The decay widths, the decay constants, and the branching fractions of a resonant state

NASA Astrophysics Data System (ADS)

de la Madrid, Rafael

2015-08-01

We introduce the differential and the total decay widths of a resonant (Gamow) state decaying into a continuum of stable states. When the resonance has several decay modes, we introduce the corresponding partial decay widths and branching fractions. In the approximation that the resonance is sharp, the expressions for the differential, partial and total decay widths of a resonant state bear a close resemblance with the Golden Rule. In such approximation, the branching fractions of a resonant state are the same as the standard branching fractions obtained by way of the Golden Rule. We also introduce dimensionless decay constants along with their associated differential decay constants, and we express experimentally measurable quantities such as the branching fractions and the energy distributions of decay events in terms of those dimensionless decay constants.

Topics in spectral methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1985-01-01

After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods. Appendix 2

NASA Technical Reports Server (NTRS)

Prudhomme, C.; Rovas, D. V.; Veroy, K.; Machiels, L.; Maday, Y.; Patera, A. T.; Turinici, G.; Zang, Thomas A., Jr. (Technical Monitor)

2002-01-01

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced basis approximations, Galerkin projection onto a space W(sub N) spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation, relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures, methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage, in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary.

PubMed

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary

PubMed Central

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations. PMID:27031232

Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Ding, Xiao-Li; Nieto, Juan J.

2017-11-01

In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

Approximations of Thermoelastic and Viscoelastic Control Systems

DTIC Science & Technology

1990-06-01

parabolic partial differential equations. The development of computational algorithms for designing controllers for such systems is an Immenselv complex...hereditary differential system on Rr , then approximate the "’historv" or -’memory- term (i.e.. the integral term in i.S)). In this paper we will use a... variation introduced by Fabiano and Ito ([FI]) of the averaging scheme considered by Banks and Burns ([BB]) for the second stage. The idea of the "’AVE

An Introduction to Computational Physics

NASA Astrophysics Data System (ADS)

Pang, Tao

2010-07-01

Preface to first edition; Preface; Acknowledgements; 1. Introduction; 2. Approximation of a function; 3. Numerical calculus; 4. Ordinary differential equations; 5. Numerical methods for matrices; 6. Spectral analysis; 7. Partial differential equations; 8. Molecular dynamics simulations; 9. Modeling continuous systems; 10. Monte Carlo simulations; 11. Genetic algorithm and programming; 12. Numerical renormalization; References; Index.

Sparse dynamics for partial differential equations

PubMed Central

Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D.; Osher, Stanley

2013-01-01

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms. PMID:23533273

Sparse dynamics for partial differential equations.

PubMed

Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D; Osher, Stanley

2013-04-23

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.

Online sequential Monte Carlo smoother for partially observed diffusion processes

NASA Astrophysics Data System (ADS)

Gloaguen, Pierre; Étienne, Marie-Pierre; Le Corff, Sylvain

2018-12-01

This paper introduces a new algorithm to approximate smoothed additive functionals of partially observed diffusion processes. This method relies on a new sequential Monte Carlo method which allows to compute such approximations online, i.e., as the observations are received, and with a computational complexity growing linearly with the number of Monte Carlo samples. The original algorithm cannot be used in the case of partially observed stochastic differential equations since the transition density of the latent data is usually unknown. We prove that it may be extended to partially observed continuous processes by replacing this unknown quantity by an unbiased estimator obtained for instance using general Poisson estimators. This estimator is proved to be consistent and its performance are illustrated using data from two models.

Time domain convergence properties of Lyapunov stable penalty methods

NASA Technical Reports Server (NTRS)

Kurdila, A. J.; Sunkel, John

1991-01-01

Linear hyperbolic partial differential equations are analyzed using standard techniques to show that a sequence of solutions generated by the Liapunov stable penalty equations approaches the solution of the differential-algebraic equations governing the dynamics of multibody problems arising in linear vibrations. The analysis does not require that the system be conservative and does not impose any specific integration scheme. Variational statements are derived which bound the error in approximation by the norm of the constraint violation obtained in the approximate solutions.

Introduction to Numerical Methods

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

Schoonover, Joseph A.

2016-06-14

These are slides for a lecture for the Parallel Computing Summer Research Internship at the National Security Education Center. This gives an introduction to numerical methods. Repetitive algorithms are used to obtain approximate solutions to mathematical problems, using sorting, searching, root finding, optimization, interpolation, extrapolation, least squares regresion, Eigenvalue problems, ordinary differential equations, and partial differential equations. Many equations are shown. Discretizations allow us to approximate solutions to mathematical models of physical systems using a repetitive algorithm and introduce errors that can lead to numerical instabilities if we are not careful.

Stable multi-domain spectral penalty methods for fractional partial differential equations

NASA Astrophysics Data System (ADS)

Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

Discovery and Optimization of Low-Storage Runge-Kutta Methods

DTIC Science & Technology

2015-06-01

NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS DISCOVERY AND OPTIMIZATION OF LOW-STORAGE RUNGE-KUTTA METHODS by Matthew T. Fletcher June 2015... methods are an important family of iterative methods for approximating the solutions of ordinary differential equations (ODEs) and differential...algebraic equations (DAEs). It is common to use an RK method to discretize in time when solving time dependent partial differential equations (PDEs) with a

An Introduction to Computational Physics - 2nd Edition

NASA Astrophysics Data System (ADS)

Pang, Tao

2006-01-01

Preface to first edition; Preface; Acknowledgements; 1. Introduction; 2. Approximation of a function; 3. Numerical calculus; 4. Ordinary differential equations; 5. Numerical methods for matrices; 6. Spectral analysis; 7. Partial differential equations; 8. Molecular dynamics simulations; 9. Modeling continuous systems; 10. Monte Carlo simulations; 11. Genetic algorithm and programming; 12. Numerical renormalization; References; Index.

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

An efficient nonlinear finite-difference approach in the computational modeling of the dynamics of a nonlinear diffusion-reaction equation in microbial ecology.

PubMed

Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E

2013-12-01

In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. Copyright © 2013 Elsevier Ltd. All rights reserved.

A Probabilistic-Numerical Approximation for an Obstacle Problem Arising in Game Theory

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

Gruen, Christine, E-mail: christine.gruen@univ-brest.fr

We investigate a two-player zero-sum stochastic differential game in which one of the players has more information on the game than his opponent. We show how to construct numerical schemes for the value function of this game, which is given by the solution of a quasilinear partial differential equation with obstacle.

PetIGA: A framework for high-performance isogeometric analysis

DOE PAGES

Dalcin, Lisandro; Collier, Nathaniel; Vignal, Philippe; ...

2016-05-25

We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with Non-Uniform Rational B-spline basis functions. We base our framework on PETSc, a high-performance library for the scalable solution of partial differential equations, which simplifies the development of large-scale scientific codes, provides a rich environment for prototyping, and separates parallelism from algorithm choice. We describe the implementation of PetIGA, and exemplify its use by solving a model nonlinear problem. To illustrate the robustness and flexibility ofmore » PetIGA, we solve some challenging nonlinear partial differential equations that include problems in both solid and fluid mechanics. Lastly, we show strong scaling results on up to 4096 cores, which confirm the suitability of PetIGA for large scale simulations.« less

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition. 2; Inclusion of Exchange

NASA Technical Reports Server (NTRS)

Shertzer, Janine; Temkin, Aaron

2004-01-01

The development of a practical method of accurately calculating the full scattering amplitude, without making a partial wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering e-H scattering in the static exchange approximation. The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial wave results.

Wavelets and distributed approximating functionals

NASA Astrophysics Data System (ADS)

Wei, G. W.; Kouri, D. J.; Hoffman, D. K.

1998-07-01

A general procedure is proposed for constructing father and mother wavelets that have excellent time-frequency localization and can be used to generate entire wavelet families for use as wavelet transforms. One interesting feature of our father wavelets (scaling functions) is that they belong to a class of generalized delta sequences, which we refer to as distributed approximating functionals (DAFs). We indicate this by the notation wavelet-DAFs. Correspondingly, the mother wavelets generated from these wavelet-DAFs are appropriately called DAF-wavelets. Wavelet-DAFs can be regarded as providing a pointwise (localized) spectral method, which furnishes a bridge between the traditional global methods and local methods for solving partial differential equations. They are shown to provide extremely accurate numerical solutions for a number of nonlinear partial differential equations, including the Korteweg-de Vries (KdV) equation, for which a previous method has encountered difficulties (J. Comput. Phys. 132 (1997) 233).

Asymptotic analysis of the local potential approximation to the Wetterich equation

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Sarkar, Sarben

2018-06-01

This paper reports a study of the nonlinear partial differential equation that arises in the local potential approximation to the Wetterich formulation of the functional renormalization group equation. A cut-off-dependent shift of the potential in this partial differential equation is performed. This shift allows a perturbative asymptotic treatment of the differential equation for large values of the infrared cut-off. To leading order in perturbation theory the differential equation becomes a heat equation, where the sign of the diffusion constant changes as the space-time dimension D passes through 2. When D  <  2, one obtains a forward heat equation whose initial-value problem is well-posed. However, for D  >  2 one obtains a backward heat equation whose initial-value problem is ill-posed. For the special case D  =  1 the asymptotic series for cubic and quartic models is extrapolated to the small infrared-cut-off limit by using Padé techniques. The effective potential thus obtained from the partial differential equation is then used in a Schrödinger-equation setting to study the stability of the ground state. For cubic potentials it is found that this Padé procedure distinguishes between a -symmetric theory and a conventional Hermitian theory (g real). For an theory the effective potential is nonsingular and has a stable ground state but for a conventional theory the effective potential is singular. For a conventional Hermitian theory and a -symmetric theory (g  >  0) the results are similar; the effective potentials in both cases are nonsingular and possess stable ground states.

A hybrid Pade-Galerkin technique for differential equations

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1993-01-01

A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters (delta(sub j)). These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated.

(N+1)-dimensional fractional reduced differential transform method for fractional order partial differential equations

NASA Astrophysics Data System (ADS)

Arshad, Muhammad; Lu, Dianchen; Wang, Jun

2017-07-01

In this paper, we pursue the general form of the fractional reduced differential transform method (DTM) to (N+1)-dimensional case, so that fractional order partial differential equations (PDEs) can be resolved effectively. The most distinct aspect of this method is that no prescribed assumptions are required, and the huge computational exertion is reduced and round-off errors are also evaded. We utilize the proposed scheme on some initial value problems and approximate numerical solutions of linear and nonlinear time fractional PDEs are obtained, which shows that the method is highly accurate and simple to apply. The proposed technique is thus an influential technique for solving the fractional PDEs and fractional order problems occurring in the field of engineering, physics etc. Numerical results are obtained for verification and demonstration purpose by using Mathematica software.

Simultaneous quaternion estimation (QUEST) and bias determination

NASA Technical Reports Server (NTRS)

Markley, F. Landis

1989-01-01

Tests of a new method for the simultaneous estimation of spacecraft attitude and sensor biases, based on a quaternion estimation algorithm minimizing Wahba's loss function are presented. The new method is compared with a conventional batch least-squares differential correction algorithm. The estimates are based on data from strapdown gyros and star trackers, simulated with varying levels of Gaussian noise for both inertially-fixed and Earth-pointing reference attitudes. Both algorithms solve for the spacecraft attitude and the gyro drift rate biases. They converge to the same estimates at the same rate for inertially-fixed attitude, but the new algorithm converges more slowly than the differential correction for Earth-pointing attitude. The slower convergence of the new method for non-zero attitude rates is believed to be due to the use of an inadequate approximation for a partial derivative matrix. The new method requires about twice the computational effort of the differential correction. Improving the approximation for the partial derivative matrix in the new method is expected to improve its convergence at the cost of increased computational effort.

A GENERAL MASS-CONSERVATIVE NUMERICAL SOLUTION FOR THE UNSATURATED FLOW EQUATION

EPA Science Inventory

Numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems. Numerical solution based on the standard h-based form of Richards equation generally yields poor results, ch...

On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions

NASA Astrophysics Data System (ADS)

Talib, Imran; Belgacem, Fethi Bin Muhammad; Asif, Naseer Ahmad; Khalil, Hammad

2017-01-01

In this research article, we derive and analyze an efficient spectral method based on the operational matrices of three dimensional orthogonal Jacobi polynomials to solve numerically the mixed partial derivatives type multi-terms high dimensions generalized class of fractional order partial differential equations. We transform the considered fractional order problem to an easily solvable algebraic equations with the aid of the operational matrices. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some test problems are considered to confirm the accuracy and validity of the proposed numerical method. The convergence of the method is ensured by comparing our Matlab software simulations based obtained results with the exact solutions in the literature, yielding negligible errors. Moreover, comparative results discussed in the literature are extended and improved in this study.

Numerical solution of differential equations by artificial neural networks

NASA Technical Reports Server (NTRS)

Meade, Andrew J., Jr.

1995-01-01

Conventionally programmed digital computers can process numbers with great speed and precision, but do not easily recognize patterns or imprecise or contradictory data. Instead of being programmed in the conventional sense, artificial neural networks (ANN's) are capable of self-learning through exposure to repeated examples. However, the training of an ANN can be a time consuming and unpredictable process. A general method is being developed by the author to mate the adaptability of the ANN with the speed and precision of the digital computer. This method has been successful in building feedforward networks that can approximate functions and their partial derivatives from examples in a single iteration. The general method also allows the formation of feedforward networks that can approximate the solution to nonlinear ordinary and partial differential equations to desired accuracy without the need of examples. It is believed that continued research will produce artificial neural networks that can be used with confidence in practical scientific computing and engineering applications.

Closed-form expressions for state-to-state charge-transfer differential cross sections in a modified Faddeev three-body approach

NASA Astrophysics Data System (ADS)

Adivi, E. Ghanbari; Brunger, M. J.; Bolorizadeh, M. A.; Campbell, L.

2007-02-01

The second-order Faddeev-Watson-Lovelace approximation in a modified form is applied to charge transfer from hydrogenlike target atoms by a fully stripped energetic projectile ion. The state-to-state, nlm→n'l'm' , partial transition amplitudes are calculated analytically. The method is specifically applied to the collision of protons with hydrogen atoms, where differential cross sections of different transitions are calculated for incident energies of 2.8 and 5.0MeV . It is shown that the Thomas peak is present in all transition cross sections. The partial cross sections are then summed and compared with the available forward-angle experimental data, showing good agreement.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

PubMed

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models

PubMed Central

Xing, W. W.; Triantafyllidis, V.

2017-01-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach. PMID:28484327

A note on the accuracy of spectral method applied to nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Wong, Peter S.

1994-01-01

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

Native low-density lipoprotein uptake by macrophage colony-stimulating factor-differentiated human macrophages is mediated by macropinocytosis and micropinocytosis.

PubMed

Anzinger, Joshua J; Chang, Janet; Xu, Qing; Buono, Chiara; Li, Yifu; Leyva, Francisco J; Park, Bum-Chan; Greene, Lois E; Kruth, Howard S

2010-10-01

To examine the pinocytotic pathways mediating native low-density lipoprotein (LDL) uptake by human macrophage colony-stimulating factor-differentiated macrophages (the predominant macrophage phenotype in human atherosclerotic plaques). We identified the kinase inhibitor SU6656 and the Rho GTPase inhibitor toxin B as inhibitors of macrophage fluid-phase pinocytosis of LDL. Assessment of macropinocytosis by time-lapse microscopy revealed that both drugs almost completely inhibited macropinocytosis, although LDL uptake and cholesterol accumulation by macrophages were only partially inhibited (approximately 40%) by these agents. Therefore, we investigated the role of micropinocytosis in mediating LDL uptake in macrophages and identified bafilomycin A1 as an additional partial inhibitor (approximately 40%) of macrophage LDL uptake that targeted micropinocytosis. When macrophages were incubated with both bafilomycin A1 and SU6656, inhibition of LDL uptake was additive (reaching 80%), showing that these inhibitors target different pathways. Microscopic analysis of fluid-phase uptake pathways in these macrophages confirmed that LDL uptake occurs through both macropinocytosis and micropinocytosis. Our findings show that human macrophage colony-stimulating factor-differentiated macrophages take up native LDL by macropinocytosis and micropinocytosis, underscoring the importance of both pathways in mediating LDL uptake by these cells.

Comparison of exact solution with Eikonal approximation for elastic heavy ion scattering

NASA Technical Reports Server (NTRS)

Dubey, Rajendra R.; Khandelwal, Govind S.; Cucinotta, Francis A.; Maung, Khin Maung

1995-01-01

A first-order optical potential is used to calculate the total and absorption cross sections for nucleus-nucleus scattering. The differential cross section is calculated by using a partial-wave expansion of the Lippmann-Schwinger equation in momentum space. The results are compared with solutions in the Eikonal approximation for the equivalent potential and with experimental data in the energy range from 25A to 1000A MeV.

On a partial differential equation method for determining the free energies and coexisting phase compositions of ternary mixtures from light scattering data.

PubMed

Ross, David S; Thurston, George M; Lutzer, Carl V

2008-08-14

In this paper we present a method for determining the free energies of ternary mixtures from light scattering data. We use an approximation that is appropriate for liquid mixtures, which we formulate as a second-order nonlinear partial differential equation. This partial differential equation (PDE) relates the Hessian of the intensive free energy to the efficiency of light scattering in the forward direction. This basic equation applies in regions of the phase diagram in which the mixtures are thermodynamically stable. In regions in which the mixtures are unstable or metastable, the appropriate PDE is the nonlinear equation for the convex hull. We formulate this equation along with continuity conditions for the transition between the two equations at cloud point loci. We show how to discretize this problem to obtain a finite-difference approximation to it, and we present an iterative method for solving the discretized problem. We present the results of calculations that were done with a computer program that implements our method. These calculations show that our method is capable of reconstructing test free energy functions from simulated light scattering data. If the cloud point loci are known, the method also finds the tie lines and tie triangles that describe thermodynamic equilibrium between two or among three liquid phases. A robust method for solving this PDE problem, such as the one presented here, can be a basis for optical, noninvasive means of characterizing the thermodynamics of multicomponent mixtures.

The large discretization step method for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Haras, Zigo; Taasan, Shlomo

1995-01-01

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

Analysis of spectral operators in one-dimensional domains

NASA Technical Reports Server (NTRS)

Maday, Y.

1985-01-01

Results are proven concerning certain projection operators on the space of all polynomials of degree less than or equal to N with respect to a class of one-dimensional weighted Sobolev spaces. The results are useful in the theory of the approximation of partial differential equations with spectral methods.

Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

NASA Technical Reports Server (NTRS)

Jameson, A.

1976-01-01

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations

NASA Astrophysics Data System (ADS)

Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei

2015-12-01

In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 ⁡ M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.

Learning partial differential equations via data discovery and sparse optimization

NASA Astrophysics Data System (ADS)

Schaeffer, Hayden

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Learning partial differential equations via data discovery and sparse optimization.

PubMed

Schaeffer, Hayden

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Learning partial differential equations via data discovery and sparse optimization

PubMed Central

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection. PMID:28265183

On conforming mixed finite element methods for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

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

1982-01-01

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

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Direct Calculation of the Scattering Amplitude Without Partial Wave Decomposition. III; Inclusion of Correlation Effects

NASA Technical Reports Server (NTRS)

Shertzer, Janine; Temkin, Aaron

2007-01-01

In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion of the article Popular summary of Direct calculation of the scattering amplitude without partial wave expansion. III ....." by J. Shertzer and A. Temkin. In this paper we continue the development of In this paper we continue the development of a new approach to the way in which researchers have traditionally used to calculate the scattering cross section of (low-energy) electrons from atoms. The basic mathematical problem is to solve the Schroedinger Equation (SE) corresponding the above physical process. Traditionally it was always the case that the SE was reduced to a sequence of one-dimensional (ordinary) differential equations - called partial waves which were solved and from the solutions "phase shifts" were extracted, from which the scattering cross section was calculated.

Numerical Algorithms Based on Biorthogonal Wavelets

NASA Technical Reports Server (NTRS)

Ponenti, Pj.; Liandrat, J.

1996-01-01

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.

On Chaotic Behavior of Temperature Distribution in a Heat Exchanger

NASA Astrophysics Data System (ADS)

Bagyalakshmi, Morachan; Gangadharan, Saisundarakrishnan; Ganesh, Madhu

The objective of this paper is to introduce the notion of fractional derivatives in the energy equations and to study the chaotic nature of the temperature distribution in a heat exchanger with variation of temperature dependent transport properties. The governing fractional partial differential equations are transformed to a set of recurrence relations using fractional differential transform method and solved using inverse transform. The approximate analytical solution obtained by the proposed method has good agreement with the existing results.

Partial differential equation techniques for analysing animal movement: A comparison of different methods.

PubMed

Wang, Yi-Shan; Potts, Jonathan R

2017-03-07

Recent advances in animal tracking have allowed us to uncover the drivers of movement in unprecedented detail. This has enabled modellers to construct ever more realistic models of animal movement, which aid in uncovering detailed patterns of space use in animal populations. Partial differential equations (PDEs) provide a popular tool for mathematically analysing such models. However, their construction often relies on simplifying assumptions which may greatly affect the model outcomes. Here, we analyse the effect of various PDE approximations on the analysis of some simple movement models, including a biased random walk, central-place foraging processes and movement in heterogeneous landscapes. Perhaps the most commonly-used PDE method dates back to a seminal paper of Patlak from 1953. However, our results show that this can be a very poor approximation in even quite simple models. On the other hand, more recent methods, based on transport equation formalisms, can provide more accurate results, as long as the kernel describing the animal's movement is sufficiently smooth. When the movement kernel is not smooth, we show that both the older and newer methods can lead to quantitatively misleading results. Our detailed analysis will aid future researchers in the appropriate choice of PDE approximation for analysing models of animal movement. Copyright © 2017 Elsevier Ltd. All rights reserved.

Analytic Regularity and Polynomial Approximation of Parametric and Stochastic Elliptic PDEs

DTIC Science & Technology

2010-05-31

Todor : Finite elements for elliptic problems with stochastic coefficients Comp. Meth. Appl. Mech. Engg. 194 (2005) 205-228. [14] R. Ghanem and P. Spanos...for elliptic partial differential equations with random input data SIAM J. Num. Anal. 46(2008), 2411–2442. [20] R. Todor , Robust eigenvalue computation...for smoothing operators, SIAM J. Num. Anal. 44(2006), 865– 878. [21] Ch. Schwab and R.A. Todor , Karhúnen-Loève Approximation of Random Fields by

A hybrid perturbation-Galerkin technique for partial differential equations

NASA Technical Reports Server (NTRS)

Geer, James F.; Anderson, Carl M.

1990-01-01

A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.

Towards information-optimal simulation of partial differential equations.

PubMed

Leike, Reimar H; Enßlin, Torsten A

2018-03-01

Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data providing information about a real physical field that is unknown. This information is sought to be conserved by the scheme as the field evolves in time. Such an information theoretic approach to simulation was pursued before by information field dynamics (IFD). In this paper we work out the theory of IFD for nonlinear PDEs in a noiseless Gaussian approximation. The result is an action that can be minimized to obtain an information-optimal simulation scheme. It can be brought into a closed form using field operators to calculate the appearing Gaussian integrals. The resulting simulation schemes are tested numerically in two instances for the Burgers equation. Their accuracy surpasses finite-difference schemes on the same resolution. The IFD scheme, however, has to be correctly informed on the subgrid correlation structure. In certain limiting cases we recover well-known simulation schemes like spectral Fourier-Galerkin methods. We discuss implications of the approximations made.

Differential cross sections for ionizations of H and H2 by 75 keV proton impact

NASA Astrophysics Data System (ADS)

Igarashi, A.; Gulyás, L.

2018-02-01

We have calculated total, partial and fully differential cross sections (FDCSs) for ionizations of H and H2 by 75 keV proton impact within the framework of the continuum-distorted-wave-eikonal-initial-state (CDW-EIS) approximation. Applying the single active electron model, the interaction between the projectile and the target ion is taken into account in the impact parameter picture. Extension of the CDW-EIS model to the molecular target is performed using the two-effective center approximation. The obtained results are compared with those of experimental and other theoretical data when available. The agreements between the theories and the experimental data are generally reasonable except for some cases of the FDCSs.

Similarity solution of the Boussinesq equation

NASA Astrophysics Data System (ADS)

Lockington, D. A.; Parlange, J.-Y.; Parlange, M. B.; Selker, J.

Similarity transforms of the Boussinesq equation in a semi-infinite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial differential equation to a boundary-value problem. Chen et al. [Trans Porous Media 1995;18:15-36] use a hodograph method to derive an integral equation formulation of the new differential equation which they solve by numerical iteration. In the present paper, the convergence of their scheme is improved such that numerical iteration can be avoided for all practical purposes. However, a simpler analytical approach is also presented which is based on Shampine's transformation of the boundary value problem to an initial value problem. This analytical approximation is remarkably simple and yet more accurate than the analytical hodograph approximations.

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.; Mozzhilkin, Vladimir V.

2006-05-01

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

Inclusion of exact exchange in the noniterative partial-differential-equation method of electron-molecule scattering - Application to e-N2

NASA Technical Reports Server (NTRS)

Weatherford, C. A.; Onda, K.; Temkin, A.

1985-01-01

The noniterative partial-differential-equation (PDE) approach to electron-molecule scattering of Onda and Temkin (1983) is modified to account for the effects of exchange explicitly. The exchange equation is reduced to a set of inhomogeneous equations containing no integral terms and solved noniteratively in a difference form; a method for propagating the solution to large values of r is described; the changes in the polarization potential of the original PDE method required by the inclusion of exact static exchange are indicated; and the results of computations for e-N2 scattering in the fixed-nuclei approximation are presented in tables and graphs and compared with previous calculations and experimental data. Better agreement is obtained using the modified PDE method.

A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems

NASA Technical Reports Server (NTRS)

Tzes, Anthony P.; Yurkovich, Stephen; Langer, F. Dieter

1989-01-01

An efficient numerical method for solving the partial differential equation (PDE) governing the flexible manipulator control dynamics is presented. A finite-dimensional model of the equation is obtained through discretization in both time and space coordinates by using finite-difference approximations to the PDE. An expert program written in the Macsyma symbolic language is utilized in order to embed the boundary conditions into the program, accounting for a mass carried at the tip of the manipulator. The advantages of the proposed algorithm are many, including the ability to (1) include any distributed actuation term in the partial differential equation, (2) provide distributed sensing of the beam displacement, (3) easily modify the boundary conditions through an expert program, and (4) modify the structure for running under a multiprocessor environment.

Hybrid theory and calculation of e-N2 scattering. [quantum mechanics - nuclei (nuclear physics)

NASA Technical Reports Server (NTRS)

Chandra, N.; Temkin, A.

1975-01-01

A theory of electron-molecule scattering was developed which was a synthesis of close coupling and adiabatic-nuclei theories. The theory is shown to be a close coupling theory with respect to vibrational degrees of freedom but is a adiabatic-nuclei theory with respect to rotation. It can be applied to any number of partial waves required, and the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations and not on experiment can be given as to which partial waves and energy domains require the various approximations. The theory allows all cross sections (i.e., pure rotational, vibrational, simultaneous vibration-rotation, differential and total) to be calculated. Explicit formulae for all the cross sections are presented.

Approximate solution of space and time fractional higher order phase field equation

NASA Astrophysics Data System (ADS)

Shamseldeen, S.

2018-03-01

This paper is concerned with a class of space and time fractional partial differential equation (STFDE) with Riesz derivative in space and Caputo in time. The proposed STFDE is considered as a generalization of a sixth-order partial phase field equation. We describe the application of the optimal homotopy analysis method (OHAM) to obtain an approximate solution for the suggested fractional initial value problem. An averaged-squared residual error function is defined and used to determine the optimal convergence control parameter. Two numerical examples are studied, considering periodic and non-periodic initial conditions, to justify the efficiency and the accuracy of the adopted iterative approach. The dependence of the solution on the order of the fractional derivative in space and time and model parameters is investigated.

Electron-pair-production cross section in the tip region of the positron spectrum

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

Sud, K.K.; Sharma, D.K.

1984-11-01

The radial integrals for electron-pair production in a point Coulomb potential have been expressed by Sud, Sharma, and Sud in terms of the matrix generalization of the GAMMA function. Two new partial differential equations in photon energy satisfied by the matrix GAMMA function are obtained. We have obtained, on integrating the partial differential equations, accurate radial integrals as a function of photon energy for the pair production by intermediate-energy photons. The cross section in the tip region of the spectrum are calculated for photons of energy 5.0 to 10.0 MeV for /sup 92/U. The new technique results in extensive savingmore » in computer time as the basic radial integrals in terms of the hypergeometric function F/sub 2/ are computed at one photon energy for each pair of partial waves. The results of our calculations are compared with plane-wave Born-approximation results and with the calculations of Dugne and of Deck, Moroi, and Alling.« less

A problem in non-linear Diophantine approximation

NASA Astrophysics Data System (ADS)

Harrap, Stephen; Hussain, Mumtaz; Kristensen, Simon

2018-05-01

In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution.

Calculation of total electron excitation cross-sections and partial electron ionization cross-sections for the elements. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Green, T. J.

1973-01-01

Computer programs were used to calculate the total electron excitation cross-section for atoms and the partial ionization cross-section. The approximations to the scattering amplitude used are as follows: (1) Born, Bethe, and Modified Bethe for non-exchange excitation; (2) Ochkur for exchange excitation; and (3) Coulomb-Born of non-exchange ionization. The amplitudes are related to the differential cross-sections which are integrated to give the total excitation (or partial ionization) cross-section for the collision. The atomic wave functions used are Hartree-Fock-Slater functions for bound states and the coulomb wave function for the continuum. The programs are presented and the results are examined.

A Measure Approximation for Distributionally Robust PDE-Constrained Optimization Problems

DOE PAGES

Kouri, Drew Philip

2017-12-19

In numerous applications, scientists and engineers acquire varied forms of data that partially characterize the inputs to an underlying physical system. This data is then used to inform decisions such as controls and designs. Consequently, it is critical that the resulting control or design is robust to the inherent uncertainties associated with the unknown probabilistic characterization of the model inputs. Here in this work, we consider optimal control and design problems constrained by partial differential equations with uncertain inputs. We do not assume a known probabilistic model for the inputs, but rather we formulate the problem as a distributionally robustmore » optimization problem where the outer minimization problem determines the control or design, while the inner maximization problem determines the worst-case probability measure that matches desired characteristics of the data. We analyze the inner maximization problem in the space of measures and introduce a novel measure approximation technique, based on the approximation of continuous functions, to discretize the unknown probability measure. Finally, we prove consistency of our approximated min-max problem and conclude with numerical results.« less

Locating the Discontinuities of a Bounded Function by the Partial Sums of its Fourier Series I: Periodical Case

NASA Technical Reports Server (NTRS)

Kvernadze, George; Hagstrom,Thomas; Shapiro, Henry

1997-01-01

A key step for some methods dealing with the reconstruction of a function with jump discontinuities is the accurate approximation of the jumps and their locations. Various methods have been suggested in the literature to obtain this valuable information. In the present paper, we develop an algorithm based on identities which determine the jumps of a 2(pi)-periodic bounded not-too-highly oscillating function by the partial sums of its differentiated Fourier series. The algorithm enables one to approximate the locations of discontinuities and the magnitudes of jumps of a bounded function. We study the accuracy of approximation and establish asymptotic expansions for the approximations of a 27(pi)-periodic piecewise smooth function with one discontinuity. By an appropriate linear combination, obtained via derivatives of different order, we significantly improve the accuracy. Next, we use Richardson's extrapolation method to enhance the accuracy even more. For a function with multiple discontinuities we establish simple formulae which "eliminate" all discontinuities of the function but one. Then we treat the function as if it had one singularity following the method described above.

Group invariant solution for a pre-existing fracture driven by a power-law fluid in impermeable rock

NASA Astrophysics Data System (ADS)

Fareo, A. G.; Mason, D. P.

2013-12-01

The effect of power-law rheology on hydraulic fracturing is investigated. The evolution of a two-dimensional fracture with non-zero initial length and driven by a power-law fluid is analyzed. Only fluid injection into the fracture is considered. The surrounding rock mass is impermeable. With the aid of lubrication theory and the PKN approximation a partial differential equation for the fracture half-width is derived. Using a linear combination of the Lie-point symmetry generators of the partial differential equation, the group invariant solution is obtained and the problem is reduced to a boundary value problem for an ordinary differential equation. Exact analytical solutions are derived for hydraulic fractures with constant volume and with constant propagation speed. The asymptotic solution near the fracture tip is found. The numerical solution for general working conditions is obtained by transforming the boundary value problem to a pair of initial value problems. Throughout the paper, hydraulic fracturing with shear thinning, Newtonian and shear thickening fluids are compared.

Pure quasi-P-wave calculation in transversely isotropic media using a hybrid method

NASA Astrophysics Data System (ADS)

Wu, Zedong; Liu, Hongwei; Alkhalifah, Tariq

2018-07-01

The acoustic approximation for anisotropic media is widely used in current industry imaging and inversion algorithms mainly because Pwaves constitute the majority of the energy recorded in seismic exploration. The resulting acoustic formulae tend to be simpler, resulting in more efficient implementations, and depend on fewer medium parameters. However, conventional solutions of the acoustic wave equation with higher-order derivatives suffer from shear wave artefacts. Thus, we derive a new acoustic wave equation for wave propagation in transversely isotropic (TI) media, which is based on a partially separable approximation of the dispersion relation for TI media and free of shear wave artefacts. Even though our resulting equation is not a partial differential equation, it is still a linear equation. Thus, we propose to implement this equation efficiently by combining the finite difference approximation with spectral evaluation of the space-independent parts. The resulting algorithm provides solutions without the constraint ɛ ≥ δ. Numerical tests demonstrate the effectiveness of the approach.

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

Extended Krylov subspaces approximations of matrix functions. Application to computational electromagnetics

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

Druskin, V.; Lee, Ping; Knizhnerman, L.

There is now a growing interest in the area of using Krylov subspace approximations to compute the actions of matrix functions. The main application of this approach is the solution of ODE systems, obtained after discretization of partial differential equations by method of lines. In the event that the cost of computing the matrix inverse is relatively inexpensive, it is sometimes attractive to solve the ODE using the extended Krylov subspaces, originated by actions of both positive and negative matrix powers. Examples of such problems can be found frequently in computational electromagnetics.

Generalized vector calculus on convex domain

NASA Astrophysics Data System (ADS)

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

DOE PAGES

Jakeman, J. D.; Wildey, T.

2015-01-01

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity. We show that utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this papermore » we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.« less

Dynamics of curved fronts in systems with power-law memory

NASA Astrophysics Data System (ADS)

Abu Hamed, M.; Nepomnyashchy, A. A.

2016-08-01

The dynamics of a curved front in a plane between two stable phases with equal potentials is modeled via two-dimensional fractional in time partial differential equation. A closed equation governing a slow motion of a small-curvature front is derived and applied for two typical examples of the potential function. Approximate axisymmetric and non-axisymmetric solutions are obtained.

Extending generalized Kubelka-Munk to three-dimensional radiative transfer.

PubMed

Sandoval, Christopher; Kim, Arnold D

2015-08-10

The generalized Kubelka-Munk (gKM) approximation is a linear transformation of the double spherical harmonics of order one (DP₁) approximation of the radiative transfer equation. Here, we extend the gKM approximation to study problems in three-dimensional radiative transfer. In particular, we derive the gKM approximation for the problem of collimated beam propagation and scattering in a plane-parallel slab composed of a uniform absorbing and scattering medium. The result is an 8×8 system of partial differential equations that is much easier to solve than the radiative transfer equation. We compare the solutions of the gKM approximation with Monte Carlo simulations of the radiative transfer equation to identify the range of validity for this approximation. We find that the gKM approximation is accurate for isotropic scattering media that are sufficiently thick and much less accurate for anisotropic, forward-peaked scattering media.

Effect of phase and orbital wave parameter choices on CS and IOS degeneracy averaged differential cross sections

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

Khare, V.; Fitz, D.E.; Kouri, D.J.

1980-09-15

The effect of phase choice and partial wave parameter choice on CS and IOS inelastic degeneracy averaged differential cross sections is studied. An approximate simplified CS scattering amplitude for l-bar=1/2(l'+l) is derived and is shown to have a form which closely resembles the McGuire--Kouri scattering amplitude for odd ..delta..j transitions and reduces to it for even ..delta..j transitions. The choice of phase in the CS wave function is shown to result in different approximations which yield significantly different shapes for the degeneracy averaged differential cross section. Time reversal symmetry arguments are employed to select the proper phase choice. IOS calculationsmore » of the degeneracy averaged differential cross sections of He--CO, He--Cl and Ne--HD using l-bar=1/2(l+l') and the phase choice which ensures proper time reversal symmetry are found to correct the phase disagreement which was previously noted for odd ..delta..j transitions using l-bar=l or l' and either the time reversal phase or other phase choices.« less

Rapid differentiation among bacteria that cause gastroenteritis by use of low-resolution Raman spectroscopy and PLS discriminant analysis.

PubMed

Mello, Cesar; Ribeiro, Diórginis; Novaes, Fábio; Poppi, Ronei J

2005-10-01

Use of classical microbiological methods to differentiate bacteria that cause gastroenteritis is cumbersome but usually very efficient. The high cost of reagents and the time required for such identifications, approximately four days, could have serious consequences, however, mainly when the patients are children, the elderly, or adults with low resistance. The search for new methods enabling rapid and reagentless differentiation of these microorganisms is, therefore, extremely relevant. In this work the main microorganisms responsible for gastroenteritis, Escherichia coli, Salmonella choleraesuis, and Shigella flexneri, were studied. For each microorganism sixty different dispersions were prepared in physiological solution. The Raman spectra of these dispersions were recorded using a diode laser operating in the near infrared region. Partial least-squares (PLS) discriminant analysis was used to differentiate among the bacteria by use of their respective Raman spectra. This approach enabled correct classification of 100% of the bacteria evaluated and unknown samples from the clinical environment, in less time ( approximately 10 h), by use of a low-cost, portable Raman spectrometer, which can be easily used in intensive care units and clinical environments.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II: Inclusion of Exchange

NASA Technical Reports Server (NTRS)

Shertzer, Janine; Temkin, A.

2003-01-01

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE), which can be reduced to a 2d partial differential equation (pde), was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation, which is reducible to a pair of coupled pde's. The resultant scattering amplitudes, both singlet and triplet, calculated as a function of energy are in excellent agreement with converged partial wave results.

Quadrature imposition of compatibility conditions in Chebyshev methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Streett, C. L.

1990-01-01

Often, in solving an elliptic equation with Neumann boundary conditions, a compatibility condition has to be imposed for well-posedness. This condition involves integrals of the forcing function. When pseudospectral Chebyshev methods are used to discretize the partial differential equation, these integrals have to be approximated by an appropriate quadrature formula. The Gauss-Chebyshev (or any variant of it, like the Gauss-Lobatto) formula can not be used here since the integrals under consideration do not include the weight function. A natural candidate to be used in approximating the integrals is the Clenshaw-Curtis formula, however it is shown that this is the wrong choice and it may lead to divergence if time dependent methods are used to march the solution to steady state. The correct quadrature formula is developed for these problems. This formula takes into account the degree of the polynomials involved. It is shown that this formula leads to a well conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

Robustness of Quadratic Hedging Strategies in Finance via Backward Stochastic Differential Equations with Jumps

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

Di Nunno, Giulia, E-mail: giulian@math.uio.no; Khedher, Asma, E-mail: asma.khedher@tum.de; Vanmaele, Michèle, E-mail: michele.vanmaele@ugent.be

We consider a backward stochastic differential equation with jumps (BSDEJ) which is driven by a Brownian motion and a Poisson random measure. We present two candidate-approximations to this BSDEJ and we prove that the solution of each candidate-approximation converges to the solution of the original BSDEJ in a space which we specify. We use this result to investigate in further detail the consequences of the choice of the model to (partial) hedging in incomplete markets in finance. As an application, we consider models in which the small variations in the price dynamics are modeled with a Poisson random measure withmore » infinite activity and models in which these small variations are modeled with a Brownian motion or are cut off. Using the convergence results on BSDEJs, we show that quadratic hedging strategies are robust towards the approximation of the market prices and we derive an estimation of the model risk.« less

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

NASA Technical Reports Server (NTRS)

Tseng, K.

1984-01-01

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

Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations

DOE PAGES

Zhang, Yang; Chong, Edwin K. P.; Hannig, Jan; ...

2013-01-01

We inmore » troduce a continuum modeling method to approximate a class of large wireless networks by nonlinear partial differential equations (PDEs). This method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N , the number of nodes in the network. As N goes to infinity, the sequence converges to a continuum limit, which is the solution of a certain nonlinear PDE. We first describe PDE models for networks with uniformly located nodes and then generalize to networks with nonuniformly located, and possibly mobile, nodes. Based on the PDE models, we develop a method to control the transmissions in nonuniform networks so that the continuum limit is invariant under perturbations in node locations. This enables the networks to maintain stable global characteristics in the presence of varying node locations.« less

A sensitivity equation approach to shape optimization in fluid flows

NASA Technical Reports Server (NTRS)

Borggaard, Jeff; Burns, John

1994-01-01

A sensitivity equation method to shape optimization problems is applied. An algorithm is developed and tested on a problem of designing optimal forebody simulators for a 2D, inviscid supersonic flow. The algorithm uses a BFGS/Trust Region optimization scheme with sensitivities computed by numerically approximating the linear partial differential equations that determine the flow sensitivities. Numerical examples are presented to illustrate the method.

A Numerical Study on Microwave Coagulation Therapy

DTIC Science & Technology

2013-01-01

hepatocellular carcinoma (small size liver tumor). Through extensive numerical simulations, we reveal the mathematical relationships between some critical parameters in the therapy, including input power, frequency, temperature, and regions of impact. It is shown that these relationships can be approximated using simple polynomial functions. Compared to solutions of partial differential equations, these functions are significantly easier to compute and simpler to analyze for engineering design and clinical

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

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

Jakeman, J.D., E-mail: jdjakem@sandia.gov; Wildey, T.

2015-01-01

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchicalmore » surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.« less

The Convergence Problems of Eigenfunction Expansions of Elliptic Differential Operators

NASA Astrophysics Data System (ADS)

Ahmedov, Anvarjon

2018-03-01

In the present research we investigate the problems concerning the almost everywhere convergence of multiple Fourier series summed over the elliptic levels in the classes of Liouville. The sufficient conditions for the almost everywhere convergence problems, which are most difficult problems in Harmonic analysis, are obtained. The methods of approximation by multiple Fourier series summed over elliptic curves are applied to obtain suitable estimations for the maximal operator of the spectral decompositions. Obtaining of such estimations involves very complicated calculations which depends on the functional structure of the classes of functions. The main idea on the proving the almost everywhere convergence of the eigenfunction expansions in the interpolation spaces is estimation of the maximal operator of the partial sums in the boundary classes and application of the interpolation Theorem of the family of linear operators. In the present work the maximal operator of the elliptic partial sums are estimated in the interpolation classes of Liouville and the almost everywhere convergence of the multiple Fourier series by elliptic summation methods are established. The considering multiple Fourier series as an eigenfunction expansions of the differential operators helps to translate the functional properties (for example smoothness) of the Liouville classes into Fourier coefficients of the functions which being expanded into such expansions. The sufficient conditions for convergence of the multiple Fourier series of functions from Liouville classes are obtained in terms of the smoothness and dimensions. Such results are highly effective in solving the boundary problems with periodic boundary conditions occurring in the spectral theory of differential operators. The investigations of multiple Fourier series in modern methods of harmonic analysis incorporates the wide use of methods from functional analysis, mathematical physics, modern operator theory and spectral decomposition. New method for the best approximation of the square-integrable function by multiple Fourier series summed over the elliptic levels are established. Using the best approximation, the Lebesgue constant corresponding to the elliptic partial sums is estimated. The latter is applied to obtain an estimation for the maximal operator in the classes of Liouville.

Development of programmable artificial neural networks

NASA Technical Reports Server (NTRS)

Meade, Andrew J.

1993-01-01

Conventionally programmed digital computers can process numbers with great speed and precision, but do not easily recognize patterns or imprecise or contradictory data. Instead of being programmed in the conventional sense, artificial neural networks are capable of self-learning through exposure to repeated examples. However, the training of an ANN can be a time consuming and unpredictable process. A general method is being developed to mate the adaptability of the ANN with the speed and precision of the digital computer. This method was successful in building feedforward networks that can approximate functions and their partial derivatives from examples in a single iteration. The general method also allows the formation of feedforward networks that can approximate the solution to nonlinear ordinary and partial differential equations to desired accuracy without the need of examples. It is believed that continued research will produce artificial neural networks that can be used with confidence in practical scientific computing and engineering applications.

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: An eigenvalue analysis

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1986-01-01

A hyperbolic initial-boundary-value problem can be approximated by a system of ordinary differential equations (ODEs) by replacing the spatial derivatives by finite-difference approximations. The resulting system of ODEs is called a semidiscrete approximation. A complication is the fact that more boundary conditions are required for the spatially discrete approximation than are specified for the partial differential equation. Consequently, additional numerical boundary conditions are required and improper treatment of these additional conditions can lead to instability. For a linear initial-boundary-value problem (IBVP) with homogeneous analytical boundary conditions, the semidiscrete approximation results in a system of ODEs of the form du/dt = Au whose solution can be written as u(t) = exp(At)u(O). Lax-Richtmyer stability requires that the matrix norm of exp(At) be uniformly bounded for O less than or = t less than or = T independent of the spatial mesh size. Although the classical Lax-Richtmyer stability definition involves a conventional vector norm, there is no known algebraic test for the uniform boundedness of the matrix norm of exp(At) for hyperbolic IBVPs. An alternative but more complicated stability definition is used in the theory developed by Gustafsson, Kreiss, and Sundstrom (GKS). The two methods are compared.

Continuation of probability density functions using a generalized Lyapunov approach

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

Baars, S., E-mail: s.baars@rug.nl; Viebahn, J.P., E-mail: viebahn@cwi.nl; Mulder, T.E., E-mail: t.e.mulder@uu.nl

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.

One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

NASA Astrophysics Data System (ADS)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

Comparative investigation of five nanoparticles in flow of viscous fluid with Joule heating and slip due to rotating disk

NASA Astrophysics Data System (ADS)

Qayyum, Sumaira; Khan, Muhammad Ijaz; Hayat, Tasawar; Alsaedi, Ahmed

2018-04-01

Present article addresses the comparative study for flow of five water based nanofluids. Flow in presence of Joule heating is generated by rotating disk with variable thickness. Nanofluids are suspension of Silver (Ag), Copper (Cu), Copper oxide (CuO), Aluminum oxide or Alumina (Al2O3), Titanium oxide or titania (TiO2) and water. Boundary layer approximation is applied to partial differential equations. Using Von Karman transformations the partial differential equations are converted to ordinary differential equations. Convergent series solutions are obtained. Graphical results are presented to examine the behaviors of axial, radial and tangential velocities, temperature, skin friction and Nusselt number. It is observed that radial, axial and tangential velocities decay for slip parameters. Axial velocity decays for larger nanoparticle volume fraction. Effect of nanofluids on velocities dominant than base material. Temperature rises for larger Eckert number and temperature of silver water nanofluid is more because of its higher thermal conductivity. Surface drag force reduces for higher slip parameters. Transfer of heat is more for larger disk thickness index.

Stable isotope ratios of carbon and nitrogen and mercury concentrations in 13 toothed whale species taken from the western Pacific Ocean off Japan.

PubMed

Endo, Tetsuya; Hisamichi, Yohsuke; Kimura, Osamu; Haraguchi, Koichi; Lavery, Shane; Dalebout, Merel L; Funahashi, Naoko; Baker, C Scott

2010-04-01

Stable isotope ratios of carbon (partial differential(13)C) and nitrogen (partial differential(15)N) and total mercury (T-Hg) concentrations were measured in red meat samples from 11 odontocete species (toothed whales, dolphins, and porpoises) sold in Japan (n = 96) and in muscle samples from stranded killer whales (n = 6) and melon-headed whales (n = 15), and the analytical data for these species were classified into three regions (northern, central, and southern Japan) depending on the locations in which they were caught or stranded. The partial differential(15)N in the samples from southern Japan tended to be lower than that in samples from the north, whereas both partial differential(13)C and T-Hg concentrations in samples from the south tended to higher than those in samples from northern Japan. Negative correlations were found between the partial differential(13)C and partial differential(15)N values and between the partial differential(15)N value and T-Hg concentrations in the combined samples all three regions (gamma= -0.238, n = 117, P < 0.01). The partial differential(13)C, partial differential(15)N, and T-Hg concentrations in the samples varied more by habitat than by species. Spatial variations in partial differential(13)C, partial differential(15)N, and T-Hg concentrations in the ocean may be the cause of these phenomena.

Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models

NASA Astrophysics Data System (ADS)

Luther, K.; Haitjema, H. M.

2000-04-01

We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.

A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Zaky, M. A.

2015-01-01

In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.

An approximation theory for the identification of nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Approximation methods for inverse problems involving the vibration of beams with tip bodies

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

Two cubic spline based approximation schemes for the estimation of structural parameters associated with the transverse vibration of flexible beams with tip appendages are outlined. The identification problem is formulated as a least squares fit to data subject to the system dynamics which are given by a hybrid system of coupled ordinary and partial differential equations. The first approximation scheme is based upon an abstract semigroup formulation of the state equation while a weak/variational form is the basis for the second. Cubic spline based subspaces together with a Rayleigh-Ritz-Galerkin approach were used to construct sequences of easily solved finite dimensional approximating identification problems. Convergence results are briefly discussed and a numerical example demonstrating the feasibility of the schemes and exhibiting their relative performance for purposes of comparison is provided.

Predatory Dinosaurs from the Sahara and Late Cretaceous Faunal Differentiation

PubMed

Sereno; Dutheil; Iarochene; Larsson; Lyon; Magwene; Sidor; Varricchio; Wilson

1996-05-17

Late Cretaceous (Cenomanian) fossils discovered in the Kem Kem region of Morocco include large predatory dinosaurs that inhabited Africa as it drifted into geographic isolation. One, represented by a skull approximately 1.6 meters in length, is an advanced allosauroid referable to the African genus Carcharodontosaurus. Another, represented by a partial skeleton with slender proportions, is a new basal coelurosaur closely resembling the Egyptian genus Bahariasaurus. Comparisons with Cretaceous theropods from other continents reveal a previously unrecognized global radiation of carcharodontosaurid predators. Substantial geographic differentiation of dinosaurian faunas in response to continental drift appears to have arisen abruptly at the beginning of the Late Cretaceous.

Thermodynamic aspect in using modified Boltzmann model as an acoustic probe for URu2Si2

NASA Astrophysics Data System (ADS)

Kwang-Hua, Chu Rainer

2018-05-01

The approximate system of equations describing ultrasonic attenuation propagating in many electrons of the heavy-fermion materials URu2Si2 under high magnetic fields were firstly derived and then calculated based on the modified Boltzmann model considering the microscopic contributions due to electronic fluids. A system of nonlinear partial differential coupled with integral equations were linearized firstly and approximately solved considering the perturbed thermodynamic equilibrium states. Our numerical data were compared with previous measurements using non-dimensional or normalized physical values. The rather good fit of our numerical calculations with experimental measurements confirms our present approach.

Regularization of moving boundaries in a laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results.

PubMed

Meulenbroek, Bernard; Ebert, Ute; Schäfer, Lothar

2005-11-04

The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial differential equation governing small perturbations of these solutions. For some parameter value, this equation can be solved analytically, which shows rigorously that the uniformly propagating solution is linearly convectively stable and that the asymptotic relaxation is universal and exponential in time.

Constructing analytic solutions on the Tricomi equation

NASA Astrophysics Data System (ADS)

Ghiasi, Emran Khoshrouye; Saleh, Reza

2018-04-01

In this paper, homotopy analysis method (HAM) and variational iteration method (VIM) are utilized to derive the approximate solutions of the Tricomi equation. Afterwards, the HAM is optimized to accelerate the convergence of the series solution by minimizing its square residual error at any order of the approximation. It is found that effect of the optimal values of auxiliary parameter on the convergence of the series solution is not negligible. Furthermore, the present results are found to agree well with those obtained through a closed-form equation available in the literature. To conclude, it is seen that the two are effective to achieve the solution of the partial differential equations.

Parametric instability analysis of truncated conical shells using the Haar wavelet method

NASA Astrophysics Data System (ADS)

Dai, Qiyi; Cao, Qingjie

2018-05-01

In this paper, the Haar wavelet method is employed to analyze the parametric instability of truncated conical shells under static and time dependent periodic axial loads. The present work is based on the Love first-approximation theory for classical thin shells. The displacement field is expressed as the Haar wavelet series in the axial direction and trigonometric functions in the circumferential direction. Then the partial differential equations are reduced into a system of coupled Mathieu-type ordinary differential equations describing dynamic instability behavior of the shell. Using Bolotin's method, the first-order and second-order approximations of principal instability regions are determined. The correctness of present method is examined by comparing the results with those in the literature and very good agreement is observed. The difference between the first-order and second-order approximations of principal instability regions for tensile and compressive loads is also investigated. Finally, numerical results are presented to bring out the influences of various parameters like static load factors, boundary conditions and shell geometrical characteristics on the domains of parametric instability of conical shells.

Asymptotic problems for stochastic partial differential equations

NASA Astrophysics Data System (ADS)

Salins, Michael

Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.

Identification and feedback control in structures with piezoceramic actuators

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.; Wang, Y.

1992-01-01

In this lecture we give fundamental well-posedness results for a variational formulation of a class of damped second order partial differential equations with unbounded input or control coefficients. Included as special cases in this class are structures with piezoceramic actuators. We consider approximation techniques leading to computational methods in the context of both parameter estimation and feedback control problems for these systems. Rigorous convergence results for parameter estimates and feedback gains are discussed.

An algorithm for solving the perturbed gas dynamic equations

NASA Technical Reports Server (NTRS)

Davis, Sanford

1993-01-01

The present application of a compact, higher-order central-difference approximation to the linearized Euler equations illustrates the multimodal character of these equations by means of computations for acoustic, vortical, and entropy waves. Such dissipationless central-difference methods are shown to propagate waves exhibiting excellent phase and amplitude resolution on the basis of relatively large time-steps; they can be applied to wave problems governed by systems of first-order partial differential equations.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II

NASA Technical Reports Server (NTRS)

Shertzer, J.; Temkin, A.

2003-01-01

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE) can be reduced to a 2d partial differential equation (pde), and was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation. The resultant equation can be reduced to a pair of coupled pde's, to which the finite element method can still be applied. The resultant scattering amplitudes, both singlet and triplet, as a function of angle can be calculated for various energies. The results are in excellent agreement with converged partial wave results.

Creating Weather System Ensembles Through Synergistic Process Modeling and Machine Learning

NASA Astrophysics Data System (ADS)

Chen, B.; Posselt, D. J.; Nguyen, H.; Wu, L.; Su, H.; Braverman, A. J.

2017-12-01

Earth's weather and climate are sensitive to a variety of control factors (e.g., initial state, forcing functions, etc). Characterizing the response of the atmosphere to a change in initial conditions or model forcing is critical for weather forecasting (ensemble prediction) and climate change assessment. Input - response relationships can be quantified by generating an ensemble of multiple (100s to 1000s) realistic realizations of weather and climate states. Atmospheric numerical models generate simulated data through discretized numerical approximation of the partial differential equations (PDEs) governing the underlying physics. However, the computational expense of running high resolution atmospheric state models makes generation of more than a few simulations infeasible. Here, we discuss an experiment wherein we approximate the numerical PDE solver within the Weather Research and Forecasting (WRF) Model using neural networks trained on a subset of model run outputs. Once trained, these neural nets can produce large number of realization of weather states from a small number of deterministic simulations with speeds that are orders of magnitude faster than the underlying PDE solver. Our neural network architecture is inspired by the governing partial differential equations. These equations are location-invariant, and consist of first and second derivations. As such, we use a 3x3 lon-lat grid of atmospheric profiles as the predictor in the neural net to provide the network the information necessary to compute the first and second moments. Results indicate that the neural network algorithm can approximate the PDE outputs with high degree of accuracy (less than 1% error), and that this error increases as a function of the prediction time lag.

CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.

CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

Numerical simulation of rarefied gas flow through a slit

NASA Technical Reports Server (NTRS)

Keith, Theo G., Jr.; Jeng, Duen-Ren; De Witt, Kenneth J.; Chung, Chan-Hong

1990-01-01

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.

FDDO and DSMC analyses of rarefied gas flow through 2D nozzles

NASA Technical Reports Server (NTRS)

Chung, Chan-Hong; De Witt, Kenneth J.; Jeng, Duen-Ren; Penko, Paul F.

1992-01-01

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas expanding through a two-dimensional nozzle and into a surrounding low-density environment. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, the variable hard sphere model is used as a molecular model and the no time counter method is employed as a collision sampling technique. The results of both the FDDO and the DSMC methods show good agreement. The FDDO method requires less computational effort than the DSMC method by factors of 10 to 40 in CPU time, depending on the degree of rarefaction.

Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

DOE PAGES

Moral, Pierre Del; Jasra, Ajay; Law, Kody J. H.; ...

2017-08-24

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the discrete approximation error must be balanced. A multilevel strategy is utilized to substantially reduce the cost to obtain a given error level in the approximation as compared to standard estimators. Two estimators are considered and relative variance bounds are given. The theoretical results are numerically illustrated for two Bayesian inverse problems arising from elliptic partial differential equations (PDEs). The examples involve the inversion of observations of themore » solution of (i) a 1-dimensional Poisson equation to infer the diffusion coefficient, and (ii) a 2-dimensional Poisson equation to infer the external forcing.« less

A multi-domain spectral method for time-fractional differential equations

NASA Astrophysics Data System (ADS)

Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

2015-07-01

This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations

NASA Astrophysics Data System (ADS)

Doha, E. H.

2002-02-01

An analytical formula expressing the ultraspherical coefficients of an expansion for an infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function is stated in a more compact form and proved in a simpler way than the formula suggested by Phillips and Karageorghis (27 (1990) 823). A new formula expressing explicitly the integrals of ultraspherical polynomials of any degree that has been integrated an arbitrary number of times of ultraspherical polynomials is given. The tensor product of ultraspherical polynomials is used to approximate a function of more than one variable. Formulae expressing the coefficients of differentiated expansions of double and triple ultraspherical polynomials in terms of the original expansion are stated and proved. Some applications of how to use ultraspherical polynomials for solving ordinary and partial differential equations are described.

Complex symmetric matrices with strongly stable iterates

NASA Technical Reports Server (NTRS)

Tadmor, E.

1985-01-01

Complex-valued symmetric matrices are studied. A simple expression for the spectral norm of such matrices is obtained, by utilizing a unitarily congruent invariant form. A sharp criterion is provided for identifying those symmetric matrices whose spectral norm is not exceeding one: such strongly stable matrices are usually sought in connection with convergent difference approximations to partial differential equations. As an example, the derived criterion is applied to conclude the strong stability of a Lax-Wendroff scheme.

A computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution, theory and users manual

NASA Technical Reports Server (NTRS)

Ball, R. E.

1972-01-01

A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.

Teaching Modeling with Partial Differential Equations: Several Successful Approaches

ERIC Educational Resources Information Center

Myers, Joseph; Trubatch, David; Winkel, Brian

2008-01-01

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

On the zero-Rossby limit for the primitive equations of the atmosphere*

NASA Astrophysics Data System (ADS)

Chen, Gui-Qiang; Zhang, Ping

2001-09-01

The zero-Rossby limit for the primitive equations governing atmospheric motions is analysed. The limit is important in geophysics for large-scale models (cf Lions 1996 Int. Conf. IAM 95 (Hamburg 1995) (Math. Res. vol 87) (Berlin: Akademie) pp 177-212) and is in the level of the zero relaxation limit for nonlinear partial differential equations (cf Chen et al 1994 Commun. Pure Appl. Math. 47 787-830). It is proved that, if the initial data appropriately approximate data of geostrophic type, the corresponding solutions of the simplified primitive equations approximate the solutions of the quasigeostrophic equations with order ɛ accuracy as the Rossby number ɛ goes to zero.

Radiation Transport Around Axisymmetric Blunt Body Vehicles Using a Modified Differential Approximation

NASA Technical Reports Server (NTRS)

Hartung, Lin C.; Hassan, H. A.

1992-01-01

A moment method for computing 3-D radiative transport is applied to axisymmetric flows in thermochemical nonequilibrium. Such flows are representative of proposed aerobrake missions. The method uses the P-1 approximation to reduce the governing system of integro-di erential equations to a coupled set of partial di erential equations. A numerical solution method for these equations given actual variations of the radiation properties in thermochemical nonequilibrium blunt body flows is developed. Initial results from the method are shown and compared to tangent slab calculations. The agreement between the transport methods is found to be about 10 percent in the stagnation region, with the difference increasing along the flank of the vehicle.

Rotationally and vibrationally inelastic scattering in the rotational IOS approximation. Ultrasimple calculation of total (differential, integral, and transport) cross sections for nonspherical molecules

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

Parker, G.A.; Pack, R.T

1978-02-15

A simple, direct derivation of the rotational infinite order sudden (IOS) approximation in molecular scattering theory is given. Connections between simple scattering amplitude formulas, choice of average partial wave parameter, and magnetic transitions are reviewed. Simple procedures for calculating cross sections for specific transitions are discussed and many older model formulas are given clear derivations. Total (summed over rotation) differential, integral, and transport cross sections, useful in the analysis of many experiments involving nonspherical molecules, are shown to be exceedingly simple: They are just averages over the potential angle of cross sections calculated using simple structureless spherical particle formulas andmore » programs. In the case of vibrationally inelastic scattering, the IOSA, without further approximation, provides a well-defined way to get fully three dimensional cross sections from calculations no more difficult than collinear calculations. Integral, differential, viscosity, and diffusion cross sections for He-CO/sub 2/ obtained from the IOSA and a realistic intermolecular potential are calculated as an example and compared with experiment. Agreement is good for the complete potential but poor when only its spherical part is used, so that one should never attempt to treat this system with a spherical model. The simplicity and accuracy of the IOSA make it a viable method for routine analysis of experiments involving collisions of nonspherical molecules.« less

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

PubMed

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

PubMed Central

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems. PMID:25811858

Large Deviations for Nonlocal Stochastic Neural Fields

PubMed Central

2014-01-01

We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers’ law for neural fields poses substantial difficulties, but that one may transfer techniques from stochastic partial differential equations to establish a large deviation principle (LDP). Then we demonstrate that an efficient finite-dimensional approximation of the stochastic neural field equation can be achieved using a Galerkin method and that the resulting finite-dimensional rate function for the LDP can have a multiscale structure in certain cases. These results form the starting point for an efficient practical computation of the LDP. Our approach also provides the technical basis for further rigorous study of noise-induced transitions in neural fields based on Galerkin approximations. Mathematics Subject Classification (2000): 60F10, 60H15, 65M60, 92C20. PMID:24742297

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

Manzini, Gianmarco

This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the numerical discretization of Partial Differential Equations (PDEs) and, in particular, the Finite Element Method (FEM). This document is not an introduction to the FEM, for which many textbooks (also free on the internet) are available. Eventually, this document is intended to evolve into a tutorial introduction to the VEM (but this is really a long-term goal).

Three-dimensional elastic stress and displacement analysis of finite circular geometry solids containing cracks

NASA Technical Reports Server (NTRS)

Gyekenyesi, J. P.; Mendelson, A.; Kring, J.

1973-01-01

A seminumerical method is presented for solving a set of coupled partial differential equations subject to mixed and coupled boundary conditions. The use of this method is illustrated by obtaining solutions for two circular geometry and mixed boundary value problems in three-dimensional elasticity. Stress and displacement distributions are calculated in an axisymmetric, circular bar of finite dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.

An analytic, approximate method for modeling steady, three-dimensional flow to partially penetrating wells

NASA Astrophysics Data System (ADS)

Bakker, Mark

2001-05-01

An analytic, approximate solution is derived for the modeling of three-dimensional flow to partially penetrating wells. The solution is written in terms of a correction on the solution for a fully penetrating well and is obtained by dividing the aquifer up, locally, in a number of aquifer layers. The resulting system of differential equations is solved by application of the theory for multiaquifer flow. The presented approach has three major benefits. First, the solution may be applied to any groundwater model that can simulate flow to a fully penetrating well; the solution may be superimposed onto the solution for the fully penetrating well to simulate the local three-dimensional drawdown and flow field. Second, the approach is applicable to isotropic, anisotropic, and stratified aquifers and to both confined and unconfined flow. Third, the solution extends over a small area around the well only; outside this area the three-dimensional effect of the partially penetrating well is negligible, and no correction to the fully penetrating well is needed. A number of comparisons are made to existing three-dimensional, analytic solutions, including radial confined and unconfined flow and a well in a uniform flow field. It is shown that a subdivision in three layers is accurate for many practical cases; very accurate solutions are obtained with more layers.

The convergence of the order sequence and the solution function sequence on fractional partial differential equation

NASA Astrophysics Data System (ADS)

Rusyaman, E.; Parmikanti, K.; Chaerani, D.; Asefan; Irianingsih, I.

2018-03-01

One of the application of fractional ordinary differential equation is related to the viscoelasticity, i.e., a correlation between the viscosity of fluids and the elasticity of solids. If the solution function develops into function with two or more variables, then its differential equation must be changed into fractional partial differential equation. As the preliminary study for two variables viscoelasticity problem, this paper discusses about convergence analysis of function sequence which is the solution of the homogenous fractional partial differential equation. The method used to solve the problem is Homotopy Analysis Method. The results show that if given two real number sequences (αn) and (βn) which converge to α and β respectively, then the solution function sequences of fractional partial differential equation with order (αn, βn) will also converge to the solution function of fractional partial differential equation with order (α, β).

Coronary heart disease mortality among Seventh-Day Adventists with differing dietary habits: a preliminary report.

PubMed

Phillips, R L; Lemon, F R; Beeson, W L; Kuzma, J W

1978-10-01

Seventh-Day Adventists (SDAs) are a conservative religious denomination who abstain from tobacco and alcohol; approximately one-half follow a lacto-ovo-vegetarian diet. In this 6-year prospective study of 24,044 California SDAs age 35 and over, coronary heart disease (CHD) mortality rates for ages 35 to 64 and 65+ are 28% and 50% respectively, of the rates for the same age groups of the total California population. This reduced risk of CHD mortality among SDAs is partially due to abstinence from smoking; however, at least half the low risk among SDAs is likely attributable to other characteristics of the SDA lifestyle. The risk of fatal CHD among nonvegetarian SDA males, ages 35 to 64, is three times greater than vegetarian SDA males of comparable age (P less than 0.01), suggesting that the SDA diet may account for a large share of their low risk. This differential was much smaller for older SDA males and SDA females. Although the differential in risk of fatal CHD for male nonvegetarians versus vegetarians may be partially accounted for by other CHD risk factors, which are more frequent among nonvegetarians, a significant differential persists after adjustment for each of six other CHD risk factors.

A differential equation for the Generalized Born radii.

PubMed

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2013-06-28

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

Almost periodic solutions to difference equations

NASA Technical Reports Server (NTRS)

Bayliss, A.

1975-01-01

The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1991-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

An analysis of turbulent diffusion flame in axisymmetric jet

NASA Technical Reports Server (NTRS)

Chung, P. M.; Im, K. H.

1980-01-01

The kinetic theory of turbulent flow was employed to study the mixing limited combustion of hydrogen in axisymmetric jets. The integro-differential equations in two spatial and three velocity coordinates describing the combustion were reduced to a set of hyperbolic partial differential equations in the two spatial coordinates by a binodal approximation. The MacCormick's finite difference method was then employed for solution. The flame length was longer than that predicted by the flame-sheet analysis, and was found to be in general agreement with a recent experimental result. Increase of the turbulence energy and scale resulted in an enhancement of the combustion rate and, hence, in a shorter flame length. Details of the numerical method as well as of the physical findings are discussed.

A numerical algorithm for optimal feedback gains in high dimensional LQR problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1986-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented.

A new mathematical solution for predicting char activation reactions

USGS Publications Warehouse

Rafsanjani, H.H.; Jamshidi, E.; Rostam-Abadi, M.

2002-01-01

The differential conservation equations that describe typical gas-solid reactions, such as activation of coal chars, yield a set of coupled second-order partial differential equations. The solution of these coupled equations by exact analytical methods is impossible. In addition, an approximate or exact solution only provides predictions for either reaction- or diffusion-controlling cases. A new mathematical solution, the quantize method (QM), was applied to predict the gasification rates of coal char when both chemical reaction and diffusion through the porous char are present. Carbon conversion rates predicted by the QM were in closer agreement with the experimental data than those predicted by the random pore model and the simple particle model. ?? 2002 Elsevier Science Ltd. All rights reserved.

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

PubMed

Einkemmer, Lukas; Ostermann, Alexander

2014-07-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.

An almost symmetric Strang splitting scheme for nonlinear evolution equations☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2014-01-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation. PMID:25844017

A moving mesh finite difference method for equilibrium radiation diffusion equations

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

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

State-of-charge estimation in lithium-ion batteries: A particle filter approach

NASA Astrophysics Data System (ADS)

Tulsyan, Aditya; Tsai, Yiting; Gopaluni, R. Bhushan; Braatz, Richard D.

2016-11-01

The dynamics of lithium-ion batteries are complex and are often approximated by models consisting of partial differential equations (PDEs) relating the internal ionic concentrations and potentials. The Pseudo two-dimensional model (P2D) is one model that performs sufficiently accurately under various operating conditions and battery chemistries. Despite its widespread use for prediction, this model is too complex for standard estimation and control applications. This article presents an original algorithm for state-of-charge estimation using the P2D model. Partial differential equations are discretized using implicit stable algorithms and reformulated into a nonlinear state-space model. This discrete, high-dimensional model (consisting of tens to hundreds of states) contains implicit, nonlinear algebraic equations. The uncertainty in the model is characterized by additive Gaussian noise. By exploiting the special structure of the pseudo two-dimensional model, a novel particle filter algorithm that sweeps in time and spatial coordinates independently is developed. This algorithm circumvents the degeneracy problems associated with high-dimensional state estimation and avoids the repetitive solution of implicit equations by defining a 'tether' particle. The approach is illustrated through extensive simulations.

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

NASA Technical Reports Server (NTRS)

Reddy C. J.

1998-01-01

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

Dual-shaped offset reflector antenna designs from solutions of the geometrical optics first-order partial differential equations

NASA Technical Reports Server (NTRS)

Galindo-Israel, V.; Imbriale, W.; Shogen, K.; Mittra, R.

1990-01-01

In obtaining solutions to the first-order nonlinear partial differential equations (PDEs) for synthesizing offset dual-shaped reflectors, it is found that previously observed computational problems can be avoided if the integration of the PDEs is started from an inner projected perimeter and integrated outward rather than starting from an outer projected perimeter and integrating inward. This procedure, however, introduces a new parameter, the main reflector inner perimeter radius p(o), when given a subreflector inner angle 0(o). Furthermore, a desired outer projected perimeter (e.g., a circle) is no longer guaranteed. Stability of the integration is maintained if some of the initial parameters are determined first from an approximate solution to the PDEs. A one-, two-, or three-parameter optimization algorithm can then be used to obtain a best set of parameters yielding a close fit to the desired projected outer rim. Good low cross-polarization mapping functions are also obtained. These methods are illustrated by synthesis of a high-gain offset-shaped Cassegrainian antenna and a low-noise offset-shaped Gregorian antenna.

Krylov subspace methods - Theory, algorithms, and applications

NASA Technical Reports Server (NTRS)

Sad, Youcef

1990-01-01

Projection methods based on Krylov subspaces for solving various types of scientific problems are reviewed. The main idea of this class of methods when applied to a linear system Ax = b, is to generate in some manner an approximate solution to the original problem from the so-called Krylov subspace span. Thus, the original problem of size N is approximated by one of dimension m, typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now becoming popular for solving nonlinear equations. The main ideas in Krylov subspace methods are shown and their use in solving linear systems, eigenvalue problems, parabolic partial differential equations, Liapunov matrix equations, and nonlinear system of equations are discussed.

Computational methods for the identification of spatially varying stiffness and damping in beams

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rosen, I. G.

1986-01-01

A numerical approximation scheme for the estimation of functional parameters in Euler-Bernoulli models for the transverse vibration of flexible beams with tip bodies is developed. The method permits the identification of spatially varying flexural stiffness and Voigt-Kelvin viscoelastic damping coefficients which appear in the hybrid system of ordinary and partial differential equations and boundary conditions describing the dynamics of such structures. An inverse problem is formulated as a least squares fit to data subject to constraints in the form of a vector system of abstract first order evolution equations. Spline-based finite element approximations are used to finite dimensionalize the problem. Theoretical convergence results are given and numerical studies carried out on both conventional (serial) and vector computers are discussed.

Optimized effective potential in real time: Problems and prospects in time-dependent density-functional theory

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

Mundt, Michael; Kuemmel, Stephan

2006-08-15

The integral equation for the time-dependent optimized effective potential (TDOEP) in time-dependent density-functional theory is transformed into a set of partial-differential equations. These equations only involve occupied Kohn-Sham orbitals and orbital shifts resulting from the difference between the exchange-correlation potential and the orbital-dependent potential. Due to the success of an analog scheme in the static case, a scheme that propagates orbitals and orbital shifts in real time is a natural candidate for an exact solution of the TDOEP equation. We investigate the numerical stability of such a scheme. An approximation beyond the Krieger-Li-Iafrate approximation for the time-dependent exchange-correlation potential ismore » analyzed.« less

Linear approximations of nonlinear systems

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Su, R.

1983-01-01

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

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.

Probabilistic density function method for nonlinear dynamical systems driven by colored noise

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

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

2016-05-01

We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integro-differential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified Large-Eddy-Diffusivity-type closure. Additionally, we introduce the generalized local linearization (LL) approximation for deriving a computable PDF equation in the form of the second-order partial differential equation (PDE). We demonstrate the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary auto-correlation time.more » We apply the proposed PDF method to the analysis of a set of Kramers equations driven by exponentially auto-correlated Gaussian colored noise to study the dynamics and stability of a power grid.« less

A Galerkin method for the estimation of parameters in hybrid systems governing the vibration of flexible beams with tip bodies

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rosen, I. G.

1985-01-01

An approximation scheme is developed for the identification of hybrid systems describing the transverse vibrations of flexible beams with attached tip bodies. In particular, problems involving the estimation of functional parameters are considered. The identification problem is formulated as a least squares fit to data subject to the coupled system of partial and ordinary differential equations describing the transverse displacement of the beam and the motion of the tip bodies respectively. A cubic spline-based Galerkin method applied to the state equations in weak form and the discretization of the admissible parameter space yield a sequence of approximating finite dimensional identification problems. It is shown that each of the approximating problems admits a solution and that from the resulting sequence of optimal solutions a convergent subsequence can be extracted, the limit of which is a solution to the original identification problem. The approximating identification problems can be solved using standard techniques and readily available software.

Fast viscosity solutions for shape from shading under a more realistic imaging model

NASA Astrophysics Data System (ADS)

Wang, Guohui; Han, Jiuqiang; Jia, Honghai; Zhang, Xinman

2009-11-01

Shape from shading (SFS) has been a classical and important problem in the domain of computer vision. The goal of SFS is to reconstruct the 3-D shape of an object from its 2-D intensity image. To this end, an image irradiance equation describing the relation between the shape of a surface and its corresponding brightness variations is used. Then it is derived as an explicit partial differential equation (PDE). Using the nonlinear programming principle, we propose a detailed solution to Prados and Faugeras's implicit scheme for approximating the viscosity solution of the resulting PDE. Furthermore, by combining implicit and semi-implicit schemes, a new approximation scheme is presented. In order to accelerate the convergence speed, we adopt the Gauss-Seidel idea and alternating sweeping strategy to the approximation schemes. Experimental results on both synthetic and real images are performed to demonstrate that the proposed methods are fast and accurate.

A Bifurcation Problem for a Nonlinear Partial Differential Equation of Parabolic Type,

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, INTEGRATION), (*PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS), BANACH SPACE , MAPPING (TRANSFORMATIONS), SET THEORY, TOPOLOGY, ITERATIONS, STABILITY, THEOREMS

Differential Geometry Applied To Least-Square Error Surface Approximations

NASA Astrophysics Data System (ADS)

Bolle, Ruud M.; Sabbah, Daniel

1987-08-01

This paper focuses on extraction of the parameters of individual surfaces from noisy depth maps. The basis for this are least-square error polynomial approximations to the range data and the curvature properties that can be computed from these approximations. The curvature properties are derived using the invariants of the Weingarten Map evaluated at the origin of local coordinate systems centered at the range points. The Weingarten Map is a well-known concept in differential geometry; a brief treatment of the differential geometry pertinent to surface curvature is given. We use the curvature properties for extracting certain surface parameters from the curvature properties of the approximations. Then we show that curvature properties alone are not enough to obtain all the parameters of the surfaces; higher order properties (information about change of curvature) are needed to obtain full parametric descriptions. This surface parameter estimation problem arises in the design of a vision system to recognize 3D objects whose surfaces are composed of planar patches and patches of quadrics of revolution. (Quadrics of revolution are quadrics that are surfaces of revolution.) A significant portion of man-made objects can be modeled using these surfaces. The actual process of recognition and parameter extraction is framed as a set of stacked parameter space transforms. The transforms are "stacked" in the sense that any one transform computes only a partial geometric description that forms the input to the next transform. Those who are interested in the organization and control of the recognition and parameter recognition process are referred to [Sabbah86], this paper briefly touches upon the organization, but concentrates mainly on geometrical aspects of the parameter extraction.

Flow in linearly sheared two-dimensional foams: From bubble to bulk scale.

PubMed

Katgert, Gijs; Latka, Andrzej; Möbius, Matthias E; van Hecke, Martin

2009-06-01

We probe the flow of two-dimensional (2D) foams, consisting of a monolayer of bubbles sandwiched between a liquid bath and glass plate, as a function of driving rate, packing fraction, and degree of disorder. First, we find that bidisperse, disordered foams exhibit strongly rate-dependent and inhomogeneous (shear-banded) velocity profiles, while monodisperse ordered foams are also shear banded but essentially rate independent. Second, we adapt a simple model [E. Janiaud, D. Weaire, and S. Hutzler, Phys. Rev. Lett. 97, 038302 (2006)] based on balancing the averaged drag forces between the bubbles and the top plate F[over ]_{bw} and the averaged bubble-bubble drag forces F[over ]_{bb} by assuming that F[over ]_{bw} approximately v;{2/3} and F[over ]_{bb} approximately ( partial differential_{y}v);{beta} , where v and ( partial differential_{y}v) denote average bubble velocities and gradients. This model captures the observed rate-dependent flows for beta approximately 0.36 , and the rate independent flows for beta approximately 0.67 . Third, we perform independent rheological measurements of F[over ]_{bw} and F[over ]_{bb} , both for ordered and disordered systems, and find these to be fully consistent with the forms assumed in the simple model. Disorder thus leads to a modified effective exponent beta . Fourth, we vary the packing fraction phi of the foam over a substantial range and find that the flow profiles become increasingly shear banded when the foam is made wetter. Surprisingly, the model describes flow profiles and rate dependence over the whole range of packing fractions with the same power-law exponents-only a dimensionless number k that measures the ratio of the prefactors of the viscous drag laws is seen to vary with packing fraction. We find that k approximately (phi-phi_{c});{-1} , where phi_{c} approximately 0.84 corresponds to the 2D jamming density, and suggest that this scaling follows from the geometry of the deformed facets between bubbles in contact. Overall, our work shows that the presence of disorder qualitatively changes the effective bubble-bubble drag forces and suggests a route to rationalize aspects of the ubiquitous Herschel-Bulkley (power-law) rheology observed in a wide range of disordered materials.

An Approach for the Adaptive Solution of Optimization Problems Governed by Partial Differential Equations with Uncertain Coefficients

DTIC Science & Technology

2012-05-01

Acad. Sci. Fennicae. Ser. A. I. Math.-Phys., 1947(37):79, 1947. [65] G. E. Karniadakis, C.-H. Su, D. Xiu, D. Lucor, C. Schwab, and R. A. Todor ...treatment of uncertainties in aerodynamic design. AIAA Journal, 47(3):646–654, 2009. [106] C. Schwab and R. A. Todor . Karhunen-Loève approximation of random...integrals. Prentice-Hall Inc., Englewood Cliffs, N.J., 1971. Prentice-Hall Series in Automatic Computation. [113] R. A. Todor and C. Schwab

On the hierarchy of partially invariant submodels of differential equations

NASA Astrophysics Data System (ADS)

Golovin, Sergey V.

2008-07-01

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

Solution of differential equations by application of transformation groups

NASA Technical Reports Server (NTRS)

Driskell, C. N., Jr.; Gallaher, L. J.; Martin, R. H., Jr.

1968-01-01

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

For numerical differentiation, dimensionality can be a blessing!

NASA Astrophysics Data System (ADS)

Anderssen, Robert S.; Hegland, Markus

Finite difference methods, such as the mid-point rule, have been applied successfully to the numerical solution of ordinary and partial differential equations. If such formulas are applied to observational data, in order to determine derivatives, the results can be disastrous. The reason for this is that measurement errors, and even rounding errors in computer approximations, are strongly amplified in the differentiation process, especially if small step-sizes are chosen and higher derivatives are required. A number of authors have examined the use of various forms of averaging which allows the stable computation of low order derivatives from observational data. The size of the averaging set acts like a regularization parameter and has to be chosen as a function of the grid size h. In this paper, it is initially shown how first (and higher) order single-variate numerical differentiation of higher dimensional observational data can be stabilized with a reduced loss of accuracy than occurs for the corresponding differentiation of one-dimensional data. The result is then extended to the multivariate differentiation of higher dimensional data. The nature of the trade-off between convergence and stability is explicitly characterized, and the complexity of various implementations is examined.

An efficient method for solving the steady Euler equations

NASA Technical Reports Server (NTRS)

Liou, M.-S.

1986-01-01

An efficient numerical procedure for solving a set of nonlinear partial differential equations, the steady Euler equations, using Newton's linearization procedure is presented. A theorem indicating quadratic convergence for the case of differential equations is demonstrated. A condition for the domain of quadratic convergence Omega(2) is obtained which indicates that whether an approximation lies in Omega(2) depends on the rate of change and the smoothness of the flow vectors, and hence is problem-dependent. The choice of spatial differencing, of particular importance for the present method, is discussed. The treatment of boundary conditions is addressed, and the system of equations resulting from the foregoing analysis is summarized and solution strategies are discussed. The convergence of calculated solutions is demonstrated by comparing them with exact solutions to one and two-dimensional problems.

Generalized self-similar unsteady gas flows behind the strong shock wave front

NASA Astrophysics Data System (ADS)

Bogatko, V. I.; Potekhina, E. A.

2018-05-01

Two-dimensional (plane and axially symmetric) nonstationary gas flows behind the front of a strong shock wave are considered. All the gas parameters are functions of the ratio of Cartesian coordinates to some degree of time tn, where n is a self-similarity index. The problem is solved in Lagrangian variables. It is shown that the resulting system of partial differential equations is suitable for constructing an iterative process. ¢he "thin shock layer" method is used to construct an approximate analytical solution of the problem. The limit solution of the problem is constructed. A formula for determining the path traversed by a gas particle in the shock layer along the front of a shock wave is obtained. A system of equations for determining the first approximation corrections is constructed.

Damageable contact between an elastic body and a rigid foundation

NASA Astrophysics Data System (ADS)

Campo, M.; Fernández, J. R.; Silva, A.

2009-02-01

In this work, the contact problem between an elastic body and a rigid obstacle is studied, including the development of material damage which results from internal compression or tension. The variational problem is formulated as a first-kind variational inequality for the displacements coupled with a parabolic partial differential equation for the damage field. The existence of a unique local weak solution is stated. Then, a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, three two-dimensional numerical simulations are performed to demonstrate the accuracy and the behaviour of the scheme.

Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

NASA Astrophysics Data System (ADS)

Collier, N.; Knepley, M.

2015-12-01

The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

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

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

Reciprocal links among differential parenting, perceived partiality, and self-worth: a three-wave longitudinal study.

PubMed

Shebloski, Barbara; Conger, Katherine J; Widaman, Keith F

2005-12-01

This study examined reciprocal links between parental differential treatment, siblings' perception of partiality, and self-worth with 3 waves of data from 384 adolescent sibling dyads. Results suggest that birth-order status was significantly associated with self-worth and perception of maternal and paternal differential treatment. There was a consistent across-time effect of self-worth on perception of parental partiality for later born siblings, but not earlier born siblings, and a consistent effect of differential treatment on perception of partiality for earlier born but not later born siblings. The results contribute new insight into the associations between perception of differential parenting and adolescents' adjustment and the role of birth order. Copyright 2006 APA, all rights reserved).

Decoupling of the Leading Order DGLAP Evolution Equation with Spin Dependent Structure Functions

NASA Astrophysics Data System (ADS)

Azadbakht, F. Teimoury; Boroun, G. R.

2018-02-01

We propose an analytical solution for DGLAP evolution equations with polarized splitting functions at the Leading Order (LO) approximation based on the Laplace transform method. It is shown that the DGLAP evolution equations can be decoupled completely into two second order differential equations which then are solved analytically by using the initial conditions δ FS(x,Q2)=F[partial δ FS0(x), δ FS0(x)] and {δ G}(x,Q2)=G[partial δ G0(x), δ G0(x)]. We used this method to obtain the polarized structure function of the proton as well as the polarized gluon distribution function inside the proton and compared the numerical results with experimental data of COMPASS, HERMES, and AAC'08 Collaborations. It was found that there is a good agreement between our predictions and the experiments.

On the solution of the complex eikonal equation in acoustic VTI media: A perturbation plus optimization scheme

NASA Astrophysics Data System (ADS)

Huang, Xingguo; Sun, Jianguo; Greenhalgh, Stewart

2018-04-01

We present methods for obtaining numerical and analytic solutions of the complex eikonal equation in inhomogeneous acoustic VTI media (transversely isotropic media with a vertical symmetry axis). The key and novel point of the method for obtaining numerical solutions is to transform the problem of solving the highly nonlinear acoustic VTI eikonal equation into one of solving the relatively simple eikonal equation for the background (isotropic) medium and a system of linear partial differential equations. Specifically, to obtain the real and imaginary parts of the complex traveltime in inhomogeneous acoustic VTI media, we generalize a perturbation theory, which was developed earlier for solving the conventional real eikonal equation in inhomogeneous anisotropic media, to the complex eikonal equation in such media. After the perturbation analysis, we obtain two types of equations. One is the complex eikonal equation for the background medium and the other is a system of linearized partial differential equations for the coefficients of the corresponding complex traveltime formulas. To solve the complex eikonal equation for the background medium, we employ an optimization scheme that we developed for solving the complex eikonal equation in isotropic media. Then, to solve the system of linearized partial differential equations for the coefficients of the complex traveltime formulas, we use the finite difference method based on the fast marching strategy. Furthermore, by applying the complex source point method and the paraxial approximation, we develop the analytic solutions of the complex eikonal equation in acoustic VTI media, both for the isotropic and elliptical anisotropic background medium. Our numerical results demonstrate the effectiveness of our derivations and illustrate the influence of the beam widths and the anisotropic parameters on the complex traveltimes.

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.

A new approach to treat discontinuities in multi-layered soils

NASA Astrophysics Data System (ADS)

Berardi, Marco; Difonzo, Fabio; Caputo, Maria; Vurro, Michele; Lopez, Luciano

2017-04-01

The water infiltration into two (or more) layered soils can give rise to preferential flow paths at the interface between different soils. The deep understanding of this phenomenon can be of great interest in modeling different environmental problems in geosciences and hydrology. Flow through layered soils arises naturally in agriculture, and layered soils are also engineered as cover liners for landfills. In particular, the treatment of the soil discontinuity is of great interest from the modeling and the numerical point of view, and is still an open problem.% (see, for example, te{Matthews_et_al,Zha_vzj_2013,DeLuca_Cepeda_ASCE_2016}). Assuming to approximate the soils with different porous media, the governing equation for this phenomenon is Richards' equation, in the following form: {eq:different_Richards_1} C_1(ψ) partial ψ/partial t = partial /partial z [ K_1(ψ) ( partial ψ/partial z - 1 ) ], \\quad if \\quad z < \\overline{z}, C_2(ψ) partial ψ/partial t = partial /partial z [ K_2(ψ) ( partial ψ/partial z - 1 ) ], \\quad if \\quad z > \\overline{z}, where \\overline{z} is the spatial threshold that identifies the change in soil structure, and C1 C_2, K_1, K_2, the hydraulic functions that describe the upper and the lower soil, respectively. The ψ-based form is used, in this work. Here we have used the Filippov's theory in order to deal with discontinuous differential systems, and we handled opportunely the numerical discretization in order to treat the abovementioned system by means of this theory, letting the discontinuity depend on the state variable. The advantage of this technique is a better insight on the solution behavior on the discontinuity surface, and the no-need to average the hydraulic conductivity field on the threshold itself, as in the existing literature.

Maximum value of the pulse energy of a passively Q-switched laser as a function of the pump power.

PubMed

Li, Jianlang; Ueda, Ken-ichi; Dong, Jun; Musha, Mitsuru; Shirakawa, Akira

2006-07-20

The finite recovery time Ts of the bleached absorber is presented as one of the possible mechanisms accounting for the increase-maximum-decrease in pulse energy E with the pumping rate Wp in cw-pumped passively Q-switched solid-state lasers, by analytically evaluating the sign of the derivative partial differentialE/ partial differentialWP. The results show that, in the low pump regime (T>Ts, T is the interpulse period), the initial population density ni remains constant, the final population density nf decreases with Wp, and this results in a monotonic increase of E with Wp. In the high pump regime (T

Partially Coherent Scattering in Stellar Chromospheres. Part 4; Analytic Wing Approximations

NASA Technical Reports Server (NTRS)

Gayley, K. G.

1993-01-01

Simple analytic expressions are derived to understand resonance-line wings in stellar chromospheres and similar astrophysical plasmas. The results are approximate, but compare well with accurate numerical simulations. The redistribution is modeled using an extension of the partially coherent scattering approximation (PCS) which we term the comoving-frame partially coherent scattering approximation (CPCS). The distinction is made here because Doppler diffusion is included in the coherent/noncoherent decomposition, in a form slightly improved from the earlier papers in this series.

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

Spatial complexity of solutions of higher order partial differential equations

NASA Astrophysics Data System (ADS)

Kukavica, Igor

2004-03-01

We address spatial oscillation properties of solutions of higher order parabolic partial differential equations. In the case of the Kuramoto-Sivashinsky equation ut + uxxxx + uxx + u ux = 0, we prove that for solutions u on the global attractor, the quantity card {x epsi [0, L]:u(x, t) = lgr}, where L > 0 is the spatial period, can be bounded by a polynomial function of L for all \\lambda\\in{\\Bbb R} . A similar property is proven for a general higher order partial differential equation u_t+(-1)^{s}\\partial_x^{2s}u+ \\sum_{k=0}^{2s-1}v_k(x,t)\\partial_x^k u =0 .

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

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

Thompson, S.

This report describes the use of several subroutines from the CORLIB core mathematical subroutine library for the solution of a model fluid flow problem. The model consists of the Euler partial differential equations. The equations are spatially discretized using the method of pseudo-characteristics. The resulting system of ordinary differential equations is then integrated using the method of lines. The stiff ordinary differential equation solver LSODE (2) from CORLIB is used to perform the time integration. The non-stiff solver ODE (4) is used to perform a related integration. The linear equation solver subroutines DECOMP and SOLVE are used to solve linearmore » systems whose solutions are required in the calculation of the time derivatives. The monotone cubic spline interpolation subroutines PCHIM and PCHFE are used to approximate water properties. The report describes the use of each of these subroutines in detail. It illustrates the manner in which modules from a standard mathematical software library such as CORLIB can be used as building blocks in the solution of complex problems of practical interest. 9 refs., 2 figs., 4 tabs.« less

The 1D Richards' equation in two layered soils: a Filippov approach to treat discontinuities

NASA Astrophysics Data System (ADS)

Berardi, Marco; Difonzo, Fabio; Vurro, Michele; Lopez, Luciano

2018-05-01

The infiltration process into the soil is generally modeled by the Richards' partial differential equation (PDE). In this paper a new approach for modeling the infiltration process through the interface of two different soils is proposed, where the interface is seen as a discontinuity surface defined by suitable state variables. Thus, the original 1D Richards' PDE, enriched by a particular choice of the boundary conditions, is first approximated by means of a time semidiscretization, that is by means of the transversal method of lines (TMOL). In such a way a sequence of discontinuous initial value problems, described by a sequence of second order differential systems in the space variable, is derived. Then, Filippov theory on discontinuous dynamical systems may be applied in order to study the relevant dynamics of the problem. The numerical integration of the semidiscretized differential system will be performed by using a one-step method, which employs an event driven procedure to locate the discontinuity surface and to adequately change the vector field.

On the Solution of Elliptic Partial Differential Equations on Regions with Corners

DTIC Science & Technology

2015-07-09

In this report we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations . We observe...that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of...efficient numerical algorithms. The results are illustrated by a number of numerical examples. On the solution of elliptic partial differential equations on

Solution of an eigenvalue problem for the Laplace operator on a spherical surface. M.S. Thesis - Maryland Univ.

NASA Technical Reports Server (NTRS)

Walden, H.

1974-01-01

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is derived. The symmetric (generally five-point) finite difference equations that develop are written in matrix form and then solved by the iterative method of point successive overrelaxation. Upon convergence of this iterative method, the fundamental eigenvalue is approximated by iteration utilizing the power method as applied to the finite Rayleigh quotient.

Towards sub-optimal stochastic control of partially observable stochastic systems

NASA Technical Reports Server (NTRS)

Ruzicka, G. J.

1980-01-01

A class of multidimensional stochastic control problems with noisy data and bounded controls encountered in aerospace design is examined. The emphasis is on suboptimal design, the optimality being taken in quadratic mean sense. To that effect the problem is viewed as a stochastic version of the Lurie problem known from nonlinear control theory. The main result is a separation theorem (involving a nonlinear Kalman-like filter) suitable for Lurie-type approximations. The theorem allows for discontinuous characteristics. As a byproduct the existence of strong solutions to a class of non-Lipschitzian stochastic differential equations in dimensions is proven.

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

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

Maccari, A.

1996-12-01

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

Use of dirichlet distributions and orthogonal projection techniques for the fluctuation analysis of steady-state multivariate birth-death systems

NASA Astrophysics Data System (ADS)

Palombi, Filippo; Toti, Simona

2015-05-01

Approximate weak solutions of the Fokker-Planck equation represent a useful tool to analyze the equilibrium fluctuations of birth-death systems, as they provide a quantitative knowledge lying in between numerical simulations and exact analytic arguments. In this paper, we adapt the general mathematical formalism known as the Ritz-Galerkin method for partial differential equations to the Fokker-Planck equation with time-independent polynomial drift and diffusion coefficients on the simplex. Then, we show how the method works in two examples, namely the binary and multi-state voter models with zealots.

Stability analysis of a liquid fuel annular combustion chamber. M.S. Thesis

NASA Technical Reports Server (NTRS)

Mcdonald, G. H.

1978-01-01

High frequency combustion instability problems in a liquid fuel annular combustion chamber are examined. A modified Galerkin method was used to produce a set of modal amplitude equations from the general nonlinear partial differential acoustic wave equation in order to analyze the problem of instability. From these modal amplitude equations, the two variable perturbation method was used to develop a set of approximate equations of a given order of magnitude. These equations were modeled to show the effects of velocity sensitive combustion instabilities by evaluating the effects of certain parameters in the given set of equations.

Flow induced force of labyrinth seal

NASA Technical Reports Server (NTRS)

Iwatsubo, T.; Motooka, N.; Kawai, R.

1982-01-01

Flow induced instability force due to a labyrinth seal is analyzed. An approximate solution is given for the partial differential equation representing the flow in labyrinth seal and it is compared with the finite difference method in order to verify the accuracy of both methods. The effects of difference of inlet and outlet pressures of the seal, deflection of pressure and mass flow from the steady state, rotor diameter, seal clearance, seal interval and seal number on the flow induced force of the seal are investigated and it is known that some of these factors are very influential on the flow induced force.

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 1: Theory document (version 1.1)

NASA Technical Reports Server (NTRS)

Magnus, A. E.; Epton, M. A.

1981-01-01

Panel aerodynamics (PAN AIR) is a system of computer programs designed to analyze subsonic and supersonic inviscid flows about arbitrary configurations. A panel method is a program which solves a linear partial differential equation by approximating the configuration surface by a set of panels. An overview of the theory of potential flow in general and PAN AIR in particular is given along with detailed mathematical formulations. Fluid dynamics, the Navier-Stokes equation, and the theory of panel methods were also discussed.

On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.

1986-01-01

Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.

Meshless Solution of the Problem on the Static Behavior of Thin and Thick Laminated Composite Beams

NASA Astrophysics Data System (ADS)

Xiang, S.; Kang, G. W.

2018-03-01

For the first time, the static behavior of laminated composite beams is analyzed using the meshless collocation method based on a thin-plate-spline radial basis function. In the approximation of a partial differential equation by using a radial basis function, the shape parameter has an important role in ensuring the numerical accuracy. The choice of a shape parameter in the thin plate spline radial basis function is easier than in other radial basis functions. The governing differential equations are derived based on Reddy's third-order shear deformation theory. Numerical results are obtained for symmetric cross-ply laminated composite beams with simple-simple and cantilever boundary conditions under a uniform load. The results found are compared with available published ones and demonstrate the accuracy of the present method.

Effect of Cattaneo-Christov heat flux on Jeffrey fluid flow with variable thermal conductivity

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Javed, Mehwish; Imtiaz, Maria; Alsaedi, Ahmed

2018-03-01

This paper presents the study of Jeffrey fluid flow by a rotating disk with variable thickness. Energy equation is constructed by using Cattaneo-Christov heat flux model with variable thermal conductivity. A system of equations governing the model is obtained by applying boundary layer approximation. Resulting nonlinear partial differential system is transformed to ordinary differential system. Homotopy concept leads to the convergent solutions development. Graphical analysis for velocities and temperature is made to examine the influence of different involved parameters. Thermal relaxation time parameter signifies that temperature for Fourier's heat law is more than Cattaneo-Christov heat flux. A constitutional analysis is made for skin friction coefficient and heat transfer rate. Effects of Prandtl number on temperature distribution and heat transfer rate are scrutinized. It is observed that larger Reynolds number gives illustrious temperature distribution.

Hartree-Fock calculation of the differential photoionization cross sections of small Li clusters

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

Galitskiy, S. A.; Artemyev, A. N.; Jänkälä, K.

2015-01-21

Cross sections and angular distribution parameters for the single-photon ionization of all electron orbitals of Li{sub 2−8} are systematically computed in a broad interval of the photoelectron kinetic energies for the energetically most stable geometry of each cluster. Calculations of the partial photoelectron continuum waves in clusters are carried out by the single center method within the Hartree-Fock approximation. We study photoionization cross sections per one electron and analyze in some details general trends in the photoionization of inner and outer shells with respect to the size and geometry of a cluster. The present differential cross sections computed for Li{submore » 2} are in a good agreement with the available theoretical data, whereas those computed for Li{sub 3−8} clusters can be considered as theoretical predictions.« less

Non-perturbative background field calculations

NASA Astrophysics Data System (ADS)

Stephens, C. R.

1988-01-01

New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation—perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation.

Semi-analytical solutions of the Schnakenberg model of a reaction-diffusion cell with feedback

NASA Astrophysics Data System (ADS)

Al Noufaey, K. S.

2018-06-01

This paper considers the application of a semi-analytical method to the Schnakenberg model of a reaction-diffusion cell. The semi-analytical method is based on the Galerkin method which approximates the original governing partial differential equations as a system of ordinary differential equations. Steady-state curves, bifurcation diagrams and the region of parameter space in which Hopf bifurcations occur are presented for semi-analytical solutions and the numerical solution. The effect of feedback control, via altering various concentrations in the boundary reservoirs in response to concentrations in the cell centre, is examined. It is shown that increasing the magnitude of feedback leads to destabilization of the system, whereas decreasing this parameter to negative values of large magnitude stabilizes the system. The semi-analytical solutions agree well with numerical solutions of the governing equations.

Sinc-Galerkin estimation of diffusivity in parabolic problems

NASA Technical Reports Server (NTRS)

Smith, Ralph C.; Bowers, Kenneth L.

1991-01-01

A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.

Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

NASA Astrophysics Data System (ADS)

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

2006-03-01

Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

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

NASA Astrophysics Data System (ADS)

Waubke, Holger; Kasess, Christian H.

2016-11-01

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

Calculation of Scattering Amplitude Without Partial Analysis. II; Inclusion of Exchange

NASA Technical Reports Server (NTRS)

Temkin, Aaron; Shertzer, J.; Fisher, Richard R. (Technical Monitor)

2002-01-01

There was a method for calculating the whole scattering amplitude, f(Omega(sub k)), directly. The idea was to calculate the complete wave function Psi numerically, and use it in an integral expression for f, which can be reduced to a 2 dimensional quadrature. The original application was for e-H scattering without exchange. There the Schrodinger reduces a 2-d partial differential equation (pde), which was solved using the finite element method (FEM). Here we extend the method to the exchange approximation. The S.E. can be reduced to a pair of coupled pde's, which are again solved by the FEM. The formal expression for f(Omega(sub k)) consists two integrals, f+/- = f(sub d) +/- f(sub e); f(sub d) is formally the same integral as the no-exchange f. We have also succeeded in reducing f(sub e) to a 2-d integral. Results will be presented at the meeting.

Dynamic least-squares kernel density modeling of Fokker-Planck equations with application to neural population.

PubMed

Shotorban, Babak

2010-04-01

The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.

ERK1/2 mediates glucose-regulated POMC gene expression in hypothalamic neurons.

PubMed

Zhang, Juan; Zhou, Yunting; Chen, Cheng; Yu, Feiyuan; Wang, Yun; Gu, Jiang; Ma, Lian; Ho, Guyu

2015-04-01

Hypothalamic glucose-sensing neurons regulate the expression of genes encoding feeding-related neuropetides POMC, AgRP, and NPY - the key components governing metabolic homeostasis. AMP-activated protein kinase (AMPK) is postulated to be the molecular mediator relaying glucose signals to regulate the expression of these neuropeptides. Whether other signaling mediator(s) plays a role is not clear. In this study, we investigated the role of ERK1/2 using primary hypothalamic neurons as the model system. The primary neurons were differentiated from hypothalamic progenitor cells. The differentiated neurons possessed the characteristic neuronal cell morphology and expressed neuronal post-mitotic markers as well as leptin-regulated orexigenic POMC and anorexigenic AgRP/NPY genes. Treatment of cells with glucose dose-dependently increased POMC and decreased AgRP/NPY expression with a concurrent suppression of AMPK phosphorylation. In addition, glucose treatment dose-dependently increased the ERK1/2 phosphorylation. Blockade of ERK1/2 activity with its specific inhibitor PD98059 partially (approximately 50%) abolished glucose-induced POMC expression, but had little effect on AgRP/NPY expression. Conversely, blockade of AMPK activity with its specific inhibitor produced a partial (approximately 50%) reversion of low-glucose-suppressed POMC expression, but almost completely blunted the low-glucose-induced AgRP/NPY expression. The results indicate that ERK1/2 mediated POMC but not AgRP/NPY expression. Confirming the in vitro findings, i.c.v. administration of PD98059 in rats similarly attenuated glucose-induced POMC expression in the hypothalamus, but again had little effect on AgRP/NPY expression. The results are indicative of a novel role of ERK1/2 in glucose-regulated POMC expression and offer new mechanistic insights into hypothalamic glucose sensing. © 2015 Society for Endocrinology.

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

NASA Astrophysics Data System (ADS)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

Time-dependent buoyant puff model for explosive sources

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

Kansa, E.J.

1997-01-01

Several models exist to predict the time dependent behavior of bouyant puffs that result from explosions. This paper presents a new model that is derived from the strong conservative form of the conservation partial differential equations that are integrated over space to yield a coupled system of time dependent nonlinear ordinary differential equations. This model permits the cloud to evolve from an intial spherical shape not an ellipsoidal shape. It ignores the Boussinesq approximation, and treats the turbulence that is generated by the puff itself and the ambient atmospheric tubulence as separate mechanisms in determining the puff history. The puffmore » cloud rise history was found to depend no only on the mass and initial temperature of the explosion, but also upon the stability conditions of the ambient atmosphere. This model was calibrated by comparison with the Roller Coaster experiments.« less

Solvability of the Initial Value Problem to the Isobe-Kakinuma Model for Water Waves

NASA Astrophysics Data System (ADS)

Nemoto, Ryo; Iguchi, Tatsuo

2017-09-01

We consider the initial value problem to the Isobe-Kakinuma model for water waves and the structure of the model. The Isobe-Kakinuma model is the Euler-Lagrange equations for an approximate Lagrangian which is derived from Luke's Lagrangian for water waves by approximating the velocity potential in the Lagrangian. The Isobe-Kakinuma model is a system of second order partial differential equations and is classified into a system of nonlinear dispersive equations. Since the hypersurface t=0 is characteristic for the Isobe-Kakinuma model, the initial data have to be restricted in an infinite dimensional manifold for the existence of the solution. Under this necessary condition and a sign condition, which corresponds to a generalized Rayleigh-Taylor sign condition for water waves, on the initial data, we show that the initial value problem is solvable locally in time in Sobolev spaces. We also discuss the linear dispersion relation to the model.

A multiscale computational model of spatially resolved calcium cycling in cardiac myocytes: from detailed cleft dynamics to the whole cell concentration profiles

PubMed Central

Vierheller, Janine; Neubert, Wilhelm; Falcke, Martin; Gilbert, Stephen H.; Chamakuri, Nagaiah

2015-01-01

Mathematical modeling of excitation-contraction coupling (ECC) in ventricular cardiac myocytes is a multiscale problem, and it is therefore difficult to develop spatially detailed simulation tools. ECC involves gradients on the length scale of 100 nm in dyadic spaces and concentration profiles along the 100 μm of the whole cell, as well as the sub-millisecond time scale of local concentration changes and the change of lumenal Ca2+ content within tens of seconds. Our concept for a multiscale mathematical model of Ca2+ -induced Ca2+ release (CICR) and whole cardiomyocyte electrophysiology incorporates stochastic simulation of individual LC- and RyR-channels, spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca2+ and Ca2+-binding molecules in the bulk of the cell. We developed a novel computational approach to resolve the concentration gradients from dyadic space to cell level by using a quasistatic approximation within the dyad and finite element methods for integrating the partial differential equations. We show whole cell Ca2+-concentration profiles using three previously published RyR-channel Markov schemes. PMID:26441674

Dynamics of temporally localized states in passively mode-locked semiconductor lasers

NASA Astrophysics Data System (ADS)

Schelte, C.; Javaloyes, J.; Gurevich, S. V.

2018-05-01

We study the emergence and the stability of temporally localized structures in the output of a semiconductor laser passively mode locked by a saturable absorber in the long-cavity regime. For large yet realistic values of the linewidth enhancement factor, we disclose the existence of secondary dynamical instabilities where the pulses develop regular and subsequent irregular temporal oscillations. By a detailed bifurcation analysis we show that additional solution branches that consist of multipulse (molecules) solutions exist. We demonstrate that the various solution curves for the single and multipeak pulses can splice and intersect each other via transcritical bifurcations, leading to a complex web of solutions. Our analysis is based on a generic model of mode locking that consists of a time-delayed dynamical system, but also on a much more numerically efficient, yet approximate, partial differential equation. We compare the results of the bifurcation analysis of both models in order to assess up to which point the two approaches are equivalent. We conclude our analysis by the study of the influence of group velocity dispersion, which is only possible in the framework of the partial differential equation model, and we show that it may have a profound impact on the dynamics of the localized states.

Backstepping boundary control: an application to the suppression of flexible beam vibration

NASA Astrophysics Data System (ADS)

Boonkumkrong, Nipon; Asadamongkon, Pichai; Chinvorarat, Sinchai

2018-01-01

This paper presents a backstepping boundary control for vibration suppression of flexible beam. The applications are such as industrial robotic arms, space structures, etc. Most slender beams can be modelled using a shear beam. The shear beam is more complex than the conventional Euler-Bernoulli beam in that a shear deformation is additionally taken into account. At present, the application of this method in industry is rather limited, because the application of controllers to the beam is difficult. In this research, we use the shear beam with moving base as a model. The beam is cantilever type. This design method allows us to deal directly with the beam’s partial differential equations (PDEs) without resorting to approximations. An observer is used to estimate the deflections along the beam. Gain kernel of the system is calculated and then used in the control law design. The control setup is anti-collocation, i.e. a sensor is placed at the beam tip and an actuator is placed at the beam moving base. Finite difference equations are used to solve the PDEs and the partial integro-differential equations (PIDEs). Control parameters are varied to see their influences that affect the control performance. The results of the control are presented via computer simulation to verify that the control scheme is effective.

Stress and transcriptional regulation of tick ferritin HC.

PubMed

Mulenga, A; Simser, J A; Macaluso, K R; Azad, A F

2004-08-01

We previously identified a partial Dermacentor variabilis cDNA encoding ferritin HC (HC) subunit homolog (DVFER) that was differentially upregulated in Rickettsia montanensis infected ticks (Mulenga et al., 2003a). We have used rapid amplification of cDNA ends to clone full-length DVFER cDNA and its apparent ortholog from the wood tick, D. andersoni (DAFER), both of which show high sequence similarity to vertebrate than insect ferritin. Both DVFER and DAFER contain the stem-loop structure of a putative iron responsive element in the 5' untranslated region (nucleotide positions, 16-42) and the feroxidase centre loop typical for vertebrate ferritin HC subunits. Quantitative Western and Northern blotting analyses of protein and RNA from unfed and partially fed whole tick as well as dissected tick tissues demonstrated that DVFER is constitutively and ubiquitously expressed. Based on densitometric analysis of detected protein and mRNA bands, DVFER is predominantly expressed in the midgut, and to a lesser extent in the salivary glands, ovary and fatbody. Sham treatment (mechanical injury) and Escherichia coli challenge of D. variabilis ticks stimulated statistically significant (approximately 1.5- and approximately 3.0-fold, respectively) increases in DVFER mRNA abundance over time point matched naive control ticks. These data suggest that DVFER mRNA is nonspecifically up regulated in response to mechanical injury or bacterial infection induced stress.

Stepwise Analysis of Differential Item Functioning Based on Multiple-Group Partial Credit Model.

ERIC Educational Resources Information Center

Muraki, Eiji

1999-01-01

Extended an Item Response Theory (IRT) method for detection of differential item functioning to the partial credit model and applied the method to simulated data using a stepwise procedure. Then applied the stepwise DIF analysis based on the multiple-group partial credit model to writing trend data from the National Assessment of Educational…

Numerical methods for the inverse problem of density functional theory

DOE PAGES

Jensen, Daniel S.; Wasserman, Adam

2017-07-17

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

A stopping criterion for the iterative solution of partial differential equations

NASA Astrophysics Data System (ADS)

Rao, Kaustubh; Malan, Paul; Perot, J. Blair

2018-01-01

A stopping criterion for iterative solution methods is presented that accurately estimates the solution error using low computational overhead. The proposed criterion uses information from prior solution changes to estimate the error. When the solution changes are noisy or stagnating it reverts to a less accurate but more robust, low-cost singular value estimate to approximate the error given the residual. This estimator can also be applied to iterative linear matrix solvers such as Krylov subspace or multigrid methods. Examples of the stopping criterion's ability to accurately estimate the non-linear and linear solution error are provided for a number of different test cases in incompressible fluid dynamics.

Simple iterative construction of the optimized effective potential for orbital functionals, including exact exchange.

PubMed

Kümmel, Stephan; Perdew, John P

2003-01-31

For exchange-correlation functionals that depend explicitly on the Kohn-Sham orbitals, the potential V(xcsigma)(r) must be obtained as the solution of the optimized effective potential (OEP) integral equation. This is very demanding and has limited the use of orbital functionals. We demonstrate that instead the OEP can be obtained iteratively by solving the partial differential equations for the orbital shifts that exactify the Krieger-Li-Iafrate approximation. Unoccupied orbitals do not need to be calculated. Accuracy and efficiency of the method are shown for atoms and clusters using the exact-exchange energy. Counterintuitive asymptotic limits of the exact OEP are presented.

Inverse Diffusion Curves Using Shape Optimization.

PubMed

Zhao, Shuang; Durand, Fredo; Zheng, Changxi

2018-07-01

The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color fields via a partial differential equation (PDE). We introduce a new approach complementary to previous methods by optimizing curve geometry. In particular, we propose a novel iterative algorithm based on the theory of shape derivatives. The resulting diffusion curves are clean and well-shaped, and the final image closely approximates the input. Our method provides a user-controlled parameter to regularize curve complexity, and generalizes to handle input color fields represented in a variety of formats.

Bivariate spline solution of time dependent nonlinear PDE for a population density over irregular domains.

PubMed

Gutierrez, Juan B; Lai, Ming-Jun; Slavov, George

2015-12-01

We study a time dependent partial differential equation (PDE) which arises from classic models in ecology involving logistic growth with Allee effect by introducing a discrete weak solution. Existence, uniqueness and stability of the discrete weak solutions are discussed. We use bivariate splines to approximate the discrete weak solution of the nonlinear PDE. A computational algorithm is designed to solve this PDE. A convergence analysis of the algorithm is presented. We present some simulations of population development over some irregular domains. Finally, we discuss applications in epidemiology and other ecological problems. Copyright © 2015 Elsevier Inc. All rights reserved.

Introduction to multigrid methods

NASA Technical Reports Server (NTRS)

Wesseling, P.

1995-01-01

These notes were written for an introductory course on the application of multigrid methods to elliptic and hyperbolic partial differential equations for engineers, physicists and applied mathematicians. The use of more advanced mathematical tools, such as functional analysis, is avoided. The course is intended to be accessible to a wide audience of users of computational methods. We restrict ourselves to finite volume and finite difference discretization. The basic principles are given. Smoothing methods and Fourier smoothing analysis are reviewed. The fundamental multigrid algorithm is studied. The smoothing and coarse grid approximation properties are discussed. Multigrid schedules and structured programming of multigrid algorithms are treated. Robustness and efficiency are considered.

Numerical methods for the inverse problem of density functional theory

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

Jensen, Daniel S.; Wasserman, Adam

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations.

PubMed

Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio

2015-01-01

We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlevé-I (P[Formula: see text]) equation or its fourth-order analogue P[Formula: see text]. As concrete examples, we discuss nonlinear Schrödinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

Approximations of thermoelastic and viscoelastic control systems

NASA Technical Reports Server (NTRS)

Burns, J. A.; Liu, Z. Y.; Miller, R. E.

1990-01-01

Well-posed models and computational algorithms are developed and analyzed for control of a class of partial differential equations that describe the motions of thermo-viscoelastic structures. An abstract (state space) framework and a general well-posedness result are presented that can be applied to a large class of thermo-elastic and thermo-viscoelastic models. This state space framework is used in the development of a computational scheme to be used in the solution of a linear quadratic regulator (LQR) control problem. A detailed convergence proof is provided for the viscoelastic model and several numerical results are presented to illustrate the theory and to analyze problems for which the theory is incomplete.

Coupled out of plane vibrations of spiral beams for micro-scale applications

NASA Astrophysics Data System (ADS)

Amin Karami, M.; Yardimoglu, Bulent; Inman, Daniel J.

2010-12-01

An analytical method is proposed to calculate the natural frequencies and the corresponding mode shape functions of an Archimedean spiral beam. The deflection of the beam is due to both bending and torsion, which makes the problem coupled in nature. The governing partial differential equations and the boundary conditions are derived using Hamilton's principle. Two factors make the vibrations of spirals different from oscillations of constant radius arcs. The first is the presence of terms with derivatives of the radius in the governing equations of spirals and the second is the fact that variations of radius of the beam causes the coefficients of the differential equations to be variable. It is demonstrated, using perturbation techniques that the derivative of the radius terms have negligible effect on structure's dynamics. The spiral is then approximated with many merging constant-radius curved sections joined together to approximate the slow change of radius along the spiral. The equations of motion are formulated in non-dimensional form and the effect of all the key parameters on natural frequencies is presented. Non-dimensional curves are used to summarize the results for clarity. We also solve the governing equations using Rayleigh's approximate method. The fundamental frequency results of the exact and Rayleigh's method are in close agreement. This to some extent verifies the exact solutions. The results show that the vibration of spirals is mostly torsional which complicates using the spiral beam as a host for a sensor or energy harvesting device.

The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices

NASA Technical Reports Server (NTRS)

Beam, Richard M.; Warming, Robert F.

1991-01-01

Toeplitz matrices occur in many mathematical, as well as, scientific and engineering investigations. This paper considers the spectra of banded Toeplitz and quasi-Toeplitz matrices with emphasis on non-normal matrices of arbitrarily large order and relatively small bandwidth. These are the type of matrices that appear in the investigation of stability and convergence of difference approximations to partial differential equations. Quasi-Toeplitz matrices are the result of non-Dirichlet boundary conditions for the difference approximations. The eigenvalue problem for a banded Toeplitz or quasi-Toeplitz matrix of large order is, in general, analytically intractable and (for non-normal matrices) numerically unreliable. An asymptotic (matrix order approaches infinity) approach partitions the eigenvalue analysis of a quasi-Toeplitz matrix into two parts, namely the analysis for the boundary condition independent spectrum and the analysis for the boundary condition dependent spectrum. The boundary condition independent spectrum is the same as the pure Toeplitz matrix spectrum. Algorithms for computing both parts of the spectrum are presented. Examples are used to demonstrate the utility of the algorithms, to present some interesting spectra, and to point out some of the numerical difficulties encountered when conventional matrix eigenvalue routines are employed for non-normal matrices of large order. The analysis for the Toeplitz spectrum also leads to a diagonal similarity transformation that improves conventional numerical eigenvalue computations. Finally, the algorithm for the asymptotic spectrum is extended to the Toeplitz generalized eigenvalue problem which occurs, for example, in the stability of Pade type difference approximations to differential equations.

Time Parallel Solution of Linear Partial Differential Equations on the Intel Touchstone Delta Supercomputer

NASA Technical Reports Server (NTRS)

Toomarian, N.; Fijany, A.; Barhen, J.

1993-01-01

Evolutionary partial differential equations are usually solved by decretization in time and space, and by applying a marching in time procedure to data and algorithms potentially parallelized in the spatial domain.

Experimental Constraints on the Chemical Differentiation of Mercurys Mantle

NASA Technical Reports Server (NTRS)

Boujibar, A.; Righter, K.; Pando, K.; Danielson, L.

2015-01-01

Mercury is known as being the most reduced terrestrial planet with the highest core/mantle ratio. Results from MESSENGER spacecraft have shown that its surface is FeO-poor (2-4 wt%) and S-rich (up to 6-7 wt%), which confirms the reducing nature of its silicate mantle. In addition several features suggest important melting stages of the Mercurian mantle: widespread volcanic deposits on its surface, a high crustal thickness (approximately 10% of the planet's volume) and chemical compositions of its surface suggesting several stages of differentiation and remelting processes. Therefore it is likely that igneous processes like magma ocean crystallization and continuous melting have induced chemical and mineralogical heterogeneities in the Mercurian mantle. The extent and nature of compositional variations produced by partial melting remains poorly constrained for the particular compositions of Mercury (very reducing conditions, low FeO-contents and high sulfur-contents). Melting experiments with bulk Mercury-analogue compositions are scarce and with poorly con-trolled starting compositions. Therefore additional experimental data are needed to better understand the differentiation processes that lead to the observed chemical compositions of Mercury's surface.

Boundary Approximation Methods for Sloving Elliptic Problems on Unbounded Domains

NASA Astrophysics Data System (ADS)

Li, Zi-Cai; Mathon, Rudolf

1990-08-01

Boundary approximation methods with partial solutions are presented for solving a complicated problem on an unbounded domain, with both a crack singularity and a corner singularity. Also an analysis of partial solutions near the singular points is provided. These methods are easy to apply, have good stability properties, and lead to highly accurate solutions. Hence, boundary approximation methods with partial solutions are recommended for the treatment of elliptic problems on unbounded domains provided that piecewise solution expansions, in particular, asymptotic solutions near the singularities and infinity, can be found.

Topographical scattering of gravity waves

NASA Astrophysics Data System (ADS)

Miles, J. W.; Chamberlain, P. G.

1998-04-01

A systematic hierarchy of partial differential equations for linear gravity waves in water of variable depth is developed through the expansion of the average Lagrangian in powers of [mid R:][nabla del, Hamilton operator][mid R:] (h=depth, [nabla del, Hamilton operator]h=slope). The first and second members of this hierarchy, the Helmholtz and conventional mild-slope equations, are second order. The third member is fourth order but may be approximated by Chamberlain & Porter's (1995) ‘modified mild-slope’ equation, which is second order and comprises terms in [nabla del, Hamilton operator]2h and ([nabla del, Hamilton operator]h)2 that are absent from the mild-slope equation. Approximate solutions of the mild-slope and modified mild-slope equations for topographical scattering are determined through an iterative sequence, starting from a geometrical-optics approximation (which neglects reflection), then a quasi-geometrical-optics approximation, and on to higher-order results. The resulting reflection coefficient for a ramp of uniform slope is compared with the results of numerical integrations of each of the mild-slope equation (Booij 1983), the modified mild-slope equation (Porter & Staziker 1995), and the full linear equations (Booij 1983). Also considered is a sequence of sinusoidal sandbars, for which Bragg resonance may yield rather strong reflection and for which the modified mild-slope approximation is in close agreement with Mei's (1985) asymptotic approximation.

Mathematical Modelling of Continuous Biotechnological Processes

ERIC Educational Resources Information Center

Pencheva, T.; Hristozov, I.; Shannon, A. G.

2003-01-01

Biotechnological processes (BTP) are characterized by a complicated structure of organization and interdependent characteristics. Partial differential equations or systems of partial differential equations are used for their behavioural description as objects with distributed parameters. Modelling of substrate without regard to dispersion…

Fault Tolerant Optimal Control.

DTIC Science & Technology

1982-08-01

subsystem is modelled by deterministic or stochastic finite-dimensional vector differential or difference equations. The parameters of these equations...is no partial differential equation that must be solved. Thus we can sidestep the inability to solve the Bellman equation for control problems with x...transition models and cost functionals can be reduced to the search for solutions of nonlinear partial differential equations using ’verification

Differential geometry techniques for sets of nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Estabrook, Frank B.

1990-01-01

An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.

A procedure to construct exact solutions of nonlinear fractional differential equations.

PubMed

Güner, Özkan; Cevikel, Adem C

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

Algebraic and geometric structures of analytic partial differential equations

NASA Astrophysics Data System (ADS)

Kaptsov, O. V.

2016-11-01

We study the problem of the compatibility of nonlinear partial differential equations. We introduce the algebra of convergent power series, the module of derivations of this algebra, and the module of Pfaffian forms. Systems of differential equations are given by power series in the space of infinite jets. We develop a technique for studying the compatibility of differential systems analogous to the Gröbner bases. Using certain assumptions, we prove that compatible systems generate infinite manifolds.

Probabilistic density function method for nonlinear dynamical systems driven by colored noise.

PubMed

Barajas-Solano, David A; Tartakovsky, Alexandre M

2016-05-01

We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integrodifferential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified large-eddy-diffusivity (LED) closure. In contrast to the classical LED closure, the proposed closure accounts for advective transport of the PDF in the approximate temporal deconvolution of the integrodifferential equation. In addition, we introduce the generalized local linearization approximation for deriving a computable PDF equation in the form of a second-order partial differential equation. We demonstrate that the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary autocorrelation time. We apply the proposed PDF method to analyze a set of Kramers equations driven by exponentially autocorrelated Gaussian colored noise to study nonlinear oscillators and the dynamics and stability of a power grid. Numerical experiments show the PDF method is accurate when the noise autocorrelation time is either much shorter or longer than the system's relaxation time, while the accuracy decreases as the ratio of the two timescales approaches unity. Similarly, the PDF method accuracy decreases with increasing standard deviation of the noise.

The solitary wave solution of coupled Klein-Gordon-Zakharov equations via two different numerical methods

NASA Astrophysics Data System (ADS)

Dehghan, Mehdi; Nikpour, Ahmad

2013-09-01

In this research, we propose two different methods to solve the coupled Klein-Gordon-Zakharov (KGZ) equations: the Differential Quadrature (DQ) and Globally Radial Basis Functions (GRBFs) methods. In the DQ method, the derivative value of a function with respect to a point is directly approximated by a linear combination of all functional values in the global domain. The principal work in this method is the determination of weight coefficients. We use two ways for obtaining these coefficients: cosine expansion (CDQ) and radial basis functions (RBFs-DQ), the former is a mesh-based method and the latter categorizes in the set of meshless methods. Unlike the DQ method, the GRBF method directly substitutes the expression of the function approximation by RBFs into the partial differential equation. The main problem in the GRBFs method is ill-conditioning of the interpolation matrix. Avoiding this problem, we study the bases introduced in Pazouki and Schaback (2011) [44]. Some examples are presented to compare the accuracy and easy implementation of the proposed methods. In numerical examples, we concentrate on Inverse Multiquadric (IMQ) and second-order Thin Plate Spline (TPS) radial basis functions. The variable shape parameter (exponentially and random) strategies are applied in the IMQ function and the results are compared with the constant shape parameter.

Primary colonic well-differentiated / dedifferentiated liposarcoma of the ascending colon: a case report.

PubMed

Sawayama, Hiroshi; Yoshida, Naoya; Miyamoto, Yuji; Uchihara, Tomoyuki; Toihata, Tasuku; Yagi, Taisuke; Hiyoshi, Yukiharu; Iwatsuki, Masaaki; Baba, Yoshifumi; Baba, Hideo

2017-08-30

Primary colonic and dedifferentiated liposarcomas are both remarkably rare. This work describes a case of primary colonic well-differentiated/dedifferentiated liposarcoma and reviews the clinical characteristics and current therapies for liposarcoma tumors. A 52-year-old woman was referred to our hospital with a submucosal tumor of the ascending colon. Clinical analysis by ultrasound colonoscopy and computed tomography revealed a partially ossified tumor with irregular edges continuous with the muscular layer. High F-18 deoxyglucose uptake was detected by positron emission tomography. Radical resection with lymph node dissection was performed, yielding a tumor specimen approximately 6.5 × 4.0 × 3.2 cm. Neoplastic spindle cell proliferation was found from submucosa to subserosa. Well-differentiated adipose tissue surrounded the tumor, but contained atypical nuclei with condensed chromosomes. Immunohistochemical staining was positive for p16, CDK4, and MDM2 expression. Based on these findings, a diagnosis of well-differentiated/dedifferentiated liposarcoma was given. Dedifferentiated liposarcomas are more aggressive than their well-differentiated, low-grade counterparts. While local recurrence can occur with both tumor types, dedifferentiated liposarcomas are more prone to developing distant metastases. The patient received no postoperative therapy, and no recurrences have been observed 12 months after surgery. Here we report an extremely rare case of well-differentiated/dedifferentiated liposarcoma of the ascending colon. The dedifferentiated component was high-grade liposarcoma and well-differentiated liposarcoma was detected around the main tumor.

On new classes of solutions of nonlinear partial differential equations in the form of convergent special series

NASA Astrophysics Data System (ADS)

Filimonov, M. Yu.

2017-12-01

The method of special series with recursively calculated coefficients is used to solve nonlinear partial differential equations. The recurrence of finding the coefficients of the series is achieved due to a special choice of functions, in powers of which the solution is expanded in a series. We obtain a sequence of linear partial differential equations to find the coefficients of the series constructed. In many cases, one can deal with a sequence of linear ordinary differential equations. We construct classes of solutions in the form of convergent series for a certain class of nonlinear evolution equations. A new class of solutions of generalized Boussinesque equation with an arbitrary function in the form of a convergent series is constructed.

Influence of two-stream relativistic electron beam parameters on the space-charge wave with broad frequency spectrum formation

NASA Astrophysics Data System (ADS)

Alexander, LYSENKO; Iurii, VOLK

2018-03-01

We developed a cubic non-linear theory describing the dynamics of the multiharmonic space-charge wave (SCW), with harmonics frequencies smaller than the two-stream instability critical frequency, with different relativistic electron beam (REB) parameters. The self-consistent differential equation system for multiharmonic SCW harmonic amplitudes was elaborated in a cubic non-linear approximation. This system considers plural three-wave parametric resonant interactions between wave harmonics and the two-stream instability effect. Different REB parameters such as the input angle with respect to focusing magnetic field, the average relativistic factor value, difference of partial relativistic factors, and plasma frequency of partial beams were investigated regarding their influence on the frequency spectrum width and multiharmonic SCW saturation levels. We suggested ways in which the multiharmonic SCW frequency spectrum widths could be increased in order to use them in multiharmonic two-stream superheterodyne free-electron lasers, with the main purpose of forming a powerful multiharmonic electromagnetic wave.

Comparison of universal approximators incorporating partial monotonicity by structure.

PubMed

Minin, Alexey; Velikova, Marina; Lang, Bernhard; Daniels, Hennie

2010-05-01

Neural networks applied in control loops and safety-critical domains have to meet more requirements than just the overall best function approximation. On the one hand, a small approximation error is required; on the other hand, the smoothness and the monotonicity of selected input-output relations have to be guaranteed. Otherwise, the stability of most of the control laws is lost. In this article we compare two neural network-based approaches incorporating partial monotonicity by structure, namely the Monotonic Multi-Layer Perceptron (MONMLP) network and the Monotonic MIN-MAX (MONMM) network. We show the universal approximation capabilities of both types of network for partially monotone functions. On a number of datasets, we investigate the advantages and disadvantages of these approaches related to approximation performance, training of the model and convergence. 2009 Elsevier Ltd. All rights reserved.

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

PubMed Central

Güner, Özkan; Cevikel, Adem C.

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972

On implicit abstract neutral nonlinear differential equations

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

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

2016-04-15

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

Oscillation of certain higher-order neutral partial functional differential equations.

PubMed

Li, Wei Nian; Sheng, Weihong

2016-01-01

In this paper, we study the oscillation of certain higher-order neutral partial functional differential equations with the Robin boundary conditions. Some oscillation criteria are established. Two examples are given to illustrate the main results in the end of this paper.

Pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations

NASA Astrophysics Data System (ADS)

Al-Islam, Najja Shakir

In this Dissertation, the existence of pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations is established. For that, (Al-Islam [4]) is first studied and then obtained under some suitable assumptions. That is, the existence of pseudo almost periodic solutions to a hyperbolic second-order partial differential equation with delay. The second-order partial differential equation (1) represents a mathematical model for the dynamics of gas absorption, given by uxt+a x,tux=Cx,t,u x,t , u0,t=4 t, 1 where a : [0, L] x RR , C : [0, L] x R x RR , and ϕ : RR are (jointly) continuous functions ( t being the greatest integer function) and L > 0. The results in this Dissertation generalize those of Poorkarimi and Wiener [22]. Secondly, a generalization of the above-mentioned system consisting of the non-linear hyperbolic second-order partial differential equation uxt+a x,tux+bx,t ut+cx,tu=f x,t,u, x∈ 0,L,t∈ R, 2 equipped with the boundary conditions ux,0 =40x, u0,t=u 0t, uxx,0=y 0x, x∈0,L, t∈R, 3 where a, b, c : [0, L ] x RR and f : [0, L] x R x RR are (jointly) continuous functions is studied. Under some suitable assumptions, the existence and uniqueness of pseudo almost periodic solutions to particular cases, as well as the general case of the second-order hyperbolic partial differential equation (2) are studied. The results of all studies contained within this text extend those obtained by Aziz and Meyers [6] in the periodic setting.

Reversible effects of oxygen partial pressure on genes associated with placental angiogenesis and differentiation in primary-term cytotrophoblast cell culture.

PubMed

Debiève, F; Depoix, C; Gruson, D; Hubinont, C

2013-09-01

Timely regulated changes in oxygen partial pressure are important for placental formation. Disturbances could be responsible for pregnancy-related diseases like preeclampsia and intrauterine growth restriction. We aimed to (i) determine the effect of oxygen partial pressure on cytotrophoblast differentiation; (ii) measure mRNA expression and protein secretion from genes associated with placental angiogenesis; and (iii) determine the reversibility of these effects at different oxygen partial pressures. Term cytotrophoblasts were incubated at 21% and 2.5% O2 for 96 hr, or were switched between the two oxygen concentrations after 48 hr. Real-time PCR and enzyme-linked immunosorbent assays (ELISAs) were used to evaluate cell fusion and differentiation, measuring transcript levels for those genes involved in cell fusion and placental angiogenesis, including VEGF, PlGF, VEGFR1, sVEGFR1, sENG, INHA, and GCM1. Cytotrophoblasts underwent fusion and differentiation in 2.5% O2 . PlGF expression was inhibited while sVEGFR1 expression increased. VEGF and sENG mRNA expressions increased in 2.5% compared to 21% O2 , but no protein was detected in the cell supernatants. Finally, GCM1 mRNA expression increased during trophoblast differentiation at 21% O2 , but was inhibited at 2.5% O2 . These mRNA expression effects were reversed by returning the cells to 21% O2 . Thus, low-oxygen partial pressure does not inhibit term-cytotrophoblast cell fusion and differentiation in vitro. Lowering the oxygen partial pressure from 21% to 2.5% caused normal-term trophoblasts to reversibly modify their expression of genes associated with placental angiogenesis. This suggests that modifications observed in pregnancy diseases such as preeclampsia or growth retardation are probably due to an extrinsic effect on trophoblasts. Copyright © 2013 Wiley Periodicals, Inc.

Lattice Boltzmann model for high-order nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Lattice Boltzmann model for high-order nonlinear partial differential equations.

PubMed

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Approximation of Quantum Stochastic Differential Equations for Input-Output Model Reduction

DTIC Science & Technology

2016-02-25

Approximation of Quantum Stochastic Differential Equations for Input-Output Model Reduction We have completed a short program of theoretical research...on dimensional reduction and approximation of models based on quantum stochastic differential equations. Our primary results lie in the area of...2211 quantum probability, quantum stochastic differential equations REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 10. SPONSOR

76 FR 51383 - Commercial Leasing for Wind Power on the Outer Continental Shelf (OCS) Offshore Rhode Island and...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-08-18

... section). This section of the Call Area is approximately 1.25 square nmi and contains 1 partial OCS lease...). This section of the Call Area is approximately 246 square nmi and contains 31 whole OCS lease blocks as... section of the Call Area is approximately 1.25 square nmi and contains 1 partial OCS lease block. The...

Entropy and convexity for nonlinear partial differential equations

PubMed Central

Ball, John M.; Chen, Gui-Qiang G.

2013-01-01

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue. PMID:24249768

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.

Entropy and convexity for nonlinear partial differential equations.

PubMed

Ball, John M; Chen, Gui-Qiang G

2013-12-28

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.

Differential phase measurements of D-region partial reflections

NASA Technical Reports Server (NTRS)

Wiersma, D. J.; Sechrist, C. F., Jr.

1972-01-01

Differential phase partial reflection measurements were used to deduce D region electron density profiles. The phase difference was measured by taking sums and differences of amplitudes received on an array of crossed dipoles. The reflection model used was derived from Fresnel reflection theory. Seven profiles obtained over the period from 13 October 1971 to 5 November 1971 are presented, along with the results from simultaneous measurements of differential absorption. Some possible sources of error and error propagation are discussed. A collision frequency profile was deduced from the electron concentration calculated from differential phase and differential absorption.

Analysis of Monte Carlo accelerated iterative methods for sparse linear systems: Analysis of Monte Carlo accelerated iterative methods for sparse linear systems

DOE PAGES

Benzi, Michele; Evans, Thomas M.; Hamilton, Steven P.; ...

2017-03-05

Here, we consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. We expect that these methods will have considerable potential for resiliency to faults when implemented on massively parallel machines. We also establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.

Review of Nuclear Physics Experiments for Space Radiation

NASA Technical Reports Server (NTRS)

Norbury, John W.; Miller, Jack; Adamczyk, Anne M.; Heilbronn, Lawrence H.; Townsend, Lawrence W.; Blattnig, Steve R.; Norman, Ryan B.; Guetersloh, Stephen B.; Zeitlin, Cary J.

2011-01-01

Human space flight requires protecting astronauts from the harmful effects of space radiation. The availability of measured nuclear cross section data needed for these studies is reviewed in the present paper. The energy range of interest for radiation protection is approximately 100 MeV/n to 10 GeV/n. The majority of data are for projectile fragmentation partial and total cross sections, including both charge changing and isotopic cross sections. The cross section data are organized into categories which include charge changing, elemental, isotopic for total, single and double differential with respect to momentum, energy and angle. Gaps in the data relevant to space radiation protection are discussed and recommendations for future experiments are made.

Thermodynamically self-consistent theory for the Blume-Capel model.

PubMed

Grollau, S; Kierlik, E; Rosinberg, M L; Tarjus, G

2001-04-01

We use a self-consistent Ornstein-Zernike approximation to study the Blume-Capel ferromagnet on three-dimensional lattices. The correlation functions and the thermodynamics are obtained from the solution of two coupled partial differential equations. The theory provides a comprehensive and accurate description of the phase diagram in all regions, including the wing boundaries in a nonzero magnetic field. In particular, the coordinates of the tricritical point are in very good agreement with the best estimates from simulation or series expansion. Numerical and analytical analysis strongly suggest that the theory predicts a universal Ising-like critical behavior along the lambda line and the wing critical lines, and a tricritical behavior governed by mean-field exponents.

Semi-analytic valuation of stock loans with finite maturity

NASA Astrophysics Data System (ADS)

Lu, Xiaoping; Putri, Endah R. M.

2015-10-01

In this paper we study stock loans of finite maturity with different dividend distributions semi-analytically using the analytical approximation method in Zhu (2006). Stock loan partial differential equations (PDEs) are established under Black-Scholes framework. Laplace transform method is used to solve the PDEs. Optimal exit price and stock loan value are obtained in Laplace space. Values in the original time space are recovered by numerical Laplace inversion. To demonstrate the efficiency and accuracy of our semi-analytic method several examples are presented, the results are compared with those calculated using existing methods. We also present a calculation of fair service fee charged by the lender for different loan parameters.

Approximation of the Newton Step by a Defect Correction Process

NASA Technical Reports Server (NTRS)

Arian, E.; Batterman, A.; Sachs, E. W.

1999-01-01

In this paper, an optimal control problem governed by a partial differential equation is considered. The Newton step for this system can be computed by solving a coupled system of equations. To do this efficiently with an iterative defect correction process, a modifying operator is introduced into the system. This operator is motivated by local mode analysis. The operator can be used also for preconditioning in Generalized Minimum Residual (GMRES). We give a detailed convergence analysis for the defect correction process and show the derivation of the modifying operator. Numerical tests are done on the small disturbance shape optimization problem in two dimensions for the defect correction process and for GMRES.

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

NASA Astrophysics Data System (ADS)

Xu, Peiliang

2018-06-01

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking, they are able to extract smallest possible gravitational signals from modern and future satellite tracking measurements, leading to the production of global high-precision, high-resolution gravitational models. By directly turning the nonlinear differential equations of satellite motion into the nonlinear integral equations, and recognizing the fact that satellite orbits are measured with random errors, we further reformulate the links between satellite tracking measurements and the global uniformly convergent solutions to the Newton's governing differential equations as a condition adjustment model with unknown parameters, or equivalently, the weighted least squares estimation of unknown differential equation parameters with equality constraints, for the reconstruction of global high-precision, high-resolution gravitational models from modern (and future) satellite tracking measurements.

ELSEPA—Dirac partial-wave calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules

NASA Astrophysics Data System (ADS)

Salvat, Francesc; Jablonski, Aleksander; Powell, Cedric J.

2005-01-01

The FORTRAN 77 code system ELSEPA for the calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules is presented. These codes perform relativistic (Dirac) partial-wave calculations for scattering by a local central interaction potential V(r). For atoms and ions, the static-field approximation is adopted, with the potential set equal to the electrostatic interaction energy between the projectile and the target, plus an approximate local exchange interaction when the projectile is an electron. For projectiles with kinetic energies up to 10 keV, the potential may optionally include a semiempirical correlation-polarization potential to describe the effect of the target charge polarizability. Also, for projectiles with energies less than 1 MeV, an imaginary absorptive potential can be introduced to account for the depletion of the projectile wave function caused by open inelastic channels. Molecular cross sections are calculated by means of a single-scattering independent-atom approximation in which the electron density of a bound atom is approximated by that of the free neutral atom. Elastic scattering by individual atoms in solids is described by means of a muffin-tin model potential. Partial-wave calculations are feasible on modest personal computers for energies up to about 5 MeV. The ELSEPA code also implements approximate factorization methods that allow the fast calculation of elastic cross sections for much higher energies. The interaction model adopted in the calculations is defined by the user by combining the different options offered by the code. The nuclear charge distribution can be selected among four analytical models (point nucleus, uniformly charged sphere, Fermi's distribution and Helm's uniform-uniform distribution). The atomic electron density is handled in numerical form. The distribution package includes data files with electronic densities of neutral atoms of the elements hydrogen to lawrencium ( Z=1-103) obtained from multiconfiguration Dirac-Fock self-consistent calculations. For comparison purposes, three simple analytical approximations to the electron density of neutral atoms (corresponding to the Thomas-Fermi, the Thomas-Fermi-Dirac and the Dirac-Hartree-Fock-Slater models) are also included. For calculations of elastic scattering by ions, the electron density should be provided by the user. The exchange potential for electron scattering can be selected among three different analytical approximations (Thomas-Fermi, Furness-McCarthy, Riley-Truhlar). The offered options for the correlation-polarization potential are based on the empirical Buckingham potential. The imaginary absorption potential is calculated from the local-density approximation proposed by Salvat [Phys. Rev. A 68 (2003) 012708]. Program summaryTitle of program:ELSEPA Catalogue identifier: ADUS Program summary URL:http://cpc.cs.qub.ac.uk/cpc/summaries/ADUS Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland License provisions: none Computer for which the program is designed and others in which it is operable: Any computer with a FORTRAN 77 compiler Operating systems under which the program has been tested: Windows XP, Windows 2000, Debian GNU/Linux 3.0r0 (sarge) Compilers:Compaq Visual Fortran v6.5 (Windows); GNU FORTRAN, g77 (Windows and Linux) Programming language used: FORTRAN 77 No. of bits in a word: 32 Memory required to execute with typical data: 0.6 Mb No. of lines in distributed program, including test data, etc.:135 489 No. of bytes in distributed program, including test data, etc.: 1 280 006 Distribution format: tar.gz Keywords: Dirac partial-wave analysis, electron elastic scattering, positron elastic scattering, differential cross sections, momentum transfer cross sections, transport cross sections, scattering amplitudes, spin polarization, scattering by complex potentials, high-energy atomic screening functions Nature of the physical problem: The code calculates differential cross sections, total cross sections and transport cross sections for single elastic scattering of electrons and positrons by neutral atoms, positive ions and randomly oriented molecules. For projectiles with kinetic energies less than about 5 MeV, the programs can also compute scattering amplitudes and spin polarization functions. Method of solution: The effective interaction between the projectile and a target atom is represented by a local central potential that can optionally include an imaginary (absorptive) part to account approximately for the coupling with inelastic channels. For projectiles with kinetic energy less that about 5 MeV, the code performs a conventional relativistic Dirac partial-wave analysis. For higher kinetic energies, where the convergence of the partial-wave series is too slow, approximate factorization methods are used. Restrictions on the complexity of the program: The calculations are based on the static-field approximation. The optional correlation-polarization and inelastic absorption corrections are obtained from approximate, semiempirical models. Calculations for molecules are based on a single-scattering independent-atom approximation. To ensure accuracy of the results for scattering by ions, the electron density of the ion must be supplied by the user. Typical running time: on a 2.8 GHz Pentium 4, the calculation of elastic scattering by atoms and ions takes between a few seconds and about two minutes, depending on the atomic number of the target, the adopted potential model and the kinetic energy of the projectile. Unusual features of the program: The program calculates elastic cross sections for electrons and positrons with kinetic energies in a wide range, from a few tens of eV up to about 1 GeV. Calculations can be performed for neutral atoms of all elements, from hydrogen to lawrencium ( Z=1-103), ions and simple molecules. Commercial products are identified to specify the calculational procedures. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, the University of Barcelona or the Polish Academy of Sciences, nor does it imply that the products are necessarily the best available for the purpose.

Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.

DTIC Science & Technology

1983-12-01

numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numer- ical evaluation of any partial differential...emphasis is being placed on numerical solution of the governing differential equations by finite difference methods . In the past two decades, considerable...original equations presented in that paper. The solution of the second problem is more difficult. 2 The method of Thompson et al. provides control for

Experts' understanding of partial derivatives using the partial derivative machine

NASA Astrophysics Data System (ADS)

Roundy, David; Weber, Eric; Dray, Tevian; Bajracharya, Rabindra R.; Dorko, Allison; Smith, Emily M.; Manogue, Corinne A.

2015-12-01

[This paper is part of the Focused Collection on Upper Division Physics Courses.] Partial derivatives are used in a variety of different ways within physics. Thermodynamics, in particular, uses partial derivatives in ways that students often find especially confusing. We are at the beginning of a study of the teaching of partial derivatives, with a goal of better aligning the teaching of multivariable calculus with the needs of students in STEM disciplines. In this paper, we report on an initial study of expert understanding of partial derivatives across three disciplines: physics, engineering, and mathematics. We report on the central research question of how disciplinary experts understand partial derivatives, and how their concept images of partial derivatives differ, with a focus on experimentally measured quantities. Using the partial derivative machine (PDM), we probed expert understanding of partial derivatives in an experimental context without a known functional form. In particular, we investigated which representations were cued by the experts' interactions with the PDM. Whereas the physicists and engineers were quick to use measurements to find a numeric approximation for a derivative, the mathematicians repeatedly returned to speculation as to the functional form; although they were comfortable drawing qualitative conclusions about the system from measurements, they were reluctant to approximate the derivative through measurement. On a theoretical front, we found ways in which existing frameworks for the concept of derivative could be expanded to include numerical approximation.

A Modified Formula of the First-order Approximation for Assessing the Contribution of Climate Change to Runoff Based on the Budyko Hypothesis

NASA Astrophysics Data System (ADS)

Liu, W.; Ning, T.; Han, X.

2015-12-01

The climate elasticity based on the Budyko curves has been widely used to evaluate the hydrological responses to climate change. The Mezentsev-Choudhury-Yang formula is one of the representative analytical equations for Budyko curves. Previous researches mostly used the variation of runoff (R) caused by the changes of annual precipitation (P) and potential evapotranspiration (ET0) as the hydrological response to climate change and evaluated it by a first-order approximation in a form of total differential, the major components of which include the partial derivatives of R to P and ET0, as well as climate elasticity on this basis. Based on analytic derivation and the characteristics of Budyko curves, this study proposed a modified formula of the first-order approximation to reduce the errors from the approximation. In the calculation of partial derivatives and climate elasticity, the values of P and ET0 were taken to the sum of their base values and half increments, respectively. The calculation was applied in 33 catchments of the Hai River basin in China and the results showed that the mean absolute value of relative error of approximated runoff change decreased from 8.4% to 0.4% and the maximum value, from 23.4% to 1.3%. Given the variation values of P, ET0 and the controlling parameter (n), the modified formula can exactly quantify the contributions of climate fluctuation and underlying surface change to runoff. Taking the Murray-Darling basin in Australia as an example of the contribution calculated by the modified formula, the reductions of mean annual runoff caused by changes of P, ET0 and n from 1895-1996 to 1997-2006 were 2.6, 0.6 and 2.9 mm, respectively, and the sum of them was 6.1 mm, which was completely consistent with the observed runoff. The modified formula of the first-order approximation proposed in this study can be not only used to assess the contributions of climate change to the runoff, but also widely used to analyze the effects of similar issues based on a certain functional relationship in hydrological and climate changes.

Genetic dissection of hybrid incompatibilities between Drosophila simulans and D. mauritiana. I. Differential accumulation of hybrid male sterility effects on the X and autosomes.

PubMed Central

Tao, Yun; Chen, Sining; Hartl, Daniel L; Laurie, Cathy C

2003-01-01

The genetic basis of hybrid incompatibility in crosses between Drosophila mauritiana and D. simulans was investigated to gain insight into the evolutionary mechanisms of speciation. In this study, segments of the D. mauritiana third chromosome were introgressed into a D. simulans genetic background and tested as homozygotes for viability, male fertility, and female fertility. The entire third chromosome was covered with partially overlapping segments. Many segments were male sterile, while none were female sterile or lethal, confirming previous reports of the rapid evolution of hybrid male sterility (HMS). A statistical model was developed to quantify the HMS accumulation. In comparison with previous work on the X chromosome, we estimate that the X has approximately 2.5 times the density of HMS factors as the autosomes. We also estimate that the whole genome contains approximately 15 HMS "equivalents"-i.e., 15 times the minimum number of incompatibility factors necessary to cause complete sterility. Although some caveats for the quantitative estimate of a 2.5-fold density difference are described, this study supports the notion that the X chromosome plays a special role in the evolution of reproductive isolation. Possible mechanisms of a "large X" effect include selective fixation of new mutations that are recessive or partially recessive and the evolution of sex-ratio distortion systems. PMID:12930747

Genetic dissection of hybrid incompatibilities between Drosophila simulans and D. mauritiana. I. Differential accumulation of hybrid male sterility effects on the X and autosomes.

PubMed

Tao, Yun; Chen, Sining; Hartl, Daniel L; Laurie, Cathy C

2003-08-01

The genetic basis of hybrid incompatibility in crosses between Drosophila mauritiana and D. simulans was investigated to gain insight into the evolutionary mechanisms of speciation. In this study, segments of the D. mauritiana third chromosome were introgressed into a D. simulans genetic background and tested as homozygotes for viability, male fertility, and female fertility. The entire third chromosome was covered with partially overlapping segments. Many segments were male sterile, while none were female sterile or lethal, confirming previous reports of the rapid evolution of hybrid male sterility (HMS). A statistical model was developed to quantify the HMS accumulation. In comparison with previous work on the X chromosome, we estimate that the X has approximately 2.5 times the density of HMS factors as the autosomes. We also estimate that the whole genome contains approximately 15 HMS "equivalents"-i.e., 15 times the minimum number of incompatibility factors necessary to cause complete sterility. Although some caveats for the quantitative estimate of a 2.5-fold density difference are described, this study supports the notion that the X chromosome plays a special role in the evolution of reproductive isolation. Possible mechanisms of a "large X" effect include selective fixation of new mutations that are recessive or partially recessive and the evolution of sex-ratio distortion systems.

Optical-model potential for electron and positron elastic scattering by atoms

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

Salvat, Francesc

2003-07-01

An optical-model potential for systematic calculations of elastic scattering of electrons and positrons by atoms and positive ions is proposed. The electrostatic interaction is determined from the Dirac-Hartree-Fock self-consistent atomic electron density. In the case of electron projectiles, the exchange interaction is described by means of the local-approximation of Furness and McCarthy. The correlation-polarization potential is obtained by combining the correlation potential derived from the local density approximation with a long-range polarization interaction, which is represented by means of a Buckingham potential with an empirical energy-dependent cutoff parameter. The absorption potential is obtained from the local-density approximation, using the Born-Ochkurmore » approximation and the Lindhard dielectric function to describe the binary collisions with a free-electron gas. The strength of the absorption potential is adjusted by means of an empirical parameter, which has been determined by fitting available absolute elastic differential cross-section data for noble gases and mercury. The Dirac partial-wave analysis with this optical-model potential provides a realistic description of elastic scattering of electrons and positrons with energies in the range from {approx}100 eV up to {approx}5 keV. At higher energies, correlation-polarization and absorption corrections are small and the usual static-exchange approximation is sufficiently accurate for most practical purposes.« less

Canonical coordinates for partial differential equations

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1988-01-01

Necessary and sufficient conditions are found under which operators of the form Sigma (m, j=1) x (2) sub j + X sub O can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type.

Canonical coordinates for partial differential equations

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

Necessary and sufficient conditions are found under which operators of the form Sigma(m, j=1) X(2)sub j + X sub 0 can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type.

QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

NASA Astrophysics Data System (ADS)

Williams, P. D.; Haine, T. W. N.; Read, P. L.; Lewis, S. R.; Yamazaki, Y. H.

2008-09-01

QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.

QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

NASA Astrophysics Data System (ADS)

Williams, P. D.; Haine, T. W. N.; Read, P. L.; Lewis, S. R.; Yamazaki, Y. H.

2009-02-01

QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.

Discontinuous Galerkin Methods for NonLinear Differential Systems

NASA Technical Reports Server (NTRS)

Barth, Timothy; Mansour, Nagi (Technical Monitor)

2001-01-01

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

DNN-state identification of 2D distributed parameter systems

NASA Astrophysics Data System (ADS)

Chairez, I.; Fuentes, R.; Poznyak, A.; Poznyak, T.; Escudero, M.; Viana, L.

2012-02-01

There are many examples in science and engineering which are reduced to a set of partial differential equations (PDEs) through a process of mathematical modelling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. Moreover, to find exact solutions of those PDEs is not a trivial task especially if the PDE is described in two or more dimensions. It is well known that neural networks can approximate a large set of continuous functions defined on a compact set to an arbitrary accuracy. In this article, a strategy based on the differential neural network (DNN) for the non-parametric identification of a mathematical model described by a class of two-dimensional (2D) PDEs is proposed. The adaptive laws for weights ensure the 'practical stability' of the DNN-trajectories to the parabolic 2D-PDE states. To verify the qualitative behaviour of the suggested methodology, here a non-parametric modelling problem for a distributed parameter plant is analysed.

Modeling biological gradient formation: combining partial differential equations and Petri nets.

PubMed

Bertens, Laura M F; Kleijn, Jetty; Hille, Sander C; Heiner, Monika; Koutny, Maciej; Verbeek, Fons J

2016-01-01

Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.

A coupled electro-thermal Discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Homsi, L.; Geuzaine, C.; Noels, L.

2017-11-01

This paper presents a Discontinuous Galerkin scheme in order to solve the nonlinear elliptic partial differential equations of coupled electro-thermal problems. In this paper we discuss the fundamental equations for the transport of electricity and heat, in terms of macroscopic variables such as temperature and electric potential. A fully coupled nonlinear weak formulation for electro-thermal problems is developed based on continuum mechanics equations expressed in terms of energetically conjugated pair of fluxes and fields gradients. The weak form can thus be formulated as a Discontinuous Galerkin method. The existence and uniqueness of the weak form solution are proved. The numerical properties of the nonlinear elliptic problems i.e., consistency and stability, are demonstrated under specific conditions, i.e. use of high enough stabilization parameter and at least quadratic polynomial approximations. Moreover the prior error estimates in the H1-norm and in the L2-norm are shown to be optimal in the mesh size with the polynomial approximation degree.

Optimal control of a coupled partial and ordinary differential equations system for the assimilation of polarimetry Stokes vector measurements in tokamak free-boundary equilibrium reconstruction with application to ITER

NASA Astrophysics Data System (ADS)

Faugeras, Blaise; Blum, Jacques; Heumann, Holger; Boulbe, Cédric

2017-08-01

The modelization of polarimetry Faraday rotation measurements commonly used in tokamak plasma equilibrium reconstruction codes is an approximation to the Stokes model. This approximation is not valid for the foreseen ITER scenarios where high current and electron density plasma regimes are expected. In this work a method enabling the consistent resolution of the inverse equilibrium reconstruction problem in the framework of non-linear free-boundary equilibrium coupled to the Stokes model equation for polarimetry is provided. Using optimal control theory we derive the optimality system for this inverse problem. A sequential quadratic programming (SQP) method is proposed for its numerical resolution. Numerical experiments with noisy synthetic measurements in the ITER tokamak configuration for two test cases, the second of which is an H-mode plasma, show that the method is efficient and that the accuracy of the identification of the unknown profile functions is improved compared to the use of classical Faraday measurements.

Use of source distributions for evaluating theoretical aerodynamics of thin finite wings at supersonic speeds

NASA Technical Reports Server (NTRS)

Evvard, John C

1950-01-01

A series of publications on the source-distribution methods for evaluating the aerodynamics of thin wings at supersonic speeds is summarized, extended, and unified. Included in the first part are the deviations of: (a) the linearized partial-differential equation for unsteady flow at a substantially constant Mach number. b) The source-distribution solution for the perturbation-velocity potential that satisfies the boundary conditions of tangential flow at the surface and in the plane of the wing; and (c) the integral equation for determining the strength and the location of sources to describe the interaction effects (as represented by upwash) of the bottom and top wing surfaces through the region between the finite wing boundary and the foremost Mach wave. The second part deals with steady-state thin-wing problems. The third part of the report approximates the integral equation for unsteady upwash and includes a solution of approximate equation. Expressions are then derived to evaluate the load distributions for time-dependent finite-wing motions.

New second order Mumford-Shah model based on Γ-convergence approximation for image processing

NASA Astrophysics Data System (ADS)

Duan, Jinming; Lu, Wenqi; Pan, Zhenkuan; Bai, Li

2016-05-01

In this paper, a second order variational model named the Mumford-Shah total generalized variation (MSTGV) is proposed for simultaneously image denoising and segmentation, which combines the original Γ-convergence approximated Mumford-Shah model with the second order total generalized variation (TGV). For image denoising, the proposed MSTGV can eliminate both the staircase artefact associated with the first order total variation and the edge blurring effect associated with the quadratic H1 regularization or the second order bounded Hessian regularization. For image segmentation, the MSTGV can obtain clear and continuous boundaries of objects in the image. To improve computational efficiency, the implementation of the MSTGV does not directly solve its high order nonlinear partial differential equations and instead exploits the efficient split Bregman algorithm. The algorithm benefits from the fast Fourier transform, analytical generalized soft thresholding equation, and Gauss-Seidel iteration. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of the proposed model.

Digital-model simulation of the glacial-outwash aquifer, Otter Creek-Dry Creek basin, Cortland County, New York

USGS Publications Warehouse

Cosner, O.J.; Harsh, J.F.

1978-01-01

The city of Cortland, New York, and surrounding areas obtain water from the highly productive glacial-outwash aquifer underlying the Otter Creek-Dry Creek basin. Pumpage from the aquifer in 1976 was approximately 6.3 million gallons per day and is expected to increase as a result of population growth and urbanization. A digital ground-water model that uses a finite-difference approximation technique to solve partial differential equations of flow through a porous medium was used to simulate the movement of water within the aquifer. The model was calibrated to equilibrium conditions by comparing water levels measured in the aquifer in March 1976 with those computed by the model. Then, from the simulated water-level surface for March, a transient-condition run was made to simulate the surface as measured in September 1976. Computed water levels presented as contours are generally in close agreement with potentiometric-surface maps prepared from field measurements of March and September 1976. (Woodard-USGS)

Structural physical approximation for the realization of the optimal singlet fraction with two measurements

NASA Astrophysics Data System (ADS)

Adhikari, Satyabrata

2018-04-01

Structural physical approximation (SPA) has been exploited to approximate nonphysical operation such as partial transpose. It has already been studied in the context of detection of entanglement and found that if the minimum eigenvalue of SPA to partial transpose is less than 2/9 then the two-qubit state is entangled. We find application of SPA to partial transpose in the estimation of the optimal singlet fraction. We show that the optimal singlet fraction can be expressed in terms of the minimum eigenvalue of SPA to partial transpose. We also show that the optimal singlet fraction can be realized using Hong-Ou-Mandel interferometry with only two detectors. Further we have shown that the generated hybrid entangled state between a qubit and a binary coherent state can be used as a resource state in quantum teleportation.

Magnetohydrodynamic Flow by a Stretching Cylinder with Newtonian Heating and Homogeneous-Heterogeneous Reactions

PubMed Central

Hayat, T.; Hussain, Zakir; Alsaedi, A.; Farooq, M.

2016-01-01

This article examines the effects of homogeneous-heterogeneous reactions and Newtonian heating in magnetohydrodynamic (MHD) flow of Powell-Eyring fluid by a stretching cylinder. The nonlinear partial differential equations of momentum, energy and concentration are reduced to the nonlinear ordinary differential equations. Convergent solutions of momentum, energy and reaction equations are developed by using homotopy analysis method (HAM). This method is very efficient for development of series solutions of highly nonlinear differential equations. It does not depend on any small or large parameter like the other methods i. e., perturbation method, δ—perturbation expansion method etc. We get more accurate result as we increase the order of approximations. Effects of different parameters on the velocity, temperature and concentration distributions are sketched and discussed. Comparison of present study with the previous published work is also made in the limiting sense. Numerical values of skin friction coefficient and Nusselt number are also computed and analyzed. It is noticed that the flow accelerates for large values of Powell-Eyring fluid parameter. Further temperature profile decreases and concentration profile increases when Powell-Eyring fluid parameter enhances. Concentration distribution is decreasing function of homogeneous reaction parameter while opposite influence of heterogeneous reaction parameter appears. PMID:27280883

Magnetohydrodynamic Flow by a Stretching Cylinder with Newtonian Heating and Homogeneous-Heterogeneous Reactions.

PubMed

Hayat, T; Hussain, Zakir; Alsaedi, A; Farooq, M

2016-01-01

This article examines the effects of homogeneous-heterogeneous reactions and Newtonian heating in magnetohydrodynamic (MHD) flow of Powell-Eyring fluid by a stretching cylinder. The nonlinear partial differential equations of momentum, energy and concentration are reduced to the nonlinear ordinary differential equations. Convergent solutions of momentum, energy and reaction equations are developed by using homotopy analysis method (HAM). This method is very efficient for development of series solutions of highly nonlinear differential equations. It does not depend on any small or large parameter like the other methods i. e., perturbation method, δ-perturbation expansion method etc. We get more accurate result as we increase the order of approximations. Effects of different parameters on the velocity, temperature and concentration distributions are sketched and discussed. Comparison of present study with the previous published work is also made in the limiting sense. Numerical values of skin friction coefficient and Nusselt number are also computed and analyzed. It is noticed that the flow accelerates for large values of Powell-Eyring fluid parameter. Further temperature profile decreases and concentration profile increases when Powell-Eyring fluid parameter enhances. Concentration distribution is decreasing function of homogeneous reaction parameter while opposite influence of heterogeneous reaction parameter appears.

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

NASA Astrophysics Data System (ADS)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

Testing for Differential Item Functioning with Measures of Partial Association

ERIC Educational Resources Information Center

Woods, Carol M.

2009-01-01

Differential item functioning (DIF) occurs when an item on a test or questionnaire has different measurement properties for one group of people versus another, irrespective of mean differences on the construct. There are many methods available for DIF assessment. The present article is focused on indices of partial association. A family of average…

THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

EPA Science Inventory

A three-point backward finite-difference method has been derived for a system of mixed hyperbolic_¯¯parabolic (convection_¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

Theory of low-energy electron-molecule collision physics in the coupled-channel method and application to e-CO/sub 2/ scattering. [0. 01 to 10 eV, potentials, partial waves

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

Morrison, M.A.

1976-08-01

A theory of electron-molecule scattering based on the fixed-nuclei approximation in a body-fixed reference frame is formulated and applied to e-CO/sub 2/ collisions in the energy range from 0.07 to 10.0 eV. The procedure used is a single-center coupled-channel method which incorporates a highly accurate static interaction potential, an approximate local exchange potential, and an induced polarization potential. Coupled equations are solved by a modification of the integral equations algorithm; several partial waves are required in the region of space near the nuclei, and a transformation procedure is developed to handle the consequent numerical problems. The potential energy is convergedmore » by separating electronic and nuclear contributions in a Legendre-polynomial expansion and including a large number of the latter. Formulas are derived for total elastic, differential, momentum transfer, and rotational excitation cross sections. The Born and asymptotic decoupling approximations are derived and discussed in the context of comparison with the coupled-channel cross sections. Both are found to be unsatisfactory in the energy range under consideration. An extensive discussion of the technical aspects of calculations for electron collisions with highly nonspherical targets is presented, including detailed convergence studies and a discussion of various numerical difficulties. The application to e-CO/sub 2/ scattering produces converged results in good agreement with observed cross sections. Various aspects of the physics of this collision are discussed, including the 3.8 eV shape resonance, which is found to possess both p and f character, and the anomalously large low-energy momentum transfer cross sections, which are found to be due to ..sigma../sub g/ symmetry. Comparison with static and static-exchange approximations are made.« less

Steady MHD free convection heat and mass transfer flow about a vertical porous surface with thermal diffusion and induced magnetic field

NASA Astrophysics Data System (ADS)

Touhid Hossain, M. M.; Afruz-Zaman, Md.; Rahman, Fouzia; Hossain, M. Arif

2013-09-01

In this study the thermal diffusion effect on the steady laminar free convection flow and heat transfer of viscous incompressible MHD electrically conducting fluid above a vertical porous surface is considered under the influence of an induced magnetic field. The governing non-dimensional equations relevant to the problem, containing the partial differential equations, are transformed by usual similarity transformations into a system of coupled non-linear ordinary differential equations and will be solved analytically by using the perturbation technique. On introducing the non-dimensional concept and applying Boussinesq's approximation, the solutions for velocity field, temperature distribution and induced magnetic field to the second order approximations are obtained for large suction with different selected values of the established dimensionless parameters. The influences of these various establish parameters on the velocity and temperature fields and on the induced magnetic fields are exhibited under certain assumptions and are studied graphically in the present analysis. It is observed that the effects of thermal-diffusion and large suction have great importance on the velocity, temperature and induced magnetic fields and mass concentration for several fluids considered, so that their effects should be taken into account with other useful parameters associated. It is also found that the dimensionless Prandtl number, Grashof number, Modified Grashof number and magnetic parameter have an appreciable influence on the concerned independent variables.

Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas

NASA Astrophysics Data System (ADS)

Ren, Zhigang; Xu, Chao; Lin, Qun; Loxton, Ryan; Teo, Kok Lay

2016-03-01

Establishing a good current spatial profile in tokamak fusion reactors is crucial to effective steady-state operation. The evolution of the current spatial profile is related to the evolution of the poloidal magnetic flux, which can be modeled in the normalized cylindrical coordinates using a parabolic partial differential equation (PDE) called the magnetic diffusion equation. In this paper, we consider the dynamic optimization problem of attaining the best possible current spatial profile during the ramp-up phase of the tokamak. We first use the Galerkin method to obtain a finite-dimensional ordinary differential equation (ODE) model based on the original magnetic diffusion PDE. Then, we combine the control parameterization method with a novel time-scaling transformation to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimization techniques such as sequential quadratic programming (SQP). This control parameterization approach involves approximating the tokamak input signals by piecewise-linear functions whose slopes and break-points are decision variables to be optimized. We show that the gradient of the objective function with respect to the decision variables can be computed by solving an auxiliary dynamic system governing the state sensitivity matrix. Finally, we conclude the paper with simulation results for an example problem based on experimental data from the DIII-D tokamak in San Diego, California.

Magnetic Evidence for a Partially Differentiated Carbonaceous Chondrite Parent Body and Possible Implications for Asteroid 21 Lutetia

NASA Astrophysics Data System (ADS)

Weiss, Benjamin; Carporzen, L.; Elkins-Tanton, L.; Shuster, D. L.; Ebel, D. S.; Gattacceca, J.; Binzel, R. P.

2010-10-01

The origin of remanent magnetization in the CV carbonaceous chondrite Allende has been a longstanding mystery. The possibility of a core dynamo like that known for achondrite parent bodies has been discounted because chondrite parent bodies are assumed to be undifferentiated. Here we report that Allende's magnetization was acquired over several million years (Ma) during metasomatism on the parent planetesimal in a > 20 microtesla field 8-9 Ma after solar system formation. This field was present too recently and directionally stable for too long to have been the generated by the protoplanetary disk or young Sun. The field intensity is in the range expected for planetesimal core dynamos (Weiss et al. 2010), suggesting that CV chondrites are derived from the outer, unmelted layer of a partially differentiated body with a convecting metallic core (Elkins-Tanton et al. 2010). This suggests that asteroids with differentiated interiors could be present today but masked under chondritic surfaces. In fact, CV chondrites are spectrally similar to many members of the Eos asteroid family whose spectral diversity has been interpreted as evidence for a partially differentiated parent asteroid (Mothe-Diniz et al. 2008). CV chondrite spectral and polarimetric data also resemble those of asteroid 21 Lutetia (e.g., Belskaya et al. 2010), recently encountered by the Rosetta spacecraft. Ground-based measurements of Lutetia indicate a high density of 2.4-5.1 g cm-3 (Drummond et al. 2010), while radar data seem to rule out a metallic surface composition (Shepard et al. 2008). If Rosetta spacecraft measurements confirm a high density and a CV-like surface composition for Lutetia, then we propose Lutetia may be an example of a partially differentiated carbonaceous chondrite parent body. Regardless, the very existence of primitive achondrites, which contain evidence of both relict chondrules and partial melting, are prima facie evidence for the formation of partially differentiated bodies.

Differential Curing In Fiber/Resin Laminates

NASA Technical Reports Server (NTRS)

Webster, Charles N.

1989-01-01

Modified layup schedule counteracts tendency toward delamination. Improved manufacturing process resembles conventional process, except prepregs partially cured laid on mold in sequence in degree of partial cure decreases from mold side to bag side. Degree of partial cure of each layer at time of layup selected by controlling storage and partial-curing temperatures of prepreg according to Arrhenius equation for rate of gel of resin as function of temperature and time from moment of mixing. Differential advancement of cure in layers made large enough to offset effect of advance bag-side heating in oven or autoclave. Technique helps prevent entrapment of volatile materials during manufacturing of fiber/resin laminates.

The method of A-harmonic approximation and optimal interior partial regularity for nonlinear elliptic systems under the controllable growth condition

NASA Astrophysics Data System (ADS)

Chen, Shuhong; Tan, Zhong

2007-11-01

In this paper, we consider the nonlinear elliptic systems under controllable growth condition. We use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. We extend previous partial regularity results under the natural growth condition to the case of the controllable growth condition, and directly establishing the optimal Hölder exponent for the derivative of a weak solution.

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.

The nonlinear modified equation approach to analyzing finite difference schemes

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1981-01-01

The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.

The influence of wind-tunnel walls on discrete frequency noise

NASA Technical Reports Server (NTRS)

Mosher, M.

1984-01-01

This paper describes an analytical model that can be used to examine the effects of wind-tunnel walls on discrete frequency noise. First, a complete physical model of an acoustic source in a wind tunnel is described, and a simplified version is then developed. This simplified model retains the important physical processes involved, yet it is more amenable to analysis. Second, the simplified physical model is formulated as a mathematical problem. An inhomogeneous partial differential equation with mixed boundary conditions is set up and then transformed into an integral equation. The integral equation has been solved with a panel program on a computer. Preliminary results from a simple model problem will be shown and compared with the approximate analytic solution.

A regularization method for extrapolation of solar potential magnetic fields

NASA Technical Reports Server (NTRS)

Gary, G. A.; Musielak, Z. E.

1992-01-01

The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.

Experimental confirmation of a PDE-based approach to design of feedback controls

NASA Technical Reports Server (NTRS)

Banks, H. T.; Smith, Ralph C.; Brown, D. E.; Silcox, R. J.; Metcalf, Vern L.

1995-01-01

Issues regarding the experimental implementation of partial differential equation based controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surface-mounted piezoceramic patches, the general techniques described here will extend to a variety of applications. The initial step is the development of a PDE model which accurately captures the physics of the underlying process. This model is then discretized to yield a vector-valued initial value problem. Optimal control theory is used to determine continuous-time voltages to the patches, and the approximations needed to facilitate discrete time implementation are addressed. Finally, experimental results demonstrating the control of both transient and steady state vibrations through these techniques are presented.

Fractional calculus in hydrologic modeling: A numerical perspective

PubMed Central

Benson, David A.; Meerschaert, Mark M.; Revielle, Jordan

2013-01-01

Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. PMID:23524449

A homotopy analysis method for the nonlinear partial differential equations arising in engineering

NASA Astrophysics Data System (ADS)

Hariharan, G.

2017-05-01

In this article, we have established the homotopy analysis method (HAM) for solving a few partial differential equations arising in engineering. This technique provides the solutions in rapid convergence series with computable terms for the problems with high degree of nonlinear terms appearing in the governing differential equations. The convergence analysis of the proposed method is also discussed. Finally, we have given some illustrative examples to demonstrate the validity and applicability of the proposed method.

Parent Ratings of ADHD Symptoms: Generalized Partial Credit Model Analysis of Differential Item Functioning across Gender

ERIC Educational Resources Information Center

Gomez, Rapson

2012-01-01

Objective: Generalized partial credit model, which is based on item response theory (IRT), was used to test differential item functioning (DIF) for the "Diagnostic and Statistical Manual of Mental Disorders" (4th ed.), inattention (IA), and hyperactivity/impulsivity (HI) symptoms across boys and girls. Method: To accomplish this, parents completed…

Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.

PubMed

Baranwal, Vipul K; Pandey, Ram K; Singh, Om P

2014-01-01

We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

Isolation of stress responsive Psb A gene from rice (Oryza sativa l.) using differential display.

PubMed

Tyagi, Aruna; Chandra, Arti

2006-08-01

Differential display (DD) experiments were performed on drought-tolerant rice (Oryza sativa L.) genotype N22 to identify both upregulated and downregulated partial cDNAs with respect to moisture stress. DNA polymorphism was detected between drought-stressed and control leaf tissues on the DD gels. A partial cDNA showing differential expression, with respect to moisture stress was isolated from the gel. Northern blotting analysis was performed using this cDNA as a probe and it was observed that mRNA corresponding to this transcript was accumulated to high level in rice leaves under water deficit stress. At the DNA sequence level, the partial cDNA showed homology with psb A gene encoding for Dl protein.

On the dynamics of approximating schemes for dissipative nonlinear equations

NASA Technical Reports Server (NTRS)

Jones, Donald A.

1993-01-01

Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.

Legendre-Tau approximation for functional differential equations. Part 3: Eigenvalue approximations and uniform stability

NASA Technical Reports Server (NTRS)

Ito, K.

1984-01-01

The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.

A COMPARISON OF EXPERIMENTS AND THREE-DIMENSIONAL ANALYSIS TECHNIQUES. PART I. UNPOISONED UNIFORM SLAB CORE WITH A PARTIALLY INSERTED HAFNIUM ROD

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

Renzi, N.E.; Roseberry, R.J.

>The experimental measurements and nuclear analysis of a uniformly loaded, unpoisoned slab core with a partially insented hafnium rod are described. Comparisons of experimental data with calculated results of the UFO code and flux synthesis techniques are given. It was concluded that one of the flux synthesis techniques and the UFO code are able to predict flux distributions to within approximately 5% of experiment for most cases. An error of approximately 10% was found in the synthesis technique for a channel near the partially inserted rod. The various calculations were able to predict neutron pulsed shutdowns to only approximately 30%.more » (auth)« less

On multilevel RBF collocation to solve nonlinear PDEs arising from endogenous stochastic volatility models

NASA Astrophysics Data System (ADS)

Bastani, Ali Foroush; Dastgerdi, Maryam Vahid; Mighani, Abolfazl

2018-06-01

The main aim of this paper is the analytical and numerical study of a time-dependent second-order nonlinear partial differential equation (PDE) arising from the endogenous stochastic volatility model, introduced in [Bensoussan, A., Crouhy, M. and Galai, D., Stochastic equity volatility related to the leverage effect (I): equity volatility behavior. Applied Mathematical Finance, 1, 63-85, 1994]. As the first step, we derive a consistent set of initial and boundary conditions to complement the PDE, when the firm is financed by equity and debt. In the sequel, we propose a Newton-based iteration scheme for nonlinear parabolic PDEs which is an extension of a method for solving elliptic partial differential equations introduced in [Fasshauer, G. E., Newton iteration with multiquadrics for the solution of nonlinear PDEs. Computers and Mathematics with Applications, 43, 423-438, 2002]. The scheme is based on multilevel collocation using radial basis functions (RBFs) to solve the resulting locally linearized elliptic PDEs obtained at each level of the Newton iteration. We show the effectiveness of the resulting framework by solving a prototypical example from the field and compare the results with those obtained from three different techniques: (1) a finite difference discretization; (2) a naive RBF collocation and (3) a benchmark approximation, introduced for the first time in this paper. The numerical results confirm the robustness, higher convergence rate and good stability properties of the proposed scheme compared to other alternatives. We also comment on some possible research directions in this field.

Optimal analytic method for the nonlinear Hasegawa-Mima equation

NASA Astrophysics Data System (ADS)

Baxter, Mathew; Van Gorder, Robert A.; Vajravelu, Kuppalapalle

2014-05-01

The Hasegawa-Mima equation is a nonlinear partial differential equation that describes the electric potential due to a drift wave in a plasma. In the present paper, we apply the method of homotopy analysis to a slightly more general Hasegawa-Mima equation, which accounts for hyper-viscous damping or viscous dissipation. First, we outline the method for the general initial/boundary value problem over a compact rectangular spatial domain. We use a two-stage method, where both the convergence control parameter and the auxiliary linear operator are optimally selected to minimize the residual error due to the approximation. To do the latter, we consider a family of operators parameterized by a constant which gives the decay rate of the solutions. After outlining the general method, we consider a number of concrete examples in order to demonstrate the utility of this approach. The results enable us to study properties of the initial/boundary value problem for the generalized Hasegawa-Mima equation. In several cases considered, we are able to obtain solutions with extremely small residual errors after relatively few iterations are computed (residual errors on the order of 10-15 are found in multiple cases after only three iterations). The results demonstrate that selecting a parameterized auxiliary linear operator can be extremely useful for minimizing residual errors when used concurrently with the optimal homotopy analysis method, suggesting that this approach can prove useful for a number of nonlinear partial differential equations arising in physics and nonlinear mechanics.

Convergence analysis of surrogate-based methods for Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Yan, Liang; Zhang, Yuan-Xiang

2017-12-01

The major challenges in the Bayesian inverse problems arise from the need for repeated evaluations of the forward model, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. Many attempts at accelerating Bayesian inference have relied on surrogates for the forward model, typically constructed through repeated forward simulations that are performed in an offline phase. Although such approaches can be quite effective at reducing computation cost, there has been little analysis of the approximation on posterior inference. In this work, we prove error bounds on the Kullback-Leibler (KL) distance between the true posterior distribution and the approximation based on surrogate models. Our rigorous error analysis show that if the forward model approximation converges at certain rate in the prior-weighted L 2 norm, then the posterior distribution generated by the approximation converges to the true posterior at least two times faster in the KL sense. The error bound on the Hellinger distance is also provided. To provide concrete examples focusing on the use of the surrogate model based methods, we present an efficient technique for constructing stochastic surrogate models to accelerate the Bayesian inference approach. The Christoffel least squares algorithms, based on generalized polynomial chaos, are used to construct a polynomial approximation of the forward solution over the support of the prior distribution. The numerical strategy and the predicted convergence rates are then demonstrated on the nonlinear inverse problems, involving the inference of parameters appearing in partial differential equations.

Generalized Lie symmetry approach for fractional order systems of differential equations. III

NASA Astrophysics Data System (ADS)

Singla, Komal; Gupta, R. K.

2017-06-01

The generalized Lie symmetry technique is proposed for the derivation of point symmetries for systems of fractional differential equations with an arbitrary number of independent as well as dependent variables. The efficiency of the method is illustrated by its application to three higher dimensional nonlinear systems of fractional order partial differential equations consisting of the (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov system, (3 + 1)-dimensional Burgers system, and (3 + 1)-dimensional Navier-Stokes equations. With the help of derived Lie point symmetries, the corresponding invariant solutions transform each of the considered systems into a system of lower-dimensional fractional partial differential equations.

Solution of some types of differential equations: operational calculus and inverse differential operators.

PubMed

Zhukovsky, K

2014-01-01

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

The Laguerre finite difference one-way equation solver

NASA Astrophysics Data System (ADS)

Terekhov, Andrew V.

2017-05-01

This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1984-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Teglas, Russell

1987-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Concatenons as the solutions for non-linear partial differential equations

NASA Astrophysics Data System (ADS)

Kudryashov, N. A.; Volkov, A. K.

2017-07-01

New class of solutions for nonlinear partial differential equations is introduced. We call them the concaten solutions. As an example we consider equations for the description of wave processes in the Fermi-Pasta-Ulam mass chain and construct the concatenon solutions for these equation. Stability of the concatenon-type solutions is investigated numerically. Interaction between the concatenon and solitons is discussed.

Hidden physics models: Machine learning of nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Raissi, Maziar; Karniadakis, George Em

2018-03-01

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

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.

Direct application of Padé approximant for solving nonlinear differential equations.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

2014-01-01

This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

Partial slip effect in the flow of MHD micropolar nanofluid flow due to a rotating disk - A numerical approach

NASA Astrophysics Data System (ADS)

Ramzan, Muhammad; Chung, Jae Dong; Ullah, Naeem

The aim of present exploration is to study the flow of micropolar nanofluid due to a rotating disk in the presence of magnetic field and partial slip condition. The governing coupled partial differential equations are reduced to nonlinear ordinary differential equations using appropriate transformations. The differential equations are solved numerically by using Maple dsolve command with option numeric which utilize Runge-Kutta fourth-fifth order Fehlberg technique. A comparison to previous study is also added to validate the present results. Moreover, behavior of different parameters on velocity, microrotation, temperature and concentration of nanofluid are presented via graphs and tables. It is noted that the slip effect and magnetic field decay the velocity and microrotation or spin component.

The Uniform Convergence of Eigenfunction Expansions of Schrödinger Operator in the Nikolskii Classes {H}_{p}^{\\alpha }(\\bar{\\Omega })

NASA Astrophysics Data System (ADS)

Jamaludin, N. A.; Ahmedov, A.

2017-09-01

Many boundary value problems in the theory of partial differential equations can be solved by separation methods of partial differential equations. When Schrödinger operator is considered then the influence of the singularity of potential on the solution of the partial differential equation is interest of researchers. In this paper the problems of the uniform convergence of the eigenfunction expansions of the functions from corresponding to the Schrödinger operator with the potential from classes of Sobolev are investigated. The spectral function corresponding to the Schrödinger operator is estimated in closed domain. The isomorphism of the Nikolskii classes is applied to prove uniform convergence of eigenfunction expansions of Schrödinger operator in closed domain.

Low-Degree Partial Melting Experiments of CR and H Chondrite Compositions: Implications for Asteroidal Magmatism Recorded in GRA 06128 and GRA 06129 T

NASA Technical Reports Server (NTRS)

Usui, T.; Jones, John H.; Mittlefehldt, D. W.

2010-01-01

Studies of differentiated meteorites have revealed a diversity of differentiation processes on their parental asteroids; these differentiation mechanisms range from whole-scale melting to partial melting without the core formation [e.g., 1]. Recently discovered paired achondrites GRA 06128 and GRA 06129 (hereafter referred to as GRA) represent unique asteroidal magmatic processes. These meteorites are characterized by high abundances of sodic plagioclase and alkali-rich whole-rock compositions, implying that they could originate from a low-degree partial melt from a volatile-rich oxidized asteroid [e.g., 2, 3, 4]. These conditions are consistent with the high abundances of highly siderophile elements, suggesting that their parent asteroid did not segregate a metallic core [2]. In this study, we test the hypothesis that low-degree partial melts of chondritic precursors under oxidizing conditions can explain the whole-rock and mineral chemistry of GRA based on melting experiments of synthesized CR- and H-chondrite compositions.

An Introduction to Lagrangian Differential Calculus.

ERIC Educational Resources Information Center

Schremmer, Francesca; Schremmer, Alain

1990-01-01

Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1988-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1990-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Trigonometric Integrals via Partial Fractions

ERIC Educational Resources Information Center

Chen, H.; Fulford, M.

2005-01-01

Parametric differentiation is used to derive the partial fractions decompositions of certain rational functions. Those decompositions enable us to integrate some new combinations of trigonometric functions.

Exp-function method for solving fractional partial differential equations.

PubMed

Zheng, Bin

2013-01-01

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

Application of partial differential equation modeling of the control/structural dynamics of flexible spacecraft

NASA Technical Reports Server (NTRS)

Taylor, Lawrence W., Jr.; Rajiyah, H.

1991-01-01

Partial differential equations for modeling the structural dynamics and control systems of flexible spacecraft are applied here in order to facilitate systems analysis and optimization of these spacecraft. Example applications are given, including the structural dynamics of SCOLE, the Solar Array Flight Experiment, the Mini-MAST truss, and the LACE satellite. The development of related software is briefly addressed.

Third Partial and 3.0L Second Partial and 2.0L Partial and Amended Consent Decree

EPA Pesticide Factsheets

The settlement partially resolves allegations that Volkswagen violated the Clean Air Act (“CAA”) by the sale of approximately 500,000 model year 2009 to 2015 motor vehicles containing 2.0 liter diesel engines equipped with “defeat devices” (“CAA 2.0 liter.

Effect of evaporative surface cooling on thermographic assessment of burn depth

NASA Technical Reports Server (NTRS)

Anselmo, V. J.; Zawacki, B. E.

1977-01-01

Differences in surface temperature between evaporating and nonevaporating, partial- and full-thickness burn injuries were studied in 20 male, white guinea pigs. Evaporative cooling can disguise the temperature differential of the partial-thickness injury and lead to a false full-thickness diagnosis. A full-thickness burn with blister intact may retain enough heat to result in a false partial-thickness diagnosis. By the fourth postburn day, formation of a dry eschar may allow a surface temperature measurement without the complication of differential evaporation. For earlier use of thermographic information, evaporation effects must be accounted for or eliminated.

Solving Differential Equations in R: Package deSolve

EPA Science Inventory

In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines appr...

Gravitational collapse of a turbulent vortex with application to star formation

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1976-01-01

The gravitational collapse of a rotating cloud or vortex is analyzed by expanding the dependent variables in the equations of motion in two-dimensional Taylor series in the space variables. It is shown that the gravitational and rotational terms in the equations are of first order in the space variables, the pressure-gradient terms are of second order, and the turbulent-viscosity term is of third order. The presence of turbulent viscosity ensures that the initial rotation is solid-body-like near the origin. The effect of pressure on the collapse process is found to depend on the shape of the initial density disturbance at the origin. Dimensionless collapse times, as well as the evolution of density and velocity, are calculated by solving numerically the system of nonlinear ordinary differential equations resulting from the series expansions. The axial flow is always inward and allows collapse to occur (axially) even when the rotation is large. An approximate solution of the governing partial differential equations is also given in order to study the spatial distributions of the density and velocity.

Gravitational collapse of a turbulent vortex with application to star formation

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1975-01-01

The gravitational collapse of a rotating cloud or vortex is analyzed by expanding the dependent variables in the equations of motion in two-dimensional Taylor series in the space variables. It is shown that the gravitation and rotation terms in the equations are of first order in the space variables, the pressure gradient terms are of second order, and the turbulent viscosity term is of third order. The presence of a turbulent viscosity insures that the initial rotation is solid-body-like near the origin. The effect of pressure on the collapse process is found to depend on the shape of the intial density disturbance at the origin. Dimensionless collapse times, as well as the evolution of density and velocity, are calculated by solving numerically the system of nonlinear ordinary differential equations resulting from the series expansions. The axial inflow plays an important role and allows collapse to occur even when the rotation is large. An approximate solution of the governing partial differential equations is also given, in order to study the spacial distributions of the density and velocity.

QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

NASA Astrophysics Data System (ADS)

Williams, P. D.; Haine, T. W. N.; Read, P. L.; Lewis, S. R.; Yamazaki, Y. H.

2009-04-01

The QUAGMIRE model has recently been made freely available for public use. QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. This presentation describes the model's main features. QUAGMIRE uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.

Geologic Evolution of North America: Geologic features suggest that the continent has grown and differentiated through geologic time.

PubMed

Engel, A E

1963-04-12

The oldest decipherable rock complexes within continents (more than 2.5 billion years old) are largely basaltic volcanics and graywacke. Recent and modern analogs are the island arcs formed along and adjacent to the unstable interface of continental and oceanic crusts. The major interfacial reactions (orogenies) incorporate pre-existing sial, oceanic crust, and mantle into crust of a more continental type. Incipient stages of continental evolution, more than 3 billion years ago, remain obscure. They may involve either a cataclysmic granite-forming event or a succession of volcanic-sedimentary and granite-forming cycles. Intermediate and recent stages of continental evolution, as indicated by data for North America, involve accretion of numerous crustal interfaces with fragments of adjacent continental crust and their partial melting, reinjection, elevation, unroofing, and stabilization. Areas of relict provinces defined by ages of granites suggest that continental growth is approximately linear. But the advanced differentiation found in many provinces and the known overlaps permit wide deviation from linearity in the direction of a more explosive early or intermediate growth.

Isolation of genes differentially expressed during development and ripening of Fragaria chiloensis fruit by suppression subtractive hybridization.

PubMed

Pimentel, Paula; Salvatierra, Ariel; Moya-León, María Alejandra; Herrera, Raúl

2010-09-15

Fragaria chiloensis, the native Chilean strawberry, is noted for its good fruit quality characters. However, it is a highly perishable fruit due to its rapid softening. With the aim to screen for genes differentially expressed during development and ripening of strawberry fruit, the subtractive suppressive hybridization (SSH) methodology was employed. Six libraries were generated contrasting transcripts from four different developmental stages. A set of 1807 genes was isolated and characterized. In our EST collection, approximately 90% of partial cDNAs showed significant similarity to proteins with known or unknown function registered in databases. Among them, proteins related to protein fate were identified in a large green fruit library and protein related with cellular transport, cell wall-related proteins, and transcription regulators were identified in a ripe fruit library. Thirteen genes were analyzed by qRT-PCR during development and ripening of the Chilean strawberry fruit. The information generated in this study provides new clues to aid the understanding of the ripening process in F. chiloensis fruit. Copyright 2010 Elsevier GmbH. All rights reserved.

Local polynomial chaos expansion for linear differential equations with high dimensional random inputs

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

Chen, Yi; Jakeman, John; Gittelson, Claude

2015-01-08

In this paper we present a localized polynomial chaos expansion for partial differential equations (PDE) with random inputs. In particular, we focus on time independent linear stochastic problems with high dimensional random inputs, where the traditional polynomial chaos methods, and most of the existing methods, incur prohibitively high simulation cost. Furthermore, the local polynomial chaos method employs a domain decomposition technique to approximate the stochastic solution locally. In each subdomain, a subdomain problem is solved independently and, more importantly, in a much lower dimensional random space. In a postprocesing stage, accurate samples of the original stochastic problems are obtained frommore » the samples of the local solutions by enforcing the correct stochastic structure of the random inputs and the coupling conditions at the interfaces of the subdomains. Overall, the method is able to solve stochastic PDEs in very large dimensions by solving a collection of low dimensional local problems and can be highly efficient. In our paper we present the general mathematical framework of the methodology and use numerical examples to demonstrate the properties of the method.« less

Görtler instability of the axisymmetric boundary layer along a cone

NASA Astrophysics Data System (ADS)

ITOH, Nobutake

2014-10-01

Exact partial differential equations are derived to describe Görtler instability, caused by a weakly concave wall, of axisymmetric boundary layers with similar velocity profiles that are decomposed into a sequence of ordinary differential systems on the assumption that the solution can be expanded into inverse powers of local Reynolds number. The leading terms of the series solution are determined by solving a non-parallel version of Görtler’s eigenvalue problem and lead to a neutral stability curve and finite values of critical Görtler number and wave number for stationary and longitudinal vortices. Higher-order terms of the series solution indicate Reynolds-number dependence of Görtler instability and a limited validity of Görtler’s approximation based on the leading terms only. The present formulation is simply applicable to two-dimensional boundary layers of similar profiles, and critical Görtler number and wave number of the Blasius boundary layer on a flat plate are given by G2c = 1.23 and β2c = 0.288, respectively, if the momentum thickness is chosen as the reference length.

Gravitational collapse of a turbulent vortex with application to star formation

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1975-01-01

The gravitational collapse of a rotating cloud or vortex is analyzed by expanding the dependent variables in the equations of motion in two-dimensional Taylor series in the space variables. It is shown that the gravitation and rotation terms in the equations are of first order in the space variables, the pressure gradient terms are of second order, and the turbulent viscosity term is of third order. The presence of a turbulent viscosity insures that the initial rotation is solid-body-like near the origin. The effect of pressure on the collapse process is found to depend on the shape of the initial density disturbance at the origin. Dimensionless collapse times, as well as the evolution of density and velocity, are calculated by solving numerically the system of nonlinear ordinary differential equations resulting from the series expansions. The axial inflow plays an important role and allows collapse to occur even when the rotation is large. An approximate solution of the governing partial differential equations is also given; the equations are used to study the spacial distributions of the density and velocity.

The numerical-analytical implementation of the cross-sections method to the open waveguide transition of the "horn" type

NASA Astrophysics Data System (ADS)

Divakov, Dmitriy; Malykh, Mikhail; Sevastianov, Leonid; Sevastianov, Anton; Tiutiunnik, Anastasiia

2017-04-01

In the paper we construct a method for approximate solution of the waveguide problem for guided modes of an open irregular waveguide transition. The method is based on straightening of the curved waveguide boundaries by introducing new variables and applying the Kantorovich method to the problem formulated in the new variables to get a system of ordinary second-order differential equations. In the method, the boundary conditions are formulated by analogy with the partial radiation conditions in the similar problem for closed waveguide transitions. The method is implemented in the symbolic-numeric form using the Maple computer algebra system. The coefficient matrices of the system of differential equations and boundary conditions are calculated symbolically, and then the obtained boundary-value problem is solved numerically using the finite difference method. The chosen coordinate functions of Kantorovich expansions provide good conditionality of the coefficient matrices. The numerical experiment simulating the propagation of guided modes in the open waveguide transition confirms the validity of the method proposed to solve the problem.

Composition and evolution of the eucrite parent body - Evidence from rare earth elements. [extraterrestrial basaltic melts

NASA Technical Reports Server (NTRS)

Consolmagno, G. J.; Drake, M. J.

1977-01-01

Quantitative modeling of the evolution of rare earth element (REE) abundances in the eucrites, which are plagioclase-pigeonite basalt achondrites, indicates that the main group of eucrites (e.g., Juvinas) might have been produced by approximately 10% equilibrium partial melting of a single type of source region with initial REE abundances which were chondritic relative and absolute. Since the age of the eucrites is about equal to that of the solar system, extensive chemical differentiation of the eucrite parent body prior to the formation of eucrites seems unlikely. If homogeneous accretion is assumed, the bulk composition of the eucrite parent body can be estimated; two estimates are provided, representing different hypotheses as to the ratio of metal to olivine in the parent body. Since a large number of differentiated olivine meteorites, which would represent material from the interior of the parent body, have not been detected, the eucrite parent body is thought to be intact. It is suggested that the asteroid 4 Vesta is the eucrite parent body.

Black Hole Firewalls and Lorentzian Relativity

NASA Astrophysics Data System (ADS)

Winterberg, Friedwardt

2013-04-01

In a paper published (Z. f. Naturforsch. 56a, 889, 2001) I had shown that the pre-Einstein theory of relativity by Lorentz and Poincare, extended to the general theory of relativity and quantum mechanics, predicts the disintegration of matter by passing through the event horizon. The zero point vacuum energy is there cut-off at the Planck energy, but Lorentz-invariant all the way up to this energy. The cut-off creates a distinguished reference system in which this energy is at rest. For non-relativistic velocities relative to this reference system, the special and general relativity remain a good approximations, with matter held together in a stable equilibrium by electrostatic forces (or forces acting like them) as a solution of an elliptic partial differential equation derived from Maxwell's equation. But in approaching and crossing the velocity of light in the distinguished reference system, which is equivalent in approaching and crossing of the event horizon, the elliptic differential equation goes over into a hyperbolic differential equation (as in fluid dynamics from subsonic to supersonic flow), and there is no such equilibrium. According to Schwarzschild's interior solution, the event horizon of a collapsing mass appears first as a point in its center, thereafter moving radially outwards, thereby converting all the mass into energy, explaining the observed gamma ray bursters.

Platelet-Rich Fibrin Promotes Periodontal Regeneration and Enhances Alveolar Bone Augmentation

PubMed Central

Li, Qi; Pan, Shuang; Dangaria, Smit J.; Gopinathan, Gokul; Kolokythas, Antonia; Chu, Shunli; Geng, Yajun; Zhou, Yanmin; Luan, Xianghong

2013-01-01

In the present study we have determined the suitability of platelet-rich fibrin (PRF) as a complex scaffold for periodontal tissue regeneration. Replacing PRF with its major component fibrin increased mineralization in alveolar bone progenitors when compared to periodontal progenitors, suggesting that fibrin played a substantial role in PRF-induced osteogenic lineage differentiation. Moreover, there was a 3.6-fold increase in the early osteoblast transcription factor RUNX2 and a 3.1-fold reduction of the mineralization inhibitor MGP as a result of PRF application in alveolar bone progenitors, a trend not observed in periodontal progenitors. Subcutaneous implantation studies revealed that PRF readily integrated with surrounding tissues and was partially replaced with collagen fibers 2 weeks after implantation. Finally, clinical pilot studies in human patients documented an approximately 5 mm elevation of alveolar bone height in tandem with oral mucosal wound healing. Together, these studies suggest that PRF enhances osteogenic lineage differentiation of alveolar bone progenitors more than of periodontal progenitors by augmenting osteoblast differentiation, RUNX2 expression, and mineralized nodule formation via its principal component fibrin. They also document that PRF functions as a complex regenerative scaffold promoting both tissue-specific alveolar bone augmentation and surrounding periodontal soft tissue regeneration via progenitor-specific mechanisms. PMID:23586051

Platelet-rich fibrin promotes periodontal regeneration and enhances alveolar bone augmentation.

PubMed

Li, Qi; Pan, Shuang; Dangaria, Smit J; Gopinathan, Gokul; Kolokythas, Antonia; Chu, Shunli; Geng, Yajun; Zhou, Yanmin; Luan, Xianghong

2013-01-01

In the present study we have determined the suitability of platelet-rich fibrin (PRF) as a complex scaffold for periodontal tissue regeneration. Replacing PRF with its major component fibrin increased mineralization in alveolar bone progenitors when compared to periodontal progenitors, suggesting that fibrin played a substantial role in PRF-induced osteogenic lineage differentiation. Moreover, there was a 3.6-fold increase in the early osteoblast transcription factor RUNX2 and a 3.1-fold reduction of the mineralization inhibitor MGP as a result of PRF application in alveolar bone progenitors, a trend not observed in periodontal progenitors. Subcutaneous implantation studies revealed that PRF readily integrated with surrounding tissues and was partially replaced with collagen fibers 2 weeks after implantation. Finally, clinical pilot studies in human patients documented an approximately 5 mm elevation of alveolar bone height in tandem with oral mucosal wound healing. Together, these studies suggest that PRF enhances osteogenic lineage differentiation of alveolar bone progenitors more than of periodontal progenitors by augmenting osteoblast differentiation, RUNX2 expression, and mineralized nodule formation via its principal component fibrin. They also document that PRF functions as a complex regenerative scaffold promoting both tissue-specific alveolar bone augmentation and surrounding periodontal soft tissue regeneration via progenitor-specific mechanisms.

Molecular and morphological differentiation between two Miocene-divergent lineages of Amazonian shrimps, with the description of a new species (Decapoda, Palaemonidae, Palaemon)

PubMed Central

Carvalho, Fabrício Lopes; Magalhães, Célio; Mantelatto, Fernando Luis

2014-01-01

Abstract Palaemon carteri (Gordon, 1935) and Palaemon ivonicus (Holthuis, 1950) are morphologically similar species of South American freshwater shrimps. Past studies have questioned the taxonomic status of both species, which are supposed to have partially sympatric geographic distributions in the Amazon basin. We analyzed a 550 bp fragment of the mitochondrial 16S rRNA gene from these Amazonian Palaemon species as well as from 11 palaemonids as the outgroup. Additionally, we checked diagnostic characters of the genus and family as well as other morphological characters that have been little explored before. Palaemon carteri and Palaemon ivonicus are allocated in two sister lineages, with wide genetic divergence and little morphological differentiation. The divergence time between these lineages was estimated as approximately 10 million years ago. Both molecular and morphological data support the taxonomic validity of both Palaemon carteri and Palaemon ivonicus, refuting the hypothesis of synonymy. In addition, a new species, Palaemon yuna sp. n., closely related to Palaemon ivonicus, is described. Our findings indicate that these species can be differentiated using the projection of the anterolateral margin and anterolateral spine of the first antennular segment, shape of the rostrum, and relative size of the appendix masculina. PMID:25561832

Taguchi method for partial differential equations with application in tumor growth.

PubMed

Ilea, M; Turnea, M; Rotariu, M; Arotăriţei, D; Popescu, Marilena

2014-01-01

The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth. Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average. First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small. Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

Geometric Model for a Parametric Study of the Blended-Wing-Body Airplane

NASA Technical Reports Server (NTRS)

Mastin, C. Wayne; Smith, Robert E.; Sadrehaghighi, Ideen; Wiese, Micharl R.

1996-01-01

A parametric model is presented for the blended-wing-body airplane, one concept being proposed for the next generation of large subsonic transports. The model is defined in terms of a small set of parameters which facilitates analysis and optimization during the conceptual design process. The model is generated from a preliminary CAD geometry. From this geometry, airfoil cross sections are cut at selected locations and fitted with analytic curves. The airfoils are then used as boundaries for surfaces defined as the solution of partial differential equations. Both the airfoil curves and the surfaces are generated with free parameters selected to give a good representation of the original geometry. The original surface is compared with the parametric model, and solutions of the Euler equations for compressible flow are computed for both geometries. The parametric model is a good approximation of the CAD model and the computed solutions are qualitatively similar. An optimal NURBS approximation is constructed and can be used by a CAD model for further refinement or modification of the original geometry.

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.

Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media: SCALE-DEPENDENT UQ

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

Tartakovsky, A. M.; Panzeri, M.; Tartakovsky, G. D.

Equations governing flow and transport in heterogeneous porous media are scale-dependent. We demonstrate that it is possible to identify a support scalemore » $$\\eta^*$$, such that the typically employed approximate formulations of Moment Equations (ME) yield accurate (statistical) moments of a target environmental state variable. Under these circumstances, the ME approach can be used as an alternative to the Monte Carlo (MC) method for Uncertainty Quantification in diverse fields of Earth and environmental sciences. MEs are directly satisfied by the leading moments of the quantities of interest and are defined on the same support scale as the governing stochastic partial differential equations (PDEs). Computable approximations of the otherwise exact MEs can be obtained through perturbation expansion of moments of the state variables in orders of the standard deviation of the random model parameters. As such, their convergence is guaranteed only for the standard deviation smaller than one. We demonstrate our approach in the context of steady-state groundwater flow in a porous medium with a spatially random hydraulic conductivity.« less

A real-time approximate optimal guidance law for flight in a plane

NASA Technical Reports Server (NTRS)

Feeley, Timothy S.; Speyer, Jason L.

1990-01-01

A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.

An Evaluation of the Scattering Law for Light and Heavy Water in ENDF-6 Format, Based on Experimental Data and Molecular Dynamics

NASA Astrophysics Data System (ADS)

Márquez Damián, J. I.; Granada, J. R.; Malaspina, D. C.

2014-04-01

In this work we present an evaluation in ENDF-6 format of the scattering law for light and heavy water computed using the LEAPR module of NJOY99. The models used in this evaluation are based on experimental data on light water dynamics measured by Novikov, partial structure factors obtained by Soper, and molecular dynamics calculations performed with GROMACS using a reparameterized version of the flexible SPC model by Toukan and Rahman. The models use the Egelstaff-Schofield diffusion equation for translational motion, and a continuous spectrum calculated from the velocity autocorrelation function computed with GROMACS. The scattering law for H in H2O is computed using the incoherent approximation, and the scattering law D and O in D2O are computed using the Sköld approximation for coherent scattering. The calculations show significant improvement over ENDF/B-VI and ENDF/B-VII when compared with measurements of the total cross section, differential scattering experiments and quasi-elastic neutron scattering experiments (QENS).

Essentially nonoscillatory postprocessing filtering methods

NASA Technical Reports Server (NTRS)

Lafon, F.; Osher, S.

1992-01-01

High order accurate centered flux approximations used in the computation of numerical solutions to nonlinear partial differential equations produce large oscillations in regions of sharp transitions. Here, we present a new class of filtering methods denoted by Essentially Nonoscillatory Least Squares (ENOLS), which constructs an upgraded filtered solution that is close to the physically correct weak solution of the original evolution equation. Our method relies on the evaluation of a least squares polynomial approximation to oscillatory data using a set of points which is determined via the ENO network. Numerical results are given in one and two space dimensions for both scalar and systems of hyperbolic conservation laws. Computational running time, efficiency, and robustness of method are illustrated in various examples such as Riemann initial data for both Burgers' and Euler's equations of gas dynamics. In all standard cases, the filtered solution appears to converge numerically to the correct solution of the original problem. Some interesting results based on nonstandard central difference schemes, which exactly preserve entropy, and have been recently shown generally not to be weakly convergent to a solution of the conservation law, are also obtained using our filters.

Distinguishing ovarian maturity of farmed white sturgeon (Acipenser transmontanus) by Fourier transform infrared spectroscopy: a potential tool for caviar production management.

PubMed

Lu, Xiaonan; Webb, Molly; Talbott, Mariah; Van Eenennaam, Joel; Palumbo, Amanda; Linares-Casenave, Javier; Doroshov, Serge; Struffenegger, Peter; Rasco, Barbara

2010-04-14

Fourier transform infrared spectroscopy (FT-IR, 4000-400 cm(-1)) was applied to blood plasma of farmed white sturgeon (N = 40) to differentiate and predict the stages of ovarian maturity. Spectral features of sex steroids (approximately 3000 cm(-1)) and vitellogenin (approximately 1080 cm(-1)) were identified. Clear segregation of maturity stages (previtellogenesis, vitellogenesis, postvitellogenesis, and follicular atresia) was achieved using principal component analysis (PCA). Progression of oocyte development in the late phase of vitellogenesis was also monitored using PCA based on changes in plasma concentrations of sex steroid and lipid content. The observed oocyte polarization index (PI, a measure of nuclear migration) was correlated with changes in plasma sex steroid levels revealed by FT-IR PCA results. A partial least squares (PLS) model predicted PI values within the range 0.12-0.40 (R = 0.95, SEP = 2.18%) from differences in spectral features. These results suggest that FT-IR may be a good tool for assessing ovarian maturity in farmed sturgeon and will reduce the need for the invasive ovarian biopsy required for PI determination.

High-beta analytic equilibria in circular, elliptical, and D-shaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows

NASA Astrophysics Data System (ADS)

López, O. E.; Guazzotto, L.

2017-03-01

The Grad-Shafranov-Bernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [E. Hameiri, Phys. Plasmas 20, 024504 (2013)], analytic approximations for high-beta equilibria in circular, elliptical, and D-shaped cross sections in the high aspect ratio approximation are found, which include finite toroidal and poloidal flows. Assuming a polynomial dependence of the free functions on the poloidal flux, the equilibrium problem is reduced to an inhomogeneous Helmholtz partial differential equation (PDE) subject to homogeneous Dirichlet conditions. An application of the Green's function method leads to a closed form for the circular solution and to a series solution in terms of Mathieu functions for the elliptical case, which is valid for arbitrary elongations. To extend the elliptical solution to a D-shaped domain, a boundary perturbation in terms of the triangularity is used. A comparison with the code FLOW [L. Guazzotto et al., Phys. Plasmas 11(2), 604-614 (2004)] is presented for relevant scenarios.

Second-order (2 +1 ) -dimensional anisotropic hydrodynamics

NASA Astrophysics Data System (ADS)

Bazow, Dennis; Heinz, Ulrich; Strickland, Michael

2014-11-01

We present a complete formulation of second-order (2 +1 ) -dimensional anisotropic hydrodynamics. The resulting framework generalizes leading-order anisotropic hydrodynamics by allowing for deviations of the one-particle distribution function from the spheroidal form assumed at leading order. We derive complete second-order equations of motion for the additional terms in the macroscopic currents generated by these deviations from their kinetic definition using a Grad-Israel-Stewart 14-moment ansatz. The result is a set of coupled partial differential equations for the momentum-space anisotropy parameter, effective temperature, the transverse components of the fluid four-velocity, and the viscous tensor components generated by deviations of the distribution from spheroidal form. We then perform a quantitative test of our approach by applying it to the case of one-dimensional boost-invariant expansion in the relaxation time approximation (RTA) in which case it is possible to numerically solve the Boltzmann equation exactly. We demonstrate that the second-order anisotropic hydrodynamics approach provides an excellent approximation to the exact (0+1)-dimensional RTA solution for both small and large values of the shear viscosity.

Multi-level adaptive finite element methods. 1: Variation problems

NASA Technical Reports Server (NTRS)

Brandt, A.

1979-01-01

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

Nonlinear model of a rotating hub-beams structure: Equations of motion

NASA Astrophysics Data System (ADS)

Warminski, Jerzy

2018-01-01

Dynamics of a rotating structure composed of a rigid hub and flexible beams is presented in the paper. A nonlinear model of a beam takes into account bending, extension and nonlinear curvature. The influence of geometric nonlinearity and nonconstant angular velocity on dynamics of the rotating structure is presented. The exact equations of motion and associated boundary conditions are derived on the basis of the Hamilton's principle. The simplification of the exact nonlinear mathematical model is proposed taking into account the second order approximation. The reduced partial differential equations of motion together with associated boundary conditions can be used to study natural or forced vibrations of a rotating structure considering constant or nonconstant angular speed of a rigid hub and an arbitrary number of flexible blades.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Comparative study for elastic electron collisions on C{sub 2}N{sub 2} isomers

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

Michelin, S. E.; Falck, A. S.; Mazon, K. T.

2006-08-15

In this work, we present a theoretical study on elastic electron collisions with the four C{sub 2}N{sub 2} isomers. More specifically, calculated differential, integral, and momentum transfer cross sections are reported in the 1-100 eV energy range. Calculations are performed at both the static-exchange-absorption and the static-exchange-polarization-absorption levels. The iterative Schwinger variational method combined with the distorted wave approximation is used to solve the scattering equations. Our study reveals an interesting trend of the calculated cross sections for the four isomers. In particular, strong isomer effect is seen at low incident energies. Also, we have identified a shape resonance whichmore » leads to a depression in the calculated partial integral cross section.« less

Advantages of multigrid methods for certifying the accuracy of PDE modeling

NASA Technical Reports Server (NTRS)

Forester, C. K.

1981-01-01

Numerical techniques for assessing and certifying the accuracy of the modeling of partial differential equations (PDE) to the user's specifications are analyzed. Examples of the certification process with conventional techniques are summarized for the three dimensional steady state full potential and the two dimensional steady Navier-Stokes equations using fixed grid methods (FG). The advantages of the Full Approximation Storage (FAS) scheme of the multigrid technique of A. Brandt compared with the conventional certification process of modeling PDE are illustrated in one dimension with the transformed potential equation. Inferences are drawn for how MG will improve the certification process of the numerical modeling of two and three dimensional PDE systems. Elements of the error assessment process that are common to FG and MG are analyzed.

The effects of Raman scattering accompanied by the soliton excitation occurring in molecular crystals

NASA Astrophysics Data System (ADS)

Pang, X. F.

2001-06-01

A theoretical research is made for the effects of Raman scattering caused by the soliton excitation occurring in the organic molecular crystals, e.g., acetanilide, on the basis of vibration model of amide-I. The energy gap between the soliton state and the vibron state have been found by partial diagonalized method in second quantized representation, which is 18.1-33 cm -1. This result is approximately consistent with the red shift value obtained from the experiments, 16 cm -1. The differential cross-section of the Raman scattering, arising from the soliton excitation, has also been obtained. Finally, we derive some properties of the Raman scattering in such a case. This result establishes spectral signatures of the soliton in the molecular crystals, which may be observed in the experiment.

Flow structure in continuous flow electrophoresis chambers

NASA Technical Reports Server (NTRS)

Deiber, J. A.; Saville, D. A.

1982-01-01

There are at least two ways that hydrodynamic processes can limit continiuous flow electrophoresis. One arises from the sensitivity of the flow to small temerature gradients, especially at low flow rates and power levels. This sensitivity can be suppressed, at least in principle, by providing a carefully tailored, stabilizing temperature gradient in the cooling system that surrounds the flow channel. At higher power levels another limitation arises due to a restructuring of the main flow. This restructuring is caused by buoyancy, which is in turn affected by the electro-osmotic crossflow. Approximate solutions to appropriate partial differential equations have been computed by finite difference methods. One set of results is described here to illustrate the strong coupling between the structure of the main (axial) flow and the electro-osmotic flow.

SCATTERING OF SLOW NEUTRONS FROM PROPANE GAS

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

Strong, K.A.; Marshall, G.D.; Brugger, R.M.

1962-02-01

Measurements of the partial differential neutron scattering cross sections for room-temperature propane gas are reported. These measurements were made at incident energies of 0.0l01, 0.0254, 0.0736, and 0.102 ev at seven scattering angles between 16.3 and 84.7 deg using the Materials Testing Reactor phased chopper velocity selector. The data are convented to the scattering-law presentation and compared with three theoretical calculations: The ideal gas, using an effective mass obtained from an average of the mass tensors for the three types of H atoms in propane, gives poor agreement. The Krieger-Nelkin approximation, which includes the effect of zero-point vibrations, gives limitedmore » agreement for energy transfer less than 0.5 k/sub b/T at intermediate momentum transfers. At large momentum transfers where vibrational effects become important it underestimates the cross section. A modification of the Krieger- Nelkin theory that includes the effects of single-quantum transitions from the three lowest vibratlonal states gives better agreement. The discrepancies still present at large momentum and energy transfers are attributed to an uncertainty in the methylgroup barrier height for the three lowest energy modes, to the harmonlc oscillator approximation for these modes, and to the approximate molecular orientation averaging used in the calculation. (auth)« less

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Ma, Wen-Xiu; Zhou, Yuan

2018-02-01

Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations u = 2(ln ⁡ f) x and u = 2(ln ⁡ f) xx, where x is one spatial variable. Applications are made for a few generalized KP and BKP equations.

Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Warsi, Z. U. A.; Mastin, C. W.

1982-01-01

A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

NASA Astrophysics Data System (ADS)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

Shift-connected SIMD array architectures for digital optical computing systems, with algorithms for numerical transforms and partial differential equations

NASA Astrophysics Data System (ADS)

Drabik, Timothy J.; Lee, Sing H.

1986-11-01

The intrinsic parallelism characteristics of easily realizable optical SIMD arrays prompt their present consideration in the implementation of highly structured algorithms for the numerical solution of multidimensional partial differential equations and the computation of fast numerical transforms. Attention is given to a system, comprising several spatial light modulators (SLMs), an optical read/write memory, and a functional block, which performs simple, space-invariant shifts on images with sufficient flexibility to implement the fastest known methods for partial differential equations as well as a wide variety of numerical transforms in two or more dimensions. Either fixed or floating-point arithmetic may be used. A performance projection of more than 1 billion floating point operations/sec using SLMs with 1000 x 1000-resolution and operating at 1-MHz frame rates is made.

Geometric properties of commutative subalgebras of partial differential operators

NASA Astrophysics Data System (ADS)

Zheglov, A. B.; Kurke, H.

2015-05-01

We investigate further algebro-geometric properties of commutative rings of partial differential operators, continuing our research started in previous articles. In particular, we start to explore the simplest and also certain known examples of quantum algebraically completely integrable systems from the point of view of a recent generalization of Sato's theory, developed by the first author. We give a complete characterization of the spectral data for a class of 'trivial' commutative algebras and strengthen geometric properties known earlier for a class of known examples. We also define a kind of restriction map from the moduli space of coherent sheaves with fixed Hilbert polynomial on a surface to an analogous moduli space on a divisor (both the surface and the divisor are part of the spectral data). We give several explicit examples of spectral data and corresponding algebras of commuting (completed) operators, producing as a by-product interesting examples of surfaces that are not isomorphic to spectral surfaces of any (maximal) commutative ring of partial differential operators of rank one. Finally, we prove that any commutative ring of partial differential operators whose normalization is isomorphic to the ring of polynomials k \\lbrack u,t \\rbrack is a Darboux transformation of a ring of operators with constant coefficients. Bibliography: 39 titles.

Comparison between numeric and approximate analytic solutions for the prediction of soil metal uptake by roots. Example of cadmium.

PubMed

Schneider, André; Lin, Zhongbing; Sterckeman, Thibault; Nguyen, Christophe

2018-04-01

The dissociation of metal complexes in the soil solution can increase the availability of metals for root uptake. When it is accounted for in models of bioavailability of soil metals, the number of partial differential equations (PDEs) increases and the computation time to numerically solve these equations may be problematic when a large number of simulations are required, for example for sensitivity analyses or when considering root architecture. This work presents analytical solutions for the set of PDEs describing the bioavailability of soil metals including the kinetics of complexation for three scenarios where the metal complex in solution was fully inert, fully labile, or partially labile. The analytical solutions are only valid i) at steady-state when the PDEs become ordinary differential equations, the transient phase being not covered, ii) when diffusion is the major mechanism of transport and therefore, when convection is negligible, iii) when there is no between-root competition. The formulation of the analytical solutions is for cylindrical geometry but the solutions rely on the spread of the depletion profile around the root, which was modelled assuming a planar geometry. The analytical solutions were evaluated by comparison with the corresponding PDEs for cadmium in the case of the French agricultural soils. Provided that convection was much lower than diffusion (Péclet's number<0.02), the cumulative uptakes calculated from the analytic solutions were in very good agreement with those calculated from the PDEs, even in the case of a partially labile complex. The analytic solutions can be used instead of the PDEs to predict root uptake of metals. The analytic solutions were also used to build an indicator of the contribution of a complex to the uptake of the metal by roots, which can be helpful to predict the effect of soluble organic matter on the bioavailability of soil metals. Copyright © 2017 Elsevier B.V. All rights reserved.

7 CFR 1000.76 - Payments by a handler operating a partially regulated distributing plant.

Code of Federal Regulations, 2010 CFR

2010-01-01

..., compute a Class I differential price by subtracting Class III price from the current month's Class I price... by which the Class I differential price exceeds the producer price differential, both prices to be... Class I differential price nor the adjusted producer price differential shall be less than zero; (3) For...

Thermal evolution of a partially differentiated H chondrite parent body

NASA Astrophysics Data System (ADS)

Abrahams, J. N. H.; Bryson, J. F. J.; Weiss, B. P.; Nimmo, F.

2016-12-01

It has traditionally been assumed that planetesimals either melted entirely or remained completely undifferentiated as they accreted. The unmelted textures and cooling histories of chondrites have been used to argue that these meteorites originated from bodies that never differentiated. However, paleomagnetic measurements indicate that some chondrites (e.g., the H chondrite Portales Valley and several CV chondrites) were magnetized by a core dynamo magnetic field, implying that their parent bodies were partially differentiated. It has been unclear, however, whether planetesimal histories consistent with dynamo production can also be consistent with the diversity of chondrite cooling rates and ages. To address this, we modeled the thermal evolution of the H chondrite parent body, considering a variety of accretion histories and parent body radii. We considered partial differentiation using two-stage accretion involving the initial formation and differentiation of a small body, followed by the later addition of low thermal conductivity chondritic material that remains mostly unmelted. We were able to reproduce the measured thermal evolution of multiple H chondrites for a range of parent body parameters, including initial radii from 70-150 km, chondritic layer thicknesses from 50 km to over 100 km, and second stage accretion times of 2.5-3 Myr after solar system formation. Our predicted rates of core cooling and crystallization are consistent with dynamo generation by compositional convection beginning 60-200 Myr after solar system formation and lasting for at least tens of millions of years. This is consistent with magnetic studies of Portales Valley [Bryson et al., this meeting]. In summary, we find that thermal models of partial differentiation are consistent the radiometric ages, magnetization, and cooling rates of a diversity H chondrites.

Some remarks on the numerical solution of parabolic partial differential equations

NASA Astrophysics Data System (ADS)

Campagna, R.; Cuomo, S.; Leveque, S.; Toraldo, G.; Giannino, F.; Severino, G.

2017-11-01

Numerous environmental/engineering applications relying upon the theory of diffusion phenomena into chaotic environments have recently stimulated the interest toward the numerical solution of parabolic partial differential equations (PDEs). In the present paper, we outline a formulation of the mathematical problem underlying a quite general diffusion mechanism in the natural environments, and we shortly emphasize some remarks concerning the applicability of the (straightforward) finite difference method. An illustration example is also presented.

The Refinement-Tree Partition for Parallel Solution of Partial Differential Equations

PubMed Central

Mitchell, William F.

1998-01-01

Dynamic load balancing is considered in the context of adaptive multilevel methods for partial differential equations on distributed memory multiprocessors. An approach that periodically repartitions the grid is taken. The important properties of a partitioning algorithm are presented and discussed in this context. A partitioning algorithm based on the refinement tree of the adaptive grid is presented and analyzed in terms of these properties. Theoretical and numerical results are given. PMID:28009355

The Refinement-Tree Partition for Parallel Solution of Partial Differential Equations.

PubMed

Mitchell, William F

1998-01-01

Dynamic load balancing is considered in the context of adaptive multilevel methods for partial differential equations on distributed memory multiprocessors. An approach that periodically repartitions the grid is taken. The important properties of a partitioning algorithm are presented and discussed in this context. A partitioning algorithm based on the refinement tree of the adaptive grid is presented and analyzed in terms of these properties. Theoretical and numerical results are given.

Observability of discretized partial differential equations

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1988-01-01

It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

2015-07-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Cellular Automata for Spatiotemporal Pattern Formation from Reaction-Diffusion Partial Differential Equations

NASA Astrophysics Data System (ADS)

Ohmori, Shousuke; Yamazaki, Yoshihiro

2016-01-01

Ultradiscrete equations are derived from a set of reaction-diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction-diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction-diffusion equations.

Numerical methods for large-scale, time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Turkel, E.

1979-01-01

A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.

Spectral methods for time dependent partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1983-01-01

The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.

Stability analysis of multigrid acceleration methods for the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Fay, John F.

1990-01-01

A calculation is made of the stability of various relaxation schemes for the numerical solution of partial differential equations. A multigrid acceleration method is introduced, and its effects on stability are explored. A detailed stability analysis of a simple case is carried out and verified by numerical experiment. It is shown that the use of multigrids can speed convergence by several orders of magnitude without adversely affecting stability.

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

NASA Astrophysics Data System (ADS)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

From crater functions to partial differential equations: a new approach to ion bombardment induced nonequilibrium pattern formation.

PubMed

Norris, Scott A; Brenner, Michael P; Aziz, Michael J

2009-06-03

We develop a methodology for deriving continuum partial differential equations for the evolution of large-scale surface morphology directly from molecular dynamics simulations of the craters formed from individual ion impacts. Our formalism relies on the separation between the length scale of ion impact and the characteristic scale of pattern formation, and expresses the surface evolution in terms of the moments of the crater function. We demonstrate that the formalism reproduces the classical Bradley-Harper results, as well as ballistic atomic drift, under the appropriate simplifying assumptions. Given an actual set of converged molecular dynamics moments and their derivatives with respect to the incidence angle, our approach can be applied directly to predict the presence and absence of surface morphological instabilities. This analysis represents the first work systematically connecting molecular dynamics simulations of ion bombardment to partial differential equations that govern topographic pattern-forming instabilities.

Partial differential equations constrained combinatorial optimization on an adiabatic quantum computer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh

Partial differential equation-constrained combinatorial optimization (PDECCO) problems are a mixture of continuous and discrete optimization problems. PDECCO problems have discrete controls, but since the partial differential equations (PDE) are continuous, the optimization space is continuous as well. Such problems have several applications, such as gas/water network optimization, traffic optimization, micro-chip cooling optimization, etc. Currently, no efficient classical algorithm which guarantees a global minimum for PDECCO problems exists. A new mapping has been developed that transforms PDECCO problem, which only have linear PDEs as constraints, into quadratic unconstrained binary optimization (QUBO) problems that can be solved using an adiabatic quantum optimizer (AQO). The mapping is efficient, it scales polynomially with the size of the PDECCO problem, requires only one PDE solve to form the QUBO problem, and if the QUBO problem is solved correctly and efficiently on an AQO, guarantees a global optimal solution for the original PDECCO problem.

On Partial Fraction Decompositions by Repeated Polynomial Divisions

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2017-01-01

We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions. This method does not involve differentiation or solving linear equations for obtaining the unknown partial fraction coefficients, which is very suitable for either…

Analytical approximate solutions for a general class of nonlinear delay differential equations.

PubMed

Căruntu, Bogdan; Bota, Constantin

2014-01-01

We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

Modelling the seismic properties of fast-spreading ridge crustal Low-Velocity Zones: insights from Oman gabbro textures

NASA Astrophysics Data System (ADS)

Lamoureux, Gwenaëlle; Ildefonse, Benoı̂t; Mainprice, David

1999-11-01

Although considerable progress has been made in the study of fast-spreading, mid-ocean ridge magma chambers over the past fifteen years, the fraction of melt present in the chamber remains poorly constrained and controversial. We present new constraints obtained by modelling the seismic properties of partially molten gabbros at the ridge axis. P-wave velocities at low frequencies are calculated in the foliation/lineation reference frame using a differential effective medium technique. The model takes into account the lattice preferred orientation of the crystalline phase and the average shape of the melt phase. The structural parameters are obtained from the Oman ophiolite. The structural reference frame is given by the general trend of the gabbro foliation and the melt fraction and shape are estimated using the textures of nine upper gabbro samples. The estimated melt fraction and shape depend on the assumptions regarding which part of the observed textures represent the melt in the gabbroic mush of the magma chamber. However, we can put limits on the reasonable values for the melt fraction and shape. Our results are consistent with a melt fraction of the order of 10 to 20% in the Low-Velocity Zone (i.e. the magma chamber), which is anisotropically distributed with the melt pockets preferentially aligned parallel to the foliation and approximated by oblate ellipsoids with approximate dimensions of 4 : 4 : 1. These results are also consistent with the seismic structure of the East Pacific rise at 9°30'. The anisotropic melt distribution can, at least partially, explain the vertical velocity gradient described in the LVZ.

Spline approximations for nonlinear hereditary control systems

NASA Technical Reports Server (NTRS)

Daniel, P. L.

1982-01-01

A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.

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.

Computer simulation of two-dimensional unsteady flows in estuaries and embayments by the method of characteristics : basic theory and the formulation of the numerical method

USGS Publications Warehouse

Lai, Chintu

1977-01-01

Two-dimensional unsteady flows of homogeneous density in estuaries and embayments can be described by hyperbolic, quasi-linear partial differential equations involving three dependent and three independent variables. A linear combination of these equations leads to a parametric equation of characteristic form, which consists of two parts: total differentiation along the bicharacteristics and partial differentiation in space. For its numerical solution, the specified-time-interval scheme has been used. The unknown, partial space-derivative terms can be eliminated first by suitable combinations of difference equations, converted from the corresponding differential forms and written along four selected bicharacteristics and a streamline. Other unknowns are thus made solvable from the known variables on the current time plane. The computation is carried to the second-order accuracy by using trapezoidal rule of integration. Means to handle complex boundary conditions are developed for practical application. Computer programs have been written and a mathematical model has been constructed for flow simulation. The favorable computer outputs suggest further exploration and development of model worthwhile. (Woodard-USGS)

Approximate optimal guidance for the advanced launch system

NASA Technical Reports Server (NTRS)

Feeley, T. S.; Speyer, J. L.

1993-01-01

A real-time guidance scheme for the problem of maximizing the payload into orbit subject to the equations of motion for a rocket over a spherical, non-rotating earth is presented. An approximate optimal launch guidance law is developed based upon an asymptotic expansion of the Hamilton - Jacobi - Bellman or dynamic programming equation. The expansion is performed in terms of a small parameter, which is used to separate the dynamics of the problem into primary and perturbation dynamics. For the zeroth-order problem the small parameter is set to zero and a closed-form solution to the zeroth-order expansion term of Hamilton - Jacobi - Bellman equation is obtained. Higher-order terms of the expansion include the effects of the neglected perturbation dynamics. These higher-order terms are determined from the solution of first-order linear partial differential equations requiring only the evaluation of quadratures. This technique is preferred as a real-time, on-line guidance scheme to alternative numerical iterative optimization schemes because of the unreliable convergence properties of these iterative guidance schemes and because the quadratures needed for the approximate optimal guidance law can be performed rapidly and by parallel processing. Even if the approximate solution is not nearly optimal, when using this technique the zeroth-order solution always provides a path which satisfies the terminal constraints. Results for two-degree-of-freedom simulations are presented for the simplified problem of flight in the equatorial plane and compared to the guidance scheme generated by the shooting method which is an iterative second-order technique.

Down-regulation of angiotensin II receptor subtypes and desensitization of cyclic GMP production in neuroblastoma N1E-115 cells.

PubMed

Reagan, L P; Ye, X; Maretzski, C H; Fluharty, S J

1993-01-01

Murine neuroblastoma N1E-115 cells possess membranous receptors for the octapeptide angiotensin II (AngII) whose density is substantially increased by in vitro differentiation. Incubation of differentiated N1E-115 cells with AngII produced a rapid decrease in receptor density, but did not alter the affinity of these receptors for either 125I-AngII or the high-affinity antagonist 125I-[Sarc1,Ile8]-AngII. This apparent down-regulation was dose related with an ED50 of 1 nM, and maximal decreases of approximately 90% were obtained with 100 nM AngII. Receptor loss from differentiated cell membranes was unaffected by incubations of membranes obtained from agonist-exposed cells with non-hydrolyzable analogues of GTP for 60 min at 37 degrees C to ensure dissociation of the ligand. Partial loss of AngII receptors was apparent within 5 min of agonist exposure, whereas maximal declines were not observed until 30 min. This temporal pattern resulted from a preferential decrease in the AT1 receptor subtype during the first 5 min, followed by a decline in both AT1 and AT2 receptors with longer periods of agonist exposure. The loss of membranous receptors was reversible with partial recovery observed after 4 h, and with nearly full recovery observed 18 h after exposure of the cells to AngII. However, the long-term recovery of receptor density was blocked by the protein synthesis inhibitor, cycloheximide. The heptapeptide angiotensin III produced a similar down-regulation of receptors, and the high-affinity antagonist [Sarc1,Thr8]-AngII blocked agonist-induced down-regulation. Finally, the apparent loss of cell surface AngII receptors decreased the ability of AngII to stimulate cyclic GMP production within intact N1E-115 cells.(ABSTRACT TRUNCATED AT 250 WORDS)

A model for foam formation, stability, and breakdown in glass-melting furnaces.

PubMed

van der Schaaf, John; Beerkens, Ruud G C

2006-03-01

A dynamic model for describing the build-up and breakdown of a glass-melt foam is presented. The foam height is determined by the gas flux to the glass-melt surface and the drainage rate of the liquid lamellae between the gas bubbles. The drainage rate is determined by the average gas bubble radius and the physical properties of the glass melt: density, viscosity, surface tension, and interfacial mobility. Neither the assumption of a fully mobile nor the assumption of a fully immobile glass-melt interface describe the observed foam formation on glass melts adequately. The glass-melt interface appears partially mobile due to the presence of surface active species, e.g., sodium sulfate and silanol groups. The partial mobility can be represented by a single, glass-melt composition specific parameter psi. The value of psi can be estimated from gas bubble lifetime experiments under furnace conditions. With this parameter, laboratory experiments of foam build-up and breakdown in a glass melt are adequately described, qualitatively and quantitatively by a set of ordinary differential equations. An approximate explicit relationship for the prediction of the steady-state foam height is derived from the fundamental model.

Group theoretic approach for solving the problem of diffusion of a drug through a thin membrane

NASA Astrophysics Data System (ADS)

Abd-El-Malek, Mina B.; Kassem, Magda M.; Meky, Mohammed L. M.

2002-03-01

The transformation group theoretic approach is applied to study the diffusion process of a drug through a skin-like membrane which tends to partially absorb the drug. Two cases are considered for the diffusion coefficient. The application of one parameter group reduces the number of independent variables by one, and consequently the partial differential equation governing the diffusion process with the boundary and initial conditions is transformed into an ordinary differential equation with the corresponding conditions. The obtained differential equation is solved numerically using the shooting method, and the results are illustrated graphically and in tables.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

PubMed

Murase, Kenya

2016-01-01

Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions

PubMed Central

Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

2015-01-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

The use of solution adaptive grids in solving partial differential equations

NASA Technical Reports Server (NTRS)

Anderson, D. A.; Rai, M. M.

1982-01-01

The grid point distribution used in solving a partial differential equation using a numerical method has a substantial influence on the quality of the solution. An adaptive grid which adjusts as the solution changes provides the best results when the number of grid points available for use during the calculation is fixed. Basic concepts used in generating and applying adaptive grids are reviewed in this paper, and examples illustrating applications of these concepts are presented.

Multirate Integration Properties of Waveform Relaxation with Applications to Circuit Simulation and Parallel Computation

DTIC Science & Technology

1985-11-18

Greenberg and K. Sakallah at Digital Equipment Corporation, and C-F. Chen, L Nagel, and P. ,. Subrahmanyam at AT&T Bell Laboratories, both for providing...Circuit Theory McGraw-Hill, 1969. [37] R. Courant and D. Hilbert , Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics...McGraw-Hill, N.Y., 1965. Page 161 [44) R. Courant and D. Hilbert , Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics

A Posteriori Finite Element Bounds for Sensitivity Derivatives of Partial-Differential-Equation Outputs. Revised

NASA Technical Reports Server (NTRS)

Lewis, Robert Michael; Patera, Anthony T.; Peraire, Jaume

1998-01-01

We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.

The Riemann-Lanczos equations in general relativity and their integrability

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2008-06-01

The aim of this paper is to examine the Riemann-Lanczos equations and how they can be made integrable. They consist of a system of linear first-order partial differential equations that arise in general relativity, whereby the Riemann curvature tensor is generated by an unknown third-order tensor potential field called the Lanczos tensor. Our approach is based on the theory of jet bundles, where all field variables and all their partial derivatives of all relevant orders are treated as independent variables alongside the local manifold coordinates (xa) on the given space-time manifold M. This approach is adopted in (a) Cartan's method of exterior differential systems, (b) Vessiot's dual method using vector field systems, and (c) the Janet-Riquier theory of systems of partial differential equations. All three methods allow for the most general situations under which integrability conditions can be found. They give equivalent results, namely, that involutivity is always achieved at all generic points of the jet manifold M after a finite number of prolongations. Two alternative methods that appear in the general relativity literature to find integrability conditions for the Riemann-Lanczos equations generate new partial differential equations for the Lanczos potential that introduce a source term, which is nonlinear in the components of the Riemann tensor. We show that such sources do not occur when either of method (a), (b), or (c) are used.

Quantitative evaluation method for differentiation of C2C12 myoblasts by ultrasonic microscopy

NASA Astrophysics Data System (ADS)

Takanashi, Kyoichi; Washiya, Mamoru; Ota, Kazuki; Yoshida, Sachiko; Hozumi, Naohiro; Kobayashi, Kazuto

2017-07-01

Cell differentiation was evaluated by ultrasonic microscopy. However, there were some regions that showed a lower acoustic impedance than the culture liquid. It was considered that, in such regions, the cells were not perfectly in contact with the film substrate. Hence, a waveform analysis was performed, and compensated acoustic impedances in such regions were in a reasonable range of values. By the same analysis, the displacements of partially floated cells were also successfully calculated. The elapsed day transitions of the compensated acoustic impedances and displacements were successfully evaluated. In the process of differentiation, actin fibers comprising the cytoskeleton are supposed to loosen in order to induce cellular fusion. In addition, the progress in cell differentiation accompanied by a change into a three-dimensional structure can partially be assessed by the displacement between a cell and a cultured film. Hence, we believe that cell differentiation can be evaluated using an ultrasonic microscope.

An Improved Heaviside Approach to Partial Fraction Expansion and Its Applications

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2009-01-01

In this note, we present an improved Heaviside approach to compute the partial fraction expansions of proper rational functions. This method uses synthetic divisions to determine the unknown partial fraction coefficients successively, without the need to use differentiation or to solve a system of linear equations. Examples of its applications in…

A numerical scheme for the identification of hybrid systems describing the vibration of flexible beams with tip bodies

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

A cubic spline based Galerkin-like method is developed for the identification of a class of hybrid systems which describe the transverse vibration to flexible beams with attached tip bodies. The identification problem is formulated as a least squares fit to data subject to the system dynamics given by a coupled system of ordnary and partial differential equations recast as an abstract evolution equation (AEE) in an appropriate infinite dimensional Hilbert space. Projecting the AEE into spline-based subspaces leads naturally to a sequence of approximating finite dimensional identification problems. The solutions to these problems are shown to exist, are relatively easily computed, and are shown to, in some sense, converge to solutions to the original identification problem. Numerical results for a variety of examples are discussed.

Thin-film Faraday patterns in three dimensions

NASA Astrophysics Data System (ADS)

Richter, Sebastian; Bestehorn, Michael

2017-04-01

We investigate the long time evolution of a thin fluid layer in three spatial dimensions located on a horizontal planar substrate. The substrate is subjected to time-periodic external vibrations in normal and in tangential direction with respect to the plane surface. The governing partial differential equation system of our model is obtained from the incompressible Navier-Stokes equations considering the limit of a thin fluid geometry and using the long wave lubrication approximation. It includes inertia and viscous friction. Numerical simulations evince the existence of persistent spatially complex surface patterns (periodic and quasiperiodic) for certain superpositions of two vertical excitations and initial conditions. Additional harmonic lateral excitations cause deformations but retain the basic structure of the patterns. Horizontal ratchet-shaped forces lead to a controllable lateral movement of the fluid. A Floquet analysis is used to determine the stability of the linearized system.

Final Report, DE-FG01-06ER25718 Domain Decomposition and Parallel Computing

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

Widlund, Olof B.

2015-06-09

The goal of this project is to develop and improve domain decomposition algorithms for a variety of partial differential equations such as those of linear elasticity and electro-magnetics.These iterative methods are designed for massively parallel computing systems and allow the fast solution of the very large systems of algebraic equations that arise in large scale and complicated simulations. A special emphasis is placed on problems arising from Maxwell's equation. The approximate solvers, the preconditioners, are combined with the conjugate gradient method and must always include a solver of a coarse model in order to have a performance which is independentmore » of the number of processors used in the computer simulation. A recent development allows for an adaptive construction of this coarse component of the preconditioner.« less

An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations

PubMed Central

Mirzaev, Inom; Byrne, Erin C.; Bortz, David M.

2016-01-01

We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach. PMID:28316360

Quantum mechanical streamlines. I - Square potential barrier

NASA Technical Reports Server (NTRS)

Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.

1974-01-01

Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.

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.

Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions

DOE PAGES

Del Moral, Pierre; Jasra, Ajay; Law, Kody J. H.

2017-01-09

We consider the multilevel sequential Monte Carlo (MLSMC) method of Beskos et al. (Stoch. Proc. Appl. [to appear]). This technique is designed to approximate expectations w.r.t. probability laws associated to a discretization. For instance, in the context of inverse problems, where one discretizes the solution of a partial differential equation. The MLSMC approach is especially useful when independent, coupled sampling is not possible. Beskos et al. show that for MLSMC the computational effort to achieve a given error, can be less than independent sampling. In this article we significantly weaken the assumptions of Beskos et al., extending the proofs tomore » non-compact state-spaces. The assumptions are based upon multiplicative drift conditions as in Kontoyiannis and Meyn (Electron. J. Probab. 10 [2005]: 61–123). The assumptions are verified for an example.« less

Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions

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

Del Moral, Pierre; Jasra, Ajay; Law, Kody J. H.

We consider the multilevel sequential Monte Carlo (MLSMC) method of Beskos et al. (Stoch. Proc. Appl. [to appear]). This technique is designed to approximate expectations w.r.t. probability laws associated to a discretization. For instance, in the context of inverse problems, where one discretizes the solution of a partial differential equation. The MLSMC approach is especially useful when independent, coupled sampling is not possible. Beskos et al. show that for MLSMC the computational effort to achieve a given error, can be less than independent sampling. In this article we significantly weaken the assumptions of Beskos et al., extending the proofs tomore » non-compact state-spaces. The assumptions are based upon multiplicative drift conditions as in Kontoyiannis and Meyn (Electron. J. Probab. 10 [2005]: 61–123). The assumptions are verified for an example.« less

An experimental and theoretical evaluation of increased thermal diffusivity phase change devices

NASA Technical Reports Server (NTRS)

White, S. P.; Golden, J. O.; Stermole, F. J.

1972-01-01

This study was to experimentally evaluate and mathematically model the performance of phase change thermal control devices containing high thermal conductivity metal matrices. Three aluminum honeycomb filters were evaluated at five different heat flux levels using n-oct-adecane as the test material. The system was mathematically modeled by approximating the partial differential equations with a three-dimensional implicit alternating direction technique. The mathematical model predicts the system quite well. All of the phase change times are predicted. The heating of solid phase is predicted exactly while there is some variation between theoretical and experimental results in the liquid phase. This variation in the liquid phase could be accounted for by the fact that there are some heat losses in the cell and there could be some convection in the experimental system.

Digital model simulation of the glacial-outwash aquifer at Dayton, Ohio

USGS Publications Warehouse

Fidler, Richard E.

1975-01-01

Dayton, Ohio and its environs obtain most of their water from wells which penetrate highly productive glacial-outwash deposits underlying the Great Miami River and its tributaries and receive recharge by induced streambed leakage. Combined municipal and industrial use of ground water in the 90-square-mile area has increased from about 180 cubic feet per second in 1960 to nearly 250 cubic feet per second in 1972. The increased pumpage has resulted in continuing water-level declines in some parts of the area. A digital model which uses a finite-difference approximation technique to solve partial differential equations of flow through a porous medium was used to evaluate the effects of pumping stresses on water levels. The simulated head values presented in map form generally are in good agreement with potentiometric-surface maps prepared from field measurements.

Application of the Sumudu Transform to Discrete Dynamic Systems

ERIC Educational Resources Information Center

Asiru, Muniru Aderemi

2003-01-01

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

Approximations of e and ?: An Exploration

ERIC Educational Resources Information Center

Brown, Philip R.

2017-01-01

Fractional approximations of e and p are discovered by searching for repetitions or partial repetitions of digit strings in their expansions in different number bases. The discovery of such fractional approximations is suggested for students and teachers as an entry point into mathematics research.

APPROXIMATION OF SOLUTIONS OF THE EQUATION \\overline\\partial^jf=0, j\\geq1, IN DOMAINS WITH QUASICONFORMAL BOUNDARY

NASA Astrophysics Data System (ADS)

Andrievskiĭ, V. V.; Belyĭ, V. I.; Maĭmeskul, V. V.

1991-02-01

This article establishes direct and inverse theorems of approximation theory (of the same type as theorems of Dzyadyk) that describe the quantitative connection between the smoothness properties of solutions of the equation \\overline\\partial^jf=0, j\\geq1, and the rate of their approximation by "module" polynomials of the form \\displaystyle P_N(z)=\\sum_{n=0}^{j-1}\\sum_{m=0}^{N-n}a_{m,n}z^m\\overline{z}^n,\\qquad N\\geq j-1.In particular, a constructive characterization is obtained for generalized Hölder classes of such functions on domains with quasiconformal boundary.Bibliography: 19 titles.

Effects of partial reinforcement and time between reinforced trials on terminal response rate in pigeon autoshaping.

PubMed

Gottlieb, Daniel A

2006-03-01

Partial reinforcement often leads to asymptotically higher rates of responding and number of trials with a response than does continuous reinforcement in pigeon autoshaping. However, comparisons typically involve a partial reinforcement schedule that differs from the continuous reinforcement schedule in both time between reinforced trials and probability of reinforcement. Two experiments examined the relative contributions of these two manipulations to asymptotic response rate. Results suggest that the greater responding previously seen with partial reinforcement is primarily due to differential probability of reinforcement and not differential time between reinforced trials. Further, once established, differences in responding are resistant to a change in stimulus and contingency. Secondary response theories of autoshaped responding (theories that posit additional response-augmenting or response-attenuating mechanisms specific to partial or continuous reinforcement) cannot fully accommodate the current body of data. It is suggested that researchers who study pigeon autoshaping train animals on a common task prior to training them under different conditions.

Partial trisomy of chromosome 22 resulting from a supernumerary marker chromosome 22 in a child with features of cat eye syndrome.

PubMed

Bélien, Valérie; Gérard-Blanluet, Marion; Serero, Stéphane; Le Dû, Nathalie; Baumann, Clarisse; Jacquemont, Marie-Line; Dupont, Céline; Krabchi, Kada; Drunat, Séverine; Elbez, Annie; Janaud, Jean-Claude; Benzacken, Brigitte; Verloes, Alain; Tabet, Anne-Claude; Aboura, Azzedine

2008-07-15

Small supernumerary marker chromosomes are present in about 0.05% of the human population. In approximately 28% of persons with these markers (excluding the approximately 60% derived from one of the acrocentric chromosomes), an abnormal phenotype is observed. We report on a 3-month-old girl with intrauterine growth retardation, craniofacial features, hypotonia, partial coloboma of iris and total anomalous pulmonary venous return. Cytogenetic analysis showed the presence of a supernumerary marker chromosome, identified by fluorescence in situ hybridization as part of chromosome 22, and conferring a proximal partial trisomy 22q22.21, not encompassing the DiGeorge critical region (RP11-154H4 + , TBX1-). This observation adds new information relevant to cat eye syndrome and partial trisomy of 22q. 2008 Wiley-Liss, Inc.

Treatment of Ion-Atom Collisions Using a Partial-Wave Expansion of the Projectile Wavefunction

ERIC Educational Resources Information Center

Wong, T. G.; Foster, M.; Colgan, J.; Madison, D. H.

2009-01-01

We present calculations of ion-atom collisions using a partial-wave expansion of the projectile wavefunction. Most calculations of ion-atom collisions have typically used classical or plane-wave approximations for the projectile wavefunction, since partial-wave expansions are expected to require prohibitively large numbers of terms to converge…

On optimal strategies in event-constrained differential games

NASA Technical Reports Server (NTRS)

Heymann, M.; Rajan, N.; Ardema, M.

1985-01-01

Combat games are formulated as zero-sum differential games with unilateral event constraints. An interior penalty function approach is employed to approximate optimal strategies for the players. The method is very attractive computationally and possesses suitable approximation and convergence properties.

Some Theoretical Aspects of Nonzero Sum Differential Games and Applications to Combat Problems

DTIC Science & Technology

1971-06-01

the Equilibrium Solution . 7 Hamilton-Jacobi-Bellman Partial Differential Equations ............. .............. 9 Influence Function Differential...Linearly .......... ............ 18 Problem Statement .......... ............ 18 Formulation of LJB Equations, Influence Function Equations and the TPBVP...19 Control Lawe . . .. ...... ........... 21 Conditions for Influence Function Continuity along Singular Surfaces

Memory Efficient Ranking.

ERIC Educational Resources Information Center

Moffat, Alistair; And Others

1994-01-01

Describes an approximate document ranking process that uses a compact array of in-memory, low-precision approximations for document length. Combined with another rule for reducing the memory required by partial similarity accumulators, the approximation heuristic allows the ranking of large document collections using less than one byte of memory…

A classical Perron method for existence of smooth solutions to boundary value and obstacle problems for degenerate-elliptic operators via holomorphic maps

NASA Astrophysics Data System (ADS)

Feehan, Paul M. N.

2017-09-01

We prove existence of solutions to boundary value problems and obstacle problems for degenerate-elliptic, linear, second-order partial differential operators with partial Dirichlet boundary conditions using a new version of the Perron method. The elliptic operators considered have a degeneracy along a portion of the domain boundary which is similar to the degeneracy of a model linear operator identified by Daskalopoulos and Hamilton [9] in their study of the porous medium equation or the degeneracy of the Heston operator [21] in mathematical finance. Existence of a solution to the partial Dirichlet problem on a half-ball, where the operator becomes degenerate on the flat boundary and a Dirichlet condition is only imposed on the spherical boundary, provides the key additional ingredient required for our Perron method. Surprisingly, proving existence of a solution to this partial Dirichlet problem with ;mixed; boundary conditions on a half-ball is more challenging than one might expect. Due to the difficulty in developing a global Schauder estimate and due to compatibility conditions arising where the ;degenerate; and ;non-degenerate boundaries; touch, one cannot directly apply the continuity or approximate solution methods. However, in dimension two, there is a holomorphic map from the half-disk onto the infinite strip in the complex plane and one can extend this definition to higher dimensions to give a diffeomorphism from the half-ball onto the infinite ;slab;. The solution to the partial Dirichlet problem on the half-ball can thus be converted to a partial Dirichlet problem on the slab, albeit for an operator which now has exponentially growing coefficients. The required Schauder regularity theory and existence of a solution to the partial Dirichlet problem on the slab can nevertheless be obtained using previous work of the author and C. Pop [16]. Our Perron method relies on weak and strong maximum principles for degenerate-elliptic operators, concepts of continuous subsolutions and supersolutions for boundary value and obstacle problems for degenerate-elliptic operators, and maximum and comparison principle estimates previously developed by the author [13].

A partial differential equation for pseudocontact shift.

PubMed

Charnock, G T P; Kuprov, Ilya

2014-10-07

It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability density. The equation enables straightforward PCS prediction and analysis in systems with delocalized unpaired electrons, particularly for the nuclei located in their immediate vicinity. It is also shown that the probability density of the unpaired electron may be extracted, using a regularization procedure, from PCS data.

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 2: Two-step method

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

A two-step semidirect procedure is developed to accelerate the one-step procedure described in NASA TP-2529. For a set of constant coefficient model problems, the acceleration factor increases from 1 to 2 as the one-step procedure convergence rate decreases from + infinity to 0. It is also shown numerically that the two-step procedure can substantially accelerate the convergence of the numerical solution of many partial differential equations (PDE's) with variable coefficients.

Nonlinear grid error effects on numerical solution of partial differential equations

NASA Technical Reports Server (NTRS)

Dey, S. K.

1980-01-01

Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.

Exact Solutions for the Integrable Sixth-Order Drinfeld-Sokolov-Satsuma-Hirota System by the Analytical Methods.

PubMed

Manafian Heris, Jalil; Lakestani, Mehrdad

2014-01-01

We establish exact solutions including periodic wave and solitary wave solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system. We employ this system by using a generalized (G'/G)-expansion and the generalized tanh-coth methods. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that these methods, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.

Parameter estimation problems for distributed systems using a multigrid method

NASA Technical Reports Server (NTRS)

Ta'asan, Shlomo; Dutt, Pravir

1990-01-01

The problem of estimating spatially varying coefficients of partial differential equations is considered from observation of the solution and of the right hand side of the equation. It is assumed that the observations are distributed in the domain and that enough observations are given. A method of discretization and an efficient multigrid method for solving the resulting discrete systems are described. Numerical results are presented for estimation of coefficients in an elliptic and a parabolic partial differential equation.

Explicit finite difference predictor and convex corrector with applications to hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Dey, C.; Dey, S. K.

1983-01-01

An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood

2018-03-01

The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

DISCHARGE AND DEPTH BEHIND A PARTIALLY BREACHED DAM.

USGS Publications Warehouse

Chen, Cheng-lung

1987-01-01

The role that the velocity-distribution correction factor plays in the determination of the flood discharge and corresponding flow depth behind a partially breached dam is investigated. Assumption of a uniformly progressive flow for an established dam-break flood in a rectangular channel of infinite extent leads to the formulation of a theoretical relation between the depth and velocity of flow expressed in differential form. Integrating this ordinary differential equation, one can express the velocity in terms of the depth.

WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS

PubMed Central

MU, LIN; WANG, JUNPING; WEI, GUOWEI; YE, XIU; ZHAO, SHAN

2013-01-01

Weak Galerkin methods refer to general finite element methods for partial differential equations (PDEs) in which differential operators are approximated by their weak forms as distributions. Such weak forms give rise to desirable flexibilities in enforcing boundary and interface conditions. A weak Galerkin finite element method (WG-FEM) is developed in this paper for solving elliptic PDEs with discontinuous coefficients and interfaces. Theoretically, it is proved that high order numerical schemes can be designed by using the WG-FEM with polynomials of high order on each element. Extensive numerical experiments have been carried to validate the WG-FEM for solving second order elliptic interface problems. High order of convergence is numerically confirmed in both L2 and L∞ norms for the piecewise linear WG-FEM. Special attention is paid to solve many interface problems, in which the solution possesses a certain singularity due to the nonsmoothness of the interface. A challenge in research is to design nearly second order numerical methods that work well for problems with low regularity in the solution. The best known numerical scheme in the literature is of order O(h) to O(h1.5) for the solution itself in L∞ norm. It is demonstrated that the WG-FEM of the lowest order, i.e., the piecewise constant WG-FEM, is capable of delivering numerical approximations that are of order O(h1.75) to O(h2) in the L∞ norm for C1 or Lipschitz continuous interfaces associated with a C1 or H2 continuous solution. PMID:24072935

Approximate controllability of a system of parabolic equations with delay

NASA Astrophysics Data System (ADS)

Carrasco, Alexander; Leiva, Hugo

2008-09-01

In this paper we give necessary and sufficient conditions for the approximate controllability of the following system of parabolic equations with delay: where [Omega] is a bounded domain in , D is an n×n nondiagonal matrix whose eigenvalues are semi-simple with nonnegative real part, the control and B[set membership, variant]L(U,Z) with , . The standard notation zt(x) defines a function from [-[tau],0] to (with x fixed) by zt(x)(s)=z(t+s,x), -[tau][less-than-or-equals, slant]s[less-than-or-equals, slant]0. Here [tau][greater-or-equal, slanted]0 is the maximum delay, which is supposed to be finite. We assume that the operator is linear and bounded, and [phi]0[set membership, variant]Z, [phi][set membership, variant]L2([-[tau],0];Z). To this end: First, we reformulate this system into a standard first-order delay equation. Secondly, the semigroup associated with the first-order delay equation on an appropriate product space is expressed as a series of strongly continuous semigroups and orthogonal projections related with the eigenvalues of the Laplacian operator (); this representation allows us to reduce the controllability of this partial differential equation with delay to a family of ordinary delay equations. Finally, we use the well-known result on the rank condition for the approximate controllability of delay system to derive our main result.

Introducing the Improved Heaviside Approach to Partial Fraction Decomposition to Undergraduate Students: Results and Implications from a Pilot Study

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2012-01-01

Partial fraction decomposition is a useful technique often taught at senior secondary or undergraduate levels to handle integrations, inverse Laplace transforms or linear ordinary differential equations, etc. In recent years, an improved Heaviside's approach to partial fraction decomposition was introduced and developed by the author. An important…

Strongly nonlinear parabolic variational inequalities.

PubMed

Browder, F E; Brézis, H

1980-02-01

An existence and uniqueness result is established for a general class of variational inequalities for parabolic partial differential equations of the form partial differentialu/ partial differentialt + A(u) + g(u) = f with g nondecreasing but satisfying no growth condition. The proof is based upon a type of compactness result for solutions of variational inequalities that should find a variety of other applications.

Anomalous diffusion associated with nonlinear fractional derivative fokker-planck-like equation: exact time-dependent solutions

PubMed

Bologna; Tsallis; Grigolini

2000-08-01

We consider the d=1 nonlinear Fokker-Planck-like equation with fractional derivatives ( partial differential/ partial differentialt)P(x,t)=D( partial differential(gamma)/ partial differentialx(gamma))[P(x,t)](nu). Exact time-dependent solutions are found for nu=(2-gamma)/(1+gamma)(-infinity

A Unified Introduction to Ordinary Differential Equations

ERIC Educational Resources Information Center

Lutzer, Carl V.

2006-01-01

This article describes how a presentation from the point of view of differential operators can be used to (partially) unify the myriad techniques in an introductory course in ordinary differential equations by providing students with a powerful, flexible paradigm that extends into (or from) linear algebra. (Contains 1 footnote.)

Non-symmetric forms of non-linear vibrations of flexible cylindrical panels and plates under longitudinal load and additive white noise

NASA Astrophysics Data System (ADS)

Krysko, V. A.; Awrejcewicz, J.; Krylova, E. Yu; Papkova, I. V.; Krysko, A. V.

2018-06-01

Parametric non-linear vibrations of flexible cylindrical panels subjected to additive white noise are studied. The governing Marguerre equations are investigated using the finite difference method (FDM) of the second-order accuracy and the Runge-Kutta method. The considered mechanical structural member is treated as a system of many/infinite number of degrees of freedom (DoF). The dependence of chaotic vibrations on the number of DoFs is investigated. Reliability of results is guaranteed by comparing the results obtained using two qualitatively different methods to reduce the problem of PDEs (partial differential equations) to ODEs (ordinary differential equations), i.e. the Faedo-Galerkin method in higher approximations and the 4th and 6th order FDM. The Cauchy problem obtained by the FDM is eventually solved using the 4th-order Runge-Kutta methods. The numerical experiment yielded, for a certain set of parameters, the non-symmetric vibration modes/forms with and without white noise. In particular, it has been illustrated and discussed that action of white noise on chaotic vibrations implies quasi-periodicity, whereas the previously non-symmetric vibration modes are closer to symmetric ones.

A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2017-12-01

In this manuscript, we consider an initial-boundary-value problem governed by a (1 + 1)-dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics. The model considers the presence of a spatial Laplacian of fractional order which is defined in terms of Riesz fractional derivatives, as well as the inclusion of a generic continuously differentiable potential. It is known that the undamped regime has an associated positive energy functional, and we show here that it is preserved throughout time under suitable boundary conditions. To approximate the solutions of this model, we propose a finite-difference discretization based on fractional centered differences. Some discrete quantities are proposed in this work to estimate the energy functional, and we show that the numerical method is capable of conserving the discrete energy under the same boundary conditions for which the continuous model is conservative. Moreover, we establish suitable computational constraints under which the discrete energy of the system is positive. The method is consistent of second order, and is both stable and convergent. The numerical simulations shown here illustrate the most important features of our numerical methodology.

Algorithmic vs. finite difference Jacobians for infrared atmospheric radiative transfer

NASA Astrophysics Data System (ADS)

Schreier, Franz; Gimeno García, Sebastián; Vasquez, Mayte; Xu, Jian

2015-10-01

Jacobians, i.e. partial derivatives of the radiance and transmission spectrum with respect to the atmospheric state parameters to be retrieved from remote sensing observations, are important for the iterative solution of the nonlinear inverse problem. Finite difference Jacobians are easy to implement, but computationally expensive and possibly of dubious quality; on the other hand, analytical Jacobians are accurate and efficient, but the implementation can be quite demanding. GARLIC, our "Generic Atmospheric Radiation Line-by-line Infrared Code", utilizes algorithmic differentiation (AD) techniques to implement derivatives w.r.t. atmospheric temperature and molecular concentrations. In this paper, we describe our approach for differentiation of the high resolution infrared and microwave spectra and provide an in-depth assessment of finite difference approximations using "exact" AD Jacobians as a reference. The results indicate that the "standard" two-point finite differences with 1 K and 1% perturbation for temperature and volume mixing ratio, respectively, can exhibit substantial errors, and central differences are significantly better. However, these deviations do not transfer into the truncated singular value decomposition solution of a least squares problem. Nevertheless, AD Jacobians are clearly recommended because of the superior speed and accuracy.

Reprint of Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-04-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-03-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Finite-difference time-domain synthesis of infrasound propagation through an absorbing atmosphere.

PubMed

de Groot-Hedlin, C

2008-09-01

Equations applicable to finite-difference time-domain (FDTD) computation of infrasound propagation through an absorbing atmosphere are derived and examined in this paper. It is shown that over altitudes up to 160 km, and at frequencies relevant to global infrasound propagation, i.e., 0.02-5 Hz, the acoustic absorption in dB/m varies approximately as the square of the propagation frequency plus a small constant term. A second-order differential equation is presented for an atmosphere modeled as a compressible Newtonian fluid with low shear viscosity, acted on by a small external damping force. It is shown that the solution to this equation represents pressure fluctuations with the attenuation indicated above. Increased dispersion is predicted at altitudes over 100 km at infrasound frequencies. The governing propagation equation is separated into two partial differential equations that are first order in time for FDTD implementation. A numerical analysis of errors inherent to this FDTD method shows that the attenuation term imposes additional stability constraints on the FDTD algorithm. Comparison of FDTD results for models with and without attenuation shows that the predicted transmission losses for the attenuating media agree with those computed from synthesized waveforms.

The coupled nonlinear dynamics of a lift system

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

Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk

2014-12-10

Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This papermore » presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.« less

Cattaneo-Christov based study of {TiO}_2 -CuO/EG Casson hybrid nanofluid flow over a stretching surface with entropy generation

NASA Astrophysics Data System (ADS)

Jamshed, Wasim; Aziz, Asim

2018-06-01

In the present research, a simplified mathematical model is presented to study the heat transfer and entropy generation analysis of thermal system containing hybrid nanofluid. Nanofluid occupies the space over an infinite horizontal surface and the flow is induced by the non-linear stretching of surface. A uniform transverse magnetic field, Cattaneo-Christov heat flux model and thermal radiation effects are also included in the present study. The similarity technique is employed to reduce the governing non-linear partial differential equations to a set of ordinary differential equation. Keller Box numerical scheme is then used to approximate the solutions for the thermal analysis. Results are presented for conventional copper oxide-ethylene glycol (CuO-EG) and hybrid titanium-copper oxide/ethylene glycol ({TiO}_2 -CuO/EG) nanofluids. The spherical, hexahedron, tetrahedron, cylindrical, and lamina-shaped nanoparticles are considered in the present analysis. The significant findings of the study is the enhanced heat transfer capability of hybrid nanofluids over the conventional nanofluids, greatest heat transfer rate for the smallest value of the shape factor parameter and the increase in Reynolds number and Brinkman number increases the overall entropy of the system.

High spatial resolution measurements of NO2 applying Topographic Target Light scattering-Differential Optical Absorption Spectroscopy (ToTaL-DOAS)

NASA Astrophysics Data System (ADS)

Frins, E.; Platt, U.; Wagner, T.

2008-06-01

Tomographic Target Light scattering - Differential Optical Absorption Spectroscopy (ToTaL-DOAS), also called Target-DOAS, is a novel experimental procedure to retrieve trace gas concentrations present in the low atmosphere. Scattered sunlight (partially or totally) reflected from natural or artificial targets of similar albedo located at different distances is analyzed to retrieve the concentration of different trace gases like NO2, SO2 and others. We report high spatial resolution measurements of NO2 mixing ratios in the city of Montevideo (Uruguay) observing three buildings as targets with a Mini-DOAS instrument. Our instrument was 146 m apart from the first building, 196 m from the second and 286 m from the third one. All three buildings are located along a main Avenue. We obtain temporal variation of NO2 mixing ratios between 30 ppb and 65 ppb (±2 ppb). Our measurements demonstrate that ToTaL-DOAS measurements can be made over very short distances. In polluted air masses, the retrieved absorption signal was found to be strong enough to allow measurements over distances in the range of several ten meters, and achieve a spatial resolution of 50 m approximately.

Role of Alternative Polyadenylation during Adipogenic Differentiation: An In Silico Approach

PubMed Central

Spangenberg, Lucía; Correa, Alejandro; Dallagiovanna, Bruno; Naya, Hugo

2013-01-01

Post-transcriptional regulation of stem cell differentiation is far from being completely understood. Changes in protein levels are not fully correlated with corresponding changes in mRNAs; the observed differences might be partially explained by post-transcriptional regulation mechanisms, such as alternative polyadenylation. This would involve changes in protein binding, transcript usage, miRNAs and other non-coding RNAs. In the present work we analyzed the distribution of alternative transcripts during adipogenic differentiation and the potential role of miRNAs in post-transcriptional regulation. Our in silico analysis suggests a modest, consistent, bias in 3′UTR lengths during differentiation enabling a fine-tuned transcript regulation via small non-coding RNAs. Including these effects in the analyses partially accounts for the observed discrepancies in relative abundance of protein and mRNA. PMID:24143171

Homogeneous partial differential equations for superpositions of indeterminate functions of several variables

NASA Astrophysics Data System (ADS)

Asai, Kazuto

2009-02-01

We determine essentially all partial differential equations satisfied by superpositions of tree type and of a further special type. These equations represent necessary and sufficient conditions for an analytic function to be locally expressible as an analytic superposition of the type indicated. The representability of a real analytic function by a superposition of this type is independent of whether that superposition involves real-analytic functions or C^{\\rho}-functions, where the constant \\rho is determined by the structure of the superposition. We also prove that the function u defined by u^n=xu^a+yu^b+zu^c+1 is generally non-representable in any real (resp. complex) domain as f\\bigl(g(x,y),h(y,z)\\bigr) with twice differentiable f and differentiable g, h (resp. analytic f, g, h).

Isotropic differential phase contrast microscopy for quantitative phase bio-imaging.

PubMed

Chen, Hsi-Hsun; Lin, Yu-Zi; Luo, Yuan

2018-05-16

Quantitative phase imaging (QPI) has been investigated to retrieve optical phase information of an object and applied to biological microscopy and related medical studies. In recent examples, differential phase contrast (DPC) microscopy can recover phase image of thin sample under multi-axis intensity measurements in wide-field scheme. Unlike conventional DPC, based on theoretical approach under partially coherent condition, we propose a new method to achieve isotropic differential phase contrast (iDPC) with high accuracy and stability for phase recovery in simple and high-speed fashion. The iDPC is simply implemented with a partially coherent microscopy and a programmable thin-film transistor (TFT) shield to digitally modulate structured illumination patterns for QPI. In this article, simulation results show consistency of our theoretical approach for iDPC under partial coherence. In addition, we further demonstrate experiments of quantitative phase images of a standard micro-lens array, as well as label-free live human cell samples. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Evaluating Feynman integrals by the hypergeometry

NASA Astrophysics Data System (ADS)

Feng, Tai-Fu; Chang, Chao-Hsi; Chen, Jian-Bin; Gu, Zhi-Hua; Zhang, Hai-Bin

2018-02-01

The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop B0 and massless C0 functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams.

Auto-Bäcklund transformations for a matrix partial differential equation

NASA Astrophysics Data System (ADS)

Gordoa, P. R.; Pickering, A.

2018-07-01

We derive auto-Bäcklund transformations, analogous to those of the matrix second Painlevé equation, for a matrix partial differential equation. We also then use these auto-Bäcklund transformations to derive matrix equations involving shifts in a discrete variable, a process analogous to the use of the auto-Bäcklund transformations of the matrix second Painlevé equation to derive a discrete matrix first Painlevé equation. The equations thus derived then include amongst other examples a semidiscrete matrix equation which can be considered to be an extension of this discrete matrix first Painlevé equation. The application of this technique to the auto-Bäcklund transformations of the scalar case of our partial differential equation has not been considered before, and so the results obtained here in this scalar case are also new. Other equations obtained here using this technique include a scalar semidiscrete equation which arises in the case of the second Painlevé equation, and which does not seem to have been thus derived previously.

Boundary-fitted curvilinear coordinate systems for solution of partial differential equations on fields containing any number of arbitrary two-dimensional bodies

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Thames, F. C.; Mastin, C. W.

1977-01-01

A method is presented for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected two-dimensional region containing any number of arbitrarily shaped bodies. No restrictions are placed on the shape of the boundaries, which may even be time-dependent, and the approach is not restricted in principle to two dimensions. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system in the physical plane. A number of examples of coordinate systems and application thereof to the solution of partial differential equations are given. The FORTRAN computer program and instructions for use are included.

Solving Partial Differential Equations in a data-driven multiprocessor environment

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

Gaudiot, J.L.; Lin, C.M.; Hosseiniyar, M.

1988-12-31

Partial differential equations can be found in a host of engineering and scientific problems. The emergence of new parallel architectures has spurred research in the definition of parallel PDE solvers. Concurrently, highly programmable systems such as data-how architectures have been proposed for the exploitation of large scale parallelism. The implementation of some Partial Differential Equation solvers (such as the Jacobi method) on a tagged token data-flow graph is demonstrated here. Asynchronous methods (chaotic relaxation) are studied and new scheduling approaches (the Token No-Labeling scheme) are introduced in order to support the implementation of the asychronous methods in a data-driven environment.more » New high-level data-flow language program constructs are introduced in order to handle chaotic operations. Finally, the performance of the program graphs is demonstrated by a deterministic simulation of a message passing data-flow multiprocessor. An analysis of the overhead in the data-flow graphs is undertaken to demonstrate the limits of parallel operations in dataflow PDE program graphs.« less

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

A symplectic integration method for elastic filaments

NASA Astrophysics Data System (ADS)

Ladd, Tony; Misra, Gaurav

2009-03-01

Elastic rods are a ubiquitous coarse-grained model of semi-flexible biopolymers such as DNA, actin, and microtubules. The Worm-Like Chain (WLC) is the standard numerical model for semi-flexible polymers, but it is only a linearized approximation to the dynamics of an elastic rod, valid for small deflections; typically the torsional motion is neglected as well. In the standard finite-difference and finite-element formulations of an elastic rod, the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integral over the contour of the filament. This discrete representation of the continuum filament can then be integrated by one of the explicit symplectic integrators frequently used in molecular dynamics. The model systematically approximates the continuum partial differential equations, but has the same level of computational complexity as molecular dynamics and is constraint free. Numerical tests show that the algorithm is much more stable than a finite-difference formulation and can be used for high aspect ratio filaments, such as actin. We present numerical results for the deterministic and stochastic motion of single filaments.

Three-dimensional modelling of thin liquid films over spinning disks

NASA Astrophysics Data System (ADS)

Zhao, Kun; Wray, Alex; Yang, Junfeng; Matar, Omar

2016-11-01

In this research the dynamics of a thin film flowing over a rapidly spinning, horizontal disk is considered. A set of non-axisymmetric evolution equations for the film thickness, radial and azimuthal flow rates are derived using a boundary-layer approximation in conjunction with the Karman-Polhausen approximation for the velocity distribution in the film. These highly nonlinear partial differential equations are then solved numerically in order to reveal the formation of two and three-dimensional large-amplitude waves that travel from the disk inlet to its periphery. The spatio-temporal profile of film thickness provides us with visualization of flow structures over the entire disk and by varying system parameters(volumetric flow rate of fluid and rotational speed of disk) different wave patterns can be observed, including spiral, concentric, smooth waves and wave break-up in exceptional conditions. Similar types of waves can be found by experimentalists in literature and CFD simulation and our results show good agreement with both experimental and CFD results. Furthermore, the semi-parabolic velocity profile assumed in our model under the waves is directly compared with CFD data in various flow regimes in order to validate our model. EPSRC UK Programme Grant EP/K003976/1.

Real-time approximate optimal guidance laws for the advanced launch system

NASA Technical Reports Server (NTRS)

Speyer, Jason L.; Feeley, Timothy; Hull, David G.

1989-01-01

An approach to optimal ascent guidance for a launch vehicle is developed using an expansion technique. The problem is to maximize the payload put into orbit subject to the equations of motion of a rocket over a rotating spherical earth. It is assumed that the thrust and gravitational forces dominate over the aerodynamic forces. It is shown that these forces can be separated by a small parameter epsilon, where epsilon is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in a series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The zeroth-order problem is that of putting maximum payload into orbit subject to the equations of motion of a rocket in a vacuum over a flat earth. The neglected inertial and aerodynamic terms are included in higher order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only quadrature integrations. These quadrature integrations can be performed rapidly, so that real-time approximate optimization can be used to construct the launch guidance law.

Fast calculation of the light differential scattering cross section of optically soft and convex bodies

NASA Astrophysics Data System (ADS)

Gruy, Frédéric

2014-02-01

Depending on the range of size and the refractive index value, an optically soft particle follows Rayleigh-Debye-Gans or RDG approximation or Van de Hulst approximation. Practically the first one is valid for small particles whereas the second one works for large particles. Klett and Sutherland (Klett JD, Sutherland RA. App. Opt. 1992;31:373) proved that the Wentzel-Kramers-Brillouin or WKB approximation leads to accurate values of the differential scattering cross section of sphere and cylinder over a wide range of size. In this paper we extend the work of Klett and Sutherland by proposing a method allowing a fast calculation of the differential scattering cross section for any shape of particle with a given orientation and illuminated by unpolarized light. Our method is based on a geometrical approximation of the particle by replacing each geometrical cross section by an ellipse and then by exactly evaluating the differential scattering cross section of the newly generated body. The latter one contains only two single integrals.

Using the phase-space imager to analyze partially coherent imaging systems: bright-field, phase contrast, differential interference contrast, differential phase contrast, and spiral phase contrast

NASA Astrophysics Data System (ADS)

Mehta, Shalin B.; Sheppard, Colin J. R.

2010-05-01

Various methods that use large illumination aperture (i.e. partially coherent illumination) have been developed for making transparent (i.e. phase) specimens visible. These methods were developed to provide qualitative contrast rather than quantitative measurement-coherent illumination has been relied upon for quantitative phase analysis. Partially coherent illumination has some important advantages over coherent illumination and can be used for measurement of the specimen's phase distribution. However, quantitative analysis and image computation in partially coherent systems have not been explored fully due to the lack of a general, physically insightful and computationally efficient model of image formation. We have developed a phase-space model that satisfies these requirements. In this paper, we employ this model (called the phase-space imager) to elucidate five different partially coherent systems mentioned in the title. We compute images of an optical fiber under these systems and verify some of them with experimental images. These results and simulated images of a general phase profile are used to compare the contrast and the resolution of the imaging systems. We show that, for quantitative phase imaging of a thin specimen with matched illumination, differential phase contrast offers linear transfer of specimen information to the image. We also show that the edge enhancement properties of spiral phase contrast are compromised significantly as the coherence of illumination is reduced. The results demonstrate that the phase-space imager model provides a useful framework for analysis, calibration, and design of partially coherent imaging methods.

Fast template matching with polynomials.

PubMed

Omachi, Shinichiro; Omachi, Masako

2007-08-01

Template matching is widely used for many applications in image and signal processing. This paper proposes a novel template matching algorithm, called algebraic template matching. Given a template and an input image, algebraic template matching efficiently calculates similarities between the template and the partial images of the input image, for various widths and heights. The partial image most similar to the template image is detected from the input image for any location, width, and height. In the proposed algorithm, a polynomial that approximates the template image is used to match the input image instead of the template image. The proposed algorithm is effective especially when the width and height of the template image differ from the partial image to be matched. An algorithm using the Legendre polynomial is proposed for efficient approximation of the template image. This algorithm not only reduces computational costs, but also improves the quality of the approximated image. It is shown theoretically and experimentally that the computational cost of the proposed algorithm is much smaller than the existing methods.

A novel principle for partial agonism of liver X receptor ligands. Competitive recruitment of activators and repressors.

PubMed

Albers, Michael; Blume, Beatrix; Schlueter, Thomas; Wright, Matthew B; Kober, Ingo; Kremoser, Claus; Deuschle, Ulrich; Koegl, Manfred

2006-02-24

Partial, selective activation of nuclear receptors is a central issue in molecular endocrinology but only partly understood. Using LXRs as an example, we show here that purely agonistic ligands can be clearly and quantitatively differentiated from partial agonists by the cofactor interactions they induce. Although a pure agonist induces a conformation that is incompatible with the binding of repressors, partial agonists such as GW3965 induce a state where the interaction not only with coactivators, but also corepressors is clearly enhanced over the unliganded state. The activities of the natural ligand 22(R)-hydroxycholesterol and of a novel quinazolinone ligand, LN6500 can be further differentiated from GW3965 and T0901317 by their weaker induction of coactivator binding. Using biochemical and cell-based assays, we show that the natural ligand of LXR is a comparably weak partial agonist. As predicted, we find that a change in the coactivator to corepressor ratio in the cell will affect NCoR recruiting compounds more dramatically than NCoR-dissociating compounds. Our data show how competitive binding of coactivators and corepressors can explain the tissue-specific behavior of partial agonists and open up new routes to a rational design of partial agonists for LXRs.

Parenting, attention and externalizing problems: testing mediation longitudinally, repeatedly and reciprocally.

PubMed

Belsky, Jay; Pasco Fearon, R M; Bell, Brian

2007-12-01

Building on prior work, this paper tests, longitudinally and repeatedly, the proposition that attentional control processes mediate the effect of earlier parenting on later externalizing problems. Repeated independent measurements of all three constructs--observed parenting, computer-tested attentional control and adult-reported externalizing problems--were subjected to structural equation modeling using data from the large-scale American study of child care and youth development. Structural equation modeling indicated (a) that greater maternal sensitivity at two different ages (54 months, approximately 6 years) predicted better attentional control on the Continuous Performance Test (CPT) of attention regulation two later ages ( approximately 6/9 years); (2) that better attentional control at three different ages (54 months, approximately 6/9 years) predicted less teacher-reported externalizing problems at three later ages ( approximately 6/8/10 years); and (3) that attentional control partially mediated the effect of parenting on externalizing problems at two different lags (i.e., 54 months--> approximately 6 years--> approximately 8 years; approximately 6 years--> approximately 9 years--> approximately 10 years), though somewhat more strongly for the first. Additionally, (4) some evidence of reciprocal effects of attentional processes on parenting emerged (54 months--> approximately 6 years; approximately 6 years--> approximately 8 years), but not of problem behavior on attention. Because attention control partially mediates the effects of parenting on externalizing problems, intervention efforts could target both parenting and attentional processes.

Morphometric analysis of epidermal differentiation in primary roots of Zea mays

NASA Technical Reports Server (NTRS)

Moore, R.; Smith, H. S.

1990-01-01

Epidermal differentiation in primary roots of Zea mays was divided into six cell types based on cellular shape and cytoplasmic appearance. These six cell types are: 1) apical protoderm, located at the tip of the root pole and characterized by periclinally flattened cells; 2) cuboidal protoderm, located approximately 230 microns from the root pole and characterized by cuboidal cells; 3) tabular epidermis, located approximately 450 microns from the root pole and characterized by anticlinally flattened cells; 4) cuboidal epidermis, located approximately 900 microns from the root pole and characterized by cuboidal cells having numerous small vacuoles; 5) vacuolate cuboidal epidermis, located approximately 1,500 microns from the root pole and characterized by cuboidal cells containing several large vacuoles; and 6) columnar epidermis, located approximately 2,200 microns from the root pole (i.e., at the beginning of the zone of elongation) and characterized by elongated cells. We also used stereology to quantify the cellular changes associated with epidermal differentiation. The quiescent center and the apical protoderm have significantly different ultrastructures. The relative volume of dictyosomes increases dramatically during the early stages of epidermal differentiation. This increase correlates inversely with the amount of coverage provided by the root cap and mucilage.

Activation of TRPV2 negatively regulates the differentiation of mouse brown adipocytes.

PubMed

Sun, Wuping; Uchida, Kunitoshi; Takahashi, Nobuyuki; Iwata, Yuko; Wakabayashi, Shigeo; Goto, Tsuyoshi; Kawada, Teruo; Tominaga, Makoto

2016-09-01

Transient receptor potential vanilloid 2 (TRPV2) acts as a Ca(2+)-permeable non-selective cation channel that has been reported to be sensitive to temperature, mechanical force, and some chemicals. We recently showed that TRPV2 is critical for maintenance of the thermogenic function of brown adipose tissue in mice. However, the involvement of TRPV2 in the differentiation of brown adipocytes remains unexplored. We found that the expression of TRPV2 was dramatically increased during the differentiation of brown adipocytes. Non-selective TRPV2 agonists (2-aminoethoxydiphenyl borate and lysophosphatidylcholine) inhibited the differentiation of brown adipocytes in a dose-dependent manner during the early stage of differentiation of brown adipocytes. The inhibition was rescued by a TRPV2-selective antagonist, SKF96365 (SKF). Mechanical force, which activates TRPV2, also inhibited the differentiation of brown adipocytes in a strength-dependent manner, and the effect was reversed by SKF. In addition, the inhibition of adipocyte differentiation by either TRPV2 ligand or mechanical stimulation was significantly smaller in the cells from TRPV2KO mice. Moreover, calcineurin inhibitors, cyclosporine A and FK506, partially reversed TRPV2 activation-induced inhibition of brown adipocyte differentiation. Thus, we conclude that TRPV2 might be involved in the modulation of brown adipocyte differentiation partially via a calcineurin pathway.

Level-Set Variational Implicit-Solvent Modeling of Biomolecules with the Coulomb-Field Approximation

PubMed Central

2011-01-01

Central in the variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett.2006, 96, 087802 and J. Chem. Phys.2006, 124, 084905] of molecular solvation is a mean-field free-energy functional of all possible solute–solvent interfaces or dielectric boundaries. Such a functional can be minimized numerically by a level-set method to determine stable equilibrium conformations and solvation free energies. Applications to nonpolar systems have shown that the level-set VISM is efficient and leads to qualitatively and often quantitatively correct results. In particular, it is capable of capturing capillary evaporation in hydrophobic confinement and corresponding multiple equilibrium states as found in molecular dynamics (MD) simulations. In this work, we introduce into the VISM the Coulomb-field approximation of the electrostatic free energy. Such an approximation is a volume integral over an arbitrary shaped solvent region, requiring no solutions to any partial differential equations. With this approximation, we obtain the effective boundary force and use it as the “normal velocity” in the level-set relaxation. We test the new approach by calculating solvation free energies and potentials of mean force for small and large molecules, including the two-domain protein BphC. Our results reveal the importance of coupling polar and nonpolar interactions in the underlying molecular systems. In particular, dehydration near the domain interface of BphC subunits is found to be highly sensitive to local electrostatic potentials as seen in previous MD simulations. This is a first step toward capturing the complex protein dehydration process by an implicit-solvent approach. PMID:22346739

Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries

NASA Astrophysics Data System (ADS)

Startsev, Sergey Ya.

2017-05-01

The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and nonlinear) partial differential systems possessing a full set of differential operators that map any function of one independent variable into a symmetry of the corresponding system. We demonstrate that a system has the above property if and only if this system admits a full set of formal integrals (i.e., differential operators which map symmetries into integrals of the system). As a consequence, such systems possess both direct and inverse Noether operators (in the terminology of a work by B. Fuchssteiner and A.S. Fokas who have used these terms for operators that map cosymmetries into symmetries and perform transformations in the opposite direction). Systems admitting Noether operators are not exhausted by Euler-Lagrange systems and the systems with formal integrals. In particular, a hyperbolic system admits an inverse Noether operator if a differential substitution maps this system into a system possessing an inverse Noether operator.

Ultrasound speckle reduction based on fractional order differentiation.

PubMed

Shao, Dangguo; Zhou, Ting; Liu, Fan; Yi, Sanli; Xiang, Yan; Ma, Lei; Xiong, Xin; He, Jianfeng

2017-07-01

Ultrasound images show a granular pattern of noise known as speckle that diminishes their quality and results in difficulties in diagnosis. To preserve edges and features, this paper proposes a fractional differentiation-based image operator to reduce speckle in ultrasound. An image de-noising model based on fractional partial differential equations with balance relation between k (gradient modulus threshold that controls the conduction) and v (the order of fractional differentiation) was constructed by the effective combination of fractional calculus theory and a partial differential equation, and the numerical algorithm of it was achieved using a fractional differential mask operator. The proposed algorithm has better speckle reduction and structure preservation than the three existing methods [P-M model, the speckle reducing anisotropic diffusion (SRAD) technique, and the detail preserving anisotropic diffusion (DPAD) technique]. And it is significantly faster than bilateral filtering (BF) in producing virtually the same experimental results. Ultrasound phantom testing and in vivo imaging show that the proposed method can improve the quality of an ultrasound image in terms of tissue SNR, CNR, and FOM values.

A simplified computer program for the prediction of the linear stability behavior of liquid propellant combustors

NASA Technical Reports Server (NTRS)

Mitchell, C. E.; Eckert, K.

1979-01-01

A program for predicting the linear stability of liquid propellant rocket engines is presented. The underlying model assumptions and analytical steps necessary for understanding the program and its input and output are also given. The rocket engine is modeled as a right circular cylinder with an injector with a concentrated combustion zone, a nozzle, finite mean flow, and an acoustic admittance, or the sensitive time lag theory. The resulting partial differential equations are combined into two governing integral equations by the use of the Green's function method. These equations are solved using a successive approximation technique for the small amplitude (linear) case. The computational method used as well as the various user options available are discussed. Finally, a flow diagram, sample input and output for a typical application and a complete program listing for program MODULE are presented.

An Artificial Neural Networks Method for Solving Partial Differential Equations

NASA Astrophysics Data System (ADS)

Alharbi, Abir

2010-09-01

While there already exists many analytical and numerical techniques for solving PDEs, this paper introduces an approach using artificial neural networks. The approach consists of a technique developed by combining the standard numerical method, finite-difference, with the Hopfield neural network. The method is denoted Hopfield-finite-difference (HFD). The architecture of the nets, energy function, updating equations, and algorithms are developed for the method. The HFD method has been used successfully to approximate the solution of classical PDEs, such as the Wave, Heat, Poisson and the Diffusion equations, and on a system of PDEs. The software Matlab is used to obtain the results in both tabular and graphical form. The results are similar in terms of accuracy to those obtained by standard numerical methods. In terms of speed, the parallel nature of the Hopfield nets methods makes them easier to implement on fast parallel computers while some numerical methods need extra effort for parallelization.

Effect of Initial Stress on the Dynamic Response of a Multi-Layered Plate-Strip Subjected to an Arbitrary Inclined Time-Harmonic Force

NASA Astrophysics Data System (ADS)

Daşdemir, A.

2017-08-01

The forced vibration of a multi-layered plate-strip with initial stress under the action of an arbitrary inclined time-harmonic force resting on a rigid foundation is considered. Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), a mathematical modelling is presented in plane strain state. It is assumed that there exists the complete contact interaction at the interface between the layers and the materials of the layer are linearly elastic, homogeneous and isotropic. The governing system of the partial differential equations of motion for the considered problem is solved approximately by employing the Finite Element Method (FEM). Further, the influence of the initial stress parameter on the dynamic response of the plate-strip is presented.

Measurement of direct f0(980) photoproduction on the proton.

PubMed

Battaglieri, M; De Vita, R; Szczepaniak, A P; Adhikari, K P; Aghasyan, M; Amaryan, M J; Ambrozewicz, P; Anghinolfi, M; Asryan, G; Avakian, H; Bagdasaryan, H; Baillie, N; Ball, J P; Baltzell, N A; Batourine, V; Bedlinskiy, I; Bellis, M; Benmouna, N; Berman, B L; Bibrzycki, L; Biselli, A S; Bookwalter, C; Bouchigny, S; Boiarinov, S; Bradford, R; Branford, D; Briscoe, W J; Brooks, W K; Bültmann, S; Burkert, V D; Calarco, J R; Careccia, S L; Carman, D S; Casey, L; Chen, S; Cheng, L; Clinton, E; Cole, P L; Collins, P; Crabb, D; Crannell, H; Crede, V; Cummings, J P; Dale, D; Daniel, A; Dashyan, N; De Masi, R; De Sanctis, E; Degtyarenko, P V; Deur, A; Dhamija, S; Dharmawardane, K V; Dickson, R; Djalali, C; Dodge, G E; Donnelly, J; Doughty, D; Dugger, M; Dzyubak, O P; Egiyan, H; Egiyan, K S; El Fassi, L; Elouadrhiri, L; Eugenio, P; Fedotov, G; Fersch, R; Forest, T A; Fradi, A; Gabrielyan, M Y; Gan, L; Garçon, M; Gasparian, A; Gavalian, G; Gevorgyan, N; Gilfoyle, G P; Giovanetti, K L; Girod, F X; Glamazdin, O; Goett, J; Goetz, J T; Gohn, W; Golovatch, E; Gordon, C I O; Gothe, R W; Graham, L; Griffioen, K A; Guidal, M; Guler, N; Guo, L; Gyurjyan, V; Hadjidakis, C; Hafidi, K; Hakobyan, H; Hakobyan, R S; Hanretty, C; Hardie, J; Hassall, N; Heddle, D; Hersman, F W; Hicks, K; Hleiqawi, I; Holtrop, M; Hyde, C E; Ilieva, Y; Ireland, D G; Ishkhanov, B S; Isupov, E L; Ito, M M; Jenkins, D; Jo, H S; Johnstone, J R; Joo, K; Juengst, H G; Kageya, T; Kalantarians, N; Keller, D; Kellie, J D; Khandaker, M; Khetarpal, P; Kim, W; Klein, A; Klein, F J; Klimenko, A V; Konczykowski, P; Kossov, M; Krahn, Z; Kramer, L H; Kubarovsky, V; Kuhn, J; Kuhn, S E; Kuleshov, S V; Kuznetsov, V; Lachniet, J; Laget, J M; Langheinrich, J; Lawrence, D; Lee, T; Lesniak, L; Li, Ji; Livingston, K; Lowry, M; Lu, H Y; Maccormick, M; Malace, S; Markov, N; Mattione, P; McCracken, M E; McKinnon, B; Mecking, B A; Melone, J J; Mestayer, M D; Meyer, C A; Mibe, T; Mikhailov, K; Mineeva, T; Minehart, R; Mirazita, M; Miskimen, R; Mochalov, V; Mokeev, V; Moreno, B; Moriya, K; Morrow, S A; Moteabbed, M; Munevar, E; Mutchler, G S; Nadel-Turonski, P; Nakagawa, I; Nasseripour, R; Niccolai, S; Niculescu, G; Niculescu, I; Niczyporuk, B B; Niroula, M R; Niyazov, R A; Nozar, M; Osipenko, M; Ostrovidov, A I; Park, K; Park, S; Pasyuk, E; Paris, M; Paterson, C; Pereira, S Anefalos; Pierce, J; Pivnyuk, N; Pocanic, D; Pogorelko, O; Pozdniakov, S; Price, J W; Prok, Y; Protopopescu, D; Raue, B A; Riccardi, G; Ricco, G; Ripani, M; Ritchie, B G; Rosner, G; Rossi, P; Sabatié, F; Saini, M S; Salamanca, J; Salgado, C; Sandorfi, A; Santoro, J P; Sapunenko, V; Schott, D; Schumacher, R A; Serov, V S; Sharabian, Y G; Sharov, D; Shvedunov, N V; Smith, E S; Smith, L C; Sober, D I; Sokhan, D; Starostin, A; Stavinsky, A; Stepanyan, S; Stepanyan, S S; Stokes, B E; Stoler, P; Stopani, K A; Strakovsky, I I; Strauch, S; Taiuti, M; Tedeschi, D J; Teymurazyan, A; Tkabladze, A; Tkachenko, S; Todor, L; Tur, C; Ungaro, M; Vineyard, M F; Vlassov, A V; Watts, D P; Wei, X; Weinstein, L B; Weygand, D P; Williams, M; Wolin, E; Wood, M H; Yegneswaran, A; Yurov, M; Zana, L; Zhang, J; Zhao, B; Zhao, Z W

2009-03-13

We report on the results of the first measurement of exclusive f_{0}(980) meson photoproduction on protons for E_{gamma}=3.0-3.8 GeV and -t=0.4-1.0 GeV2. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility. The resonance was detected via its decay in the pi;{+}pi;{-} channel by performing a partial wave analysis of the reaction gammap-->ppi;{+}pi;{-}. Clear evidence of the f_{0}(980) meson was found in the interference between P and S waves at M_{pi;{+}pi;{-}} approximately 1 GeV. The S-wave differential cross section integrated in the mass range of the f_{0}(980) was found to be a factor of about 50 smaller than the cross section for the rho meson. This is the first time the f_{0}(980) meson has been measured in a photoproduction experiment.

Stability analysis of a liquid fuel annular combustion chamber. M.S. Thesis

NASA Technical Reports Server (NTRS)

Mcdonald, G. H.

1979-01-01

The problems of combustion instability in an annular combustion chamber are investigated. A modified Galerkin method was used to produce a set of modal amplitude equations from the general nonlinear partial differential acoustic wave equation. From these modal amplitude equations, the two variable perturbation method was used to develop a set of approximate equations of a given order of magnitude. These equations were modeled to show the effects of velocity sensitive combustion instabilities by evaluating the effects of certain parameters in the given set of equations. By evaluating these effects, parameters which cause instabilities to occur in the combustion chamber can be ascertained. It is assumed that in the annular combustion chamber, the liquid propellants are injected uniformly across the injector face, the combustion processes are distributed throughout the combustion chamber, and that no time delay occurs in the combustion processes.

The contact sport of rough surfaces

NASA Astrophysics Data System (ADS)

Carpick, Robert W.

2018-01-01

Describing the way two surfaces touch and make contact may seem simple, but it is not. Fully describing the elastic deformation of ideally smooth contacting bodies, under even low applied pressure, involves second-order partial differential equations and fourth-rank elastic constant tensors. For more realistic rough surfaces, the problem becomes a multiscale exercise in surface-height statistics, even before including complex phenomena such as adhesion, plasticity, and fracture. A recent research competition, the “Contact Mechanics Challenge” (1), was designed to test various approximate methods for solving this problem. A hypothetical rough surface was generated, and the community was invited to model contact with this surface with competing theories for the calculation of properties, including contact area and pressure. A supercomputer-generated numerical solution was kept secret until competition entries were received. The comparison of results (2) provides insights into the relative merits of competing models and even experimental approaches to the problem.

Multiplicative noise removal through fractional order tv-based model and fast numerical schemes for its approximation

NASA Astrophysics Data System (ADS)

Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad

2017-07-01

This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.

When push comes to shove: Exclusion processes with nonlocal consequences

NASA Astrophysics Data System (ADS)

Almet, Axel A.; Pan, Michael; Hughes, Barry D.; Landman, Kerry A.

2015-11-01

Stochastic agent-based models are useful for modelling collective movement of biological cells. Lattice-based random walk models of interacting agents where each site can be occupied by at most one agent are called simple exclusion processes. An alternative motility mechanism to simple exclusion is formulated, in which agents are granted more freedom to move under the compromise that interactions are no longer necessarily local. This mechanism is termed shoving. A nonlinear diffusion equation is derived for a single population of shoving agents using mean-field continuum approximations. A continuum model is also derived for a multispecies problem with interacting subpopulations, which either obey the shoving rules or the simple exclusion rules. Numerical solutions of the derived partial differential equations compare well with averaged simulation results for both the single species and multispecies processes in two dimensions, while some issues arise in one dimension for the multispecies case.

Extracellular Matrix Scaffold Technology for Bioartificial Pancreas Engineering

PubMed Central

Salvatori, Marcus; Katari, Ravi; Patel, Timil; Peloso, Andrea; Mugweru, Jon; Owusu, Kofi

2014-01-01

Emergent technologies in regenerative medicine may soon overcome the limitations of conventional diabetes therapies. Collaborative efforts across the subfields of stem cell technology, islet encapsulation, and biomaterial carriers seek to produce a bioengineered pancreas capable of restoring endocrine function in patients with insulin-dependent diabetes. These technologies rely on a robust understanding of the extracellular matrix (ECM), the supportive 3-dimensional network of proteins necessary for cellular attachment, proliferation, and differentiation. Although these functions can be partially approximated by biosynthetic carriers, novel decellularization protocols have allowed researchers to discover the advantages afforded by the native pancreatic ECM. The native ECM has proven to be an optimal platform for recellularization and whole-organ pancreas bioengineering, an exciting new field with the potential to resolve the dire shortage of transplantable organs. This review seeks to contextualize recent findings, discuss current research goals, and identify future challenges of regenerative medicine as it applies to diabetes management. PMID:24876552

A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: Application to a model of cell migration and chemotaxis.

PubMed

MacDonald, G; Mackenzie, J A; Nolan, M; Insall, R H

2016-03-15

In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk-surface reaction-diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk-surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane.

Inclusion of electron correlation for the target wave function in low- to intermediate-energy e-N2 scattering

NASA Technical Reports Server (NTRS)

Weatherford, C. A.; Brown, F. B.; Temkin, A.

1987-01-01

In a recent calculation, an exact exchange method was developed for use in the partial-differential-equation approach to electron-molecule scattering and was applied to e-N2 scattering in the fixed-nuclei approximation with an adiabatic polarization potential at low energies (0-10 eV). Integrated elastic cross sections were calculated and found to be lower than experiment at energies both below and above the Pi(g) resonance. It was speculated at that time that improved experimental agreement could be obtained if a correlated target representation were used in place of the uncorrelated one. The present paper implements this suggestion and demonstrates the improved agreement. These calculations are also extended to higher energies (0-30 eV) so asd to include the Sigma(u) resonance. Some discrepancies among the experiments and between experiment and the various calculations at very low energy are noted.

Dynamic one-dimensional modeling of secondary settling tanks and system robustness evaluation.

PubMed

Li, Ben; Stenstrom, M K

2014-01-01

One-dimensional secondary settling tank models are widely used in current engineering practice for design and optimization, and usually can be expressed as a nonlinear hyperbolic or nonlinear strongly degenerate parabolic partial differential equation (PDE). Reliable numerical methods are needed to produce approximate solutions that converge to the exact analytical solutions. In this study, we introduced a reliable numerical technique, the Yee-Roe-Davis (YRD) method as the governing PDE solver, and compared its reliability with the prevalent Stenstrom-Vitasovic-Takács (SVT) method by assessing their simulation results at various operating conditions. The YRD method also produced a similar solution to the previously developed Method G and Enquist-Osher method. The YRD and SVT methods were also used for a time-to-failure evaluation, and the results show that the choice of numerical method can greatly impact the solution. Reliable numerical methods, such as the YRD method, are strongly recommended.

Optimal estimation of spatially variable recharge and transmissivity fields under steady-state groundwater flow. Part 1. Theory

NASA Astrophysics Data System (ADS)

Graham, Wendy D.; Tankersley, Claude D.

1994-05-01

Stochastic methods are used to analyze two-dimensional steady groundwater flow subject to spatially variable recharge and transmissivity. Approximate partial differential equations are developed for the covariances and cross-covariances between the random head, transmissivity and recharge fields. Closed-form solutions of these equations are obtained using Fourier transform techniques. The resulting covariances and cross-covariances can be incorporated into a Bayesian conditioning procedure which provides optimal estimates of the recharge, transmissivity and head fields given available measurements of any or all of these random fields. Results show that head measurements contain valuable information for estimating the random recharge field. However, when recharge is treated as a spatially variable random field, the value of head measurements for estimating the transmissivity field can be reduced considerably. In a companion paper, the method is applied to a case study of the Upper Floridan Aquifer in NE Florida.

Meshfree truncated hierarchical refinement for isogeometric analysis

NASA Astrophysics Data System (ADS)

Atri, H. R.; Shojaee, S.

2018-05-01

In this paper truncated hierarchical B-spline (THB-spline) is coupled with reproducing kernel particle method (RKPM) to blend advantages of the isogeometric analysis and meshfree methods. Since under certain conditions, the isogeometric B-spline and NURBS basis functions are exactly represented by reproducing kernel meshfree shape functions, recursive process of producing isogeometric bases can be omitted. More importantly, a seamless link between meshfree methods and isogeometric analysis can be easily defined which provide an authentic meshfree approach to refine the model locally in isogeometric analysis. This procedure can be accomplished using truncated hierarchical B-splines to construct new bases and adaptively refine them. It is also shown that the THB-RKPM method can provide efficient approximation schemes for numerical simulations and represent a promising performance in adaptive refinement of partial differential equations via isogeometric analysis. The proposed approach for adaptive locally refinement is presented in detail and its effectiveness is investigated through well-known benchmark examples.

Fractal ladder models and power law wave equations

PubMed Central

Kelly, James F.; McGough, Robert J.

2009-01-01

The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers–Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters. PMID:19813816

Cattaneo-Christov Heat Flux Model for MHD Three-Dimensional Flow of Maxwell Fluid over a Stretching Sheet.

PubMed

Rubab, Khansa; Mustafa, M

2016-01-01

This letter investigates the MHD three-dimensional flow of upper-convected Maxwell (UCM) fluid over a bi-directional stretching surface by considering the Cattaneo-Christov heat flux model. This model has tendency to capture the characteristics of thermal relaxation time. The governing partial differential equations even after employing the boundary layer approximations are non linear. Accurate analytic solutions for velocity and temperature distributions are computed through well-known homotopy analysis method (HAM). It is noticed that velocity decreases and temperature rises when stronger magnetic field strength is accounted. Penetration depth of temperature is a decreasing function of thermal relaxation time. The analysis for classical Fourier heat conduction law can be obtained as a special case of the present work. To our knowledge, the Cattaneo-Christov heat flux model law for three-dimensional viscoelastic flow problem is just introduced here.

GENASIS Mathematics : Object-oriented manifolds, operations, and solvers for large-scale physics simulations

NASA Astrophysics Data System (ADS)

Cardall, Christian Y.; Budiardja, Reuben D.

2018-01-01

The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.

The use of Galerkin finite-element methods to solve mass-transport equations

USGS Publications Warehouse

Grove, David B.

1977-01-01

The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.; Estabrook, F. B.

1975-01-01

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

Numerical method based on the lattice Boltzmann model for the Fisher equation.

PubMed

Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng

2008-06-01

In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.

Generation of three-dimensional body-fitted grids by solving hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, an extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Generation of three-dimensional body-fitted grids by solving hyperbolic and parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Computer transformation of partial differential equations into any coordinate system

NASA Technical Reports Server (NTRS)

Sullivan, R. D.

1977-01-01

The use of tensors to provide a compact way of writing partial differential equations in a form valid in all coordinate systems is discussed. In order to find solutions to the equations with their boundary conditions they must be expressed in terms of the coordinate system under consideration. The process of arriving at these expressions from the tensor formulation was automated by a software system, TENSR. An allied system that analyzes the resulting expressions term by term and drops those that are negligible is also described.

Partial differential equation models in macroeconomics.

PubMed

Achdou, Yves; Buera, Francisco J; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin

2014-11-13

The purpose of this article is to get mathematicians interested in studying a number of partial differential equations (PDEs) that naturally arise in macroeconomics. These PDEs come from models designed to study some of the most important questions in economics. At the same time, they are highly interesting for mathematicians because their structure is often quite difficult. We present a number of examples of such PDEs, discuss what is known about their properties, and list some open questions for future research. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

On the continuous differentiability of inter-spike intervals of synaptically connected cortical spiking neurons in a neuronal network.

PubMed

Kumar, Gautam; Kothare, Mayuresh V

2013-12-01

We derive conditions for continuous differentiability of inter-spike intervals (ISIs) of spiking neurons with respect to parameters (decision variables) of an external stimulating input current that drives a recurrent network of synaptically connected neurons. The dynamical behavior of individual neurons is represented by a class of discontinuous single-neuron models. We report here that ISIs of neurons in the network are continuously differentiable with respect to decision variables if (1) a continuously differentiable trajectory of the membrane potential exists between consecutive action potentials with respect to time and decision variables and (2) the partial derivative of the membrane potential of spiking neurons with respect to time is not equal to the partial derivative of their firing threshold with respect to time at the time of action potentials. Our theoretical results are supported by showing fulfillment of these conditions for a class of known bidimensional spiking neuron models.

Rational trigonometric approximations using Fourier series partial sums

NASA Technical Reports Server (NTRS)

Geer, James F.

1993-01-01

A class of approximations (S(sub N,M)) to a periodic function f which uses the ideas of Pade, or rational function, approximations based on the Fourier series representation of f, rather than on the Taylor series representation of f, is introduced and studied. Each approximation S(sub N,M) is the quotient of a trigonometric polynomial of degree N and a trigonometric polynomial of degree M. The coefficients in these polynomials are determined by requiring that an appropriate number of the Fourier coefficients of S(sub N,M) agree with those of f. Explicit expressions are derived for these coefficients in terms of the Fourier coefficients of f. It is proven that these 'Fourier-Pade' approximations converge point-wise to (f(x(exp +))+f(x(exp -)))/2 more rapidly (in some cases by a factor of 1/k(exp 2M)) than the Fourier series partial sums on which they are based. The approximations are illustrated by several examples and an application to the solution of an initial, boundary value problem for the simple heat equation is presented.

Existence and discrete approximation for optimization problems governed by fractional differential equations

NASA Astrophysics Data System (ADS)

Bai, Yunru; Baleanu, Dumitru; Wu, Guo-Cheng

2018-06-01

We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe ´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.

Pseudospectral collocation methods for fourth order differential equations

NASA Technical Reports Server (NTRS)

Malek, Alaeddin; Phillips, Timothy N.

1994-01-01

Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.

Nucleation type instabilities in partially wetting nanoscale nematic liquid films

NASA Astrophysics Data System (ADS)

Lam, Michael; Cummings, Linda; Kondic, Lou

2016-11-01

Nucleation type instabilities are studied in nematic liquid crystal (NLC) films with thicknesses less than a micrometer. Within the framework of the long wave approximation, a 4th order nonlinear partial differential equation is proposed for the free surface height. Unlike simple fluids, NLC molecules have a dipole moment which induces an elastic response due to deformation in the bulk of the fluid. The model includes the balance between the bulk elasticity energy and the anchoring (boundary) energy at the substrate and free surface, and van der Waals' intermolecular forces, by means of a structural disjoining pressure. In this presentation, we focus on two-dimensional flow and present simulation results for a flat film with a localized perturbation. We are interested in the morphology of the dewetted film as a function of the initial film thickness. We will show that there exists a range of film thicknesses within the linearly unstable flat film regime where stability analysis does not explain the morphology of the dewetted film. Marginal stability criterion (MSC) is used to derive an analytical expression for the velocity at which a perturbation propagates into the unstable flat film. Finally, we discuss the degree to which MSC can be used to explain the observed morphology.

Edge-augmented Fourier partial sums with applications to Magnetic Resonance Imaging (MRI)

NASA Astrophysics Data System (ADS)

Larriva-Latt, Jade; Morrison, Angela; Radgowski, Alison; Tobin, Joseph; Iwen, Mark; Viswanathan, Aditya

2017-08-01

Certain applications such as Magnetic Resonance Imaging (MRI) require the reconstruction of functions from Fourier spectral data. When the underlying functions are piecewise-smooth, standard Fourier approximation methods suffer from the Gibbs phenomenon - with associated oscillatory artifacts in the vicinity of edges and an overall reduced order of convergence in the approximation. This paper proposes an edge-augmented Fourier reconstruction procedure which uses only the first few Fourier coefficients of an underlying piecewise-smooth function to accurately estimate jump information and then incorporate it into a Fourier partial sum approximation. We provide both theoretical and empirical results showing the improved accuracy of the proposed method, as well as comparisons demonstrating superior performance over existing state-of-the-art sparse optimization-based methods.

Effect of partial heating at mid of vertical plate adjacent to porous medium

NASA Astrophysics Data System (ADS)

Mulla, Mohammed Fahimuddin; Pallan, Khalid. M.; Al-Rashed, A. A. A. A.

2018-05-01

Heat and mass transfer in porous medium due to heating of vertical plate at mid-section is analyzed for various physical parameters. The heat and mass transfer in porous medium is modeled with the help of momentum, energy and concentration equations in terms of non-dimensional partial differential equations. The partial differential equations are converted into simpler form of algebraic equations with the help of finite element method. A computer code is developed to assemble the matrix form of algebraic equations into global matrices and then to solve them in an iterative manner to obtain the temperature, concentration and streamline distribution inside the porous medium. It is found that the heat transfer behavior of porous medium heated at middle section is considerably different from other cases.

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras

PubMed Central

Gazizov, R. K.

2017-01-01

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures. PMID:28265184

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras.

PubMed

Gainetdinova, A A; Gazizov, R K

2017-01-01

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.

Paleomagnetic Evidence for Partial Differentiation of the Silicate-Bearing IIE Iron Meteorite Parent Body

NASA Astrophysics Data System (ADS)

Maurel, C.; Bryson, J. F. J.; Weiss, B. P.; Scholl, A.

2016-12-01

The identification of dozens of petrologically diverse chondritic and achondritic meteoritic groups indicates that a diversity of planetesimals formed in the early solar system. It is commonly thought that planetesimals formed as either unmelted or else fully differentiated bodies, implying that chondrites and achondrites cannot have originated on a single body. However, it has been suggested that partially melted bodies with chondritic crusts and achondritic interiors may also have formed. This alternative proposal is supported by the recent identification of post-accretional remanent magnetization in CV, H chondrites, and also possibly in CM chondrites, which has been interpreted as possible evidence for a core dynamo on their parent bodies. Other piece of evidence suggesting the existence of partially differentiated bodies is the existence of the silicate-bearing IIE iron meteorites. The IIEs are composed of a Fe-Ni alloy matrix containing a mixture of chondritic, primitive achondritic, and chondritic silicate inclusions that likely formed on a single parent body. Therefore, IIEs may sample all three putative layers of a layered, partially differentiated body. On the other hand, the siderophile element compositions of the matrix metal demonstrate that it is not the product of fractional crystallization of a molten core. This suggests that the matrix metal is derived from isolated reservoirs of metal in the mantle and/or crust. It is unknown whether a large-scale metallic core, not represented by known meteorite samples, also formed on the same parent planetesimal. We can search for evidence of a molten, advecting core by assessing whether IIE irons contain remanent magnetization produced by a core dynamo. With this goal, we studied the paleomagnetism of a cloudy zone (CZ) interface in the Fe-Ni matrix of the IIE iron Colomera using X-ray photoelectron emission microscopy (XPEEM). Our initial results suggest that a steady, intense magnetic field was present during the gradual formation of the CZ. This may indicate the existence of an advecting core on the IIE parent body, which would support the hypothesis of a partially differentiated structure. We are continuing to test this conclusion with further XPEEM measurements on Colomera and other IIE irons.