H. Y.

1994-01-01

In the first part of this contribution we show that the master equation derived from the generalized version of the nonlinear Doebner-Goldin equation leads to the squeezing of one of the quadratures. In the second part we consider two familiar Hamiltonians, the Bateman- Caldirola-Kanai and the optical parametric oscillator; going back to their classical Lagrangian form we introduce a stochastic force and a dissipative factor. From this new Lagrangian we obtain a modified Hamiltonian that treats adequately the simultaneous amplification and dissipation phenomena, presenting squeezing, too.

GFSSP Training Course Lectures

NASA Technical Reports Server (NTRS)

Majumdar, Alok K.

2008-01-01

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

The thermodynamic properties of oxygen and nitrogen

NASA Technical Reports Server (NTRS)

Stewart, R. B.; Jacobsen, R. T.; Myers, A. F.

1972-01-01

The development of a single equation of state for oxygen and nitrogen based on the thermodynamic properties of the gases is described. The coefficients of the equation of state were determined by simultaneous least squares fits to values of isochoric heat capacity and saturation density values used to define the criteria for phase equilibrium. Tables of data for the conditions of both gases are included.

On One Possible Generalization of the Regression Theorem

NASA Astrophysics Data System (ADS)

Bogolubov, N. N.; Soldatov, A. V.

2018-03-01

A general approach to derivation of formally exact closed time-local or time-nonlocal evolution equations for non-equilibrium multi-time correlations functions made of observables of an open quantum system interacting simultaneously with external time-dependent classical fields and dissipative environment is discussed. The approach allows for the subsequent treatment of these equations within a perturbative scheme assuming that the system-environment interaction is weak.

Exact self-similarity solution of the Navier-Stokes equations for a porous channel with orthogonally moving walls

NASA Astrophysics Data System (ADS)

Dauenhauer, Eric C.; Majdalani, Joseph

2003-06-01

This article describes a self-similarity solution of the Navier-Stokes equations for a laminar, incompressible, and time-dependent flow that develops within a channel possessing permeable, moving walls. The case considered here pertains to a channel that exhibits either injection or suction across two opposing porous walls while undergoing uniform expansion or contraction. Instances of direct application include the modeling of pulsating diaphragms, sweat cooling or heating, isotope separation, filtration, paper manufacturing, irrigation, and the grain regression during solid propellant combustion. To start, the stream function and the vorticity equation are used in concert to yield a partial differential equation that lends itself to a similarity transformation. Following this similarity transformation, the original problem is reduced to solving a fourth-order differential equation in one similarity variable η that combines both space and time dimensions. Since two of the four auxiliary conditions are of the boundary value type, a numerical solution becomes dependent upon two initial guesses. In order to achieve convergence, the governing equation is first transformed into a function of three variables: The two guesses and η. At the outset, a suitable numerical algorithm is applied by solving the resulting set of twelve first-order ordinary differential equations with two unspecified start-up conditions. In seeking the two unknown initial guesses, the rapidly converging inverse Jacobian method is applied in an iterative fashion. Numerical results are later used to ascertain a deeper understanding of the flow character. The numerical scheme enables us to extend the solution range to physical settings not considered in previous studies. Moreover, the numerical approach broadens the scope to cover both suction and injection cases occurring with simultaneous wall motion.

Using a fast Fourier method to model sound propagation in a stratified atmosphere over a stratified porous-elastic ground

NASA Technical Reports Server (NTRS)

Tooms, S.; Attenborough, K.

1990-01-01

Using a Fast Fourier integration method and a global matrix method for solution of the boundary condition equations at all interfaces simultaneously, a useful tool for predicting acoustic propagation in a stratified fluid over a stratified porous-elastic solid was developed. The model for the solid is a modified Biot-Stoll model incorporating four parameters describing the pore structure corresponding to the Rayleigh-Attenborough rigid-porous structure model. The method is also compared to another Fast Fourier code (CERL-FFP) which models the ground as an impedance surface under a horizontally stratified air. Agreement with the CERL FFP is good. The effects on sound propagation of a combination of ground elasticity, complex ground structure, and atmospheric conditions are demonstrated by theoretical results over a snow layer, and experimental results over a model ground surface.

Multivariate Autoregressive Modeling and Granger Causality Analysis of Multiple Spike Trains

PubMed Central

Krumin, Michael; Shoham, Shy

2010-01-01

Recent years have seen the emergence of microelectrode arrays and optical methods allowing simultaneous recording of spiking activity from populations of neurons in various parts of the nervous system. The analysis of multiple neural spike train data could benefit significantly from existing methods for multivariate time-series analysis which have proven to be very powerful in the modeling and analysis of continuous neural signals like EEG signals. However, those methods have not generally been well adapted to point processes. Here, we use our recent results on correlation distortions in multivariate Linear-Nonlinear-Poisson spiking neuron models to derive generalized Yule-Walker-type equations for fitting ‘‘hidden” Multivariate Autoregressive models. We use this new framework to perform Granger causality analysis in order to extract the directed information flow pattern in networks of simulated spiking neurons. We discuss the relative merits and limitations of the new method. PMID:20454705

International Conference on Numerical Methods in Fluid Dynamics, 7th, Stanford University, Stanford and Moffett Field, CA, June 23-27, 1980, Proceedings

NASA Technical Reports Server (NTRS)

Reynolds, W. C. (Editor); Maccormack, R. W.

1981-01-01

Topics discussed include polygon transformations in fluid mechanics, computation of three-dimensional horseshoe vortex flow using the Navier-Stokes equations, an improved surface velocity method for transonic finite-volume solutions, transonic flow calculations with higher order finite elements, the numerical calculation of transonic axial turbomachinery flows, and the simultaneous solutions of inviscid flow and boundary layer at transonic speeds. Also considered are analytical solutions for the reflection of unsteady shock waves and relevant numerical tests, reformulation of the method of characteristics for multidimensional flows, direct numerical simulations of turbulent shear flows, the stability and separation of freely interacting boundary layers, computational models of convective motions at fluid interfaces, viscous transonic flow over airfoils, and mixed spectral/finite difference approximations for slightly viscous flows.

Uniformity Masks Design Method Based on the Shadow Matrix for Coating Materials with Different Condensation Characteristics

PubMed Central

2013-01-01

An intuitionistic method is proposed to design shadow masks to achieve thickness profile control for evaporation coating processes. The proposed method is based on the concept of the shadow matrix, which is a matrix that contains coefficients that build quantitive relations between shape parameters of masks and shadow quantities of substrate directly. By using the shadow matrix, shape parameters of shadow masks could be derived simply by solving a matrix equation. Verification experiments were performed on a special case where coating materials have different condensation characteristics. By using the designed mask pair with complementary shapes, thickness uniformities of better than 98% are demonstrated for MgF2 (m = 1) and LaF3 (m = 0.5) simultaneously on a 280 mm diameter spherical substrate with the radius curvature of 200 mm. PMID:24227996

Two-Layer Elastographic 3-D Traction Force Microscopy

PubMed Central

Álvarez-González, Begoña; Zhang, Shun; Gómez-González, Manuel; Meili, Ruedi; Firtel, Richard A.; Lasheras, Juan C.; del Álamo, Juan C.

2017-01-01

Cellular traction force microscopy (TFM) requires knowledge of the mechanical properties of the substratum where the cells adhere to calculate cell-generated forces from measurements of substratum deformation. Polymer-based hydrogels are broadly used for TFM due to their linearly elastic behavior in the range of measured deformations. However, the calculated stresses, particularly their spatial patterns, can be highly sensitive to the substratum’s Poisson’s ratio. We present two-layer elastographic TFM (2LETFM), a method that allows for simultaneously measuring the Poisson’s ratio of the substratum while also determining the cell-generated forces. The new method exploits the analytical solution of the elastostatic equation and deformation measurements from two layers of the substratum. We perform an in silico analysis of 2LETFM concluding that this technique is robust with respect to TFM experimental parameters, and remains accurate even for noisy measurement data. We also provide experimental proof of principle of 2LETFM by simultaneously measuring the stresses exerted by migrating Physarum amoeboae on the surface of polyacrylamide substrata, and the Poisson’s ratio of the substrata. The 2LETFM method could be generalized to concurrently determine the mechanical properties and cell-generated forces in more physiologically relevant extracellular environments, opening new possibilities to study cell-matrix interactions. PMID:28074837

Estimation of homogeneous nucleation flux via a kinetic model

NASA Technical Reports Server (NTRS)

Wilcox, C. F.; Bauer, S. H.

1991-01-01

The proposed kinetic model for condensation under homogeneous conditions, and the onset of unidirectional cluster growth in supersaturated gases, does not suffer from the conceptual flaws that characterize classical nucleation theory. When a full set of simultaneous rate equation is solved, a characteristic time emerges, for each cluster size, at which the production rate, and its rate of conversion to the next size (n + 1) are equal. Procedures for estimating the essential parameters are proposed; condensation fluxes J(kin) exp ss are evaluated. Since there are practical limits to the cluster size that can be incorporated in the set of simultaneous first-order differential equations, a code was developed for computing an approximate J(th) exp ss based on estimates of a 'constrained equilibrium' distribution, and identification of its minimum.

Deblending of simultaneous-source data using iterative seislet frame thresholding based on a robust slope estimation

NASA Astrophysics Data System (ADS)

Zhou, Yatong; Han, Chunying; Chi, Yue

2018-06-01

In a simultaneous source survey, no limitation is required for the shot scheduling of nearby sources and thus a huge acquisition efficiency can be obtained but at the same time making the recorded seismic data contaminated by strong blending interference. In this paper, we propose a multi-dip seislet frame based sparse inversion algorithm to iteratively separate simultaneous sources. We overcome two inherent drawbacks of traditional seislet transform. For the multi-dip problem, we propose to apply a multi-dip seislet frame thresholding strategy instead of the traditional seislet transform for deblending simultaneous-source data that contains multiple dips, e.g., containing multiple reflections. The multi-dip seislet frame strategy solves the conflicting dip problem that degrades the performance of the traditional seislet transform. For the noise issue, we propose to use a robust dip estimation algorithm that is based on velocity-slope transformation. Instead of calculating the local slope directly using the plane-wave destruction (PWD) based method, we first apply NMO-based velocity analysis and obtain NMO velocities for multi-dip components that correspond to multiples of different orders, then a fairly accurate slope estimation can be obtained using the velocity-slope conversion equation. An iterative deblending framework is given and validated through a comprehensive analysis over both numerical synthetic and field data examples.

Development of Finite Elements for Two-Dimensional Structural Analysis Using the Integrated Force Method

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Patnaik, Surya N.; Hopkins, Dale A.

1996-01-01

The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations.

Finite-frequency sensitivity kernels for global seismic wave propagation based upon adjoint methods

NASA Astrophysics Data System (ADS)

Liu, Qinya; Tromp, Jeroen

2008-07-01

We determine adjoint equations and Fréchet kernels for global seismic wave propagation based upon a Lagrange multiplier method. We start from the equations of motion for a rotating, self-gravitating earth model initially in hydrostatic equilibrium, and derive the corresponding adjoint equations that involve motions on an earth model that rotates in the opposite direction. Variations in the misfit function χ then may be expressed as , where δlnm = δm/m denotes relative model perturbations in the volume V, δlnd denotes relative topographic variations on solid-solid or fluid-solid boundaries Σ, and ∇Σδlnd denotes surface gradients in relative topographic variations on fluid-solid boundaries ΣFS. The 3-D Fréchet kernel Km determines the sensitivity to model perturbations δlnm, and the 2-D kernels Kd and Kd determine the sensitivity to topographic variations δlnd. We demonstrate also how anelasticity may be incorporated within the framework of adjoint methods. Finite-frequency sensitivity kernels are calculated by simultaneously computing the adjoint wavefield forward in time and reconstructing the regular wavefield backward in time. Both the forward and adjoint simulations are based upon a spectral-element method. We apply the adjoint technique to generate finite-frequency traveltime kernels for global seismic phases (P, Pdiff, PKP, S, SKS, depth phases, surface-reflected phases, surface waves, etc.) in both 1-D and 3-D earth models. For 1-D models these adjoint-generated kernels generally agree well with results obtained from ray-based methods. However, adjoint methods do not have the same theoretical limitations as ray-based methods, and can produce sensitivity kernels for any given phase in any 3-D earth model. The Fréchet kernels presented in this paper illustrate the sensitivity of seismic observations to structural parameters and topography on internal discontinuities. These kernels form the basis of future 3-D tomographic inversions.

Interactive calculation procedure for supersonic flows. Ph.D. Thesis - Case Western Reserve Univ., 1976. Final Report

NASA Technical Reports Server (NTRS)

Tassa, Y.; Anderson, B. H.; Reshotko, E.

1977-01-01

An interactive procedure was developed for supersonic viscous flows that can be used for either two-dimensional or axisymmetric configurations. The procedure is directed to supersonic internal flows as well as those supersonic external flows that require consideration of mutual interaction between the outer flow and the boundary layer flow. The flow field is divided into two regions: an inner region which is highly viscous and mostly subsonic and an outer region where the flow is supersonic and in which viscous effects are small but not negligible. For the outer region a numerical solution is obtained by applying the method of characteristics to a system of equations which includes viscous and conduction transport terms only normal to the streamlines. The inner region is treated by a system of equations of the boundary layer type that includes higher order effects such as longitudinal and transverse curvature and normal pressure gradients. These equations are coupled and solved simultaneously in the physical coordinates by using an implicit finite difference scheme. This system can also be used to calculate laminar and turbulent boundary layers using a scalar eddy viscosity concept.

Use of loading-unloading compression curves in medical device design

NASA Astrophysics Data System (ADS)

Ciornei, M. C.; Alaci, S.; Ciornei, F. C.; Romanu, I. C.

2017-08-01

The paper presents a method and experimental results regarding mechanical testing of soft materials. In order to characterize the mechanical behaviour of technological materials used in prosthesis, a large number of material constants are required, as well as the comparison to the original. The present paper proposes as methodology the comparison between compression loading-unloading curves corresponding to a soft biological tissue and to a synthetic material. To this purpose, a device was designed based on the principle of the dynamic harness test. A moving load is considered and the force upon the indenter is controlled for loading-unloading phases. The load and specimen deformation are simultaneously recorded. A significant contribution of this paper is the interpolation of experimental data by power law functions, a difficult task because of the instability of the system of equations to be optimized. Finding the interpolation function was simplified, from solving a system of transcendental equations to solving a unique equation. The characteristic parameters of the experimentally curves must be compared to the ones corresponding to actual tissue. The tests were performed for two cases: first, using a spherical punch, and second, for a flat-ended cylindrical punch.

Design optimization of axial flow hydraulic turbine runner: Part I - an improved Q3D inverse method

NASA Astrophysics Data System (ADS)

Peng, Guoyi; Cao, Shuliang; Ishizuka, Masaru; Hayama, Shinji

2002-06-01

With the aim of constructing a comprehensive design optimization procedure of axial flow hydraulic turbine, an improved quasi-three-dimensional inverse method has been proposed from the viewpoint of system and a set of rotational flow governing equations as well as a blade geometry design equation has been derived. The computation domain is firstly taken from the inlet of guide vane to the far outlet of runner blade in the inverse method and flows in different regions are solved simultaneously. So the influence of wicket gate parameters on the runner blade design can be considered and the difficulty to define the flow condition at the runner blade inlet is surmounted. As a pre-computation of initial blade design on S2m surface is newly adopted, the iteration of S1 and S2m surfaces has been reduced greatly and the convergence of inverse computation has been improved. The present model has been applied to the inverse computation of a Kaplan turbine runner. Experimental results and the direct flow analysis have proved the validation of inverse computation. Numerical investigations show that a proper enlargement of guide vane distribution diameter is advantageous to improve the performance of axial hydraulic turbine runner. Copyright

Synchronized parameter optimization of the double freeform lenses illumination system used for the CF-LCoS pico-projectors

NASA Astrophysics Data System (ADS)

Chen, Enguo; Liu, Peng; Yu, Feihong

2012-10-01

A novel synchronized optimization method of multiple freeform surfaces is proposed and applied to double lenses illumination system design of CF-LCoS pico-projectors. Based on Snell's law and the energy conservation law, a series of first-order partial differential equations are derived for the multiple freeform surfaces of the initial system. By assigning the light deflection angle to each freeform surface, multiple surfaces can be obtained simultaneously by solving the corresponding equations, meanwhile the restricted angle on CF-LCoS is guaranteed. In order to improve the spatial uniformity, the multi-surfaces are synchronously optimized by using simplex algorithm for an extended LED source. Design example shows that the double lenses based illumination system, which employs a single 2 mm×2 mm LED chip and a CF-LCoS panel with a diagonal of 0.59 inches satisfies the needs of pico-projector. Moreover, analytical result indicates that the design method represents substantial improvement and practical significance over traditional CF-LCoS projection system, which could offer outstanding performance with both portability and low cost. The synchronized optimization design method could not only realize collimating and uniform illumination, but also could be introduced to other specific light conditions.

Modeling of diatomic molecule using the Morse potential and the Verlet algorithm

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

Fidiani, Elok

Performing molecular modeling usually uses special software for Molecular Dynamics (MD) such as: GROMACS, NAMD, JMOL etc. Molecular dynamics is a computational method to calculate the time dependent behavior of a molecular system. In this work, MATLAB was used as numerical method for a simple modeling of some diatomic molecules: HCl, H{sub 2} and O{sub 2}. MATLAB is a matrix based numerical software, in order to do numerical analysis, all the functions and equations describing properties of atoms and molecules must be developed manually in MATLAB. In this work, a Morse potential was generated to describe the bond interaction betweenmore » the two atoms. In order to analyze the simultaneous motion of molecules, the Verlet Algorithm derived from Newton’s Equations of Motion (classical mechanics) was operated. Both the Morse potential and the Verlet algorithm were integrated using MATLAB to derive physical properties and the trajectory of the molecules. The data computed by MATLAB is always in the form of a matrix. To visualize it, Visualized Molecular Dynamics (VMD) was performed. Such method is useful for development and testing some types of interaction on a molecular scale. Besides, this can be very helpful for describing some basic principles of molecular interaction for educational purposes.« less

Simultaneous measurement of translation and tilt using digital speckle photography

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

Bhaduri, Basanta; Quan, Chenggen; Tay, Cho Jui

2010-06-20

A Michelson-type digital speckle photographic system has been proposed in which one light beam produces a Fourier transform and another beam produces an image at a recording plane, without interfering between themselves. Because the optical Fourier transform is insensitive to translation and the imaging technique is insensitive to tilt, the proposed system is able to simultaneously and independently determine both surface tilt and translation by two separate recordings, one before and another after the surface motion, without the need to obtain solutions for simultaneous equations. Experimental results are presented to verify the theoretical analysis.

Simultaneous optical flow and source estimation: Space–time discretization and preconditioning

PubMed Central

Andreev, R.; Scherzer, O.; Zulehner, W.

2015-01-01

We consider the simultaneous estimation of an optical flow field and an illumination source term in a movie sequence. The particular optical flow equation is obtained by assuming that the image intensity is a conserved quantity up to possible sources and sinks which represent varying illumination. We formulate this problem as an energy minimization problem and propose a space–time simultaneous discretization for the optimality system in saddle-point form. We investigate a preconditioning strategy that renders the discrete system well-conditioned uniformly in the discretization resolution. Numerical experiments complement the theory. PMID:26435561

Millimeter wave generation by relativistic electron beams

NASA Astrophysics Data System (ADS)

Kuo, S. S.; Cheo, B. R.; Tiong, K. K.; Whang, M. H.

1985-11-01

The classical technique of transformation and characteristics is employed to analyze the problem of strong turbulence in unmagnetized plasmas. The effects of resonance broadening and perturbation expansion are treated simultaneously without time securities. The renormalization procedure is used in the transformed Vlasov equation to analyze the turbulence and to derive explicitly a diffusion equation. Analyses are extended to imhomogeneous plasma and the relationship between the transformation and ponderomotive force is obtained.

The Impact of Input and Output Prices on The Household Economic Behavior of Rice-Livestock Integrated Farming System (Rlifs) and Non Rlifs Farmers

NASA Astrophysics Data System (ADS)

Lindawati, L.; Kusnadi, N.; Kuntjoro, S. U.; Swastika, D. K. S.

2018-02-01

Integrated farming system is a system that emphasized linkages and synergism of farming units waste utilization. The objective of the study was to analyze the impact of input and output prices on both Rice Livestock Integrated Farming System (RLIFS) and non RLIFS farmers. The study used econometric model in the form of a simultaneous equations system consisted of 36 equations (18 behavior and 18 identity equations). The impact of changes in some variables was obtained through simulation of input and output prices on simultaneous equations. The results showed that the price increasing of the seed, SP-36, urea, medication/vitamins, manure, bran, straw had negative impact on production of the rice, cow, manure, bran, straw and household income. The decrease in the rice and cow production, production input usage, allocation of family labor, rice and cow business income was greater in RLIFS than non RLIFS farmers. The impact of rising rice and cow cattle prices in the two groups of farmers was not too much different because (1) farming waste wasn’t used effectively (2) manure and straw had small proportion of production costs. The increase of input and output price didn’t have impact on production costs and household expenditures on RLIFS.

A linear programming manual

NASA Technical Reports Server (NTRS)

Tuey, R. C.

1972-01-01

Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.

Surrogate modelling for the prediction of spatial fields based on simultaneous dimensionality reduction of high-dimensional input/output spaces.

PubMed

Crevillén-García, D

2018-04-01

Time-consuming numerical simulators for solving groundwater flow and dissolution models of physico-chemical processes in deep aquifers normally require some of the model inputs to be defined in high-dimensional spaces in order to return realistic results. Sometimes, the outputs of interest are spatial fields leading to high-dimensional output spaces. Although Gaussian process emulation has been satisfactorily used for computing faithful and inexpensive approximations of complex simulators, these have been mostly applied to problems defined in low-dimensional input spaces. In this paper, we propose a method for simultaneously reducing the dimensionality of very high-dimensional input and output spaces in Gaussian process emulators for stochastic partial differential equation models while retaining the qualitative features of the original models. This allows us to build a surrogate model for the prediction of spatial fields in such time-consuming simulators. We apply the methodology to a model of convection and dissolution processes occurring during carbon capture and storage.

Extracting survival parameters from isothermal, isobaric, and "iso-concentration" inactivation experiments by the "3 end points method".

PubMed

Corradini, M G; Normand, M D; Newcomer, C; Schaffner, D W; Peleg, M

2009-01-01

Theoretically, if an organism's resistance can be characterized by 3 survival parameters, they can be found by solving 3 simultaneous equations that relate the final survival ratio to the lethal agent's intensity. (For 2 resistance parameters, 2 equations will suffice.) In practice, the inevitable experimental scatter would distort the results of such a calculation or render the method unworkable. Averaging the results obtained with more than 3 final survival ratio triplet combinations, determined in four or more treatments, can remove this impediment. This can be confirmed by the ability of a kinetic inactivation model derived from the averaged parameters to predict survival patterns under conditions not employed in their determination, as demonstrated with published isothermal survival data of Clostridium botulinum spores, isobaric data of Escherichia coli under HPP, and Pseudomonas exposed to hydrogen peroxide. Both the method and the underlying assumption that the inactivation followed a Weibull-Log logistic (WeLL) kinetics were confirmed in this way, indicating that when an appropriate survival model is available, it is possible to predict the entire inactivation curves from several experimental final survival ratios alone. Where applicable, the method could simplify the experimental procedure and lower the cost of microbial resistance determinations. In principle, the methodology can be extended to deteriorative chemical reactions if they too can be characterized by 2 or 3 kinetic parameters.

The externally corrected coupled cluster approach with four- and five-body clusters from the CASSCF wave function.

PubMed

Xu, Enhua; Li, Shuhua

2015-03-07

An externally corrected CCSDt (coupled cluster with singles, doubles, and active triples) approach employing four- and five-body clusters from the complete active space self-consistent field (CASSCF) wave function (denoted as ecCCSDt-CASSCF) is presented. The quadruple and quintuple excitation amplitudes within the active space are extracted from the CASSCF wave function and then fed into the CCSDt-like equations, which can be solved in an iterative way as the standard CCSDt equations. With a size-extensive CASSCF reference function, the ecCCSDt-CASSCF method is size-extensive. When the CASSCF wave function is readily available, the computational cost of the ecCCSDt-CASSCF method scales as the popular CCSD method (if the number of active orbitals is small compared to the total number of orbitals). The ecCCSDt-CASSCF approach has been applied to investigate the potential energy surface for the simultaneous dissociation of two O-H bonds in H2O, the equilibrium distances and spectroscopic constants of 4 diatomic molecules (F2(+), O2(+), Be2, and NiC), and the reaction barriers for the automerization reaction of cyclobutadiene and the Cl + O3 → ClO + O2 reaction. In most cases, the ecCCSDt-CASSCF approach can provide better results than the CASPT2 (second order perturbation theory with a CASSCF reference function) and CCSDT methods.

On systems having Poincaré and Galileo symmetry

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

Holland, Peter, E-mail: peter.holland@gtc.ox.ac.uk

Using the wave equation in d≥1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincaré and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d=1 the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated withmore » the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d>1 is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwell’s equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics.« less

Dynamic sensitivity analysis of biological systems

PubMed Central

Wu, Wu Hsiung; Wang, Feng Sheng; Chang, Maw Shang

2008-01-01

Background A mathematical model to understand, predict, control, or even design a real biological system is a central theme in systems biology. A dynamic biological system is always modeled as a nonlinear ordinary differential equation (ODE) system. How to simulate the dynamic behavior and dynamic parameter sensitivities of systems described by ODEs efficiently and accurately is a critical job. In many practical applications, e.g., the fed-batch fermentation systems, the system admissible input (corresponding to independent variables of the system) can be time-dependent. The main difficulty for investigating the dynamic log gains of these systems is the infinite dimension due to the time-dependent input. The classical dynamic sensitivity analysis does not take into account this case for the dynamic log gains. Results We present an algorithm with an adaptive step size control that can be used for computing the solution and dynamic sensitivities of an autonomous ODE system simultaneously. Although our algorithm is one of the decouple direct methods in computing dynamic sensitivities of an ODE system, the step size determined by model equations can be used on the computations of the time profile and dynamic sensitivities with moderate accuracy even when sensitivity equations are more stiff than model equations. To show this algorithm can perform the dynamic sensitivity analysis on very stiff ODE systems with moderate accuracy, it is implemented and applied to two sets of chemical reactions: pyrolysis of ethane and oxidation of formaldehyde. The accuracy of this algorithm is demonstrated by comparing the dynamic parameter sensitivities obtained from this new algorithm and from the direct method with Rosenbrock stiff integrator based on the indirect method. The same dynamic sensitivity analysis was performed on an ethanol fed-batch fermentation system with a time-varying feed rate to evaluate the applicability of the algorithm to realistic models with time-dependent admissible input. Conclusion By combining the accuracy we show with the efficiency of being a decouple direct method, our algorithm is an excellent method for computing dynamic parameter sensitivities in stiff problems. We extend the scope of classical dynamic sensitivity analysis to the investigation of dynamic log gains of models with time-dependent admissible input. PMID:19091016

Analysis with electron microscope of multielement samples using pure element standards

DOEpatents

King, W.E.

1986-01-06

This disclosure describes a method and modified analytical electron microscope for determining the concentration of elements in a multielement sample by exposing samples with differing thicknesses for each element to a beam of electrons. Simultaneously the electron dosage and x-ray intensities are measured for each sample of element to determine a ''K/sub AB/'' value to be used in the equation (I/sub A/I/sub B/) = K/sub AB/ (C/sub A//C/sub B/), where I is intensity and C is concentration for elements A and B. The multielement sample is exposed to determine the concentrations of the elements in the sample.

Reduction by invariants and projection of linear representations of Lie algebras applied to the construction of nonlinear realizations

NASA Astrophysics Data System (ADS)

Campoamor-Stursberg, R.

2018-03-01

A procedure for the construction of nonlinear realizations of Lie algebras in the context of Vessiot-Guldberg-Lie algebras of first-order systems of ordinary differential equations (ODEs) is proposed. The method is based on the reduction of invariants and projection of lowest-dimensional (irreducible) representations of Lie algebras. Applications to the description of parameterized first-order systems of ODEs related by contraction of Lie algebras are given. In particular, the kinematical Lie algebras in (2 + 1)- and (3 + 1)-dimensions are realized simultaneously as Vessiot-Guldberg-Lie algebras of parameterized nonlinear systems in R3 and R4, respectively.

A theoretically based determination of bowen-ratio fetch requirements

USGS Publications Warehouse

Stannard, D.I.

1997-01-01

Determination of fetch requirements for accurate Bowen-ratio measurements of latent- and sensible-heat fluxes is more involved than for eddy-correlation measurements because Bowen-ratio sensors are located at two heights, rather than just one. A simple solution to the diffusion equation is used to derive an expression for Bowen-ratio fetch requirements, downwind of a step change in surface fluxes. These requirements are then compared to eddy-correlation fetch requirements based on the same diffusion equation solution. When the eddy-correlation and upper Bowen-ratio sensor heights are equal, and the available energy upwind and downwind of the step change is constant, the Bowen-ratio method requires less fetch than does eddy correlation. Differences in fetch requirements between the two methods are greatest over relatively smooth surfaces. Bowen-ratio fetch can be reduced significantly by lowering the lower sensor, as well as the upper sensor. The Bowen-ratio fetch model was tested using data from a field experiment where multiple Bowen-ratio systems were deployed simultaneously at various fetches and heights above a field of bermudagrass. Initial comparisons were poor, but improved greatly when the model was modified (and operated numerically) to account for the large roughness of the upwind cotton field.

Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.

PubMed

Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong

2015-11-01

The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.

Iterative absolute electroanalytical approach to characterization of bulk redox conducting systems.

PubMed

Lewera, Adam; Miecznikowski, Krzysztof; Chojak, Malgorzata; Makowski, Oktawian; Golimowski, Jerzy; Kulesza, Pawel J

2004-05-15

A novel electroanalytical approach is proposed here, and it is demonstrated with the direct and simultaneous determination of two unknowns: the concentration of redox sites and the apparent diffusion coefficient for charge propagation in a single crystal of dodecatungstophosphoric acid. This Keggin-type polyoxometalate serves as a model bulk redox conducting inorganic material for solid-state voltammetry. The system has been investigated using an ultramicrodisk working electrode in the absence of external liquid supporting electrolyte. The analytical method requires numerical solution of the combination of two equations in which the first one describes current (or charge) in a well-defined (either spherical or linear) diffusional regime and the second general equation describes chronoamperometric (or normal pulse voltammetric current) under mixed (linear-spherical) conditions. The iterative approach is based on successive approximations through calculation and minimizing the least-squares error function. The method is fairly universal, and in principle, it can be extended to the investigation of other bulk systems including sol-gel processed materials, redox melts, and solutions on condition that they are electroactive and well behaved, they contain redox centers at sufficiently high level, and a number of electrons for the redox reaction considered is known.

Completed Beltrami-Michell Formulation for Analyzing Radially Symmetrical Bodies

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Saigal, Sunil; Hopkins, Dale A.; Patnaik, Surya N.

1994-01-01

A force method formulation, the completed Beltrami-Michell formulation (CBMF), has been developed for analyzing boundary value problems in elastic continua. The CBMF is obtained by augmenting the classical Beltrami-Michell formulation with novel boundary compatibility conditions. It can analyze general elastic continua with stress, displacement, or mixed boundary conditions. The CBMF alleviates the limitations of the classical formulation, which can solve stress boundary value problems only. In this report, the CBMF is specialized for plates and shells. All equations of the CBMF, including the boundary compatibility conditions, are derived from the variational formulation of the integrated force method (IFM). These equations are defined only in terms of stresses. Their solution for kinematically stable elastic continua provides stress fields without any reference to displacements. In addition, a stress function formulation for plates and shells is developed by augmenting the classical Airy's formulation with boundary compatibility conditions expressed in terms of the stress function. The versatility of the CBMF and the augmented stress function formulation is demonstrated through analytical solutions of several mixed boundary value problems. The example problems include a composite circular plate and a composite circular cylindrical shell under the simultaneous actions of mechanical and thermal loads.

Nuclear scissors modes and hidden angular momenta

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

Balbutsev, E. B., E-mail: balbuts@theor.jinr.ru; Molodtsova, I. V.; Schuck, P.

The coupled dynamics of low-lying modes and various giant resonances are studied with the help of the Wigner Function Moments method generalized to take into account spin degrees of freedom and pair correlations simultaneously. The method is based on Time-Dependent Hartree–Fock–Bogoliubov equations. The model of the harmonic oscillator including spin–orbit potential plus quadrupole–quadrupole and spin–spin interactions is considered. New low-lying spin-dependent modes are analyzed. Special attention is paid to the scissors modes. A new source of nuclear magnetism, connected with counter-rotation of spins up and down around the symmetry axis (hidden angular momenta), is discovered. Its inclusion into the theorymore » allows one to improve substantially the agreement with experimental data in the description of energies and transition probabilities of scissors modes.« less

Remote sensing of environmental particulate pollutants - Optical methods for determinations of size distribution and complex refractive index

NASA Technical Reports Server (NTRS)

Fymat, A. L.

1978-01-01

A unifying approach, based on a generalization of Pearson's differential equation of statistical theory, is proposed for both the representation of particulate size distribution and the interpretation of radiometric measurements in terms of this parameter. A single-parameter gamma-type distribution is introduced, and it is shown that inversion can only provide the dimensionless parameter, r/ab (where r = particle radius, a = effective radius, b = effective variance), at least when the distribution vanishes at both ends. The basic inversion problem in reconstructing the particle size distribution is analyzed, and the existing methods are reviewed (with emphasis on their capabilities) and classified. A two-step strategy is proposed for simultaneously determining the complex refractive index and reconstructing the size distribution of atmospheric particulates.

Analysis and improvement measures of flight delay in China

NASA Astrophysics Data System (ADS)

Zang, Yuhang

2017-03-01

Firstly, this paper establishes the principal component regression model to analyze the data quantitatively, based on principal component analysis to get the three principal component factors of flight delays. Then the least square method is used to analyze the factors and obtained the regression equation expression by substitution, and then found that the main reason for flight delays is airlines, followed by weather and traffic. Aiming at the above problems, this paper improves the controllable aspects of traffic flow control. For reasons of traffic flow control, an adaptive genetic queuing model is established for the runway terminal area. This paper, establish optimization method that fifteen planes landed simultaneously on the three runway based on Beijing capital international airport, comparing the results with the existing FCFS algorithm, the superiority of the model is proved.

Potential flow about arbitrary biplane wing sections

NASA Technical Reports Server (NTRS)

Garrick, I E

1937-01-01

A rigorous treatment is given of the problem of determining the two-dimensional potential flow around arbitrary biplane cellules. The analysis involves the use of elliptic functions and is sufficiently general to include the effects of such elements as the section shapes, the chord ratio, gap, stagger, and decalage, which elements may be specified arbitrarily. The flow problem is resolved by making use of the methods of conformal representation. Thus the solution of the problem of transforming conformally two arbitrary contours into two circles is expressed by a pair of simultaneous integral equations, for which a method of numerical solution is outlined. As an example of the numerical process, the pressure distribution over certain arrangements of the NACA 4412 airfoil in biplane combinations is presented and compared with the monoplane pressure distribution.

A Solution Space for a System of Null-State Partial Differential Equations: Part 2

NASA Astrophysics Data System (ADS)

Flores, Steven M.; Kleban, Peter

2015-01-01

This article is the second of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE). The system comprises 2 N null-state equations and three conformal Ward identities which govern CFT correlation functions of 2 N one-leg boundary operators. In the first article (Flores and Kleban, Commun Math Phys, arXiv:1212.2301, 2012), we use methods of analysis and linear algebra to prove that dim , with C N the Nth Catalan number. The analysis of that article is complete except for the proof of a lemma that it invokes. The purpose of this article is to provide that proof. The lemma states that if every interval among ( x 2, x 3), ( x 3, x 4),…,( x 2 N-1, x 2 N ) is a two-leg interval of (defined in Flores and Kleban, Commun Math Phys, arXiv:1212.2301, 2012), then F vanishes. Proving this lemma by contradiction, we show that the existence of such a nonzero function implies the existence of a non-vanishing CFT two-point function involving primary operators with different conformal weights, an impossibility. This proof (which is rigorous in spite of our occasional reference to CFT) involves two different types of estimates, those that give the asymptotic behavior of F as the length of one interval vanishes, and those that give this behavior as the lengths of two intervals vanish simultaneously. We derive these estimates by using Green functions to rewrite certain null-state PDEs as integral equations, combining other null-state PDEs to obtain Schauder interior estimates, and then repeatedly integrating the integral equations with these estimates until we obtain optimal bounds. Estimates in which two interval lengths vanish simultaneously divide into two cases: two adjacent intervals and two non-adjacent intervals. The analysis of the latter case is similar to that for one vanishing interval length. In contrast, the analysis of the former case is more complicated, involving a Green function that contains the Jacobi heat kernel as its essential ingredient.

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

NASA Technical Reports Server (NTRS)

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

1984-01-01

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

An all-at-once reduced Hessian SQP scheme for aerodynamic design optimization

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1995-01-01

This paper introduces a computational scheme for solving a class of aerodynamic design problems that can be posed as nonlinear equality constrained optimizations. The scheme treats the flow and design variables as independent variables, and solves the constrained optimization problem via reduced Hessian successive quadratic programming. It updates the design and flow variables simultaneously at each iteration and allows flow variables to be infeasible before convergence. The solution of an adjoint flow equation is never needed. In addition, a range space basis is chosen so that in a certain sense the 'cross term' ignored in reduced Hessian SQP methods is minimized. Numerical results for a nozzle design using the quasi-one-dimensional Euler equations show that this scheme is computationally efficient and robust. The computational cost of a typical nozzle design is only a fraction more than that of the corresponding analysis flow calculation. Superlinear convergence is also observed, which agrees with the theoretical properties of this scheme. All optimal solutions are obtained by starting far away from the final solution.

Computation of multi-dimensional viscous supersonic jet flow

NASA Technical Reports Server (NTRS)

Kim, Y. N.; Buggeln, R. C.; Mcdonald, H.

1986-01-01

A new method has been developed for two- and three-dimensional computations of viscous supersonic flows with embedded subsonic regions adjacent to solid boundaries. The approach employs a reduced form of the Navier-Stokes equations which allows solution as an initial-boundary value problem in space, using an efficient noniterative forward marching algorithm. Numerical instability associated with forward marching algorithms for flows with embedded subsonic regions is avoided by approximation of the reduced form of the Navier-Stokes equations in the subsonic regions of the boundary layers. Supersonic and subsonic portions of the flow field are simultaneously calculated by a consistently split linearized block implicit computational algorithm. The results of computations for a series of test cases relevant to internal supersonic flow is presented and compared with data. Comparison between data and computation are in general excellent thus indicating that the computational technique has great promise as a tool for calculating supersonic flow with embedded subsonic regions. Finally, a User's Manual is presented for the computer code used to perform the calculations.

Simultaneous heat and mass transfer inside a vertical channel in evaporating a heated falling glycols liquid film

NASA Astrophysics Data System (ADS)

Nait Alla, Abderrahman; Feddaoui, M'barek; Meftah, Hicham

2015-12-01

The interactive effects of heat and mass transfer in the evaporation of ethylene and propylene glycol flowing as falling films on vertical channel was investigated. The liquid film falls along a left plate which is externally subjected to a uniform heat flux while the right plate is the dry wall and is kept thermally insulated. The model solves the coupled governing equations in both phases together with the boundary and interfacial conditions. The systems of equations obtained by using an implicit finite difference method are solved by Tridiagonal Matrix Algorithm. The influence of the inlet liquid flow, Reynolds number in the gas flow and the wall heat flux on the intensity of heat and mass transfers are examined. A comparison between the results obtained for studied glycols and water in the same conditions is made. The results indicate that water evaporates in more intense way in comparison to glycols and the increase of gas flow rate tends to improve slightly the evaporation.

Computation of multi-dimensional viscous supersonic flow

NASA Technical Reports Server (NTRS)

Buggeln, R. C.; Kim, Y. N.; Mcdonald, H.

1986-01-01

A method has been developed for two- and three-dimensional computations of viscous supersonic jet flows interacting with an external flow. The approach employs a reduced form of the Navier-Stokes equations which allows solution as an initial-boundary value problem in space, using an efficient noniterative forward marching algorithm. Numerical instability associated with forward marching algorithms for flows with embedded subsonic regions is avoided by approximation of the reduced form of the Navier-Stokes equations in the subsonic regions of the boundary layers. Supersonic and subsonic portions of the flow field are simultaneously calculated by a consistently split linearized block implicit computational algorithm. The results of computations for a series of test cases associated with supersonic jet flow is presented and compared with other calculations for axisymmetric cases. Demonstration calculations indicate that the computational technique has great promise as a tool for calculating a wide range of supersonic flow problems including jet flow. Finally, a User's Manual is presented for the computer code used to perform the calculations.

Acoustic resonances in cylinder bundles oscillating in a compressibile fluid

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

Lin, W.H.; Raptis, A.C.

1984-12-01

This paper deals with an analytical study on acoustic resonances of elastic oscillations of a group of parallel, circular, thin cylinders in an unbounded volume of barotropic, compressible, inviscid fluid. The perturbed motion of the fluid is assumed due entirely to the flexural oscillations of the cylinders. The motion of the fluid disturbances is first formulated in a three-dimensional wave form and then casted into a two-dimensional Helmholtz equation for the harmonic motion in time and in axial space. The acoustic motion in the fluid and the elastic motion in the cylinders are solved simultaneously. Acoustic resonances were approximately determinedmore » from the secular (eigenvalue) equation by the method of successive iteration with the use of digital computers for a given set of the fluid properties and the cylinders' geometry and properties. Effects of the flexural wavenumber and the configuration of and the spacing between the cylinders on the acoustic resonances were thoroughly investigated.« less

User`s guide for UTCHEM implicit (1.0) a three dimensional chemical flood simulator. Final report, September 30, 1992--December 31, 1995

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

NONE

1996-07-01

UTCHEM IMPLICIT is a three-dimensional chemical flooding simulator. The solution scheme is fully implicit. The pressure equation and the mass conservation equations are solved simultaneously for the aqueous phase pressure and the total concentrations of each component. A third-order-in-space, second-order-in-time finite-difference method and a new total-variation-diminishing (TVD) third-order flux limiter are used to reduce numerical dispersion effects. Saturations and phase concentrations are solved in a flash routine. The major physical phenomena modeled in the simulator are: dispersion, adsorption, aqueous-oleic-microemulsion phase behavior, interfacial tension, relative permeability, capillary trapping, compositional phase viscosity, capillary pressure, phase density, polymer properties: shear thinning viscosity, inaccessiblemore » pore volume, permeability reduction, and adsorption. The following options are available in the simulator: constant or variable time-step sizes, uniform or nonuniform grid, pressure or rate constrained wells, horizontal and vertical wells.« less

The shape and location of the sector boundary surface in the inner solar system. [Helios observations

NASA Technical Reports Server (NTRS)

Villante, U.; Bruno, R.; Mariani, F.; Burlaga, L. F.; Ness, N. F.

1979-01-01

Simultaneous observations by Helios-1 and Helios-2 over four solar rotations were used to determine the latitudinal dependence of the polarity of the interplanetary magnetic field within plus or minus 7.23 deg of the solar equator and within 1 AU. The longitudinal and latitudinal positions of the sector boundary crossing are consistent with a warped sector boundary which extended from the sun to 1 AU and was inclined approximately 10 deg with respect to the heliographic equator. This is consistent with simultaneous Pioneer 11 observations, which showed unipolar fields at latitude approximately 16 deg at heliocentric distances greater than 3.5 AU. Two sectors were observed at southern latitudes; however, four sectors were observed at northern latitudes on two rotations, indicating a distortion from planarity of the sectory boundary surface.

Parameter Estimation for Simultaneous Saccharification and Fermentation of Food Waste Into Ethanol Using Matlab Simulink

NASA Astrophysics Data System (ADS)

Davis, Rebecca Anne

The increase in waste disposal and energy costs has provided an incentive to convert carbohydrate-rich food waste streams into fuel. For example, dining halls and restaurants discard foods that require tipping fees for removal. An effective use of food waste may be the enzymatic hydrolysis of the waste to simple sugars and fermentation of the sugars to ethanol. As these wastes have complex compositions which may change day-to-day, experiments were carried out to test fermentability of two different types of food waste at 27° C using Saccharomyces cerevisiae yeast (ATCC4124) and Genencor's STARGEN™ enzyme in batch simultaneous saccharification and fermentation (SSF) experiments. A mathematical model of SSF based on experimentally matched rate equations for enzyme hydrolysis and yeast fermentation was developed in Matlab Simulink®. Using Simulink® parameter estimation 1.1.3, parameters for hydrolysis and fermentation were estimated through modified Michaelis-Menten and Monod-type equations with the aim of predicting changes in the levels of ethanol and glycerol from different initial concentrations of glucose, fructose, maltose, and starch. The model predictions and experimental observations agree reasonably well for the two food waste streams and a third validation dataset. The approach of using Simulink® as a dynamic visual model for SSF represents a simple method which can be applied to a variety of biological pathways and may be very useful for systems approaches in metabolic engineering in the future.

Constructing diabatic representations using adiabatic and approximate diabatic data--Coping with diabolical singularities.

PubMed

Zhu, Xiaolei; Yarkony, David R

2016-01-28

We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, H(d), and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility, has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of H(d) individually provides a starting point (seed) from which convergence of the full H(d) construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4(1)A states of phenol and the 1,2(1)A states of NH3, states which are coupled by conical intersections.

A mathematical approach for the simultaneous in vitro spectrophotometric analysis of rifampicin and isoniazid from modified-release anti-TB drug delivery systems.

PubMed

du Toit, Lisa; Pillay, Viness; Choonara, Yahya

2010-01-01

Dissolution testing with subsequent analysis is considered as an imperative tool for quality evaluation of the combination rifampicin-isoniazid (RIF-INH) combination. Partial least squares (PLS) regression has been successfully undertaken to select suitable predictor variables and to identify outliers for the generation of equations for RIF and INH determination in fixed-dose combinations (FDCs). The aim of this investigation was to ascertain the applicability of the described technique in testing a novel oral FDC anti-TB drug delivery system and currently available two-drug FDCs, in comparison to the United States Pharmacopeial method for analysis of RIF and INH Capsules with chromatographic determination of INH and colorimetric RIF determination. Regression equations generated employing the statistical coefficients satisfactorily predicted RIF release at each sampling point (R(2)>or=0.9350). There was an acceptable degree of correlation between the drug release data, as predicted by regressional analysis of UV spectrophotometric data, and chromatographic and colorimetric determination of INH (R(2)=0.9793 and R(2)=0.9739) and RIF (R(2)= 0.9976 and R(2)=0.9996) for the two-drug FDC and the novel oral anti-TB drug delivery system, respectively. Regressional analysis of UV spectrophotometric data for simultaneous RIF and INH prediction thus provides a simplified methodology for use in diverse research settings for the assurance of RIF bioavailability from FDC formulations, specifically modified-release forms.

Qualitative properties of large buckled states of spherical shells

NASA Technical Reports Server (NTRS)

Shih, K. G.; Antman, S. S.

1985-01-01

A system of 6th-order quasi-linear Ordinary Differential Equations is analyzed to show the global existence of axisymmetrically buckled states. A surprising nodal property is obtained which shows that everywhere along a branch of solutions that bifurcates from a simple eigenvalue of the linearized equation, the number of simultaneously vanishing points of both shear resultant and circumferential bending moment resultant remains invariant, provided that a certain auxiliary condition is satisfied.

Energy loss in spark gap switches

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

Oreshkin, V. I., E-mail: oreshkin@ovpe.hcei.tsc.ru; Lavrinovich, I. V.; National Research Tomsk Polytechnic University, Lenin Avenue 30, 634050 Tomsk

2014-04-15

The paper reports on numerical study of the energy loss in spark gap switches. The operation of the switches is analyzed using the Braginsky model which allows calculation of the time dependence of the spark channel resistance. The Braginsky equation is solved simultaneously with generator circuit equations for different load types. Based on the numerical solutions, expressions which determine both the energy released in a spark gap switch and the switching time are derived.

Non-linear instability analysis of the two-dimensional Navier-Stokes equation: The Taylor-Green vortex problem

NASA Astrophysics Data System (ADS)

Sengupta, Tapan K.; Sharma, Nidhi; Sengupta, Aditi

2018-05-01

An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This problem admits a time-dependent analytical solution as the base flow, whose instability is traced here. The numerical study of the evolution of the Taylor-Green vortices shows that the flow becomes turbulent, but an explanation for this transition has not been advanced so far. The deviation of the numerical solution from the analytical solution is studied here using a high accuracy compact scheme on a non-uniform grid (NUC6), with the fourth-order Runge-Kutta method. The stream function-vorticity (ψ, ω) formulation of the governing equations is solved here in a periodic square domain with four vortices at t = 0. Simulations performed at different Reynolds numbers reveal that numerical errors in computations induce a breakdown of symmetry and simultaneous fragmentation of vortices. It is shown that the actual physical instability is triggered by the growth of disturbances and is explained by the evolution of disturbance mechanical energy and enstrophy. The disturbance evolution equations have been traced by looking at (a) disturbance mechanical energy of the Navier-Stokes equation, as described in the work of Sengupta et al., "Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003), and (b) the creation of rotationality via the enstrophy transport equation in the work of Sengupta et al., "Diffusion in inhomogeneous flows: Unique equilibrium state in an internal flow," Comput. Fluids 88, 440-451 (2013).

Some New Results in Astrophysical Problems of Nonlinear Theory of Radiative Transfer

NASA Astrophysics Data System (ADS)

Pikichyan, H. V.

2017-07-01

In the interpretation of the observed astrophysical spectra, a decisive role is related to nonlinear problems of radiative transfer, because the processes of multiple interactions of matter of cosmic medium with the exciting intense radiation ubiquitously occur in astrophysical objects, and in their vicinities. Whereas, the intensity of the exciting radiation changes the physical properties of the original medium, and itself was modified, simultaneously, in a self-consistent manner under its influence. In the present report, we show that the consistent application of the principle of invariance in the nonlinear problem of bilateral external illumination of a scattering/absorbing one-dimensional anisotropic medium of finite geometrical thickness allows for simplifications that were previously considered as a prerogative only of linear problems. The nonlinear problem is analyzed through the three methods of the principle of invariance: (i) an adding of layers, (ii) its limiting form, described by differential equations of invariant imbedding, and (iii) a transition to the, so-called, functional equations of the "Ambartsumyan's complete invariance". Thereby, as an alternative to the Boltzmann equation, a new type of equations, so-called "kinetic equations of equivalence", are obtained. By the introduction of new functions - the so-called "linear images" of solution of nonlinear problem of radiative transfer, the linear structure of the solution of the nonlinear problem under study is further revealed. Linear images allow to convert naturally the statistical characteristics of random walk of a "single quantum" or their "beam of unit intensity", as well as widely known "probabilistic interpretation of phenomena of transfer", to the field of nonlinear problems. The structure of the equations obtained for determination of linear images is typical of linear problems.

Parallel computation of three-dimensional aeroelastic fluid-structure interaction

NASA Astrophysics Data System (ADS)

Sadeghi, Mani

This dissertation presents a numerical method for the parallel computation of aeroelasticity (ParCAE). A flow solver is coupled to a structural solver by use of a fluid-structure interface method. The integration of the three-dimensional unsteady Navier-Stokes equations is performed in the time domain, simultaneously to the integration of a modal three-dimensional structural model. The flow solution is accelerated by using a multigrid method and a parallel multiblock approach. Fluid-structure coupling is achieved by subiteration. A grid-deformation algorithm is developed to interpolate the deformation of the structural boundaries onto the flow grid. The code is formulated to allow application to general, three-dimensional, complex configurations with multiple independent structures. Computational results are presented for various configurations, such as turbomachinery blade rows and aircraft wings. Investigations are performed on vortex-induced vibrations, effects of cascade mistuning on flutter, and cases of nonlinear cascade and wing flutter.

Reaction Mechanisms on Multiwell Potential Energy Surfaces in Combustion (and Atmospheric) Chemistry

DOE PAGES

Osborn, David L.

2017-03-15

Chemical reactions occurring on a potential energy surface with multiple wells are ubiquitous in low temperature combustion and the oxidation of volatile organic compounds in earth’s atmosphere. The rich variety of structural isomerizations that compete with collisional stabilization make characterizing such complex-forming reactions challenging. This review describes recent experimental and theoretical advances that deliver increasingly complete views of their reaction mechanisms. New methods for creating reactive intermediates coupled with multiplexed measurements provide many experimental observables simultaneously. Automated methods to explore potential energy surfaces can uncover hidden reactive pathways, while master equation methods enable a holistic treatment of both sequential andmore » well-skipping pathways. Our ability to probe and understand nonequilibrium effects and reaction sequences is increasing. These advances provide the fundamental science base for predictive models of combustion and the atmosphere that are crucial to address global challenges.« less

Reaction Mechanisms on Multiwell Potential Energy Surfaces in Combustion (and Atmospheric) Chemistry

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

Osborn, David L.

Chemical reactions occurring on a potential energy surface with multiple wells are ubiquitous in low temperature combustion and the oxidation of volatile organic compounds in earth’s atmosphere. The rich variety of structural isomerizations that compete with collisional stabilization make characterizing such complex-forming reactions challenging. This review describes recent experimental and theoretical advances that deliver increasingly complete views of their reaction mechanisms. New methods for creating reactive intermediates coupled with multiplexed measurements provide many experimental observables simultaneously. Automated methods to explore potential energy surfaces can uncover hidden reactive pathways, while master equation methods enable a holistic treatment of both sequential andmore » well-skipping pathways. Our ability to probe and understand nonequilibrium effects and reaction sequences is increasing. These advances provide the fundamental science base for predictive models of combustion and the atmosphere that are crucial to address global challenges.« less

Reconstructing signals from noisy data with unknown signal and noise covariance.

PubMed

Oppermann, Niels; Robbers, Georg; Ensslin, Torsten A

2011-10-01

We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle of minimum Gibbs free energy, which was previously used to derive a signal reconstruction algorithm handling uncertainties in the signal covariance. We extend this algorithm to simultaneously uncertain noise and signal covariances using the same principles in the derivation. The resulting equations are general enough to be applied in many different contexts. We demonstrate the performance of the algorithm by applying it to specific example situations and compare it to algorithms not allowing for uncertainties in the noise covariance. The results show that the method we suggest performs very well under a variety of circumstances and is indeed qualitatively superior to the other methods in cases where uncertainty in the noise covariance is present.

Non-LTE radiative transfer with lambda-acceleration - Convergence properties using exact full and diagonal lambda-operators

NASA Technical Reports Server (NTRS)

Macfarlane, J. J.

1992-01-01

We investigate the convergence properties of Lambda-acceleration methods for non-LTE radiative transfer problems in planar and spherical geometry. Matrix elements of the 'exact' A-operator are used to accelerate convergence to a solution in which both the radiative transfer and atomic rate equations are simultaneously satisfied. Convergence properties of two-level and multilevel atomic systems are investigated for methods using: (1) the complete Lambda-operator, and (2) the diagonal of the Lambda-operator. We find that the convergence properties for the method utilizing the complete Lambda-operator are significantly better than those of the diagonal Lambda-operator method, often reducing the number of iterations needed for convergence by a factor of between two and seven. However, the overall computational time required for large scale calculations - that is, those with many atomic levels and spatial zones - is typically a factor of a few larger for the complete Lambda-operator method, suggesting that the approach should be best applied to problems in which convergence is especially difficult.

Will learning to solve one-step equations pose a challenge to 8th grade students?

NASA Astrophysics Data System (ADS)

Ngu, Bing Hiong; Phan, Huy P.

2017-08-01

Assimilating multiple interactive elements simultaneously in working memory to allow understanding to occur, while solving an equation, would impose a high cognitive load. Element interactivity arises from the interaction between elements within and across operational and relational lines. Moreover, operating with special features (e.g. negative pronumeral) poses additional challenge to master equation solving skills. In an experiment, 41 8th grade students (girls = 16, boys = 25) sat for a pre-test, attended a session about equation solving, completed an acquisition phase which constituted the main intervention and were tested again in a post-test. The results showed that at post-test, students performed better on one-step equations tapping low rather than high element interactivity knowledge. In addition, students performed better on those one-step equations that contained no special features. Thus, both the degree of element interactivity and the operation with special features affect the challenge posed to 8th grade students on learning how to solve one-step equations.

Simultaneous detection of assembly and disassembly of multivalent HA tag and anti-HA antibody in single in-capillary assay.

PubMed

Wang, Jianhao; Qin, Yuqin; Qin, Haifang; Liu, Li; Ding, Shumin; Teng, Yiwan; Ji, Junling; Qiu, Lin; Jiang, Pengju

2016-08-01

Herein, we have developed an in-capillary assay for simultaneous detection of the assembly and disassembly of the multivalent HA tag peptide and antibody. HA tag with hexahistidine at C terminus (YPYDVPDYAG4 H6 , termed YPYDH6 ) was conjugated with quantum dots (QDs) by metal-affinity force to form a multivalent HA tag (QD-YPYDH6 ). QD-YPYDH6 and monoclonal anti-HA antibody (anti-HA) were sequentially injected into the capillary. They were mixed and assembled inside the capillary. The reaction products were online discriminated and detected by fluorescence coupled capillary electrophoresis (CE-FL). For the in-capillary assay, the binding efficiency of the multivalent HA tag and antibody on was influenced by the molar ratio and injection time. Such novel assay could even give out the self-assembly kinetic constant of QDs and YPYDH6 as KD of 34.1 μM with n (binding cooperativeness) of 2.2 by Hill equation. More importantly, the simultaneous detection of the assembly and imidazole (Im) induced disassembly of the QD-YPYDH6 -anti-HA complex was achieved in a single in-capillary assay. Our study demonstrated a new method for the online detection of antigen-antibody interactions. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The structural identifiability and parameter estimation of a multispecies model for the transmission of mastitis in dairy cows with postmilking teat disinfection.

PubMed

White, L J; Evans, N D; Lam, T J G M; Schukken, Y H; Medley, G F; Godfrey, K R; Chappell, M J

2002-01-01

A mathematical model for the transmission of two interacting classes of mastitis causing bacterial pathogens in a herd of dairy cows is presented and applied to a specific data set. The data were derived from a field trial of a specific measure used in the control of these pathogens, where half the individuals were subjected to the control and in the others the treatment was discontinued. The resultant mathematical model (eight non-linear simultaneous ordinary differential equations) therefore incorporates heterogeneity in the host as well as the infectious agent and consequently the effects of control are intrinsic in the model structure. A structural identifiability analysis of the model is presented demonstrating that the scope of the novel method used allows application to high order non-linear systems. The results of a simultaneous estimation of six unknown system parameters are presented. Previous work has only estimated a subset of these either simultaneously or individually. Therefore not only are new estimates provided for the parameters relating to the transmission and control of the classes of pathogens under study, but also information about the relationships between them. We exploit the close link between mathematical modelling, structural identifiability analysis, and parameter estimation to obtain biological insights into the system modelled.

A Bayesian Framework for Coupled Estimation of Key Unknown Parameters of Land Water and Energy Balance Equations

NASA Astrophysics Data System (ADS)

Farhadi, L.; Abdolghafoorian, A.

2015-12-01

The land surface is a key component of climate system. It controls the partitioning of available energy at the surface between sensible and latent heat, and partitioning of available water between evaporation and runoff. Water and energy cycle are intrinsically coupled through evaporation, which represents a heat exchange as latent heat flux. Accurate estimation of fluxes of heat and moisture are of significant importance in many fields such as hydrology, climatology and meteorology. In this study we develop and apply a Bayesian framework for estimating the key unknown parameters of terrestrial water and energy balance equations (i.e. moisture and heat diffusion) and their uncertainty in land surface models. These equations are coupled through flux of evaporation. The estimation system is based on the adjoint method for solving a least-squares optimization problem. The cost function consists of aggregated errors on state (i.e. moisture and temperature) with respect to observation and parameters estimation with respect to prior values over the entire assimilation period. This cost function is minimized with respect to parameters to identify models of sensible heat, latent heat/evaporation and drainage and runoff. Inverse of Hessian of the cost function is an approximation of the posterior uncertainty of parameter estimates. Uncertainty of estimated fluxes is estimated by propagating the uncertainty for linear and nonlinear function of key parameters through the method of First Order Second Moment (FOSM). Uncertainty analysis is used in this method to guide the formulation of a well-posed estimation problem. Accuracy of the method is assessed at point scale using surface energy and water fluxes generated by the Simultaneous Heat and Water (SHAW) model at the selected AmeriFlux stations. This method can be applied to diverse climates and land surface conditions with different spatial scales, using remotely sensed measurements of surface moisture and temperature states

MEASURING THE MASS OF 4UO900-40 DYNAMICALLY

NASA Technical Reports Server (NTRS)

Dolan, J. F.; Etzel, Paul B.; Boyd, Patricia T.

2006-01-01

Accurate measurements of neutron star masses are needed to constrain the equation of state of neutron star matter - of importance to both particle physics and the astrophysics of neutron stars - and to identify the evolutionary track of the progenitor stars that form neutron stars. The best measured values of the mass of 4UO900-40 (= Vela XR-l), 1.86 +/- 0.16 Msun (Barziv et al. 2001) and 1.93 +/- 0.20 Msun (Abubekerov et al. 2004), make it a leading candidate for the most massive neutron star known. The direct relationship between the maximum mass of neutron stars and the equation of state of ultra-dense matter makes 4UO900-40 an important neutron star mass to determine accurately. The confidence interval on previous mass estimates, obtained from observations that include parameters determined by non-dynamical methods, are not small enough to significantly restrict possible equations of state. We describe here a purely dynamical method for determining the mass of 4UO900-40, an X-ray pulsar, using the reprocessed UV pulses emitted by its BO.5Ib companion. One can derive the instantaneous radial velocity of each component by simultaneous X-ray and UV observations at the two quadratures of the system. The Doppler shift caused by the primary's rotational velocity and the illumination pattern of the X-rays on the primary, two of the three principal contributors to the uncertainty on the derived mass of the neutron star, almost exactly cancel by symmetry in this method. A heuristic measurement of the mass of 4UO900-40 using observations obtained previously with the High Speed Photometer on HST is given in Appendix A.

Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

NASA Astrophysics Data System (ADS)

Pathak, Harshavardhana S.; Shukla, Ratnesh K.

2016-08-01

A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of discontinuous propagating shocks with simultaneous resolution of smooth yet complex small scale unsteady flow features to an exceptional detail.

Estimation of shortwave hemispherical reflectance (albedo) from bidirectionally reflected radiance data

NASA Technical Reports Server (NTRS)

Starks, Patrick J.; Norman, John M.; Blad, Blaine L.; Walter-Shea, Elizabeth A.; Walthall, Charles L.

1991-01-01

An equation for estimating albedo from bidirectional reflectance data is proposed. The estimates of albedo are found to be greater than values obtained with simultaneous pyranometer measurements. Particular attention is given to potential sources of systematic errors including extrapolation of bidirectional reflectance data out to a view zenith angle of 90 deg, the use of inappropriate weighting coefficients in the numerator of the albedo equation, surface shadowing caused by the A-frame instrumentation used to measure the incoming and outgoing radiation fluxes, errors in estimates of the denominator of the proposed albedo equation, and a 'hot spot' contribution in bidirectional data measured by a modular multiband radiometer.

Adaptive Arrays for Multiple Simultaneous Desired Signals.

DTIC Science & Technology

1983-08-01

weights [Equation (4)]. Using Equation (6), the inverse of the covariance matrix is given by 5 4 i *ŕm * T ". -1 1 I d Z dij (7) L -I + UT U* 4 di x di...Equations (11) and (12) p k = A k Ik d (14) dk aki*~~* ( ~ dk LJk Udk) and 1 t IjI II di l() 27 x = (1 + t UT U*) Thus, the output SNR of the kth desired...signals are assumed to be of the same frequency. There is no jammer 9 0 dB SIGNAL 10 dB SIGNAL 90 % 90 180 Fiur .dptdpatrnofalier rayo tn strpc lmet

Development of optimal models of porous media by combining static and dynamic data: the permeability and porosity distributions.

PubMed

Hamzehpour, Hossein; Rasaei, M Reza; Sahimi, Muhammad

2007-05-01

We describe a method for the development of the optimal spatial distributions of the porosity phi and permeability k of a large-scale porous medium. The optimal distributions are constrained by static and dynamic data. The static data that we utilize are limited data for phi and k, which the method honors in the optimal model and utilizes their correlation functions in the optimization process. The dynamic data include the first-arrival (FA) times, at a number of receivers, of seismic waves that have propagated in the porous medium, and the time-dependent production rates of a fluid that flows in the medium. The method combines the simulated-annealing method with a simulator that solves numerically the three-dimensional (3D) acoustic wave equation and computes the FA times, and a second simulator that solves the 3D governing equation for the fluid's pressure as a function of time. To our knowledge, this is the first time that an optimization method has been developed to determine simultaneously the global minima of two distinct total energy functions. As a stringent test of the method's accuracy, we solve for flow of two immiscible fluids in the same porous medium, without using any data for the two-phase flow problem in the optimization process. We show that the optimal model, in addition to honoring the data, also yields accurate spatial distributions of phi and k, as well as providing accurate quantitative predictions for the single- and two-phase flow problems. The efficiency of the computations is discussed in detail.

Computational method for the correction of proximity effect in electron-beam lithography (Poster Paper)

NASA Astrophysics Data System (ADS)

Chang, Chih-Yuan; Owen, Gerry; Pease, Roger Fabian W.; Kailath, Thomas

1992-07-01

Dose correction is commonly used to compensate for the proximity effect in electron lithography. The computation of the required dose modulation is usually carried out using 'self-consistent' algorithms that work by solving a large number of simultaneous linear equations. However, there are two major drawbacks: the resulting correction is not exact, and the computation time is excessively long. A computational scheme, as shown in Figure 1, has been devised to eliminate this problem by the deconvolution of the point spread function in the pattern domain. The method is iterative, based on a steepest descent algorithm. The scheme has been successfully tested on a simple pattern with a minimum feature size 0.5 micrometers , exposed on a MEBES tool at 10 KeV in 0.2 micrometers of PMMA resist on a silicon substrate.

Calculation of symmetric and asymmetric vortex seperation on cones and tangent ogives based on discrete vortex models

NASA Technical Reports Server (NTRS)

Chin, S.; Lan, C. Edward

1988-01-01

An inviscid discrete vortex model, with newly derived expressions for the tangential velocity imposed at the separation points, is used to investigate the symmetric and asymmetric vortex separation on cones and tangent ogives. The circumferential locations of separation are taken from experimental data. Based on a slender body theory, the resulting simultaneous nonlinear algebraic equations in a cross-flow plane are solved with Broyden's modified Newton-Raphson method. Total force coefficients are obtained through momentum principle with new expressions for nonconical flow. It is shown through the method of function deflation that multiple solutions exist at large enough angles of attack, even with symmetric separation points. These additional solutions are asymmetric in vortex separation and produce side force coefficients which agree well with data for cones and tangent ogives.

Magnetotelluric inversion via reverse time migration algorithm of seismic data

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

Ha, Taeyoung; Shin, Changsoo

2007-07-01

We propose a new algorithm for two-dimensional magnetotelluric (MT) inversion. Our algorithm is an MT inversion based on the steepest descent method, borrowed from the backpropagation technique of seismic inversion or reverse time migration, introduced in the middle 1980s by Lailly and Tarantola. The steepest descent direction can be calculated efficiently by using the symmetry of numerical Green's function derived from a mixed finite element method proposed by Nedelec for Maxwell's equation, without calculating the Jacobian matrix explicitly. We construct three different objective functions by taking the logarithm of the complex apparent resistivity as introduced in the recent waveform inversionmore » algorithm by Shin and Min. These objective functions can be naturally separated into amplitude inversion, phase inversion and simultaneous inversion. We demonstrate our algorithm by showing three inversion results for synthetic data.« less

Numerical Analysis of Coolant Flow and Heat Transfer in ITER Diagnostic First Wall

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

Khodak, A.; Loesser, G.; Zhai, Y.

2015-07-24

We performed numerical simulations of the ITER Diagnostic First Wall (DFW) using ANSYS workbench. During operation DFW will include solid main body as well as liquid coolant. Thus thermal and hydraulic analysis of the DFW was performed using conjugated heat transfer approach, in which heat transfer was resolved in both solid and liquid parts, and simultaneously fluid dynamics analysis was performed only in the liquid part. This approach includes interface between solid and liquid part of the systemAnalysis was performed using ANSYS CFX software. CFX software allows solution of heat transfer equations in solid and liquid part, and solution ofmore » the flow equations in the liquid part. Coolant flow in the DFW was assumed turbulent and was resolved using Reynolds averaged Navier-Stokes equations with Shear Stress Transport turbulence model. Meshing was performed using CFX method available within ANSYS. The data cloud for thermal loading consisting of volumetric heating and surface heating was imported into CFX Volumetric heating source was generated using Attila software. Surface heating was obtained using radiation heat transfer analysis. Our results allowed us to identify areas of excessive heating. Proposals for cooling channel relocation were made. Additional suggestions were made to improve hydraulic performance of the cooling system.« less

Structural Equation Modeling: Applications in ecological and evolutionary biology research

USGS Publications Warehouse

Pugesek, Bruce H.; von Eye, Alexander; Tomer, Adrian

2003-01-01

This book presents an introduction to the methodology of structural equation modeling, illustrates its use, and goes on to argue that it has revolutionary implications for the study of natural systems. A major theme of this book is that we have, up to this point, attempted to study systems primarily using methods (such as the univariate model) that were designed only for considering individual processes. Understanding systems requires the capacity to examine simultaneous influences and responses. Structural equation modeling (SEM) has such capabilities. It also possesses many other traits that add strength to its utility as a means of making scientific progress. In light of the capabilities of SEM, it can be argued that much of ecological theory is currently locked in an immature state that impairs its relevance. It is further argued that the principles of SEM are capable of leading to the development and evaluation of multivariate theories of the sort vitally needed for the conservation of natural systems. Supplementary information can be found at the authors website, http://www.jamesbgrace.com/. • Details why multivariate analyses should be used to study ecological systems • Exposes unappreciated weakness in many current popular analyses • Emphasizes the future methodological developments needed to advance our understanding of ecological systems.

Velocity boundary conditions for vorticity formulations of the incompressible Navier-Stokes equations

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

Kempka, S.N.; Strickland, J.H.; Glass, M.W.

1995-04-01

formulation to satisfy velocity boundary conditions for the vorticity form of the incompressible, viscous fluid momentum equations is presented. The tangential and normal components of the velocity boundary condition are satisfied simultaneously by creating vorticity adjacent to boundaries. The newly created vorticity is determined using a kinematical formulation which is a generalization of Helmholtz` decomposition of a vector field. Though it has not been generally recognized, these formulations resolve the over-specification issue associated with creating voracity to satisfy velocity boundary conditions. The generalized decomposition has not been widely used, apparently due to a lack of a useful physical interpretation. Anmore » analysis is presented which shows that the generalized decomposition has a relatively simple physical interpretation which facilitates its numerical implementation. The implementation of the generalized decomposition is discussed in detail. As an example the flow in a two-dimensional lid-driven cavity is simulated. The solution technique is based on a Lagrangian transport algorithm in the hydrocode ALEGRA. ALEGRA`s Lagrangian transport algorithm has been modified to solve the vorticity transport equation and the generalized decomposition, thus providing a new, accurate method to simulate incompressible flows. This numerical implementation and the new boundary condition formulation allow vorticity-based formulations to be used in a wider range of engineering problems.« less

An axisymmetric single-path model for gas transport in the conducting airways.

PubMed

Madasu, Srinath; Borhan, All; Ultman, James S

2006-02-01

In conventional one-dimensional single-path models, radially averaged concentration is calculated as a function of time and longitudinal position in the lungs, and coupled convection and diffusion are accounted for with a dispersion coefficient. The axisymmetric single-path model developed in this paper is a two-dimensional model that incorporates convective-diffusion processes in a more fundamental manner by simultaneously solving the Navier-Stokes and continuity equations with the convection-diffusion equation. A single airway path was represented by a series of straight tube segments interconnected by leaky transition regions that provide for flow loss at the airway bifurcations. As a sample application, the model equations were solved by a finite element method to predict the unsteady state dispersion of an inhaled pulse of inert gas along an airway path having dimensions consistent with Weibel's symmetric airway geometry. Assuming steady, incompressible, and laminar flow, a finite element analysis was used to solve for the axisymmetric pressure, velocity and concentration fields. The dispersion calculated from these numerical solutions exhibited good qualitative agreement with the experimental values, but quantitatively was in error by 20%-30% due to the assumption of axial symmetry and the inability of the model to capture the complex recirculatory flows near bifurcations.

Kinetics of binary nucleation of vapors in size and composition space.

PubMed

Fisenko, Sergey P; Wilemski, Gerald

2004-11-01

We reformulate the kinetic description of binary nucleation in the gas phase using two natural independent variables: the total number of molecules g and the molar composition x of the cluster. The resulting kinetic equation can be viewed as a two-dimensional Fokker-Planck equation describing the simultaneous Brownian motion of the clusters in size and composition space. Explicit expressions for the Brownian diffusion coefficients in cluster size and composition space are obtained. For characterization of binary nucleation in gases three criteria are established. These criteria establish the relative importance of the rate processes in cluster size and composition space for different gas phase conditions and types of liquid mixtures. The equilibrium distribution function of the clusters is determined in terms of the variables g and x. We obtain an approximate analytical solution for the steady-state binary nucleation rate that has the correct limit in the transition to unary nucleation. To further illustrate our description, the nonequilibrium steady-state cluster concentrations are found by numerically solving the reformulated kinetic equation. For the reformulated transient problem, the relaxation or induction time for binary nucleation was calculated using Galerkin's method. This relaxation time is affected by processes in both size and composition space, but the contributions from each process can be separated only approximately.

A reformulation of mechanics and electrodynamics.

PubMed

Pinheiro, Mario J

2017-07-01

Classical mechanics, as commonly taught in engineering and science, are confined to the conventional Newtonian theory. But classical mechanics has not really changed in substance since Newton formulation, describing simultaneous rotation and translation of objects with somewhat complicate drawbacks, risking interpretation of forces in non-inertial frames. In this work we introduce a new variational principle for out-of-equilibrium, rotating systems, obtaining a set of two first order differential equations that introduces a thermodynamic-mechanistic time into Newton's dynamical equation, and revealing the same formal symplectic structure shared by classical mechanics, fluid mechanics and thermodynamics. The results is a more consistent formulation of dynamics and electrodynamics, explaining natural phenomena as the outcome from a balance between energy and entropy, embedding translational with rotational motion into a single equation, showing centrifugal and Coriolis force as derivatives from the transport of angular momentum, and offering a natural method to handle variational problems, as shown with the brachistochrone problem. In consequence, a new force term appears, the topological torsion current, important for spacecraft dynamics. We describe a set of solved problems showing the potential of a competing technique, with significant interest to electrodynamics as well. We expect this new approach to have impact in a large class of scientific and technological problems.

Validity test and its consistency in the construction of patient loyalty model

NASA Astrophysics Data System (ADS)

Yanuar, Ferra

2016-04-01

The main objective of this present study is to demonstrate the estimation of validity values and its consistency based on structural equation model. The method of estimation was then implemented to an empirical data in case of the construction the patient loyalty model. In the hypothesis model, service quality, patient satisfaction and patient loyalty were determined simultaneously, each factor were measured by any indicator variables. The respondents involved in this study were the patients who ever got healthcare at Puskesmas in Padang, West Sumatera. All 394 respondents who had complete information were included in the analysis. This study found that each construct; service quality, patient satisfaction and patient loyalty were valid. It means that all hypothesized indicator variables were significant to measure their corresponding latent variable. Service quality is the most measured by tangible, patient satisfaction is the most mesured by satisfied on service and patient loyalty is the most measured by good service quality. Meanwhile in structural equation, this study found that patient loyalty was affected by patient satisfaction positively and directly. Service quality affected patient loyalty indirectly with patient satisfaction as mediator variable between both latent variables. Both structural equations were also valid. This study also proved that validity values which obtained here were also consistence based on simulation study using bootstrap approach.

Macroscopic kinematics of the Hall electric field under influence of carrier magnetic moments

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

Sakai, Masamichi, E-mail: sakai@fms.saitama-u.ac.jp

2016-06-15

The relativistic effect on electromagnetic forces yields two types of forces which depend on the velocity of the relevant particles: (i) the usual Lorentz force exerted on a moving charged particle and (ii) the apparent Lorentz force exerted on a moving magnetic moment. In sharp contrast with type (i), the type (ii) force originates due to the transverse field induced by the Hall effect (HE). This study incorporates both forces into a Drude-type equation with a fully spin-polarized condition to investigate the effects of self-consistency of the source and the resultant fields on the HE. We also examine the self-consistencymore » of the carrier kinematics and electromagnetic dynamics by simultaneously considering the Drude type equation and Maxwell equations at low frequencies. Thus, our approach can predict both the dc and ac characteristics of the HE, demonstrating that the dc current condition solely yields the ordinary HE, while the ac current condition yields generation of both fundamental and second harmonic modes of the HE field. When the magnetostatic field is absent, the simultaneous presence of dc and ac longitudinal currents generates the ac HE that has both fundamental frequency and second harmonic.« less

In vivo stationary flux analysis by 13C labeling experiments.

PubMed

Wiechert, W; de Graaf, A A

1996-01-01

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

Partial compensation interferometry for measurement of surface parameter error of high-order aspheric surfaces

NASA Astrophysics Data System (ADS)

Hao, Qun; Li, Tengfei; Hu, Yao

2018-01-01

Surface parameters are the properties to describe the shape characters of aspheric surface, which mainly include vertex radius of curvature (VROC) and conic constant (CC). The VROC affects the basic properties, such as focal length of an aspheric surface, while the CC is the basis of classification for aspheric surface. The deviations of the two parameters are defined as surface parameter error (SPE). Precisely measuring SPE is critical for manufacturing and aligning aspheric surface. Generally, SPE of aspheric surface is measured directly by curvature fitting on the absolute profile measurement data from contact or non-contact testing. And most interferometry-based methods adopt null compensators or null computer-generated holograms to measure SPE. To our knowledge, there is no effective way to measure SPE of highorder aspheric surface with non-null interferometry. In this paper, based on the theory of slope asphericity and the best compensation distance (BCD) established in our previous work, we propose a SPE measurement method for high-order aspheric surface in partial compensation interferometry (PCI) system. In the procedure, firstly, we establish the system of two element equations by utilizing the SPE-caused BCD change and surface shape change. Then, we can simultaneously obtain the VROC error and CC error in PCI system by solving the equations. Simulations are made to verify the method, and the results show a high relative accuracy.

A Moving Mesh Finite Element Algorithm for Singular Problems in Two and Three Space Dimensions

NASA Astrophysics Data System (ADS)

Li, Ruo; Tang, Tao; Zhang, Pingwen

2002-04-01

A framework for adaptive meshes based on the Hamilton-Schoen-Yau theory was proposed by Dvinsky. In a recent work (2001, J. Comput. Phys.170, 562-588), we extended Dvinsky's method to provide an efficient moving mesh algorithm which compared favorably with the previously proposed schemes in terms of simplicity and reliability. In this work, we will further extend the moving mesh methods based on harmonic maps to deal with mesh adaptation in three space dimensions. In obtaining the variational mesh, we will solve an optimization problem with some appropriate constraints, which is in contrast to the traditional method of solving the Euler-Lagrange equation directly. The key idea of this approach is to update the interior and boundary grids simultaneously, rather than considering them separately. Application of the proposed moving mesh scheme is illustrated with some two- and three-dimensional problems with large solution gradients. The numerical experiments show that our methods can accurately resolve detail features of singular problems in 3D.

Analytical study of striated nozzle flow with small radius of curvature ratio throats

NASA Technical Reports Server (NTRS)

Norton, D. J.; White, R. E.

1972-01-01

An analytical method was developed which is capable of estimating the chamber and throat conditions in a nozzle with a low radius of curvature throat. The method was programmed using standard FORTRAN 4 language and includes chemical equilibrium calculation subprograms (modified NASA Lewis program CEC71) as an integral part. The method determines detailed and gross rocket characteristics in the presence of striated flows and gives detailed results for the motor chamber and throat plane with as many as 20 discrete zones. The method employs a simultaneous solution of the mass, momentum, and energy equations and allows propellant types, 0/F ratios, propellant distribution, nozzle geometry, and injection schemes to be varied so to predict spatial velocity, density, pressure, and other thermodynamic variable distributions in the chamber as well as the throat. Results for small radius of curvature have shown good comparison to experimental results. Both gaseous and liquid injection may be considered with frozen or equilibrium flow calculations.

Implicit high-order discontinuous Galerkin method with HWENO type limiters for steady viscous flow simulations

NASA Astrophysics Data System (ADS)

Jiang, Zhen-Hua; Yan, Chao; Yu, Jian

2013-08-01

Two types of implicit algorithms have been improved for high order discontinuous Galerkin (DG) method to solve compressible Navier-Stokes (NS) equations on triangular grids. A block lower-upper symmetric Gauss-Seidel (BLU-SGS) approach is implemented as a nonlinear iterative scheme. And a modified LU-SGS (LLU-SGS) approach is suggested to reduce the memory requirements while retain the good convergence performance of the original LU-SGS approach. Both implicit schemes have the significant advantage that only the diagonal block matrix is stored. The resulting implicit high-order DG methods are applied, in combination with Hermite weighted essentially non-oscillatory (HWENO) limiters, to solve viscous flow problems. Numerical results demonstrate that the present implicit methods are able to achieve significant efficiency improvements over explicit counterparts and for viscous flows with shocks, and the HWENO limiters can be used to achieve the desired essentially non-oscillatory shock transition and the designed high-order accuracy simultaneously.

[Evaluation of vaporizers by anesthetic gas monitors corrected with a new method for preparation of calibration gases].

PubMed

Kurashiki, T

1996-11-01

For resolving the discrepancy of concentrations found among anesthetic gas monitors, the author proposed a new method using a vaporizer as a standard anesthetic gas generator for calibration. In this method, the carrier gas volume is measured by a mass flow meter (SEF-510 + FI-101) installed before the inlet of the vaporizer. The vaporized weight of volatile anesthetic agent is simultaneously measured by an electronic force balance (E12000S), on which the vaporizer is placed directly. The molar percent of the anesthetic is calculated using these data and is transformed into the volume percent. These gases discharging from the vaporizer are utilized for calibrating anesthetic gas monitors. These monitors are normalized by the linear equation describing the relationship between concentrations of calibration gases and readings of the anesthetic gas monitors. By using normalized monitors, flow rate-concentration performance curves of several anesthetic vaporizers were obtained. The author concludes that this method can serve as a standard in evaluating anesthetic vaporizers.

Wave-vector and polarization dependent impedance model for a hexagonal periodic metasurface exemplified through finite-difference time-domain simulations.

PubMed

Ding, Yi S; He, Yang

2017-08-21

An isotropic impedance sheet model is proposed for a loop-type hexagonal periodic metasurface. Both frequency and wave-vector dispersion are considered near the resonance frequency. Therefore both the angle and polarization dependences of the metasurface impedance can be properly and simultaneously described in our model. The constitutive relation of this model is transformed into auxiliary differential equations which are integrated into the finite-difference time-domain algorithm. Finally, a finite large metasurface sample under oblique illumination is used to test the model and the algorithm. Our model and algorithm can significantly increase the accuracy of the homogenization methods for modeling periodic metasurfaces.

A flexible model for correlated medical costs, with application to medical expenditure panel survey data.

PubMed

Chen, Jinsong; Liu, Lei; Shih, Ya-Chen T; Zhang, Daowen; Severini, Thomas A

2016-03-15

We propose a flexible model for correlated medical cost data with several appealing features. First, the mean function is partially linear. Second, the distributional form for the response is not specified. Third, the covariance structure of correlated medical costs has a semiparametric form. We use extended generalized estimating equations to simultaneously estimate all parameters of interest. B-splines are used to estimate unknown functions, and a modification to Akaike information criterion is proposed for selecting knots in spline bases. We apply the model to correlated medical costs in the Medical Expenditure Panel Survey dataset. Simulation studies are conducted to assess the performance of our method. Copyright © 2015 John Wiley & Sons, Ltd.

Structural similitude and scaling laws for laminated beam-plates

NASA Technical Reports Server (NTRS)

Simitses, George J.; Rezaeepazhand, Jalil

1992-01-01

The establishment of similarity conditions between two structural systems is discussed. Similarity conditions provide the relationship between a scale model and its prototype and can be used to predict the behavior of the prototype by extrapolating the experimental data of the corresponding small-scale model. Since satisfying all the similarity conditions simultaneously is difficult or even impossible, distorted models with partial similarity (with at least one similarity condition relaxed) are more practical. Establishing similarity conditions based on both dimensional analysis and direct use of governing equations is discussed, and the possibility of designing distorted models is investigated. The method is demonstrated through analysis of the cylindrical bending of orthotropic laminated beam-plates subjected to transverse line loads.

A method for analyzing clustered interval-censored data based on Cox's model.

PubMed

Kor, Chew-Teng; Cheng, Kuang-Fu; Chen, Yi-Hau

2013-02-28

Methods for analyzing interval-censored data are well established. Unfortunately, these methods are inappropriate for the studies with correlated data. In this paper, we focus on developing a method for analyzing clustered interval-censored data. Our method is based on Cox's proportional hazard model with piecewise-constant baseline hazard function. The correlation structure of the data can be modeled by using Clayton's copula or independence model with proper adjustment in the covariance estimation. We establish estimating equations for the regression parameters and baseline hazards (and a parameter in copula) simultaneously. Simulation results confirm that the point estimators follow a multivariate normal distribution, and our proposed variance estimations are reliable. In particular, we found that the approach with independence model worked well even when the true correlation model was derived from Clayton's copula. We applied our method to a family-based cohort study of pandemic H1N1 influenza in Taiwan during 2009-2010. Using the proposed method, we investigate the impact of vaccination and family contacts on the incidence of pH1N1 influenza. Copyright © 2012 John Wiley & Sons, Ltd.

Fidelity of the Integrated Force Method Solution

NASA Technical Reports Server (NTRS)

Hopkins, Dale; Halford, Gary; Coroneos, Rula; Patnaik, Surya

2002-01-01

The theory of strain compatibility of the solid mechanics discipline was incomplete since St. Venant's 'strain formulation' in 1876. We have addressed the compatibility condition both in the continuum and the discrete system. This has lead to the formulation of the Integrated Force Method. A dual Integrated Force Method with displacement as the primal variable has also been formulated. A modest finite element code (IFM/Analyzers) based on the IFM theory has been developed. For a set of standard test problems the IFM results were compared with the stiffness method solutions and the MSC/Nastran code. For the problems IFM outperformed the existing methods. Superior IFM performance is attributed to simultaneous compliance of equilibrium equation and compatibility condition. MSC/Nastran organization expressed reluctance to accept the high fidelity IFM solutions. This report discusses the solutions to the examples. No inaccuracy was detected in the IFM solutions. A stiffness method code with a small programming effort can be improved to reap the many IFM benefits when implemented with the IFMD elements. Dr. Halford conducted a peer-review on the Integrated Force Method. Reviewers' response is included.

Time-stable overset grid method for hyperbolic problems using summation-by-parts operators

NASA Astrophysics Data System (ADS)

Sharan, Nek; Pantano, Carlos; Bodony, Daniel J.

2018-05-01

A provably time-stable method for solving hyperbolic partial differential equations arising in fluid dynamics on overset grids is presented in this paper. The method uses interface treatments based on the simultaneous approximation term (SAT) penalty method and derivative approximations that satisfy the summation-by-parts (SBP) property. Time-stability is proven using energy arguments in a norm that naturally relaxes to the standard diagonal norm when the overlap reduces to a traditional multiblock arrangement. The proposed overset interface closures are time-stable for arbitrary overlap arrangements. The information between grids is transferred using Lagrangian interpolation applied to the incoming characteristics, although other interpolation schemes could also be used. The conservation properties of the method are analyzed. Several one-, two-, and three-dimensional, linear and non-linear numerical examples are presented to confirm the stability and accuracy of the method. A performance comparison between the proposed SAT-based interface treatment and the commonly-used approach of injecting the interpolated data onto each grid is performed to highlight the efficacy of the SAT method.

Sensitivity of control-augmented structure obtained by a system decomposition method

NASA Technical Reports Server (NTRS)

Sobieszczanskisobieski, Jaroslaw; Bloebaum, Christina L.; Hajela, Prabhat

1988-01-01

The verification of a method for computing sensitivity derivatives of a coupled system is presented. The method deals with a system whose analysis can be partitioned into subsets that correspond to disciplines and/or physical subsystems that exchange input-output data with each other. The method uses the partial sensitivity derivatives of the output with respect to input obtained for each subset separately to assemble a set of linear, simultaneous, algebraic equations that are solved for the derivatives of the coupled system response. This sensitivity analysis is verified using an example of a cantilever beam augmented with an active control system to limit the beam's dynamic displacements under an excitation force. The verification shows good agreement of the method with reference data obtained by a finite difference technique involving entire system analysis. The usefulness of a system sensitivity method in optimization applications by employing a piecewise-linear approach to the same numerical example is demonstrated. The method's principal merits are its intrinsically superior accuracy in comparison with the finite difference technique, and its compatibility with the traditional division of work in complex engineering tasks among specialty groups.

Numerical Simulation of Subsonic and Transonic Propeller Flow. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Snyder, Aaron

1988-01-01

The numerical simulation of 3-D transonic flow about a system of propeller blades is investigated. In particular, it is shown that the use of helical coordinates significantly simplifies the form of the governing equation when the propeller system is assumed to be surrounded by an irrotational flow field of an inviscid fluid. The unsteady small disturbance equation, valid for lightly loaded blades and expressed in helical coordinates, is derived from the general blade-fixed potential equation, given for an arbitrary coordinate system. The use of a coordinate system which inherently adapts to the mean flow results in a disturbance equation requiring relatively few terms to accurately model the physics of the flow. Furthermore, the helical coordinate system presented here is novel in that it is periodic in the circumferential direction while, simultaneously, maintaining orthogonal properties at the mean blade locations. The periodic characteristic allows a complete cascade of blades to be treated, and the orthogonality property affords straightforward treatment of blade boundary conditions. An ADI numerical scheme is used to compute the solution of the steady flow as an asymptotic limit of an unsteady flow. As an example of the method, solutions are presented for subsonic and transonic flow about a 5 percent thick bicircular arc blade of an 8-bladed cascade. Both high and low advance ratio cases are computed and include a lifting as well as nonlifting cases. The nonlifting solutions obtained are compared to solutions from a Euler code.

Simultaneous quantification of flavonoids and triterpenoids in licorice using HPLC.

PubMed

Wang, Yuan-Chuen; Yang, Yi-Shan

2007-05-01

Numerous bioactive compounds are present in licorice (Glycyrrhizae Radix), including flavonoids and triterpenoids. In this study, a reversed-phase high-performance liquid chromatography (HPLC) method for simultaneous quantification of three flavonoids (liquiritin, liquiritigenin and isoliquiritigenin) and four triterpenoids (glycyrrhizin, 18alpha-glycyrrhetinic acid, 18beta-glycyrrhetinic acid and 18beta-glycyrrhetinic acid methyl ester) from licorice was developed, and further, to quantify these 7 compounds from 20 different licorice samples. Specifically, the reverse-phase HPLC was performed with a gradient mobile phase composed of 25 mM phosphate buffer (pH 2.5)-acetonitrile featuring gradient elution steps as follows: 0 min, 100:0; 10 min, 80:20; 50 min, 70:30; 73 min, 50:50; 110 min, 50:50; 125 min, 20:80; 140 min, 20:80, and peaks were detected at 254 nm. By using our technique, a rather good specificity was obtained regarding to the separation of these seven compounds. The regression coefficient for the linear equations for the seven compounds lay between 0.9978 and 0.9992. The limits of detection and quantification lay in the range of 0.044-0.084 and 0.13-0.25 microg/ml, respectively. The relative recovery rates for the seven compounds lay between 96.63+/-2.43 and 103.55+/-2.77%. Coefficient variation for intra-day and inter-day precisions lay in the range of 0.20-1.84 and 0.28-1.86%, respectively. Based upon our validation results, this analytical technique is a convenient method to simultaneous quantify numerous bioactive compounds derived from licorice, featuring good quantification parameters, accuracy and precision.

Simultaneous Determination of Miconazole Nitrate and Metronidazole in Different Pharmaceutical Dosage Forms by Gas Chromatography and Flame Ionization Detector (GC-FID).

PubMed

Ashour, Safwan; Kattan, Nuha

2010-03-01

A simple, rapid and precise gas chromatographic method has been developed for the simultaneous determination of miconazole nitrate (MIZ) and metronidazole (MNZ) in tablets and ovules, using a capillary column AE.SE-54 (15 m × 0.53 mm, i.d.) and nitrogen as a carrier gas at a flow rate of 9 mL min(-1). The oven temperature was programmed at 140°C for 3 min, with a rise of 40°C min(-1) up to 180°C (held for 2 min) and then increased to a final temperature of 250°C. The injector and detector port temperatures were maintained at 260°C. Detection was carried out using flame ionization detector. Results of assay and recovery studies were statistically evaluated for its accuracy and precision. The retention times were about 3.50 and 12.90 min for MNZ and MIZ, respectively. Linearity ranges were 50.0-6030.0 and 62.5-2000.0 μg mL(-1) for MNZ and MIZ, with limit of detection values of 2.5 and 3.1 μg mL(-1), respectively. Correlation coefficients (R(2)) of the regression equations were greater than 0.999 in all cases. No interference from any components of pharmaceutical dosage forms or degradation products was observed. According to the validation results, the proposed method was found to be specific, accurate, precise and could be applied to the simultaneous quantitative analysis of MIZ and MNZ in tablets and ovules.

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

NASA Astrophysics Data System (ADS)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

Parallel-vector out-of-core equation solver for computational mechanics

NASA Technical Reports Server (NTRS)

Qin, J.; Agarwal, T. K.; Storaasli, O. O.; Nguyen, D. T.; Baddourah, M. A.

1993-01-01

A parallel/vector out-of-core equation solver is developed for shared-memory computers, such as the Cray Y-MP machine. The input/ output (I/O) time is reduced by using the a synchronous BUFFER IN and BUFFER OUT, which can be executed simultaneously with the CPU instructions. The parallel and vector capability provided by the supercomputers is also exploited to enhance the performance. Numerical applications in large-scale structural analysis are given to demonstrate the efficiency of the present out-of-core solver.

Multiple-generator errors are unavoidable under model misspecification.

PubMed

Jewett, D L; Zhang, Z

1995-08-01

Model misspecification poses a major problem for dipole source localization (DSL) because it causes insidious multiple-generator errors (MulGenErrs) to occur in the fitted dipole parameters. This paper describes how and why this occurs, based upon simple algebraic considerations. MulGenErrs must occur, to some degree, in any DSL analysis of real data because there is model misspecification and mathematically the equations used for the simultaneously active generators must be of a different form than the equations for each generator active alone.

Mechanical Properties of EPON 826/DEA Epoxy

DTIC Science & Technology

2008-07-26

Eβ ( ε̇− ε̇pβ ) . (5b) Equations (2) and (5) are solved simultaneously as a system of time-dependant differential equations to determine the stress in...this implies that estimates of these underlying physical parameters are highly uncertain but also has a weak effect on the stress -strain relationships...20), 4923–4928 (1998) Chou, S.C., Robertson, K.D., et al.: The effect of strain rate and heat developed during deformation on the stress -strain curve

An analysis of curvature effects for the control of wall-bounded shear flows

NASA Technical Reports Server (NTRS)

Gatski, T. B.; Savill, A. M.

1989-01-01

The Reynolds stress transport equations are used to predict the effects of simultaneous and sequential combinations of distortions on turbulent boundary layers. The equations are written in general orthogonal curvilinear coordinates, with the curvature terms expressed in terms of the principal radii of curvature of the respective coordinate surfaces. Results are obtained for the cases of two-dimensional and three-dimensional flows in the limit where production and pressure-strain redistribution dominate over diffusion effects.

N-soliton interactions: Effects of linear and nonlinear gain and loss

NASA Astrophysics Data System (ADS)

Carretero-González, R.; Gerdjikov, V. S.; Todorov, M. D.

2017-10-01

We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the nonlinear Schrödinger equation perturbed simultaneously by linear and nonlinear gain/loss terms. We derive the corresponding perturbed complex Toda chain in the case of a combination of linear, cubic, and/or quintic terms. We show that the soliton interactions dynamics for this reduced PCTC model compares favorably to full numerical results of the original perturbed nonlinear Schrödinger equation.

TH-CD-201-03: A Real-Time Method to Simultaneously Measure Linear Energy Transfer and Dose for Proton Therapy Using Organic Scintillators

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

Alsanea, F; Therriault-Proulx, F; Sawakuchi, G

Purpose: The light generated in organic scintillators depends on both the radiation dose and the linear energy transfer (LET). The LET dependence leads to an under-response of the detector in the Bragg peak of proton beams. This phenomenon, called ionization quenching, must be corrected to obtain accurate dose measurements of proton beams. This work exploits the ionization quenching phenomenon to provide a method of measuring LET and auto correcting quenching. Methods: We exposed simultaneously four different organic scintillators (BCF-12, PMMA, PVT, and LSD; 1mm in diameter) and a plane parallel ionization chamber in passively scattered proton beams to doses betweenmore » 32 and 43 cGy and fluence averaged LET values from 0.47 to 1.26 keV/µm. The LET values for each irradiation condition were determined using a validated Monte Carlo model of the beam line. We determined the quenching parameter in the Birk’s equation for scintillation in BCF-12 for dose measurements. One set of irradiation conditions was used to correlate the scintillation response ratio to the LET values and plot a scintillation response ratio versus LET calibration curve. Irradiation conditions independent from the calibration ones were used to validate this method. Comparisons to the expected values were made on both the basis of dose and LET. Results: Among all the scintillators investigated, the ratio of PMMA to BCF-12 provided the best correlation to LET values and was used as the LET calibration curve. The expected LET values in the validation set were within 2%±6%, which resulted in dose accuracy of 1.5%±5.8% for the range of LET values investigated in this work. Conclusion: We have demonstrated the feasibility of using the ratio between the light output of two organic scintillators to simultaneously measure LET and dose of therapeutic proton beams. Further studies are needed to verify the response in higher LET values.« less

SU-C-9A-03: Simultaneous Deconvolution and Segmentation for PET Tumor Delineation Using a Variational Method

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

Li, L; Tan, S; Lu, W

2014-06-01

Purpose: To implement a new method that integrates deconvolution with segmentation under the variational framework for PET tumor delineation. Methods: Deconvolution and segmentation are both challenging problems in image processing. The partial volume effect (PVE) makes tumor boundaries in PET image blurred which affects the accuracy of tumor segmentation. Deconvolution aims to obtain a PVE-free image, which can help to improve the segmentation accuracy. Conversely, a correct localization of the object boundaries is helpful to estimate the blur kernel, and thus assist in the deconvolution. In this study, we proposed to solve the two problems simultaneously using a variational methodmore » so that they can benefit each other. The energy functional consists of a fidelity term and a regularization term, and the blur kernel was limited to be the isotropic Gaussian kernel. We minimized the energy functional by solving the associated Euler-Lagrange equations and taking the derivative with respect to the parameters of the kernel function. An alternate minimization method was used to iterate between segmentation, deconvolution and blur-kernel recovery. The performance of the proposed method was tested on clinic PET images of patients with non-Hodgkin's lymphoma, and compared with seven other segmentation methods using the dice similarity index (DSI) and volume error (VE). Results: Among all segmentation methods, the proposed one (DSI=0.81, VE=0.05) has the highest accuracy, followed by the active contours without edges (DSI=0.81, VE=0.25), while other methods including the Graph Cut and the Mumford-Shah (MS) method have lower accuracy. A visual inspection shows that the proposed method localizes the real tumor contour very well. Conclusion: The result showed that deconvolution and segmentation can contribute to each other. The proposed variational method solve the two problems simultaneously, and leads to a high performance for tumor segmentation in PET. This work was supported in part by National Natural Science Foundation of China (NNSFC), under Grant Nos. 60971112 and 61375018, and Fundamental Research Funds for the Central Universities, under Grant No. 2012QN086. Wei Lu was supported in part by the National Institutes of Health (NIH) Grant No. R01 CA172638.« less

Modeling, estimation and identification methods for static shape determination of flexible structures. [for large space structure design

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Scheid, R. E., Jr.

1986-01-01

This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.

A backward Monte Carlo method for efficient computation of runaway probabilities in runaway electron simulation

NASA Astrophysics Data System (ADS)

Zhang, Guannan; Del-Castillo-Negrete, Diego

2017-10-01

Kinetic descriptions of RE are usually based on the bounced-averaged Fokker-Planck model that determines the PDFs of RE. Despite of the simplification involved, the Fokker-Planck equation can rarely be solved analytically and direct numerical approaches (e.g., continuum and particle-based Monte Carlo (MC)) can be time consuming specially in the computation of asymptotic-type observable including the runaway probability, the slowing-down and runaway mean times, and the energy limit probability. Here we present a novel backward MC approach to these problems based on backward stochastic differential equations (BSDEs). The BSDE model can simultaneously describe the PDF of RE and the runaway probabilities by means of the well-known Feynman-Kac theory. The key ingredient of the backward MC algorithm is to place all the particles in a runaway state and simulate them backward from the terminal time to the initial time. As such, our approach can provide much faster convergence than the brute-force MC methods, which can significantly reduce the number of particles required to achieve a prescribed accuracy. Moreover, our algorithm can be parallelized as easy as the direct MC code, which paves the way for conducting large-scale RE simulation. This work is supported by DOE FES and ASCR under the Contract Numbers ERKJ320 and ERAT377.

Radial orbit error reduction and sea surface topography determination using satellite altimetry

NASA Technical Reports Server (NTRS)

Engelis, Theodossios

1987-01-01

A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface topography with minimum wavelengths of about 500 km and to reduce the radial orbit error caused by geopotential errors. The modeling of the radial orbit error is made using the linearized Lagrangian perturbation theory. Secular and second order effects are also included. After a rather extensive validation of the linearized equations, alternative expressions of the radial orbit error are derived. Numerical estimates for the radial orbit error and geoid undulation error are computed using the differences of two geopotential models as potential coefficient errors, for a SEASAT orbit. To provide statistical estimates of the radial distances and the geoid, a covariance propagation is made based on the full geopotential covariance. Accuracy estimates for the SEASAT orbits are given which agree quite well with already published results. Observation equations are develped using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information provides estimates of parameters representing the sea surface topography and corrections to the gravity field that is used for the orbit generation. The simulation results show that the method can be used to effectively reduce the radial orbit error and recover the sea surface topography.

A Maxwell-Schrödinger solver for quantum optical few-level systems

NASA Astrophysics Data System (ADS)

Fleischhaker, Robert; Evers, Jörg

2011-03-01

The msprop program presented in this work is capable of solving the Maxwell-Schrödinger equations for one or several laser fields propagating through a medium of quantum optical few-level systems in one spatial dimension and in time. In particular, it allows to numerically treat systems in which a laser field interacts with the medium with both its electric and magnetic component at the same time. The internal dynamics of the few-level system is modeled by a quantum optical master equation which includes coherent processes due to optical transitions driven by the laser fields as well as incoherent processes due to decay and dephasing. The propagation dynamics of the laser fields is treated in slowly varying envelope approximation resulting in a first order wave equation for each laser field envelope function. The program employs an Adams predictor formula second order in time to integrate the quantum optical master equation and a Lax-Wendroff scheme second order in space and time to evolve the wave equations for the fields. The source function in the Lax-Wendroff scheme is specifically adapted to allow taking into account the simultaneous coupling of a laser field to the polarization and the magnetization of the medium. To reduce execution time, a customized data structure is implemented and explained. In three examples the features of the program are demonstrated and the treatment of a system with a phase-dependent cross coupling of the electric and magnetic field component of a laser field is shown. Program summaryProgram title: msprop Catalogue identifier: AEHR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHR_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 507 625 No. of bytes in distributed program, including test data, etc.: 10 698 552 Distribution format: tar.gz Programming language: C (C99 standard), Mathematica, bash script, gnuplot script Computer: Tested on x86 architecture Operating system: Unix/Linux environment RAM: Less than 30 MB Classification: 2.5 External routines: Standard C math library, accompanying bash script uses gnuplot, bc (basic calculator), and convert (ImageMagick) Nature of problem: We consider a system of quantum optical few-level atoms exposed to several near-resonant continuous-wave or pulsed laser fields. The complexity of the problem arises from the combination of the coherent and incoherent time evolution of the atoms and its dependence on the spatially varying fields. In systems with a coupling to the electric and magnetic field component the simultaneous treatment of both field components poses an additional challenge. Studying the system dynamics requires solving the quantum optical master equation coupled to the wave equations governing the spatio-temporal dynamics of the fields [1,2]. Solution method: We numerically integrate the equations of motion using a second order Adams predictor method for the time evolution of the atomic density matrix and a second order Lax-Wendroff scheme for iterating the fields in space [3]. For the Lax-Wendroff scheme, the source function is adapted such that a simultaneous coupling to the polarization and the magnetization of the medium can be taken into account. Restrictions: The evolution of the fields is treated in slowly varying envelope approximation [2] such that variations of the fields in space and time must be on a scale larger than the wavelength and the optical cycle. Propagation is restricted to the forward direction and to one dimension. Concerning the description of the atomic system, only a finite number of basis states can be treated and the laser-driven transitions have to be near-resonant such that the rotating-wave approximation can be applied [2]. Unusual features: The program allows the dipole interaction of both the electric and the magnetic component of a laser field to be taken into account at the same time. Thus, a system with a phase-dependent cross coupling of electric and magnetic field component can be treated (see Section 4.2 and [4]). Concerning the implementation of the data structure, it has been optimized for faster memory access. Compared to using standard memory allocation methods, shorter run times are achieved (see Section 3.2). Additional comments: Three examples are given. They each include a readme file, a Mathematica notebook to generate the C-code form of the quantum optical master equation, a parameter file, a bash script which runs the program and converts the numerical data into a movie, two gnuplot scripts, and all files that are produced by running the bash script. Running time: For the first two examples the running time is less than a minute, the third example takes about 12 minutes. On a Pentium 4 (3 GHz) system, a rough estimate can be made with a value of 1 second per million grid points and per field variable.

A finite element model of conduction, convection, and phase change near a solid/melt interface. Ph.D. Thesis - Michigan Univ.

NASA Technical Reports Server (NTRS)

Viterna, Larry A.

1991-01-01

Detailed understanding of heat transfer and fluid flow is required for many aerospace thermal systems. These systems often include phase change and operate over a range of accelerations or effective gravitational fields. An approach to analyzing such systems is presented which requires the simultaneous solution of the conservation laws of energy, momentum, and mass, as well as an equation of state. The variable property form of the governing equations are developed in two-dimensional Cartesian coordinates for a Newtonian fluid. A numerical procedure for solving the governing equations is presented and implemented in a computer program. The Galerkin form of the finite element method is used to solve the spatial variation of the field variables, along with the implicit Crank-Nicolson time marching algorithm. Quadratic Langrangian elements are used for the internal energy and the two components of velocity. Linear Lagrangian elements are used for the pressure. The location of the solid/liquid interface as well as the temperatures are determined form the calculated internal energy and pressure. This approach is quite general in that it can describe heat transfer without phase change, phase change with a sharp interface, and phase change without an interface. Analytical results from this model are compared to those of other researchers studying transient conduction, convection, and phase change and are found to be in good agreement. The numerical procedure presented requires significant computer resources, but this is not unusual when compared to similar studies by other researchers. Several methods are suggested to reduce the computational times.

Constructing diabatic representations using adiabatic and approximate diabatic data – Coping with diabolical singularities

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

Zhu, Xiaolei, E-mail: virtualzx@gmail.com; Yarkony, David R., E-mail: yarkony@jhu.edu

2016-01-28

We have recently introduced a diabatization scheme, which simultaneously fits and diabatizes adiabatic ab initio electronic wave functions, Zhu and Yarkony J. Chem. Phys. 140, 024112 (2014). The algorithm uses derivative couplings in the defining equations for the diabatic Hamiltonian, H{sup d}, and fits all its matrix elements simultaneously to adiabatic state data. This procedure ultimately provides an accurate, quantifiably diabatic, representation of the adiabatic electronic structure data. However, optimizing the large number of nonlinear parameters in the basis functions and adjusting the number and kind of basis functions from which the fit is built, which provide the essential flexibility,more » has proved challenging. In this work, we introduce a procedure that combines adiabatic state and diabatic state data to efficiently optimize the nonlinear parameters and basis function expansion. Further, we consider using direct properties based diabatizations to initialize the fitting procedure. To address this issue, we introduce a systematic method for eliminating the debilitating (diabolical) singularities in the defining equations of properties based diabatizations. We exploit the observation that if approximate diabatic data are available, the commonly used approach of fitting each matrix element of H{sup d} individually provides a starting point (seed) from which convergence of the full H{sup d} construction algorithm is rapid. The optimization of nonlinear parameters and basis functions and the elimination of debilitating singularities are, respectively, illustrated using the 1,2,3,4{sup 1}A states of phenol and the 1,2{sup 1}A states of NH{sub 3}, states which are coupled by conical intersections.« less

Simultaneous waste activated sludge disintegration and biological hydrogen production using an ozone/ultrasound pretreatment.

PubMed

Yang, Shan-Shan; Guo, Wan-Qian; Cao, Guang-Li; Zheng, He-Shan; Ren, Nan-Qi

2012-11-01

This paper offers an effective pretreatment method that can simultaneously achieve excess sludge reduction and bio-hydrogen production from sludge self-fermentation. Batch tests demonstrated that the combinative use of ozone/ultrasound pretreatment had an advantage over the individual ozone and ultrasound pretreatments. The optimal condition (ozone dose of 0.158 g O(3)/g DS and ultrasound energy density of 1.423 W/mL) was recommended by response surface methodology. The maximum hydrogen yield was achieved at 9.28 mL H(2)/g DS under the optimal condition. According to the kinetic analysis, the highest hydrogen production rate (1.84 mL/h) was also obtained using combined pretreatment, which well fitted the predicted equation (the squared regression statistic was 0.9969). The disintegration degrees (DD) were limited to 19.57% and 46.10% in individual ozone and ultrasound pretreatments, while it reached up to 60.88% in combined pretreatment. The combined ozone/ultrasound pretreatment provides an ideal and environmental friendly solution to the problem of sludge disposal. Copyright © 2012 Elsevier Ltd. All rights reserved.

Simultaneous effects of coagulation and variable magnetic field on peristaltically induced motion of Jeffrey nanofluid containing gyrotactic microorganism.

PubMed

Bhatti, M M; Zeeshan, A; Ellahi, R

2017-03-01

In this article, simultaneous effects of coagulation (blood clot) and variable magnetic field on peristaltically induced motion of non-Newtonian Jeffrey nanofluid containing gyrotactic microorganism through an annulus have been studied. The effects of an endoscope also taken into consideration in our study as a special case. The governing flow problem is simplified by taking the approximation of long wavelength and creeping flow regime. The resulting highly coupled differential equations are solved analytically with the help of perturbation method and series solution have been presented up to second order approximation. The impact of all the sundry parameters is discussed for velocity profile, temperature profile, nanoparticle concentration profile, motile microorganism density profile, pressure rise and friction forces. Moreover, numerical integration is also used to evaluate the expressions for pressure rise and friction forces for outer tube and inner tube. It is found that velocity of a fluid diminishes near the walls due to the increment in the height of clot. However, the influence of magnetic field depicts opposite behavior near the walls. Copyright © 2016 Elsevier Inc. All rights reserved.

Phase-Shifted Based Numerical Method for Modeling Frequency-Dependent Effects on Seismic Reflections

NASA Astrophysics Data System (ADS)

Chen, Xuehua; Qi, Yingkai; He, Xilei; He, Zhenhua; Chen, Hui

2016-08-01

The significant velocity dispersion and attenuation has often been observed when seismic waves propagate in fluid-saturated porous rocks. Both the magnitude and variation features of the velocity dispersion and attenuation are frequency-dependent and related closely to the physical properties of the fluid-saturated porous rocks. To explore the effects of frequency-dependent dispersion and attenuation on the seismic responses, in this work, we present a numerical method for seismic data modeling based on the diffusive and viscous wave equation (DVWE), which introduces the poroelastic theory and takes into account diffusive and viscous attenuation in diffusive-viscous-theory. We derive a phase-shift wave extrapolation algorithm in frequencywavenumber domain for implementing the DVWE-based simulation method that can handle the simultaneous lateral variations in velocity, diffusive coefficient and viscosity. Then, we design a distributary channels model in which a hydrocarbon-saturated sand reservoir is embedded in one of the channels. Next, we calculated the synthetic seismic data to analytically and comparatively illustrate the seismic frequency-dependent behaviors related to the hydrocarbon-saturated reservoir, by employing DVWE-based and conventional acoustic wave equation (AWE) based method, respectively. The results of the synthetic seismic data delineate the intrinsic energy loss, phase delay, lower instantaneous dominant frequency and narrower bandwidth due to the frequency-dependent dispersion and attenuation when seismic wave travels through the hydrocarbon-saturated reservoir. The numerical modeling method is expected to contribute to improve the understanding of the features and mechanism of the seismic frequency-dependent effects resulted from the hydrocarbon-saturated porous rocks.

Monte Carlo, Probability, Algebra, and Pi.

ERIC Educational Resources Information Center

Hinders, Duane C.

1981-01-01

The uses of random number generators are illustrated in three ways: (1) the solution of a probability problem using a coin; (2) the solution of a system of simultaneous linear equations using a die; and (3) the approximation of pi using darts. (MP)

A new model for the blown film process

NASA Astrophysics Data System (ADS)

Demay, Yves; Clamond, Didier

2011-11-01

Polymer films are generally manufactured by film blowing. In this process the polymer (a polyethylene for example) is molten in a screw extruder and forced into a tubular die (typical dimensions are several decimeters in diameter and about one mm in thickness). At extrusion, it forms a liquid tube which is simultaneously drawn in the vertical direction by nip rolls, inflated by an internal pressure and cooled by external air rings. Typical dimensions of the bubble at take up are 1 m or more in diameter and several 10 μm in thickness. From a mechanical point of view, it is an extensional thin layer flow. Readers not familiar with this process will find easily pictures and schematic descriptions with a web research using keywords blown film extrusion. In order to simplify, it is assumed that the temperature profile is known and that the molten polymer behaves as a Newtonian fluid. This crude rheological behavior allows to capture qualitatively an important part of observed phenomena. The classical model introduced by Pearson and Petrie in 1970 is based on three hypothesis: the polymer flow in air is steady and axisymmetric and the film is thin. It uses a tangent frame affixed to the membrane to describe kinematics and to compute stress and strain tensors. In this model the balance equations are written using a stretching force and a curvature equation. It results in a nonlinear system of differential equations for velocity, thickness, radius and stress components according to distance z to extrusion. Solution is then computed using a tedious shooting method to determine force and internal pressure. For stability reasons this system of equations is solved from take up to extrusion. In this Note we derive also balance equations according to a curvilinear abscissa s. It allows us to derive a coupled system of equations for velocity and geometry according to radius r. This strategy which is classically used to determine surfaces of revolution with given mean curvature is rather disconcerting to compute a stretching flow in z direction. However it leads to a model constituted of two coupled equations: Velocity is then solution of a Dirichlet boundary value problem of order two easily solved using a finite elements method; The profile curve of the bubble is solution of a highly nonlinear differential equation of order one leading to a singular integral. Internal pressure appears as a parameter allowing to impose an additional boundary condition. Despite the fact that the computation of the solution remains technical, this new model seems more natural from a mathematical point of view as it leads, on the one hand, to an elliptic equation to compute velocity, and on the other hand, to an equation of a classical type in differential geometry to determine the generatrix.

Validation of continuous-wave Doppler echocardiographic measurements of mitral and tricuspid prosthetic valve gradients: a simultaneous Doppler-catheter study.

PubMed

Wilkins, G T; Gillam, L D; Kritzer, G L; Levine, R A; Palacios, I F; Weyman, A E

1986-10-01

For patients with stenotic native valves, the modified Bernoulli equation (delta P = 4V2) may be applied to Doppler-measured transvalvular velocities to yield an accurate estimate of transvalvular gradients. Although it would be useful if the same approach could be used for those with stenotic prosthetic valves, no previous study has validated the Doppler technique in this setting. We therefore recorded simultaneous continuous-wave Doppler flow profiles and transvalvular manometric gradients in 12 catheterized patients in whom all atrial and ventricular pressures were directly measured (transseptal left atrial catheterization and transthoracic ventricular puncture were performed where necessary). A total of 13 prostheses were studied: 11 mitral (seven porcine, three Starr-Edwards, and one Björk-Shiley) and two tricuspid (one porcine and one Björk-Shiley). The Doppler-determined mean gradient was calculated as the mean of the instantaneous gradients (delta P = 4V2) at 10 msec intervals throughout diastole. The correlation of simultaneous Doppler (DMG) and manometric mean gradients (MG) for the whole group (n = 13) demonstrated a highly significant relationship (MG = 1.07 DMG + 0.28; r = .96, p = .0001). The correlation was equally good for porcine valves alone (n = 8) (MG = 1.06 DMG + 0.55; r = .96, p = .001) and for mechanical valves alone (n = 5) (MG = 1.06 DMG - 0.04; r = .93, p = .02). In a subset of patients without regurgitation (n = 8), prosthetic valve areas were estimated by two Doppler methods originally described by Holen and Hatle, as well as by the invasive Gorlin method. As expected from theoretical considerations, a close correlation was not demonstrated between results of the Gorlin method and those of either Hatle's Doppler method (r = .65, fp = NS) or Holen's method (r = .14, p = NS). Comparison of the results of the two Doppler methods yielded a somewhat closer correlation (r = .73, p less than or equal to .05). These results suggest that in patients with disk-occluder, ball-occluder, and porcine prosthetic valves, Doppler estimates of transvalvular gradients are virtually identical to those obtained invasively.

A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry

NASA Astrophysics Data System (ADS)

Jaouen, Stéphane

2007-07-01

In many physical applications, one wishes to control the development of multi-dimensional instabilities around a one-dimensional (1D) complex flow. For predicting the growth rates of these perturbations, a general numerical approach is viable which consists in solving simultaneously the one-dimensional equations and their linearized form for three-dimensional perturbations. In Clarisse et al. [J.-M. Clarisse, S. Jaouen, P.-A. Raviart, A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys. 198 (2004) 80-105], a class of Godunov-type schemes for planar-symmetric flows of gas dynamics has been proposed. Pursuing this effort, we extend these results to spherically symmetric flows. A new method to derive the Lagrangian perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian systems, Arch. Rational Mech. Anal. 178 (2005) 327-372] is also described. It leads to many advantages. First of all, many physical problems we are interested in enter this formalism (gas dynamics, two-temperature plasma equations, ideal magnetohydrodynamics, etc.) whatever is the geometry. Secondly, a class of numerical entropic schemes is available for the basic flow [11]. Last, linearizing and devising numerical schemes for the perturbed flow is straightforward. The numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that - due to its simplicity and its low computational cost - the Linear Perturbations Code (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.

Modified Chebyshev Picard Iteration for Efficient Numerical Integration of Ordinary Differential Equations

NASA Astrophysics Data System (ADS)

Macomber, B.; Woollands, R. M.; Probe, A.; Younes, A.; Bai, X.; Junkins, J.

2013-09-01

Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method for approximating solutions of linear or non-linear Ordinary Differential Equations (ODEs) to obtain time histories of system state trajectories. Unlike other step-by-step differential equation solvers, the Runge-Kutta family of numerical integrators for example, MCPI approximates long arcs of the state trajectory with an iterative path approximation approach, and is ideally suited to parallel computation. Orthogonal Chebyshev Polynomials are used as basis functions during each path iteration; the integrations of the Picard iteration are then done analytically. Due to the orthogonality of the Chebyshev basis functions, the least square approximations are computed without matrix inversion; the coefficients are computed robustly from discrete inner products. As a consequence of discrete sampling and weighting adopted for the inner product definition, Runge phenomena errors are minimized near the ends of the approximation intervals. The MCPI algorithm utilizes a vector-matrix framework for computational efficiency. Additionally, all Chebyshev coefficients and integrand function evaluations are independent, meaning they can be simultaneously computed in parallel for further decreased computational cost. Over an order of magnitude speedup from traditional methods is achieved in serial processing, and an additional order of magnitude is achievable in parallel architectures. This paper presents a new MCPI library, a modular toolset designed to allow MCPI to be easily applied to a wide variety of ODE systems. Library users will not have to concern themselves with the underlying mathematics behind the MCPI method. Inputs are the boundary conditions of the dynamical system, the integrand function governing system behavior, and the desired time interval of integration, and the output is a time history of the system states over the interval of interest. Examples from the field of astrodynamics are presented to compare the output from the MCPI library to current state-of-practice numerical integration methods. It is shown that MCPI is capable of out-performing the state-of-practice in terms of computational cost and accuracy.

The four fixed points of scale invariant single field cosmological models

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

Xue, BingKan, E-mail: bxue@princeton.edu

2012-10-01

We introduce a new set of flow parameters to describe the time dependence of the equation of state and the speed of sound in single field cosmological models. A scale invariant power spectrum is produced if these flow parameters satisfy specific dynamical equations. We analyze the flow of these parameters and find four types of fixed points that encompass all known single field models. Moreover, near each fixed point we uncover new models where the scale invariance of the power spectrum relies on having simultaneously time varying speed of sound and equation of state. We describe several distinctive new modelsmore » and discuss constraints from strong coupling and superluminality.« less

Calculation of turbulent boundary layers with heat transfer and pressure gradient utilizing a compressibility transformation. Part 3: Computer program manual

NASA Technical Reports Server (NTRS)

Schneider, J.; Boccio, J.

1972-01-01

A computer program is described capable of determining the properties of a compressible turbulent boundary layer with pressure gradient and heat transfer. The program treats the two-dimensional problem assuming perfect gas and Crocco integral energy solution. A compressibility transformation is applied to the equation for the conservation of mass and momentum, which relates this flow to a low speed constant property flow with simultaneous mass transfer and pressure gradient. The resulting system of describing equations consists of eight ordinary differential equations which are solved numerically. For Part 1, see N72-12226; for Part 2, see N72-15264.

Multiscale Concrete Modeling of Aging Degradation

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

Hammi, Yousseff; Gullett, Philipp; Horstemeyer, Mark F.

In this work a numerical finite element framework is implemented to enable the integration of coupled multiscale and multiphysics transport processes. A User Element subroutine (UEL) in Abaqus is used to simultaneously solve stress equilibrium, heat conduction, and multiple diffusion equations for 2D and 3D linear and quadratic elements. Transport processes in concrete structures and their degradation mechanisms are presented along with the discretization of the governing equations. The multiphysics modeling framework is theoretically extended to the linear elastic fracture mechanics (LEFM) by introducing the eXtended Finite Element Method (XFEM) and based on the XFEM user element implementation of Ginermore » et al. [2009]. A damage model that takes into account the damage contribution from the different degradation mechanisms is theoretically developed. The total contribution of damage is forwarded to a Multi-Stage Fatigue (MSF) model to enable the assessment of the fatigue life and the deterioration of reinforced concrete structures in a nuclear power plant. Finally, two examples are presented to illustrate the developed multiphysics user element implementation and the XFEM implementation of Giner et al. [2009].« less

A discontinuous Galerkin approach for conservative modeling of fully nonlinear and weakly dispersive wave transformations

NASA Astrophysics Data System (ADS)

Sharifian, Mohammad Kazem; Kesserwani, Georges; Hassanzadeh, Yousef

2018-05-01

This work extends a robust second-order Runge-Kutta Discontinuous Galerkin (RKDG2) method to solve the fully nonlinear and weakly dispersive flows, within a scope to simultaneously address accuracy, conservativeness, cost-efficiency and practical needs. The mathematical model governing such flows is based on a variant form of the Green-Naghdi (GN) equations decomposed as a hyperbolic shallow water system with an elliptic source term. Practical features of relevance (i.e. conservative modeling over irregular terrain with wetting and drying and local slope limiting) have been restored from an RKDG2 solver to the Nonlinear Shallow Water (NSW) equations, alongside new considerations to integrate elliptic source terms (i.e. via a fourth-order local discretization of the topography) and to enable local capturing of breaking waves (i.e. via adding a detector for switching off the dispersive terms). Numerical results are presented, demonstrating the overall capability of the proposed approach in achieving realistic prediction of nearshore wave processes involving both nonlinearity and dispersion effects within a single model.

The relationship between eddy-transport and second-order closure models for stratified media and for vortices

NASA Technical Reports Server (NTRS)

Donaldson, C. D.

1973-01-01

The question is considered of how complex a model should be used for the calculation of turbulent shear flows. At the present time there are models varying in complexity from very simple eddy-transport models to models in which all the equations for the nonzero second-order correlations are solved simultaneously with the equations for the mean variables. A discussion is presented of the relationship between these two models of turbulent shear flow. Two types of motion are discussed: first, turbulent shear flow in a stratified medium and, second, the motion in a turbulent line vortex. These two cases are instructive because in the first example eddy-transport methods have proven reasonably effective, whereas in the second, they have led to erroneous conclusions. It is not generally appreciated that the simplest form of eddy-transport theory can be derived from second-order closure models of turbulent flow by a suitably limiting process. This limiting process and the suitability of eddy-transport modeling for stratified media and line vortices are discussed.

Multiple pathways from the neighborhood food environment to increased body mass index through dietary behaviors: A structural equation-based analysis in the CARDIA study

PubMed Central

Richardson, Andrea S.; Meyer, Katie A.; Howard, Annie Green; Boone-Heinonen, Janne; Popkin, Barry M.; Evenson, Kelly R.; Shikany, James M.; Lewis, Cora E.; Gordon-Larsen, Penny

2016-01-01

Objectives To examine longitudinal pathways from multiple types of neighborhood restaurants and food stores to BMI, through dietary behaviors. Methods We used data from participants (n=5114) in the United States-based Coronary Artery Risk Development in Young Adults study and a structural equation model to estimate longitudinal (1985–86 to 2005–06) pathways simultaneously from neighborhood fast food restaurants, sit-down restaurants, supermarkets, and convenience stores to BMI through dietary behaviors, controlling for socioeconomic status (SES) and physical activity. Results Higher numbers of neighborhood fast food restaurants and lower numbers of sit-down restaurants were associated with higher consumption of an obesogenic fast food-type diet. The pathways from food stores to BMI through diet were inconsistent in magnitude and statistical significance. Conclusions Efforts to decrease the numbers of neighborhood fast food restaurants and to increase the numbers of sit-down restaurant options could influence diet behaviors. Availability of neighborhood fast food and sit-down restaurants may play comparatively stronger roles than food stores in shaping dietary behaviors and BMI. PMID:26454248

A solution procedure for behavior of thick plates on a nonlinear foundation and postbuckling behavior of long plates

NASA Technical Reports Server (NTRS)

Stein, M.; Stein, P. A.

1978-01-01

Approximate solutions for three nonlinear orthotropic plate problems are presented: (1) a thick plate attached to a pad having nonlinear material properties which, in turn, is attached to a substructure which is then deformed; (2) a long plate loaded in inplane longitudinal compression beyond its buckling load; and (3) a long plate loaded in inplane shear beyond its buckling load. For all three problems, the two dimensional plate equations are reduced to one dimensional equations in the y-direction by using a one dimensional trigonometric approximation in the x-direction. Each problem uses different trigonometric terms. Solutions are obtained using an existing algorithm for simultaneous, first order, nonlinear, ordinary differential equations subject to two point boundary conditions. Ordinary differential equations are derived to determine the variable coefficients of the trigonometric terms.

Thermal shaft effects on load-carrying capacity of a fully coupled, variable-properties cryogenic journal bearing

NASA Technical Reports Server (NTRS)

Braun, M. J.; Wheeler, R. L., III; Hendricks, R. C.

1986-01-01

The purpose of this work was to perform a rather complete analysis for a cryogenic (oxygen) journal bearing. The Reynolds equation required coupling and simultaneous solution with the fluid energy equation. To correctly account for the changes in the fluid viscosity, the fluid energy equation was coupled with the shaft and bearing heat conduction energy equations. The effects of pressure and temperature on the density, viscosity, and load-carrying capacity were further discussed as analysis parameters, with respect to relative eccentricity and the angular velocity. The isothermal fluid case and the adiabatic fluid case represented the limiting boundaries. The discussion was further extrapolated to study the Sommerfeld number dependency on the fluid Nusselt number and its consequence on possible total loss of load-carrying capacity and/or seizure (catastrophic failure).

Global uniqueness in an inverse problem for time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Kian, Y.; Oksanen, L.; Soccorsi, E.; Yamamoto, M.

2018-01-01

Given (M , g), a compact connected Riemannian manifold of dimension d ⩾ 2, with boundary ∂M, we consider an initial boundary value problem for a fractional diffusion equation on (0 , T) × M, T > 0, with time-fractional Caputo derivative of order α ∈ (0 , 1) ∪ (1 , 2). We prove uniqueness in the inverse problem of determining the smooth manifold (M , g) (up to an isometry), and various time-independent smooth coefficients appearing in this equation, from measurements of the solutions on a subset of ∂M at fixed time. In the "flat" case where M is a compact subset of Rd, two out the three coefficients ρ (density), a (conductivity) and q (potential) appearing in the equation ρ ∂tα u - div (a∇u) + qu = 0 on (0 , T) × M are recovered simultaneously.

Simultaneously removal of inorganic arsenic species from stored rainwater in arsenic endemic area by leaves of Tecomella undulata: a multivariate study.

PubMed

Brahman, Kapil Dev; Kazi, Tasneem Gul; Afridi, Hassan Imran; Baig, Jameel Ahmed; Abro, Muhammad Ishaque; Arain, Sadaf Sadia; Ali, Jamshed; Khan, Sumaira

2016-08-01

In the present study, an indigenous biosorbent (leaves of Tecomella undulata) was used for the simultaneous removal of inorganic arsenic species (As(III) and As(V)) from the stored rainwater in Tharparkar, Pakistan. The Plackett-Burman experimental design was used as a multivariate strategy for the evaluation of the effects of six factors/variables on the biosorption of inorganic arsenic species, simultaneously. Central composite design (CCD) was used to found the optimum values of significant factors for the removal of As(III) and As(V). Initial concentrations of both inorganic As species, pH, biosorbent dose, and contact time were selected as independent factors in CCD, while the adsorption capacity (q e) was considered as a response function. The separation of inorganic As species in water samples before and after biosorption was carried out by cloud point and solid-phase extraction methods. Theoretical values of pH, concentration of analytes, biosorbent dose, and contact time were calculated by quadratic equation for 100 % biosorption of both inorganic As species in aqueous media. Experimental data were modeled by Langmuir and Freundlich isotherms. Thermodynamic and kinetic study indicated that the biosorption of As(III) and As(V) was followed by pseudo second order. It was concluded that the indigenous biosorbent material efficiently and simultaneously removed both As species in the range of 70.8 to 98.5 % of total contents in studied ground water samples. Graphical abstract Optimizing the significant varable by central 2(3) + star orthogonal composite design.

Comparison of Kernel Equating and Item Response Theory Equating Methods

ERIC Educational Resources Information Center

Meng, Yu

2012-01-01

The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

A high-order positivity-preserving single-stage single-step method for the ideal magnetohydrodynamic equations

NASA Astrophysics Data System (ADS)

Christlieb, Andrew J.; Feng, Xiao; Seal, David C.; Tang, Qi

2016-07-01

We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage (i.e., it has no internal stages to store), single-step (i.e., it has no time history that needs to be stored), maintains a discrete divergence-free condition on the magnetic field, and has the capacity to preserve the positivity of the density and pressure. To accomplish this, we use a Taylor discretization of the Picard integral formulation (PIF) of the finite difference WENO method proposed in Christlieb et al. (2015) [23], where the focus is on a high-order discretization of the fluxes (as opposed to the conserved variables). We use the version where fluxes are expanded to third-order accuracy in time, and for the fluid variables space is discretized using the classical fifth-order finite difference WENO discretization. We use constrained transport in order to obtain divergence-free magnetic fields, which means that we simultaneously evolve the magnetohydrodynamic (that has an evolution equation for the magnetic field) and magnetic potential equations alongside each other, and set the magnetic field to be the (discrete) curl of the magnetic potential after each time step. In this work, we compute these derivatives to fourth-order accuracy. In order to retain a single-stage, single-step method, we develop a novel Lax-Wendroff discretization for the evolution of the magnetic potential, where we start with technology used for Hamilton-Jacobi equations in order to construct a non-oscillatory magnetic field. The end result is an algorithm that is similar to our previous work Christlieb et al. (2014) [8], but this time the time stepping is replaced through a Taylor method with the addition of a positivity-preserving limiter. Finally, positivity preservation is realized by introducing a parameterized flux limiter that considers a linear combination of high and low-order numerical fluxes. The choice of the free parameter is then given in such a way that the fluxes are limited towards the low-order solver until positivity is attained. Given the lack of additional degrees of freedom in the system, this positivity limiter lacks energy conservation where the limiter turns on. However, this ingredient can be dropped for problems where the pressure does not become negative. We present two and three dimensional numerical results for several standard test problems including a smooth Alfvén wave (to verify formal order of accuracy), shock tube problems (to test the shock-capturing ability of the scheme), Orszag-Tang, and cloud shock interactions. These results assert the robustness and verify the high-order of accuracy of the proposed scheme.

A Comparison of Kernel Equating and Traditional Equipercentile Equating Methods and the Parametric Bootstrap Methods for Estimating Standard Errors in Equipercentile Equating

ERIC Educational Resources Information Center

Choi, Sae Il

2009-01-01

This study used simulation (a) to compare the kernel equating method to traditional equipercentile equating methods under the equivalent-groups (EG) design and the nonequivalent-groups with anchor test (NEAT) design and (b) to apply the parametric bootstrap method for estimating standard errors of equating. A two-parameter logistic item response…

Method and program product for determining a radiance field in an optical environment

NASA Technical Reports Server (NTRS)

Reinersman, Phillip N. (Inventor); Carder, Kendall L. (Inventor)

2007-01-01

A hybrid method is presented by which Monte Carlo techniques are combined with iterative relaxation techniques to solve the Radiative Transfer Equation in arbitrary one-, two- or three-dimensional optical environments. The optical environments are first divided into contiguous regions, or elements, with Monte Carlo techniques then being employed to determine the optical response function of each type of element. The elements are combined, and the iterative relaxation techniques are used to determine simultaneously the radiance field on the boundary and throughout the interior of the modeled environment. This hybrid model is capable of providing estimates of the under-water light field needed to expedite inspection of ship hulls and port facilities. It is also capable of providing estimates of the subaerial light field for structured, absorbing or non-absorbing environments such as shadows of mountain ranges within and without absorption spectral bands such as water vapor or CO.sub.2 bands.

Attenuated coupled cluster: a heuristic polynomial similarity transformation incorporating spin symmetry projection into traditional coupled cluster theory

NASA Astrophysics Data System (ADS)

Gomez, John A.; Henderson, Thomas M.; Scuseria, Gustavo E.

2017-11-01

In electronic structure theory, restricted single-reference coupled cluster (CC) captures weak correlation but fails catastrophically under strong correlation. Spin-projected unrestricted Hartree-Fock (SUHF), on the other hand, misses weak correlation but captures a large portion of strong correlation. The theoretical description of many important processes, e.g. molecular dissociation, requires a method capable of accurately capturing both weak and strong correlation simultaneously, and would likely benefit from a combined CC-SUHF approach. Based on what we have recently learned about SUHF written as particle-hole excitations out of a symmetry-adapted reference determinant, we here propose a heuristic CC doubles model to attenuate the dominant spin collective channel of the quadratic terms in the CC equations. Proof of principle results presented here are encouraging and point to several paths forward for improving the method further.

Calculation of three dimensional viscous flows in annular cascades using parabolized Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Lawerenz, M.

Numerical algorithms for describing the endwall boundary layers and secondary flows in high turning turbine cascades are described. Partially-parabolic methods which cover three-dimensional viscous flow effects are outlined. Introduction of tip-clearance models and modifications of no-slip conditions without the use of wall functions expand the range of application and improve accuracy. Simultaneous computation of the profile boundary layers by refinement of the mesh size in the circumferential direction makes it possible to describe the boundary layer interaction in the corners formed by the bladings and the endwalls. The partially-parabolic method means that the streamwise elliptic coupling is well represented by the given pressure field and that separation does not occur, but it is not possible to describe the separation of the endwall boundary layer near the leading edge and the horse-shoe vortex there properly.

Interactive application of quadratic expansion of chi-square statistic to nonlinear curve fitting

NASA Technical Reports Server (NTRS)

Badavi, F. F.; Everhart, Joel L.

1987-01-01

This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.

Modeling heat transfer and inactivation of Escherichia coli O157:H7 in precooked meat products in Argentina using the finite element method.

PubMed

Santos, M V; Zaritzky, N; Califano, A

2008-07-01

The presence of Escherichia coli is linked with sanitary deficiencies and undercooking of meat products. Recent studies have detected E. coli O157:H7 in black blood sausages. Minimum time-temperature specifications to kill the bacteria were obtained by numerical simulations of the microscopic heat conduction equation using the finite element method, and calculating the temperature profile of the sausage and the population of E. coli at the coldest point during heating. The model was validated by heating sausages in a water-bath. The effects of heat transfer coefficients and water temperatures on the required time to achieve an inactivation value (IV) of 12(log) are reported. Macroscopic heat balances were simultaneously solved to consider the temperature drop in the water batch as a function of the ratio between the mass of thermally treated sausage and the heat capacity of the system.

Solar Corona Simulation Model With Positivity-preserving Property

NASA Astrophysics Data System (ADS)

Feng, X. S.

2015-12-01

Positivity-preserving is one of crucial problems in solar corona simulation. In such numerical simulation of low plasma β region, keeping density and pressure is a first of all matter to obtain physical sound solution. In the present paper, we utilize the maximum-principle-preserving flux limiting technique to develop a class of second order positivity-preserving Godunov finite volume HLL methods for the solar wind plasma MHD equations. Based on the underlying first order building block of positivity preserving Lax-Friedrichs, our schemes, under the constrained transport (CT) and generalized Lagrange multiplier (GLM) framework, can achieve high order accuracy, a discrete divergence-free condition and positivity of the numerical solution simultaneously without extra CFL constraints. Numerical results in four Carrington rotation during the declining, rising, minimum and maximum solar activity phases are provided to demonstrate the performance of modeling small plasma beta with positivity-preserving property of the proposed method.

Supernova constraints on neutrino oscillation and EoS for proto-neutron star

NASA Astrophysics Data System (ADS)

Kajino, T.; Aoki, W.; Cheoun, M.-K.; Hayakawa, T.; Hidaka, J.; Hirai, Y.; Mathews, G. J.; Nakamura, K.; Shibagaki, S.; Suzuki, T.

2014-05-01

Core-collapse supernovae eject huge amount of flux of energetic neutrinos which affect explosive nucleosynthesis of rare isotopes like 7Li, 11B, 92Nb, 138La and Ta and r-process elements. Several isotopes depend strongly on the neutrino flavor oscillation due to the Mikheyev-Smirnov-Wolfenstein (MSW) effect. We here discuss how to determine the neutrino temperatures and propose a method to determine still unknown neutrino oscillation parameters, mass hierarchy and θ13, simultaneously. Combining the recent experimental constraints on θ13 with isotopic ratios of the light elements discovered in presolar grains from the Murchison meteorite, we show that our method suggests at a marginal preference for an inverted neutrino mass hierarchy. We also discuss supernova relic neutrinos that may indicate the softness of the equation of state (EoS) of nuclear matter as well as adiabatic conditions of the neutrino oscillation.

Efficient sparse matrix-matrix multiplication for computing periodic responses by shooting method on Intel Xeon Phi

NASA Astrophysics Data System (ADS)

Stoykov, S.; Atanassov, E.; Margenov, S.

2016-10-01

Many of the scientific applications involve sparse or dense matrix operations, such as solving linear systems, matrix-matrix products, eigensolvers, etc. In what concerns structural nonlinear dynamics, the computations of periodic responses and the determination of stability of the solution are of primary interest. Shooting method iswidely used for obtaining periodic responses of nonlinear systems. The method involves simultaneously operations with sparse and dense matrices. One of the computationally expensive operations in the method is multiplication of sparse by dense matrices. In the current work, a new algorithm for sparse matrix by dense matrix products is presented. The algorithm takes into account the structure of the sparse matrix, which is obtained by space discretization of the nonlinear Mindlin's plate equation of motion by the finite element method. The algorithm is developed to use the vector engine of Intel Xeon Phi coprocessors. It is compared with the standard sparse matrix by dense matrix algorithm and the one developed by Intel MKL and it is shown that by considering the properties of the sparse matrix better algorithms can be developed.

Role of short-range correlation in facilitation of wave propagation in a long-range ladder chain

NASA Astrophysics Data System (ADS)

Farzadian, O.; Niry, M. D.

2018-09-01

We extend a new method for generating a random chain, which has a kind of short-range correlation induced by a repeated sequence while retaining long-range correlation. Three distinct methods are considered to study the localization-delocalization transition of mechanical waves in one-dimensional disordered media with simultaneous existence of short and long-range correlation. First, a transfer-matrix method was used to calculate numerically the localization length of a wave in a binary chain. We found that the existence of short-range correlation in a long-range correlated chain can increase the localization length at the resonance frequency Ωc. Then, we carried out an analytical study of the delocalization properties of the waves in correlated disordered media around Ωc. Finally, we apply a dynamical method based on the direct numerical simulation of the wave equation to study the propagation of waves in the correlated chain. Imposing short-range correlation on the long-range background will lead the propagation to super-diffusive transport. The results obtained with all three methods are in agreement with each other.

Inversion of very large matrices encountered in large scale problems of photogrammetry and photographic astrometry

NASA Technical Reports Server (NTRS)

Brown, D. C.

1971-01-01

The simultaneous adjustment of very large nets of overlapping plates covering the celestial sphere becomes computationally feasible by virtue of a twofold process that generates a system of normal equations having a bordered-banded coefficient matrix, and solves such a system in a highly efficient manner. Numerical results suggest that when a well constructed spherical net is subjected to a rigorous, simultaneous adjustment, the exercise of independently established control points is neither required for determinancy nor for production of accurate results.

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.

A Numerical Method for Obtaining Monoenergetic Neutron Flux Distributions and Transmissions in Multiple-Region Slabs

NASA Technical Reports Server (NTRS)

Schneider, Harold

1959-01-01

This method is investigated for semi-infinite multiple-slab configurations of arbitrary width, composition, and source distribution. Isotropic scattering in the laboratory system is assumed. Isotropic scattering implies that the fraction of neutrons scattered in the i(sup th) volume element or subregion that will make their next collision in the j(sup th) volume element or subregion is the same for all collisions. These so-called "transfer probabilities" between subregions are calculated and used to obtain successive-collision densities from which the flux and transmission probabilities directly follow. For a thick slab with little or no absorption, a successive-collisions technique proves impractical because an unreasonably large number of collisions must be followed in order to obtain the flux. Here the appropriate integral equation is converted into a set of linear simultaneous algebraic equations that are solved for the average total flux in each subregion. When ordinary diffusion theory applies with satisfactory precision in a portion of the multiple-slab configuration, the problem is solved by ordinary diffusion theory, but the flux is plotted only in the region of validity. The angular distribution of neutrons entering the remaining portion is determined from the known diffusion flux and the remaining region is solved by higher order theory. Several procedures for applying the numerical method are presented and discussed. To illustrate the calculational procedure, a symmetrical slab ia vacuum is worked by the numerical, Monte Carlo, and P(sub 3) spherical harmonics methods. In addition, an unsymmetrical double-slab problem is solved by the numerical and Monte Carlo methods. The numerical approach proved faster and more accurate in these examples. Adaptation of the method to anisotropic scattering in slabs is indicated, although no example is included in this paper.

Numerical Modelling of Three-Fluid Flow Using The Level-set Method

NASA Astrophysics Data System (ADS)

Li, Hongying; Lou, Jing; Shang, Zhi

2014-11-01

This work presents a numerical model for simulation of three-fluid flow involving two different moving interfaces. These interfaces are captured using the level-set method via two different level-set functions. A combined formulation with only one set of conservation equations for the whole physical domain, consisting of the three different immiscible fluids, is employed. Numerical solution is performed on a fixed mesh using the finite volume method. Surface tension effect is incorporated using the Continuum Surface Force model. Validation of the present model is made against available results for stratified flow and rising bubble in a container with a free surface. Applications of the present model are demonstrated by a variety of three-fluid flow systems including (1) three-fluid stratified flow, (2) two-fluid stratified flow carrying the third fluid in the form of drops and (3) simultaneous rising and settling of two drops in a stationary third fluid. The work is supported by a Thematic and Strategic Research from A*STAR, Singapore (Ref. #: 1021640075).

Methods for Equating Mental Tests.

DTIC Science & Technology

1984-11-01

1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth

A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

PubMed Central

Motsa, S. S.; Magagula, V. M.; Sibanda, P.

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252

A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

PubMed

Motsa, S S; Magagula, V M; Sibanda, P

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

Hierarchical imputation of systematically and sporadically missing data: An approximate Bayesian approach using chained equations.

PubMed

Jolani, Shahab

2018-03-01

In health and medical sciences, multiple imputation (MI) is now becoming popular to obtain valid inferences in the presence of missing data. However, MI of clustered data such as multicenter studies and individual participant data meta-analysis requires advanced imputation routines that preserve the hierarchical structure of data. In clustered data, a specific challenge is the presence of systematically missing data, when a variable is completely missing in some clusters, and sporadically missing data, when it is partly missing in some clusters. Unfortunately, little is known about how to perform MI when both types of missing data occur simultaneously. We develop a new class of hierarchical imputation approach based on chained equations methodology that simultaneously imputes systematically and sporadically missing data while allowing for arbitrary patterns of missingness among them. Here, we use a random effect imputation model and adopt a simplification over fully Bayesian techniques such as Gibbs sampler to directly obtain draws of parameters within each step of the chained equations. We justify through theoretical arguments and extensive simulation studies that the proposed imputation methodology has good statistical properties in terms of bias and coverage rates of parameter estimates. An illustration is given in a case study with eight individual participant datasets. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Flight Investigation of Prescribed Simultaneous Independent Surface Excitations for Real-Time Parameter Identification

NASA Technical Reports Server (NTRS)

Moes, Timothy R.; Smith, Mark S.; Morelli, Eugene A.

2003-01-01

Near real-time stability and control derivative extraction is required to support flight demonstration of Intelligent Flight Control System (IFCS) concepts being developed by NASA, academia, and industry. Traditionally, flight maneuvers would be designed and flown to obtain stability and control derivative estimates using a postflight analysis technique. The goal of the IFCS concept is to be able to modify the control laws in real time for an aircraft that has been damaged in flight. In some IFCS implementations, real-time parameter identification (PID) of the stability and control derivatives of the damaged aircraft is necessary for successfully reconfiguring the control system. This report investigates the usefulness of Prescribed Simultaneous Independent Surface Excitations (PreSISE) to provide data for rapidly obtaining estimates of the stability and control derivatives. Flight test data were analyzed using both equation-error and output-error PID techniques. The equation-error PID technique is known as Fourier Transform Regression (FTR) and is a frequency-domain real-time implementation. Selected results were compared with a time-domain output-error technique. The real-time equation-error technique combined with the PreSISE maneuvers provided excellent derivative estimation in the longitudinal axis. However, the PreSISE maneuvers as presently defined were not adequate for accurate estimation of the lateral-directional derivatives.

Enzyme inhibition studies by integrated Michaelis-Menten equation considering simultaneous presence of two inhibitors when one of them is a reaction product.

PubMed

Bezerra, Rui M F; Pinto, Paula A; Fraga, Irene; Dias, Albino A

2016-03-01

To determine initial velocities of enzyme catalyzed reactions without theoretical errors it is necessary to consider the use of the integrated Michaelis-Menten equation. When the reaction product is an inhibitor, this approach is particularly important. Nevertheless, kinetic studies usually involved the evaluation of other inhibitors beyond the reaction product. The occurrence of these situations emphasizes the importance of extending the integrated Michaelis-Menten equation, assuming the simultaneous presence of more than one inhibitor because reaction product is always present. This methodology is illustrated with the reaction catalyzed by alkaline phosphatase inhibited by phosphate (reaction product, inhibitor 1) and urea (inhibitor 2). The approach is explained in a step by step manner using an Excel spreadsheet (available as a template in Appendix). Curve fitting by nonlinear regression was performed with the Solver add-in (Microsoft Office Excel). Discrimination of the kinetic models was carried out based on Akaike information criterion. This work presents a methodology that can be used to develop an automated process, to discriminate in real time the inhibition type and kinetic constants as data (product vs. time) are achieved by the spectrophotometer. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.