Undergraduate Students' Mental Operations in Systems of Differential Equations

ERIC Educational Resources Information Center

Whitehead, Karen; Rasmussen, Chris

2003-01-01

This paper reports on research conducted to understand undergraduate students' ways of reasoning about systems of differential equations (SDEs). As part of a semester long classroom teaching experiment in a first course in differential equations, we conducted task-based interviews with six students after their study of first order differential…

Matrix differentiation formulas

NASA Technical Reports Server (NTRS)

Usikov, D. A.; Tkhabisimov, D. K.

1983-01-01

A compact differentiation technique (without using indexes) is developed for scalar functions that depend on complex matrix arguments which are combined by operations of complex conjugation, transposition, addition, multiplication, matrix inversion and taking the direct product. The differentiation apparatus is developed in order to simplify the solution of extremum problems of scalar functions of matrix arguments.

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.

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.

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.

Differential operators on the supercircle S1|2 and symbol map

NASA Astrophysics Data System (ADS)

Hamza, Raouafi; Selmi, Zeineb; Boujelben, Jamel

2017-09-01

We consider the supercircle S1|2 equipped with the standard contact structure. The conformal Lie superalgebra 𝒦(2) acts on S1|2 as the Lie superalgebra of contact vector fields; it contains the Möbius superalgebra 𝔬𝔰𝔭(2|2). We study the space of linear differential operators on weighted densities as a module over 𝔬𝔰𝔭(2|2). We introduce the canonical isomorphism between this space and the corresponding space of symbols. This result allows us to give, in contrast to the classical setting, a classification of the 𝒦(2)-modules 𝔇λ,μk of linear differential operators of order k acting on the superspaces of weighted densities. This work is the simplest superization of a result by Gargoubi and Ovsienko [Modules of differential operators on the real line, Funct. Anal. Appl. 35(1) (2001) 13-18.

Model-order reduction of lumped parameter systems via fractional calculus

NASA Astrophysics Data System (ADS)

Hollkamp, John P.; Sen, Mihir; Semperlotti, Fabio

2018-04-01

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.

IFR approval of differential global positioning system (DGPS) special category I instrument approaches using private ground facilities

DOT National Transportation Integrated Search

1994-08-14

This order identifies specific criteria, not presently found in existing standards, which shall be satisfied before Instrument Flight Rules (IFR) operations can be authorized using differential global positioning systems (DGPS) Special Instrument App...

Nonlinear differential equations

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

Dresner, L.

1988-01-01

This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis ismore » on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.« less

The spectral function of a singular differential operator of order 2m

NASA Astrophysics Data System (ADS)

Kozko, Artem I.; Pechentsov, Alexander S.

2010-12-01

We study the spectral function of a self-adjoint semibounded below differential operator on a Hilbert space L_2 \\lbrack 0,\\infty) and obtain the formulae for the spectral function of the operator (-1)^{m}y^{(2m)}(x) with general boundary conditions at the zero. In particular, for the boundary conditions y(0)=y'(0)=\\dots=y^{(m-1)}(0)=0 we find the explicit form of the spectral function \\Theta_{mB'}(x,x,\\lambda) on the diagonal x=y for \\lambda \\ge 0.

A Fresh Look at Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

ERIC Educational Resources Information Center

Camporesi, Roberto

2016-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…

Fractional-order difference equations for physical lattices and some applications

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

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2015-10-15

Fractional-order operators for physical lattice models based on the Grünwald-Letnikov fractional differences are suggested. We use an approach based on the models of lattices with long-range particle interactions. The fractional-order operators of differentiation and integration on physical lattices are represented by kernels of lattice long-range interactions. In continuum limit, these discrete operators of non-integer orders give the fractional-order derivatives and integrals with respect to coordinates of the Grünwald-Letnikov types. As examples of the fractional-order difference equations for physical lattices, we give difference analogs of the fractional nonlocal Navier-Stokes equations and the fractional nonlocal Maxwell equations for lattices with long-range interactions.more » Continuum limits of these fractional-order difference equations are also suggested.« less

Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations

PubMed Central

Song, Junqiang; Leng, Hongze; Lu, Fengshun

2014-01-01

We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. PMID:24511303

Additive schemes for certain operator-differential equations

NASA Astrophysics Data System (ADS)

Vabishchevich, P. N.

2010-12-01

Unconditionally stable finite difference schemes for the time approximation of first-order operator-differential systems with self-adjoint operators are constructed. Such systems arise in many applied problems, for example, in connection with nonstationary problems for the system of Stokes (Navier-Stokes) equations. Stability conditions in the corresponding Hilbert spaces for two-level weighted operator-difference schemes are obtained. Additive (splitting) schemes are proposed that involve the solution of simple problems at each time step. The results are used to construct splitting schemes with respect to spatial variables for nonstationary Navier-Stokes equations for incompressible fluid. The capabilities of additive schemes are illustrated using a two-dimensional model problem as an example.

Differential Drag Demonstration: A Post-Mission Experiment with the EO-1 Spacecraft

NASA Technical Reports Server (NTRS)

Hull, Scott; Shelton, Amanda; Richardson, David

2017-01-01

Differential drag is a technique for altering the semi-major axis, velocity, and along-track position of a spacecraft in low Earth orbit. It involves varying the spacecrafts cross-sectional area relative to its velocity direction by temporarily changing attitude and solar array angles, thus varying the amount of atmospheric drag on the spacecraft. The technique has recently been proposed and used by at least three satellite systems for initial separation of constellation spacecraft after launch, stationkeeping during the mission, and potentially for conjunction avoidance. Similarly, differential drag has been proposed as a control strategy for rendezvous, removing the need for active propulsion. In theory, some operational missions that lack propulsion capability could use this approach for conjunction avoidance, though options are typically constrained for spacecraft that are already in orbit. Shortly before the spacecraft was decommissioned, an experiment was performed using NASAs EO-1 spacecraft in order to demonstrate differential drag on an operational spacecraft in orbit, and discover some of the effects differential drag might manifest. EO-1 was not designed to maintain off-nominal orientations for long periods, and as a result the team experienced unanticipated challenges during the experiment. This paper will discuss operations limitations identified before the experiment, as well as those discovered during the experiment. The effective displacement that resulted from increasing the drag area for 39 hours will be compared to predictions as well as the expected position if the spacecraft maintained nominal operations. A hypothetical scenario will also be examined, studying the relative risks of maintaining an operational spacecraft bus in order to maintain the near-maximum drag area orientation and hasten reentry.

Differential Drag Demonstration: A Post-Mission Experiment with the EO-1 Spacecraft

NASA Technical Reports Server (NTRS)

Hull, Scott; Shelton, Amanda; Richardson, David

2017-01-01

Differential drag is a technique for altering the semimajor axis, velocity, and along-track position of a spacecraft in low Earth orbit. It involves varying the spacecraft's cross-sectional area relative to its velocity direction by temporarily changing attitude and solar array angles, thus varying the amount of atmospheric drag on the spacecraft. The technique has recently been proposed and used by at least three satellite systems for initial separation of constellation spacecraft after launch, stationkeeping during the mission, and potentially for conjunction avoidance. Similarly, differential drag has been proposed as a control strategy for rendezvous, removing the need for active propulsion. In theory, some operational missions that lack propulsion capability could use this approach for conjunction avoidance, though options are typically constrained for spacecraft that are already in orbit. Shortly before the spacecraft was decommissioned, an experiment was performed using NASA's EO-1 spacecraft in order to demonstrate differential drag on an operational spacecraft in orbit, and discover some of the effects differential drag might manifest. EO-1 was not designed to maintain off-nominal orientations for long periods, and as a result the team experienced unanticipated challenges during the experiment. This paper will discuss operations limitations identified before the experiment, as well as those discovered during the experiment. The effective displacement that resulted from increasing the drag area for 39 hours will be compared to predictions as well as the expected position if the spacecraft maintained nominal operations. A hypothetical scenario will also be examined, studying the relative risks of maintaining an operational spacecraft bus in order to maintain the near-maximum drag area orientation and hasten reentry.

A comparison of second order derivative based models for time domain reflectometry wave form analysis

USDA-ARS?s Scientific Manuscript database

Adaptive waveform interpretation with Gaussian filtering (AWIGF) and second order bounded mean oscillation operator Z square 2(u,t,r) are TDR analysis methods based on second order differentiation. AWIGF was originally designed for relatively long probe (greater than 150 mm) TDR waveforms, while Z s...

Differential calculus and gauge transformations on a deformed space

NASA Astrophysics Data System (ADS)

Wess, Julius

2007-08-01

We consider a formalism by which gauge theories can be constructed on noncommutative space time structures. The coordinates are supposed to form an algebra, restricted by certain requirements that allow us to realise the algebra in terms of star products. In this formulation it is useful to define derivatives and to extend the algebra of coordinates by these derivatives. The elements of this extended algebra are deformed differential operators. We then show that there is a morphism between these deformed differential operators and the usual higher order differential operators acting on functions of commuting coordinates. In this way we obtain deformed gauge transformations and a deformed version of the algebra of diffeomorphisms. The deformation of these algebras can be clearly seen in the category of Hopf algebras. The comultiplication will be twisted. These twisted algebras can be realised on noncommutative spaces and allow the construction of deformed gauge theories and deformed gravity theory.

Solution of second order supersymmetrical intertwining relations in Minkowski plane

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

Ioffe, M. V., E-mail: m.ioffe@spbu.ru; Kolevatova, E. V., E-mail: e.v.kolev@yandex.ru; Nishnianidze, D. N., E-mail: cutaisi@yahoo.com

2016-08-15

Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives, the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest—constant—ansatzes for the “metric” matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of “metric” matrices, and their properties are discussed.

Design of distributed PID-type dynamic matrix controller for fractional-order systems

NASA Astrophysics Data System (ADS)

Wang, Dawei; Zhang, Ridong

2018-01-01

With the continuous requirements for product quality and safety operation in industrial production, it is difficult to describe the complex large-scale processes with integer-order differential equations. However, the fractional differential equations may precisely represent the intrinsic characteristics of such systems. In this paper, a distributed PID-type dynamic matrix control method based on fractional-order systems is proposed. First, the high-order approximate model of integer order is obtained by utilising the Oustaloup method. Then, the step response model vectors of the plant is obtained on the basis of the high-order model, and the online optimisation for multivariable processes is transformed into the optimisation of each small-scale subsystem that is regarded as a sub-plant controlled in the distributed framework. Furthermore, the PID operator is introduced into the performance index of each subsystem and the fractional-order PID-type dynamic matrix controller is designed based on Nash optimisation strategy. The information exchange among the subsystems is realised through the distributed control structure so as to complete the optimisation task of the whole large-scale system. Finally, the control performance of the designed controller in this paper is verified by an example.

Semi-classical analysis and pseudo-spectra

NASA Astrophysics Data System (ADS)

Davies, E. B.

We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second-order differential operators in the semi-classical limit. This leads to the construction of a twisted FBI transform. We also investigate the connections between pseudo-spectra and boundary conditions in the semi-classical limit.

Modular forms, Schwarzian conditions, and symmetries of differential equations in physics

NASA Astrophysics Data System (ADS)

Abdelaziz, Y.; Maillard, J.-M.

2017-05-01

We give examples of infinite order rational transformations that leave linear differential equations covariant. These examples are non-trivial yet simple enough illustrations of exact representations of the renormalization group. We first illustrate covariance properties on order-two linear differential operators associated with identities relating the same {}_2F1 hypergeometric function with different rational pullbacks. These rational transformations are solutions of a differentially algebraic equation that already emerged in a paper by Casale on the Galoisian envelopes. We provide two new and more general results of the previous covariance by rational functions: a new Heun function example and a higher genus {}_2F1 hypergeometric function example. We then focus on identities relating the same {}_2F1 hypergeometric function with two different algebraic pullback transformations: such remarkable identities correspond to modular forms, the algebraic transformations being solution of another differentially algebraic Schwarzian equation that also emerged in Casale’s paper. Further, we show that the first differentially algebraic equation can be seen as a subcase of the last Schwarzian differential condition, the restriction corresponding to a factorization condition of some associated order-two linear differential operator. Finally, we also explore generalizations of these results, for instance, to {}_3F2 , hypergeometric functions, and show that one just reduces to the previous {}_2F1 cases through a Clausen identity. The question of the reduction of these Schwarzian conditions to modular correspondences remains an open question. In a _2F1 hypergeometric framework the Schwarzian condition encapsulates all the modular forms and modular equations of the theory of elliptic curves, but these two conditions are actually richer than elliptic curves or {}_2F1 hypergeometric functions, as can be seen on the Heun and higher genus example. This work is a strong incentive to develop more differentially algebraic symmetry analysis in physics.

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

Application of the moving frame method to deformed Willmore surfaces in space forms

NASA Astrophysics Data System (ADS)

Paragoda, Thanuja

2018-06-01

The main goal of this paper is to use the theory of exterior differential forms in deriving variations of the deformed Willmore energy in space forms and study the minimizers of the deformed Willmore energy in space forms. We derive both first and second order variations of deformed Willmore energy in space forms explicitly using moving frame method. We prove that the second order variation of deformed Willmore energy depends on the intrinsic Laplace Beltrami operator, the sectional curvature and some special operators along with mean and Gauss curvatures of the surface embedded in space forms, while the first order variation depends on the extrinsic Laplace Beltrami operator.

A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator

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

Haut, T. S.; Babb, T.; Martinsson, P. G.

2015-06-16

Our manuscript demonstrates a technique for efficiently solving the classical wave equation, the shallow water equations, and, more generally, equations of the form ∂u/∂t=Lu∂u/∂t=Lu, where LL is a skew-Hermitian differential operator. The idea is to explicitly construct an approximation to the time-evolution operator exp(τL)exp(τL) for a relatively large time-step ττ. Recently developed techniques for approximating oscillatory scalar functions by rational functions, and accelerated algorithms for computing functions of discretized differential operators are exploited. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many characteristic wavelengths and large speed-ups over existingmore » methods in situations where simulation over long times are required. Numerical examples involving the 2D rotating shallow water equations and the 2D wave equation in an inhomogenous medium are presented, and the method is compared to the 4th order Runge–Kutta (RK4) method and to the use of Chebyshev polynomials. The new method achieved high accuracy over long-time intervals, and with speeds that are orders of magnitude faster than both RK4 and the use of Chebyshev polynomials.« less

Exact linearized Coulomb collision operator in the moment expansion

DOE PAGES

Ji, Jeong -Young; Held, Eric D.

2006-10-05

In the moment expansion, the Rosenbluth potentials, the linearized Coulomb collision operators, and the moments of the collision operators are analytically calculated for any moment. The explicit calculation of Rosenbluth potentials converts the integro-differential form of the Coulomb collision operator into a differential operator, which enables one to express the collision operator in a simple closed form for any arbitrary mass and temperature ratios. In addition, it is shown that gyrophase averaging the collision operator acting on arbitrary distribution functions is the same as the collision operator acting on the corresponding gyrophase averaged distribution functions. The moments of the collisionmore » operator are linear combinations of the fluid moments with collision coefficients parametrized by mass and temperature ratios. Furthermore, useful forms involving the small mass-ratio approximation are easily found since the collision operators and their moments are expressed in terms of the mass ratio. As an application, the general moment equations are explicitly written and the higher order heat flux equation is derived.« less

An improved high order texture features extraction method with application to pathological diagnosis of colon lesions for CT colonography

NASA Astrophysics Data System (ADS)

Song, Bowen; Zhang, Guopeng; Lu, Hongbing; Wang, Huafeng; Han, Fangfang; Zhu, Wei; Liang, Zhengrong

2014-03-01

Differentiation of colon lesions according to underlying pathology, e.g., neoplastic and non-neoplastic, is of fundamental importance for patient management. Image intensity based textural features have been recognized as a useful biomarker for the differentiation task. In this paper, we introduce high order texture features, beyond the intensity, such as gradient and curvature, for that task. Based on the Haralick texture analysis method, we introduce a virtual pathological method to explore the utility of texture features from high order differentiations, i.e., gradient and curvature, of the image intensity distribution. The texture features were validated on database consisting of 148 colon lesions, of which 35 are non-neoplastic lesions, using the random forest classifier and the merit of area under the curve (AUC) of the receiver operating characteristics. The results show that after applying the high order features, the AUC was improved from 0.8069 to 0.8544 in differentiating non-neoplastic lesion from neoplastic ones, e.g., hyperplastic polyps from tubular adenomas, tubulovillous adenomas and adenocarcinomas. The experimental results demonstrated that texture features from the higher order images can significantly improve the classification accuracy in pathological differentiation of colorectal lesions. The gain in differentiation capability shall increase the potential of computed tomography (CT) colonography for colorectal cancer screening by not only detecting polyps but also classifying them from optimal polyp management for the best outcome in personalized medicine.

An Algebraic Construction of the First Integrals of the Stationary KdV Hierarchy

NASA Astrophysics Data System (ADS)

Matsushima, Masatomo; Ohmiya, Mayumi

2009-09-01

The stationary KdV hierarchy is constructed using a kind of recursion operator called Λ-operator. The notion of the maximal solution of the n-th stationary KdV equation is introduced. Using this maximal solution, a specific differential polynomial with the auxiliary spectral parameter called the spectral M-function is constructed as the quadratic form of the fundamental system of the eigenvalue problem for the 2-nd order linear ordinary differential equation which is related to the linearizing operator of the hierarchy. By calculating a perfect square condition of the quadratic form by an elementary algebraic method, the complete set of first integrals of this hierarchy is constructed.

Spherical integral transforms of second-order gravitational tensor components onto third-order gravitational tensor components

NASA Astrophysics Data System (ADS)

Šprlák, Michal; Novák, Pavel

2017-02-01

New spherical integral formulas between components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second- and third-order gravitational tensors. Initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are also summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (1) vertical-vertical, (2) vertical-horizontal and (3) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the consistency of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy.

Chaotic Oscillations of Second Order Linear Hyperbolic Equations with Nonlinear Boundary Conditions: A Factorizable but Noncommutative Case

NASA Astrophysics Data System (ADS)

Li, Liangliang; Huang, Yu; Chen, Goong; Huang, Tingwen

If a second order linear hyperbolic partial differential equation in one-space dimension can be factorized as a product of two first order operators and if the two first order operators commute, with one boundary condition being the van der Pol type and the other being linear, one can establish the occurrence of chaos when the parameters enter a certain regime [Chen et al., 2014]. However, if the commutativity of the two first order operators fails to hold, then the treatment in [Chen et al., 2014] no longer works and significant new challenges arise in determining nonlinear boundary conditions that engenders chaos. In this paper, we show that by incorporating a linear memory effect, a nonlinear van der Pol boundary condition can cause chaotic oscillations when the parameter enters a certain regime. Numerical simulations illustrating chaotic oscillations are also presented.

Dynamic equations for an isotropic spherical shell using the power series method and surface differential operators

NASA Astrophysics Data System (ADS)

Okhovat, Reza; Boström, Anders

2017-04-01

Dynamic equations for an isotropic spherical shell are derived by using a series expansion technique. The displacement field is split into a scalar (radial) part and a vector (tangential) part. Surface differential operators are introduced to decrease the length of all equations. The starting point is a power series expansion of the displacement components in the thickness coordinate relative to the mid-surface of the shell. By using the expansions of the displacement components, the three-dimensional elastodynamic equations yield a set of recursion relations among the expansion functions that can be used to eliminate all but the four of lowest order and to express higher order expansion functions in terms of those of lowest orders. Applying the boundary conditions on the surfaces of the spherical shell and eliminating all but the four lowest order expansion functions give the shell equations as a power series in the shell thickness. After lengthy manipulations, the final four shell equations are obtained in a relatively compact form which are given to second order in shell thickness explicitly. The eigenfrequencies are compared to exact three-dimensional theory with excellent agreement and to membrane theory.

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.

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.

On the singular perturbations for fractional differential equation.

PubMed

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

Differential Validity of a Differential Aptitude Test

DTIC Science & Technology

1990-05-01

Sir Francis Galton in 1883 first espoused the concept of general mental ability or g, it was not until 1904 that empirical evidence was analyzed...81150) and Apprentice Radio Communications Analysis Specialist ( intelligence ) (AFSC 20230), respectively. Table 7. Educational and Demographic Description...numerical order, with a brief categorization such as "Aircrew Operations," "Precision Measurement," or " Intelligence ." Selection and classification

Theory of repetitively pulsed operation of diode lasers subject to delayed feedback

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

Napartovich, A P; Sukharev, A G

2015-03-31

Repetitively pulsed operation of a diode laser with delayed feedback has been studied theoretically at varying feedback parameters and pump power levels. A new approach has been proposed that allows one to reduce the system of Lang–Kobayashi equations for a steady-state repetitively pulsed operation mode to a first-order nonlinear differential equation. We present partial solutions that allow the pulse shape to be predicted. (lasers)

PREFACE: Fractional Differentiation and its Applications (FDA08) Fractional Differentiation and its Applications (FDA08)

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Tenreiro Machado, J. A.

2009-10-01

The international workshop, Fractional Differentiation and its Applications (FDA08), held at Cankaya University, Ankara, Turkey on 5-7 November 2008, was the third in an ongoing series of conferences dedicated to exploring applications of fractional calculus in science, engineering, economics and finance. Fractional calculus, which deals with derivatives and integrals of any order, is now recognized as playing an important role in modeling multi-scale problems that span a wide range of time or length scales. Fractional calculus provides a natural link to the intermediate-order dynamics that often reflects the complexity of micro- and nanostructures through fractional-order differential equations. Unlike the more established techniques of mathematical physics, the methods of fractional differentiation are still under development; while it is true that the ideas of fractional calculus are as old as the classical integer-order differential operators, modern work is proceeding by both expanding the capabilities of this mathematical tool and by widening its range of applications. Hence, the interested reader will find papers here that focus on the underlying mathematics of fractional calculus, that extend fractional-order operators into new domains, and that apply well established methods to experimental and theoretical problems. The organizing committee invited presentations from experts representing the international community of scholars in fractional calculus and welcomed contributions from the growing number of researchers who are applying fractional differentiation to complex technical problems. The selection of papers in this topical issue of Physica Scripta reflects the success of the FDA08 workshop, with the emergence of a variety of novel areas of application. With these ideas in mind, the guest editors would like to honor the many distinguished scientists that have promoted the development of fractional calculus and, in particular, Professor George M Zaslavsky who supported this special issue but passed away recently. The organizing committee wishes to thank the sponsors and supporters of FDA08, namely Cankaya University represented by the President of the Board of Trustees Sitki Alp and Rector Professor Ziya B Güvenc, The Scientfic and Technological Research Council of Turkey (TUBITAK) and the IFAC for providing the resources needed to hold the workshop, the invited speakers for sharing their expertise and knowledge of fractional calculus, and the participants for their enthusiastic contributions to the discussions and debates.

Insights Into the Fractional Order Initial Value Problem via Semi-Infinite Systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper considers various aspects of the initial value problem for fractional order differential equations. The main contribution of this paper is to use the solutions to known spatially distributed systems to demonstrate that fractional differintegral operators require an initial condition term that is time-varying due to past distributed storage of information.

On singlet s-wave electron-hydrogen scattering.

NASA Technical Reports Server (NTRS)

Madan, R. N.

1973-01-01

Discussion of various zeroth-order approximations to s-wave scattering of electrons by hydrogen atoms below the first excitation threshold. The formalism previously developed by the author (1967, 1968) is applied to Feshbach operators to derive integro-differential equations, with the optical-potential set equal to zero, for the singlet and triplet cases. Phase shifts of s-wave scattering are computed in the zeroth-order approximation of the Feshbach operator method and in the static-exchange approximation. It is found that the convergence of numerical computations is faster in the former approximation than in the latter.

On the Singularity Structure of WKB Solution of the Boosted Whittaker Equation: its Relevance to Resurgent Functions with Essential Singularities

NASA Astrophysics Data System (ADS)

Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya

2016-12-01

Inspired by the symbol calculus of linear differential operators of infinite order applied to the Borel transformed WKB solutions of simple-pole type equation [Kamimoto et al. (RIMS Kôkyûroku Bessatsu B 52:127-146, 2014)], which is summarized in Section 1, we introduce in Section 2 the space of simple resurgent functions depending on a parameter with an infra-exponential type growth order, and then we define the assigning operator A which acts on the space and produces resurgent functions with essential singularities. In Section 3, we apply the operator A to the Borel transforms of the Voros coefficient and its exponentiation for the Whittaker equation with a large parameter so that we may find the Borel transforms of the Voros coefficient and its exponentiation for the boosted Whittaker equation with a large parameter. In Section 4, we use these results to find the explicit form of the alien derivatives of the Borel transformed WKB solutions of the boosted Whittaker equation with a large parameter. The results in this paper manifest the importance of resurgent functions with essential singularities in developing the exact WKB analysis, the WKB analysis based on the resurgent function theory. It is also worth emphasizing that the concrete form of essential singularities we encounter is expressed by the linear differential operators of infinite order.

Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations

NASA Astrophysics Data System (ADS)

Liu, Changying; Wu, Xinyuan

2017-07-01

In this paper we explore arbitrarily high-order Lagrange collocation-type time-stepping schemes for effectively solving high-dimensional nonlinear Klein-Gordon equations with different boundary conditions. We begin with one-dimensional periodic boundary problems and first formulate an abstract ordinary differential equation (ODE) on a suitable infinity-dimensional function space based on the operator spectrum theory. We then introduce an operator-variation-of-constants formula which is essential for the derivation of our arbitrarily high-order Lagrange collocation-type time-stepping schemes for the nonlinear abstract ODE. The nonlinear stability and convergence are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix under some suitable smoothness assumptions. With regard to the two dimensional Dirichlet or Neumann boundary problems, our new time-stepping schemes coupled with discrete Fast Sine / Cosine Transformation can be applied to simulate the two-dimensional nonlinear Klein-Gordon equations effectively. All essential features of the methodology are present in one-dimensional and two-dimensional cases, although the schemes to be analysed lend themselves with equal to higher-dimensional case. The numerical simulation is implemented and the numerical results clearly demonstrate the advantage and effectiveness of our new schemes in comparison with the existing numerical methods for solving nonlinear Klein-Gordon equations in the literature.

Time-ordered product expansions for computational stochastic system biology.

PubMed

Mjolsness, Eric

2013-06-01

The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie's stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems.

An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order

PubMed Central

Almeida, Ricardo

2013-01-01

We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type. PMID:24319382

An efficient computer based wavelets approximation method to solve Fuzzy boundary value differential equations

NASA Astrophysics Data System (ADS)

Alam Khan, Najeeb; Razzaq, Oyoon Abdul

2016-03-01

In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.

Periodicity computation of generalized mathematical biology problems involving delay differential equations.

PubMed

Jasim Mohammed, M; Ibrahim, Rabha W; Ahmad, M Z

2017-03-01

In this paper, we consider a low initial population model. Our aim is to study the periodicity computation of this model by using neutral differential equations, which are recognized in various studies including biology. We generalize the neutral Rayleigh equation for the third-order by exploiting the model of fractional calculus, in particular the Riemann-Liouville differential operator. We establish the existence and uniqueness of a periodic computational outcome. The technique depends on the continuation theorem of the coincidence degree theory. Besides, an example is presented to demonstrate the finding.

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

NASA Astrophysics Data System (ADS)

Liu, Changying; Iserles, Arieh; Wu, Xinyuan

2018-03-01

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

Integration by parts and Pohozaev identities for space-dependent fractional-order operators

NASA Astrophysics Data System (ADS)

Grubb, Gerd

2016-08-01

Consider a classical elliptic pseudodifferential operator P on Rn of order 2a (0 < a < 1) with even symbol. For example, P = A(x , D) a where A (x , D) is a second-order strongly elliptic differential operator; the fractional Laplacian (- Δ) a is a particular case. For solutions u of the Dirichlet problem on a bounded smooth subset Ω ⊂Rn, we show an integration-by-parts formula with a boundary integral involving (d-a u)|∂Ω, where d (x) = dist (x , ∂ Ω). This extends recent results of Ros-Oton, Serra and Valdinoci, to operators that are x-dependent, nonsymmetric, and have lower-order parts. We also generalize their formula of Pohozaev-type, that can be used to prove unique continuation properties, and nonexistence of nontrivial solutions of semilinear problems. An illustration is given with P =(- Δ +m2) a. The basic step in our analysis is a factorization of P, P ∼P-P+, where we set up a calculus for the generalized pseudodifferential operators P± that come out of the construction.

A class of fractional differential hemivariational inequalities with application to contact problem

NASA Astrophysics Data System (ADS)

Zeng, Shengda; Liu, Zhenhai; Migorski, Stanislaw

2018-04-01

In this paper, we study a class of generalized differential hemivariational inequalities of parabolic type involving the time fractional order derivative operator in Banach spaces. We use the Rothe method combined with surjectivity of multivalued pseudomonotone operators and properties of the Clarke generalized gradient to establish existence of solution to the abstract inequality. As an illustrative application, a frictional quasistatic contact problem for viscoelastic materials with adhesion is investigated, in which the friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals, and the constitutive relation is modeled by the fractional Kelvin-Voigt law.

On the Singular Perturbations for Fractional Differential Equation

PubMed Central

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method. PMID:24683357

A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

NASA Astrophysics Data System (ADS)

Camporesi, Roberto

2016-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors.

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

NASA Astrophysics Data System (ADS)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

Explicit least squares system parameter identification for exact differential input/output models

NASA Technical Reports Server (NTRS)

Pearson, A. E.

1993-01-01

The equation error for a class of systems modeled by input/output differential operator equations has the potential to be integrated exactly, given the input/output data on a finite time interval, thereby opening up the possibility of using an explicit least squares estimation technique for system parameter identification. The paper delineates the class of models for which this is possible and shows how the explicit least squares cost function can be obtained in a way that obviates dealing with unknown initial and boundary conditions. The approach is illustrated by two examples: a second order chemical kinetics model and a third order system of Lorenz equations.

Differential Equations and Computational Simulations

DTIC Science & Technology

1999-06-18

divergence operator of a vector field, which can be defined in terms of the Levi - Civita connection. Let $(x, t) be the orbit passing through x g M...differential equations 31 Junping Chen and Dadi Yang The limit cycle of two species predator-prey model with general functional response > 34 S. S...analysis of two -species nonlinear competition system with periodic coefficients 286 X. H. Tang and J. S. Yu Oscillation of first order delay

A problem with inverse time for a singularly perturbed integro-differential equation with diagonal degeneration of the kernel of high order

NASA Astrophysics Data System (ADS)

Bobodzhanov, A. A.; Safonov, V. F.

2016-04-01

We consider an algorithm for constructing asymptotic solutions regularized in the sense of Lomov (see [1], [2]). We show that such problems can be reduced to integro-differential equations with inverse time. But in contrast to known papers devoted to this topic (see, for example, [3]), in this paper we study a fundamentally new case, which is characterized by the absence, in the differential part, of a linear operator that isolates, in the asymptotics of the solution, constituents described by boundary functions and by the fact that the integral operator has kernel with diagonal degeneration of high order. Furthermore, the spectrum of the regularization operator A(t) (see below) may contain purely imaginary eigenvalues, which causes difficulties in the application of the methods of construction of asymptotic solutions proposed in the monograph [3]. Based on an analysis of the principal term of the asymptotics, we isolate a class of inhomogeneities and initial data for which the exact solution of the original problem tends to the limit solution (as \\varepsilon\\to+0) on the entire time interval under consideration, also including a boundary-layer zone (that is, we solve the so-called initialization problem). The paper is of a theoretical nature and is designed to lead to a greater understanding of the problems in the theory of singular perturbations. There may be applications in various applied areas where models described by integro-differential equations are used (for example, in elasticity theory, the theory of electrical circuits, and so on).

Soliton structure versus singularity analysis: Third-order completely intergrable nonlinear differential equations in 1 + 1-dimensions

NASA Astrophysics Data System (ADS)

Fuchssteiner, Benno; Carillo, Sandra

1989-01-01

Bäcklund transformations between all known completely integrable third-order differential equations in (1 + 1)-dimensions are established and the corresponding transformations formulas for their hereditary operators and Hamiltonian formulations are exhibited. Some of these Bäcklund transformations are not injective; therefore additional non-commutative symmetry groups are found for some equations. These non-commutative symmetry groups are classified as having a semisimple part isomorphic to the affine algebra A(1)1. New completely integrable third-order integro-differential equations, some depending explicitly on x, are given. These new equations give rise to nonin equation. Connections between the singularity equations (from the Painlevé analysis) and the nonlinear equations for interacting solitons are established. A common approach to singularity analysis and soliton structure is introduced. The Painlevé analysis is modified in such a sense that it carries over directly and without difficulty to the time evolution of singularity manifolds of equations like the sine-Gordon and nonlinear Schrödinger equation. A method to recover the Painlevé series from its constant level term is exhibit. The soliton-singularity transform is recognized to be connected to the Möbius group. This gives rise to a Darboux-like result for the spectral properties of the recursion operator. These connections are used in order to explain why poles of soliton equations move like trajectories of interacting solitons. Furthermore it is explicitly computed how solitons of singularity equations behave under the effect of this soliton-singularity transform. This then leads to the result that only for scaling degrees α = -1 and α = -2 the usual Painlevé analysis can be carried out. A new invariance principle, connected to kernels of differential operators is discovered. This new invariance, for example, connects the explicit solutions of the Liouville equation with the Miura transform. Simple methods are exhibited which allow to compute out of N-soliton solutions of the KdV (Bargman potentials) explicit solutions of equations like the Harry Dym equation. Certain solutions are plotted.

Boundary conditions in Chebyshev and Legendre methods

NASA Technical Reports Server (NTRS)

Canuto, C.

1984-01-01

Two different ways of treating non-Dirichlet boundary conditions in Chebyshev and Legendre collocation methods are discussed for second order differential problems. An error analysis is provided. The effect of preconditioning the corresponding spectral operators by finite difference matrices is also investigated.

Differential optoacoustic absorption detector

NASA Technical Reports Server (NTRS)

Shumate, M. S. (Inventor)

1978-01-01

A differential optoacoustic absorption detector employed two tapered cells in tandem or in parallel. When operated in tandem, two mirrors were used at one end remote from the source of the beam of light directed into one cell back through the other, and a lens to focus the light beam into the one cell at a principal focus half way between the reflecting mirror. Each cell was tapered to conform to the shape of the beam so that the volume of one was the same as for the other, and the volume of each received maximum illumination. The axes of the cells were placed as close to each other as possible in order to connect a differential pressure detector to the cells with connecting passages of minimum length. An alternative arrangement employed a beam splitter and two lenses to operate the cells in parallel.

Differential thermal voltammetry for tracking of degradation in lithium-ion batteries

NASA Astrophysics Data System (ADS)

Wu, Billy; Yufit, Vladimir; Merla, Yu; Martinez-Botas, Ricardo F.; Brandon, Nigel P.; Offer, Gregory J.

2015-01-01

Monitoring of lithium-ion batteries is of critical importance in electric vehicle applications in order to manage the operational condition of the cells. Measurements on a vehicle often involve current, voltage and temperature which enable in-situ diagnostic techniques. This paper presents a novel diagnostic technique, termed differential thermal voltammetry, which is capable of monitoring the state of the battery using voltage and temperature measurements in galvanostatic operating modes. This tracks battery degradation through phase transitions, and the resulting entropic heat, occurring in the electrodes. Experiments to monitor battery degradation using the new technique are compared with a pseudo-2D cell model. Results show that the differential thermal voltammetry technique provides information comparable to that of slow rate cyclic voltammetry at shorter timescale and with load conditions easier to replicate in a vehicle.

An Automatic Orthonormalization Method for Solving Stiff Boundary-Value Problems

NASA Astrophysics Data System (ADS)

Davey, A.

1983-08-01

A new initial-value method is described, based on a remark by Drury, for solving stiff linear differential two-point cigenvalue and boundary-value problems. The method is extremely reliable, it is especially suitable for high-order differential systems, and it is capable of accommodating realms of stiffness which other methods cannot reach. The key idea behind the method is to decompose the stiff differential operator into two non-stiff operators, one of which is nonlinear. The nonlinear one is specially chosen so that it advances an orthonormal frame, indeed the method is essentially a kind of automatic orthonormalization; the second is auxiliary but it is needed to determine the required function. The usefulness of the method is demonstrated by calculating some eigenfunctions for an Orr-Sommerfeld problem when the Reynolds number is as large as 10°.

Mean, covariance, and effective dimension of stochastic distributed delay dynamics

NASA Astrophysics Data System (ADS)

René, Alexandre; Longtin, André

2017-11-01

Dynamical models are often required to incorporate both delays and noise. However, the inherently infinite-dimensional nature of delay equations makes formal solutions to stochastic delay differential equations (SDDEs) challenging. Here, we present an approach, similar in spirit to the analysis of functional differential equations, but based on finite-dimensional matrix operators. This results in a method for obtaining both transient and stationary solutions that is directly amenable to computation, and applicable to first order differential systems with either discrete or distributed delays. With fewer assumptions on the system's parameters than other current solution methods and no need to be near a bifurcation, we decompose the solution to a linear SDDE with arbitrary distributed delays into natural modes, in effect the eigenfunctions of the differential operator, and show that relatively few modes can suffice to approximate the probability density of solutions. Thus, we are led to conclude that noise makes these SDDEs effectively low dimensional, which opens the possibility of practical definitions of probability densities over their solution space.

IFR Approval of Differential Global Positioning System (DGPS) Special Category I Instrument Approaches Using Private Ground Facilities

DOT National Transportation Integrated Search

1994-08-19

This order establishes interim procedures to approve special instrument approach : operations using privately owned DGPS installations at U.S. and foreign airports/ : runways. It identifies specific criteria, not presently found in existing : standar...

Numerical Bifurcation Analysis of Delayed Recycle Stream in a Continuously Stirred Tank Reactor

NASA Astrophysics Data System (ADS)

Gangadhar, Nalwala Rohitbabu; Balasubramanian, Periyasamy

2010-10-01

In this paper, we present the stability analysis of delay differential equations which arise as a result of transportation lag in the CSTR-mechanical separator recycle system. A first order irreversible elementary reaction is considered to model the system and is governed by the delay differential equations. The DDE-BIFTOOL software package is used to analyze the stability of the delay system. The present analysis reveals that the system exhibits delay independent stability for isothermal operation of the CSTR. In the absence of delay, the system is dynamically unstable for non-isothermal operation of the CSTR, and as a result of delay, the system exhibits delay dependent stability.

Numerical analysis for trajectory controllability of a coupled multi-order fractional delay differential system via the shifted Jacobi method

NASA Astrophysics Data System (ADS)

Priya, B. Ganesh; Muthukumar, P.

2018-02-01

This paper deals with the trajectory controllability for a class of multi-order fractional linear systems subject to a constant delay in state vector. The solution for the coupled fractional delay differential equation is established by the Mittag-Leffler function. The necessary and sufficient condition for the trajectory controllability is formulated and proved by the generalized Gronwall's inequality. The approximate trajectory for the proposed system is obtained through the shifted Jacobi operational matrix method. The numerical simulation of the approximate solution shows the theoretical results. Finally, some remarks and comments on the existing results of constrained controllability for the fractional dynamical system are also presented.

Interior radiances in optically deep absorbing media. 1: Exact solutions for one-dimensional model

NASA Technical Reports Server (NTRS)

Kattawar, G. W.; Plass, G. N.

1973-01-01

The exact solutions are obtained for a one dimensional model of a scattering and absorbing medium. The results are given for both the reflected and transmitted radiance for any arbitrary surface albedo as well as for the interior radiance. These same quantities are calculated by the matrix operator method. The relative error of the solutions is obtained by comparison with the exact solutions as well as by an error analysis of the equations. The importance of an accurate starting value for the reflection and transmission operators is shown. A fourth order Runge-Kutta method can be used to solve the differential equations satisfied by these operators in order to obtain such accurate starting values.

A strictly Markovian expansion for plasma turbulence theory

NASA Technical Reports Server (NTRS)

Jones, F. C.

1976-01-01

The collision operator that appears in the equation of motion for a particle distribution function that was averaged over an ensemble of random Hamiltonians is non-Markovian. It is non-Markovian in that it involves a propagated integral over the past history of the ensemble averaged distribution function. All formal expansions of this nonlinear collision operator to date preserve this non-Markovian character term by term yielding an integro-differential equation that must be converted to a diffusion equation by an additional approximation. An expansion is derived for the collision operator that is strictly Markovian to any finite order and yields a diffusion equation as the lowest nontrivial order. The validity of this expansion is seen to be the same as that of the standard quasilinear expansion.

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

NASA Astrophysics Data System (ADS)

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-05-01

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

A nonlinear macromodel of the bipolar integrated circuit operational amplifier for electromagnetic interference analysis

NASA Astrophysics Data System (ADS)

Chen, G. K. C.

1981-06-01

A nonlinear macromodel for the bipolar transistor integrated circuit operational amplifier is derived from the macromodel proposed by Boyle. The nonlinear macromodel contains only two nonlinear transistors in the input stage in a differential amplifier configuration. Parasitic capacitance effects are represented by capacitors placed at the collectors and emitters of the input transistors. The nonlinear macromodel is effective in predicting the second order intermodulation effect of operational amplifiers in a unity gain buffer amplifier configuration. The nonlinear analysis computer program NCAP is used for the analysis. Accurate prediction of demodulation of amplitude modulated RF signals with RF carrier frequencies in the 0.05 to 100 MHz range is achieved. The macromodel predicted results, presented in the form of second order nonlinear transfer function, come to within 6 dB of the full model predictions for the 741 type of operational amplifiers for values of the second order transfer function greater than -40 dB.

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 is given, specifically for the steady Euler equations. Solutions of the equations were obtained by Newton's linearization procedure, commonly used to solve the roots of nonlinear algebraic equations. In application of the same procedure for solving a set of differential equations we give a theorem showing that a quadratic convergence rate can be achieved. While the domain of quadratic convergence depends on the problems studied and is unknown a priori, we show that firstand second-order derivatives of flux vectors determine whether the condition for quadratic convergence is satisfied. The first derivatives enter as an implicit operator for yielding new iterates and the second derivatives indicates smoothness of the flows considered. Consequently flows involving shocks are expected to require larger number of iterations. First-order upwind discretization in conjunction with the Steger-Warming flux-vector splitting is employed on the implicit operator and a diagonal dominant matrix results. However the explicit operator is represented by first- and seond-order upwind differencings, using both Steger-Warming's and van Leer's splittings. We discuss treatment of boundary conditions and solution procedures for solving the resulting block matrix system. With a set of test problems for one- and two-dimensional flows, we show detailed study as to the efficiency, accuracy, and convergence of the present method.

A non-local model of fractional heat conduction in rigid bodies

NASA Astrophysics Data System (ADS)

Borino, G.; di Paola, M.; Zingales, M.

2011-03-01

In recent years several applications of fractional differential calculus have been proposed in physics, chemistry as well as in engineering fields. Fractional order integrals and derivatives extend the well-known definitions of integer-order primitives and derivatives of the ordinary differential calculus to real-order operators. Engineering applications of fractional operators spread from viscoelastic models, stochastic dynamics as well as with thermoelasticity. In this latter field one of the main actractives of fractional operators is their capability to interpolate between the heat flux and its time-rate of change, that is related to the well-known second sound effect. In other recent studies a fractional, non-local thermoelastic model has been proposed as a particular case of the non-local, integral, thermoelasticity introduced at the mid of the seventies. In this study the autors aim to introduce a different non-local model of extended irreverible thermodynamics to account for second sound effect. Long-range heat flux is defined and it involves the integral part of the spatial Marchaud fractional derivatives of the temperature field whereas the second-sound effect is accounted for introducing time-derivative of the heat flux in the transport equation. It is shown that the proposed model does not suffer of the pathological problems of non-homogenoeus boundary conditions. Moreover the proposed model coalesces with the Povstenko fractional models in unbounded domains.

Multi-Rate Digital Control Systems with Simulation Applications. Volume I. Technical Report

DTIC Science & Technology

1980-09-01

108 45. A Pseudo Differentiation Configuration ........................ 110 46. Bode Plot, Pseudo Differentiation ...symbolically in Fig. 7a and for 11 x 2 in Fig. 7b. (* notation on x2is used here to indicate an "unconven- tional" sampling operation.) 115 TXi ,A! T...the general multi-rate/multiple-order open-loop system of Fig. 21 have a sine wave input. In Fig 2L, = (GIRj) (114) CT/N = [GGRt]T/N ( 115 ) where a, B

Anisotropic fractal media by vector calculus in non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-08-01

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations

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

Moryakov, A. V., E-mail: sailor@orc.ru

2016-12-15

An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.

Recent Development of Multigrid Algorithms for Mixed and Noncomforming Methods for Second Order Elliptical Problems

NASA Technical Reports Server (NTRS)

Chen, Zhangxin; Ewing, Richard E.

1996-01-01

Multigrid algorithms for nonconforming and mixed finite element methods for second order elliptic problems on triangular and rectangular finite elements are considered. The construction of several coarse-to-fine intergrid transfer operators for nonconforming multigrid algorithms is discussed. The equivalence between the nonconforming and mixed finite element methods with and without projection of the coefficient of the differential problems into finite element spaces is described.

Preliminary Test Results of a Non-Contacting Finger Seal on a Herringbone-Grooved Rotor

NASA Technical Reports Server (NTRS)

Proctor, Margaret P.; Degado, Irebert R.

2008-01-01

Low leakage, non-contacting finger seals have potential to reduce gas turbine engine specific fuel consumption by 2 to 3 percent and to reduce direct operating costs by increasing the time between engine overhauls. A non-contacting finger seal with concentric lift-pads operating adjacent to a test rotor with herringbone grooves was statically tested at 300, 533, and 700 K inlet air temperatures at pressure differentials up to 576 kPa. Leakage flow factors were approximately 70 percent less than state-of-the-art labyrinth seals. Leakage rates are compared to first order predictions. Initial spin tests at 5000 rpm, 300 K inlet air temperature and pressure differentials to 241 kPa produced no measurable wear.

75 FR 49928 - California Independent System Operator Corporation; Green Energy Express LLC; 21st Century...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-08-16

... (CAISO) proposed Revised Transmission Planning Process (RTPP).\\1\\ Take notice that such conference will... California Transmission Planning Group, and complies with the transmission planning principles of Order No. 890; How the various categories of transmission projects will be defined and differentiated; To what...

46 CFR 201.76 - Applications for Government aid.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 46 Shipping 8 2011-10-01 2011-10-01 false Applications for Government aid. 201.76 Section 201.76... Government aid. Applications for operating-differential subsidies, charter of Government-owned vessels, and other types of Government aid shall conform to the requirements set forth in the various general orders...

46 CFR 201.76 - Applications for Government aid.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 46 Shipping 8 2010-10-01 2010-10-01 false Applications for Government aid. 201.76 Section 201.76... Government aid. Applications for operating-differential subsidies, charter of Government-owned vessels, and other types of Government aid shall conform to the requirements set forth in the various general orders...

A strictly Markovian expansion for plasma turbulence theory

NASA Technical Reports Server (NTRS)

Jones, F. C.

1978-01-01

The collision operator that appears in the equation of motion for a particle distribution function that has been averaged over an ensemble of random Hamiltonians is non-Markovian. It is non-Markovian in that it involves a propagated integral over the past history of the ensemble averaged distribution function. All formal expansions of this nonlinear collision operator to date preserve this non-Markovian character term by term yielding an integro-differential equation that must be converted to a diffusion equation by an additional approximation. In this note we derive an expansion of the collision operator that is strictly Markovian to any finite order and yields a diffusion equation as the lowest non-trivial order. The validity of this expansion is seen to be the same as that of the standard quasi-linear expansion.

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.

Third-Order Elliptic Lowpass Filter for Multi-Standard Baseband Chain Using Highly Linear Digitally Programmable OTA

NASA Astrophysics Data System (ADS)

Elamien, Mohamed B.; Mahmoud, Soliman A.

2018-03-01

In this paper, a third-order elliptic lowpass filter is designed using highly linear digital programmable balanced OTA. The filter exhibits a cutoff frequency tuning range from 2.2 MHz to 7.1 MHz, thus, it covers W-CDMA, UMTS, and DVB-H standards. The programmability concept in the filter is achieved by using digitally programmable operational transconductors amplifier (DPOTA). The DPOTA employs three linearization techniques which are the source degeneration, double differential pair and the adaptive biasing. Two current division networks (CDNs) are used to control the value of the transconductance. For the DPOTA, the third-order harmonic distortion (HD3) remains below -65 dB up to 0.4 V differential input voltage at 1.2 V supply voltage. The DPOTA and the filter are designed and simulated in 90 nm CMOS technology with LTspice simulator.

Hidden symmetry in the presence of fluxes

NASA Astrophysics Data System (ADS)

Kubizňák, David; Warnick, Claude M.; Krtouš, Pavel

2011-03-01

We derive the most general first-order symmetry operator for the Dirac equation coupled to arbitrary fluxes. Such an operator is given in terms of an inhomogeneous form ω which is a solution to a coupled system of first-order partial differential equations which we call the generalized conformal Killing-Yano system. Except trivial fluxes, solutions of this system are subject to additional constraints. We discuss various special cases of physical interest. In particular, we demonstrate that in the case of a Dirac operator coupled to the skew symmetric torsion and U(1) field, the system of generalized conformal Killing-Yano equations decouples into the homogeneous conformal Killing-Yano equations with torsion introduced in D. Kubiznak et al. (2009) [8] and the symmetry operator is essentially the one derived in T. Houri et al. (2010) [9]. We also discuss the Dirac field coupled to a scalar potential and in the presence of 5-form and 7-form fluxes.

A remark on fractional differential equation involving I-function

NASA Astrophysics Data System (ADS)

Mishra, Jyoti

2018-02-01

The present paper deals with the solution of the fractional differential equation using the Laplace transform operator and its corresponding properties in the fractional calculus; we derive an exact solution of a complex fractional differential equation involving a special function known as I-function. The analysis of the some fractional integral with two parameters is presented using the suggested Theorem 1. In addition, some very useful corollaries are established and their proofs presented in detail. Some obtained exact solutions are depicted to see the effect of each fractional order. Owing to the wider applicability of the I-function, we can conclude that, the obtained results in our work generalize numerous well-known results obtained by specializing the parameters.

46 CFR 281.1 - Information and procedure required under liner operating-differential subsidy agreements.

Code of Federal Regulations, 2010 CFR

2010-10-01

... Administration, Washington, DC 20590. (b) Condition of vessels, inspection and repairs. (1) In order that the Maritime Administration may have an opportunity to participate in the inspection of the vessels, the... time and place of making inspections. In the event the Maritime Administration's representative is not...

46 CFR 281.1 - Information and procedure required under liner operating-differential subsidy agreements.

Code of Federal Regulations, 2011 CFR

2011-10-01

... Administration, Washington, DC 20590. (b) Condition of vessels, inspection and repairs. (1) In order that the Maritime Administration may have an opportunity to participate in the inspection of the vessels, the... time and place of making inspections. In the event the Maritime Administration's representative is not...

Improved diffusion Monte Carlo propagators for bosonic systems using Itô calculus

NASA Astrophysics Data System (ADS)

Hâkansson, P.; Mella, M.; Bressanini, Dario; Morosi, Gabriele; Patrone, Marta

2006-11-01

The construction of importance sampled diffusion Monte Carlo (DMC) schemes accurate to second order in the time step is discussed. A central aspect in obtaining efficient second order schemes is the numerical solution of the stochastic differential equation (SDE) associated with the Fokker-Plank equation responsible for the importance sampling procedure. In this work, stochastic predictor-corrector schemes solving the SDE and consistent with Itô calculus are used in DMC simulations of helium clusters. These schemes are numerically compared with alternative algorithms obtained by splitting the Fokker-Plank operator, an approach that we analyze using the analytical tools provided by Itô calculus. The numerical results show that predictor-corrector methods are indeed accurate to second order in the time step and that they present a smaller time step bias and a better efficiency than second order split-operator derived schemes when computing ensemble averages for bosonic systems. The possible extension of the predictor-corrector methods to higher orders is also discussed.

Even-order harmonic cancellation for off-quadrature biased Mach-Zehnder modulator with improved RF metrics using dual wavelength inputs and dual outputs.

PubMed

Devgan, Preetpaul S; Diehl, John F; Urick, Vincent J; Sunderman, Christopher E; Williams, Keith J

2009-05-25

We present a technique using a dual-output Mach-Zehnder modulator (MZM) with two wavelength inputs, one operating at low-bias and the other operating at high-bias, in order to cancel unwanted even-order harmonics in analog optical links. By using a dual-output MZM, this technique allows for two suppressed optical carriers to be transmitted to the receiver. Combined with optical amplification and balanced differential detection, the RF power of the fundamental is increased by 2 dB while the even-order harmonic is reduced by 47 dB, simultaneously. The RF noise figure and third-order spurious-free dynamic range (SFDR(3)) are improved by 5.4 dB and 3.6 dB, respectively. Using a wavelength sensitive, low V(pi) MZM allows the two wavelengths to be within 5.5 nm of each other for a frequency band from 10 MHz to 100 MHz and 10 nm for 1 GHz.

Approximate analytical solutions of a pair of coupled anharmonic oscillators

NASA Astrophysics Data System (ADS)

Alam, Nasir; Mandal, Swapan; Öhberg, Patrik

2015-02-01

The Hamiltonian and the corresponding equations of motion involving the field operators of two quartic anharmonic oscillators indirectly coupled via a linear oscillator are constructed. The approximate analytical solutions of the coupled differential equations involving the non-commuting field operators are solved up to the second order in the anharmonic coupling. In the absence of nonlinearity these solutions are used to calculate the second order variances and hence the squeezing in pure and in mixed modes. The higher order quadrature squeezing and the amplitude squared squeezing of various field modes are also investigated where the squeezing in pure and in mixed modes are found to be suppressed. Moreover, the absence of a nonlinearity prohibits the higher order quadrature and higher ordered amplitude squeezing of the input coherent states. It is established that the mere coupling of two oscillators through a third one is unable to produce any squeezing effects of input coherent light, but the presence of a nonlinear interaction may provide squeezed states and other nonclassical phenomena.

Noncommutative de Rham Cohomology of Finite Groups

NASA Astrophysics Data System (ADS)

Castellani, L.; Catenacci, R.; Debernardi, M.; Pagani, C.

We study de Rham cohomology for various differential calculi on finite groups G up to order 8. These include the permutation group S3, the dihedral group D4 and the quaternion group Q. Poincaré duality holds in every case, and under some assumptions (essentially the existence of a top form) we find that it must hold in general. A short review of the bicovariant (noncommutative) differential calculus on finite G is given for selfconsistency. Exterior derivative, exterior product, metric, Hodge dual, connections, torsion, curvature, and biinvariant integration can be defined algebraically. A projector decomposition of the braiding operator is found, and used in constructing the projector on the space of two-forms. By means of the braiding operator and the metric a knot invariant is defined for any finite group.

Closed Loop solar array-ion thruster system with power control circuitry

NASA Technical Reports Server (NTRS)

Gruber, R. P. (Inventor)

1979-01-01

A power control circuit connected between a solar array and an ion thruster receives voltage and current signals from the solar array. The control circuit multiplies the voltage and current signals together to produce a power signal which is differentiated with respect to time. The differentiator output is detected by a zero crossing detector and, after suitable shaping, the detector output is phase compared with a clock in a phase demodulator. An integrator receives no output from the phase demodulator when the operating point is at the maximum power but is driven toward the maximum power point for non-optimum operation. A ramp generator provides minor variations in the beam current reference signal produced by the integrator in order to obtain the first derivative of power.

Anisotropic fractal media by vector calculus in non-integer dimensional space

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

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2014-08-15

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensionalmore » space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.« less

An efficient transport solver for tokamak plasmas

DOE PAGES

Park, Jin Myung; Murakami, Masanori; St. John, H. E.; ...

2017-01-03

A simple approach to efficiently solve a coupled set of 1-D diffusion-type transport equations with a stiff transport model for tokamak plasmas is presented based on the 4th order accurate Interpolated Differential Operator scheme along with a nonlinear iteration method derived from a root-finding algorithm. Here, numerical tests using the Trapped Gyro-Landau-Fluid model show that the presented high order method provides an accurate transport solution using a small number of grid points with robust nonlinear convergence.

Noncommutative spherically symmetric spacetimes at semiclassical order

NASA Astrophysics Data System (ADS)

Fritz, Christopher; Majid, Shahn

2017-07-01

Working within the recent formalism of Poisson-Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order O(λ) . Here λ is the deformation parameter, plausibly the Planck scale. We find that r, t, d r, d t are all forced to be central, i.e. undeformed at order λ, while for each value of r, t we are forced to have a fuzzy sphere of radius r with a unique differential calculus which is necessarily nonassociative at order λ2 . We give the spherically symmetric quantisation of the FLRW cosmology in detail and also recover a previous analysis for the Schwarzschild black hole, now showing that the quantum Ricci tensor for the latter vanishes at order λ. The quantum Laplace-Beltrami operator for spherically symmetric models turns out to be undeformed at order λ while more generally in Poisson-Riemannian geometry we show that it deforms to □f+λ2ωαβ(Ricγα-Sγα)(∇^βdf)γ+O(λ2) in terms of the classical Levi-Civita connection \\widehat\

Fourth order difference methods for hyperbolic IBVP's

NASA Technical Reports Server (NTRS)

Gustafsson, Bertil; Olsson, Pelle

1994-01-01

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

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.

Differential evolution enhanced with multiobjective sorting-based mutation operators.

PubMed

Wang, Jiahai; Liao, Jianjun; Zhou, Ying; Cai, Yiqiao

2014-12-01

Differential evolution (DE) is a simple and powerful population-based evolutionary algorithm. The salient feature of DE lies in its mutation mechanism. Generally, the parents in the mutation operator of DE are randomly selected from the population. Hence, all vectors are equally likely to be selected as parents without selective pressure at all. Additionally, the diversity information is always ignored. In order to fully exploit the fitness and diversity information of the population, this paper presents a DE framework with multiobjective sorting-based mutation operator. In the proposed mutation operator, individuals in the current population are firstly sorted according to their fitness and diversity contribution by nondominated sorting. Then parents in the mutation operators are proportionally selected according to their rankings based on fitness and diversity, thus, the promising individuals with better fitness and diversity have more opportunity to be selected as parents. Since fitness and diversity information is simultaneously considered for parent selection, a good balance between exploration and exploitation can be achieved. The proposed operator is applied to original DE algorithms, as well as several advanced DE variants. Experimental results on 48 benchmark functions and 12 real-world application problems show that the proposed operator is an effective approach to enhance the performance of most DE algorithms studied.

Applications of conformal field theory to problems in 2D percolation

NASA Astrophysics Data System (ADS)

Simmons, Jacob Joseph Harris

This thesis explores critical two-dimensional percolation in bounded regions in the continuum limit. The main method which we employ is conformal field theory (CFT). Our specific results follow from the null-vector structure of the c = 0 CFT that applies to critical two-dimensional percolation. We also make use of the duality symmetry obeyed at the percolation point, and the fact that percolation may be understood as the q-state Potts model in the limit q → 1. Our first results describe the correlations between points in the bulk and boundary intervals or points, i.e. the probability that the various points or intervals are in the same percolation cluster. These quantities correspond to order-parameter profiles under the given conditions, or cluster connection probabilities. We consider two specific cases: an anchoring interval, and two anchoring points. We derive results for these and related geometries using the CFT null-vectors for the corresponding boundary condition changing (bcc) operators. In addition, we exhibit several exact relationships between these probabilities. These relations between the various bulk-boundary connection probabilities involve parameters of the CFT called operator product expansion (OPE) coefficients. We then compute several of these OPE coefficients, including those arising in our new probability relations. Beginning with the familiar CFT operator φ1,2, which corresponds to a free-fixed spin boundary change in the q-state Potts model, we then develop physical interpretations of the bcc operators. We argue that, when properly normalized, higher-order bcc operators correspond to successive fusions of multiple φ1,2, operators. Finally, by identifying the derivative of φ1,2 with the operator φ1,4, we derive several new quantities called first crossing densities. These new results are then combined and integrated to obtain the three previously known crossing quantities in a rectangle: the probability of a horizontal crossing cluster, the probability of a cluster crossing both horizontally and vertically, and the expected number of horizontal crossing clusters. These three results were known to be solutions to a certain fifth-order differential equation, but until now no physically meaningful explanation had appeared. This differential equation arises naturally in our derivation.

Spectral approach to homogenization of hyperbolic equations with periodic coefficients

NASA Astrophysics Data System (ADS)

Dorodnyi, M. A.; Suslina, T. A.

2018-06-01

In L2 (Rd ;Cn), we consider selfadjoint strongly elliptic second order differential operators Aε with periodic coefficients depending on x / ε, ε > 0. We study the behavior of the operators cos ⁡ (Aε1/2 τ) and Aε-1/2 sin ⁡ (Aε1/2 τ), τ ∈ R, for small ε. Approximations for these operators in the (Hs →L2)-operator norm with a suitable s are obtained. The results are used to study the behavior of the solution vε of the Cauchy problem for the hyperbolic equation ∂τ2 vε = -Aεvε + F. General results are applied to the acoustics equation and the system of elasticity theory.

Using the MCNP Taylor series perturbation feature (efficiently) for shielding problems

NASA Astrophysics Data System (ADS)

Favorite, Jeffrey

2017-09-01

The Taylor series or differential operator perturbation method, implemented in MCNP and invoked using the PERT card, can be used for efficient parameter studies in shielding problems. This paper shows how only two PERT cards are needed to generate an entire parameter study, including statistical uncertainty estimates (an additional three PERT cards can be used to give exact statistical uncertainties). One realistic example problem involves a detailed helium-3 neutron detector model and its efficiency as a function of the density of its high-density polyethylene moderator. The MCNP differential operator perturbation capability is extremely accurate for this problem. A second problem involves the density of the polyethylene reflector of the BeRP ball and is an example of first-order sensitivity analysis using the PERT capability. A third problem is an analytic verification of the PERT capability.

Feasibility of Higher-Order Differential Ion Mobility Separations Using New Asymmetric Waveforms

PubMed Central

Shvartsburg, Alexandre A.; Mashkevich, Stefan V.; Smith, Richard D.

2011-01-01

Technologies for separating and characterizing ions based on their transport properties in gases have been around for three decades. The early method of ion mobility spectrometry (IMS) distinguished ions by absolute mobility that depends on the collision cross section with buffer gas atoms. The more recent technique of field asymmetric waveform IMS (FAIMS) measures the difference between mobilities at high and low electric fields. Coupling IMS and FAIMS to soft ionization sources and mass spectrometry (MS) has greatly expanded their utility, enabling new applications in biomedical and nanomaterials research. Here, we show that time-dependent electric fields comprising more than two intensity levels could, in principle, effect an infinite number of distinct differential separations based on the higher-order terms of expression for ion mobility. These analyses could employ the hardware and operational procedures similar to those utilized in FAIMS. Methods up to the 4th or 5th order (where conventional IMS is 1st order and FAIMS is 2nd order) should be practical at field intensities accessible in ambient air, with still higher orders potentially achievable in insulating gases. Available experimental data suggest that higher-order separations should be largely orthogonal to each other and to FAIMS, IMS, and MS. PMID:16494377

High-order space charge effects using automatic differentiation

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

Reusch, Michael F.; Bruhwiler, David L.; Computer Accelerator Physics Conference Williamsburg, Virginia 1996

1997-02-01

The Northrop Grumman Topkark code has been upgraded to Fortran 90, making use of operator overloading, so the same code can be used to either track an array of particles or construct a Taylor map representation of the accelerator lattice. We review beam optics and beam dynamics simulations conducted with TOPKARK in the past and we present a new method for modeling space charge forces to high-order with automatic differentiation. This method generates an accurate, high-order, 6-D Taylor map of the phase space variable trajectories for a bunched, high-current beam. The spatial distribution is modeled as the product of amore » Taylor Series times a Gaussian. The variables in the argument of the Gaussian are normalized to the respective second moments of the distribution. This form allows for accurate representation of a wide range of realistic distributions, including any asymmetries, and allows for rapid calculation of the space charge fields with free space boundary conditions. An example problem is presented to illustrate our approach.« less

Second-order differential equations for bosons with spin j ≥ 1 and in the bases of general tensor-spinors of rank 2j

NASA Astrophysics Data System (ADS)

Banda Guzmán, V. M.; Kirchbach, M.

2016-09-01

A boson of spin j≥ 1 can be described in one of the possibilities within the Bargmann-Wigner framework by means of one sole differential equation of order twice the spin, which however is known to be inconsistent as it allows for non-local, ghost and acausally propagating solutions, all problems which are difficult to tackle. The other possibility is provided by the Fierz-Pauli framework which is based on the more comfortable to deal with second-order Klein-Gordon equation, but it needs to be supplemented by an auxiliary condition. Although the latter formalism avoids some of the pathologies of the high-order equations, it still remains plagued by some inconsistencies such as the acausal propagation of the wave fronts of the (classical) solutions within an electromagnetic environment. We here suggest a method alternative to the above two that combines their advantages while avoiding the related difficulties. Namely, we suggest one sole strictly D^{(j,0)oplus (0,j)} representation specific second-order differential equation, which is derivable from a Lagrangian and whose solutions do not violate causality. The equation under discussion presents itself as the product of the Klein-Gordon operator with a momentum-independent projector on Lorentz irreducible representation spaces constructed from one of the Casimir invariants of the spin-Lorentz group. The basis used is that of general tensor-spinors of rank 2 j.

SIVA/DIVA- INITIAL VALUE ORDINARY DIFFERENTIAL EQUATION SOLUTION VIA A VARIABLE ORDER ADAMS METHOD

NASA Technical Reports Server (NTRS)

Krogh, F. T.

1994-01-01

The SIVA/DIVA package is a collection of subroutines for the solution of ordinary differential equations. There are versions for single precision and double precision arithmetic. These solutions are applicable to stiff or nonstiff differential equations of first or second order. SIVA/DIVA requires fewer evaluations of derivatives than other variable order Adams predictor-corrector methods. There is an option for the direct integration of second order equations which can make integration of trajectory problems significantly more efficient. Other capabilities of SIVA/DIVA include: monitoring a user supplied function which can be separate from the derivative; dynamically controlling the step size; displaying or not displaying output at initial, final, and step size change points; saving the estimated local error; and reverse communication where subroutines return to the user for output or computation of derivatives instead of automatically performing calculations. The user must supply SIVA/DIVA with: 1) the number of equations; 2) initial values for the dependent and independent variables, integration stepsize, error tolerance, etc.; and 3) the driver program and operational parameters necessary for subroutine execution. SIVA/DIVA contains an extensive diagnostic message library should errors occur during execution. SIVA/DIVA is written in FORTRAN 77 for batch execution and is machine independent. It has a central memory requirement of approximately 120K of 8 bit bytes. This program was developed in 1983 and last updated in 1987.

Belavkin filter for mixture of quadrature and photon counting process with some control techniques

NASA Astrophysics Data System (ADS)

Garg, Naman; Parthasarathy, Harish; Upadhyay, D. K.

2018-03-01

The Belavkin filter for the H-P Schrödinger equation is derived when the measurement process consists of a mixture of quantum Brownian motions and conservation/Poisson process. Higher-order powers of the measurement noise differentials appear in the Belavkin dynamics. For simulation, we use a second-order truncation. Control of the Belavkin filtered state by infinitesimal unitary operators is achieved in order to reduce the noise effects in the Belavkin filter equation. This is carried out along the lines of Luc Bouten. Various optimization criteria for control are described like state tracking and Lindblad noise removal.

Computer program documentation for the dynamic analysis of a noncontacting mechanical face seal

NASA Technical Reports Server (NTRS)

Auer, B. M.; Etsion, I.

1980-01-01

A computer program is presented which achieves a numerical solution for the equations of motion of a noncontacting mechanical face seal. The flexibly-mounted primary seal ring motion is expressed by a set of second order differential equations for three degrees of freedom. These equations are reduced to a set of first order equations and the GEAR software package is used to solve the set of first order equations. Program input includes seal design parameters and seal operating conditions. Output from the program includes velocities and displacements of the seal ring about the axis of an inertial reference system. One example problem is described.

Dirac’s magnetic monopole and the Kontsevich star product

NASA Astrophysics Data System (ADS)

Soloviev, M. A.

2018-03-01

We examine relationships between various quantization schemes for an electrically charged particle in the field of a magnetic monopole. Quantization maps are defined in invariant geometrical terms, appropriate to the case of nontrivial topology, and are constructed for two operator representations. In the first setting, the quantum operators act on the Hilbert space of sections of a nontrivial complex line bundle associated with the Hopf bundle, whereas the second approach uses instead a quaternionic Hilbert module of sections of a trivial quaternionic line bundle. We show that these two quantizations are naturally related by a bundle morphism and, as a consequence, induce the same phase-space star product. We obtain explicit expressions for the integral kernels of star-products corresponding to various operator orderings and calculate their asymptotic expansions up to the third order in the Planck constant \\hbar . We also show that the differential form of the magnetic Weyl product corresponding to the symmetric ordering agrees completely with the Kontsevich formula for deformation quantization of Poisson structures and can be represented by Kontsevich’s graphs.

On functional determinants of matrix differential operators with multiple zero modes

NASA Astrophysics Data System (ADS)

Falco, G. M.; Fedorenko, Andrei A.; Gruzberg, Ilya A.

2017-12-01

We generalize the method of computing functional determinants with a single excluded zero eigenvalue developed by McKane and Tarlie to differential operators with multiple zero eigenvalues. We derive general formulas for such functional determinants of r× r matrix second order differential operators O with 0 < n ≤slant 2r linearly independent zero modes. We separately discuss the cases of the homogeneous Dirichlet boundary conditions, when the number of zero modes cannot exceed r, and the case of twisted boundary conditions, including the periodic and anti-periodic ones, when the number of zero modes is bounded above by 2r. In all cases the determinants with excluded zero eigenvalues can be expressed only in terms of the n zero modes and other r-n or 2r-n (depending on the boundary conditions) solutions of the homogeneous equation O h=0 , in the spirit of Gel’fand-Yaglom approach. In instanton calculations, the contribution of the zero modes is taken into account by introducing the so-called collective coordinates. We show that there is a remarkable cancellation of a factor (involving scalar products of zero modes) between the Jacobian of the transformation to the collective coordinates and the functional fluctuation determinant with excluded zero eigenvalues. This cancellation drastically simplifies instanton calculations when one uses our formulas.

A spectral mimetic least-squares method

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

Bochev, Pavel; Gerritsma, Marc

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less

A spectral mimetic least-squares method

DOE PAGES

Bochev, Pavel; Gerritsma, Marc

2014-09-01

We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less

Computations involving differential operators and their actions on functions

NASA Technical Reports Server (NTRS)

Crouch, Peter E.; Grossman, Robert; Larson, Richard

1991-01-01

The algorithms derived by Grossmann and Larson (1989) are further developed for rewriting expressions involving differential operators. The differential operators involved arise in the local analysis of nonlinear dynamical systems. These algorithms are extended in two different directions: the algorithms are generalized so that they apply to differential operators on groups and the data structures and algorithms are developed to compute symbolically the action of differential operators on functions. Both of these generalizations are needed for applications.

Multiplexing Transducers Based on Tunnel-Diode Oscillators

NASA Technical Reports Server (NTRS)

Chui, Talso; Penanen, Konstantin; Young, Joseph

2006-01-01

Multiplexing and differential transducers based on tunnel-diode oscillators (TDOs) would be developed, according to a proposal, for operation at very low and/or widely varying temperatures in applications that involve requirements to minimize the power and mass of transducer electronic circuitry. It has been known since 1975 that TDOs are useful for making high-resolution (of the order of 10(exp -9)) measurements at low temperatures. Since that time, TDO transducers have been found to offer the following additional advantages, which the present proposal is intended to exploit: TDO transducers can operate at temperatures ranging from 1 K to about 400 K. Most electronic components other than tunnel diodes do not operate over such a wide temperature range. TDO transducers can be made to operate at very low power - typically, <1 mW. Inasmuch as the response of a TDO transducer is a small change in an arbitrarily set oscillation frequency, the outputs of many TDOs operating at sufficiently different set frequencies can be multiplexed through a single wire. Inasmuch as frequencies can be easily subtracted by means of mixing circuitry, one can easily use two TDOs to make differential measurements. Differential measurements are generally more precise and less susceptible to environmental variations than are absolute measurements. TDO transducers are tolerant to ionizing radiation. Ultimately, the response of a TDO transducer is measured by use of a frequency counter. Because frequency counting can be easily implemented by use of clock signals available from most microprocessors, it is not necessary to incorporate additional readout circuitry that would, if included, add to the mass and power consumption of the transducer circuitry. In one example of many potential variations on the basic theme of the proposal, the figure schematically depicts a conceptual differential-pressure transducer containing a symmetrical pair of TDOs. The differential pressure would be exerted on an electrically conductive and grounded diaphragm, which, at zero differential pressure, would nominally be sprung to a middle position between two capacitor plates that would be parts of the two TDOs. The frequencies of the two TDOs would vary in opposite directions as variations in differential pressure bent the diaphragm away from one capacitor plate and toward the other. The outputs of the TDOs would be mixed and lowpass filtered to obtain a signal at the difference between the frequencies of the two TDOs. The difference frequency would be measured by a frequency counter and converted to differential pressure by a computer.

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation

PubMed Central

Müller, Eike H.; Scheichl, Rob; Shardlow, Tony

2015-01-01

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy. PMID:27547075

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation.

PubMed

Müller, Eike H; Scheichl, Rob; Shardlow, Tony

2015-04-08

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.

Stability analysis of coupled torsional vibration and pressure in oilwell drillstring system

NASA Astrophysics Data System (ADS)

Toumi, S.; Beji, L.; Mlayeh, R.; Abichou, A.

2018-01-01

To address security issues in oilwell drillstring system, the drilling operation handling which is in generally not autonomous but ensured by an operator may be drill bit destructive or fatal for the machine. To control of stick-slip phenomenon, the drillstring control at the right speed taking only the drillstring vibration is not sufficient as the mud dynamics and the pressure change around the drill pipes cannot be neglected. A coupled torsional vibration and pressure model is presented, and the well-posedness problem is addressed. As a Partial Differential Equation-Ordinary Differential Equation (PDE-ODE) coupled system, and in order to maintain a non destructive downhole pressure, we investigate the control stability with and without the damping term in the wave PDE. In terms of, the torsional variable, the downhole pressure, and the annulus pressure, the coupled system equilibrium is shown to be exponentially stable.

Simulation and optimization of pressure swing adsorption systmes using reduced-order modeling

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

Agarwal, A.; Biegler, L.; Zitney, S.

2009-01-01

Over the past three decades, pressure swing adsorption (PSA) processes have been widely used as energyefficient gas separation techniques, especially for high purity hydrogen purification from refinery gases. Models for PSA processes are multiple instances of partial differential equations (PDEs) in time and space with periodic boundary conditions that link the processing steps together. The solution of this coupled stiff PDE system is governed by steep fronts moving with time. As a result, the optimization of such systems represents a significant computational challenge to current differential algebraic equation (DAE) optimization techniques and nonlinear programming algorithms. Model reduction is one approachmore » to generate cost-efficient low-order models which can be used as surrogate models in the optimization problems. This study develops a reducedorder model (ROM) based on proper orthogonal decomposition (POD), which is a low-dimensional approximation to a dynamic PDE-based model. The proposed method leads to a DAE system of significantly lower order, thus replacing the one obtained from spatial discretization and making the optimization problem computationally efficient. The method has been applied to the dynamic coupled PDE-based model of a twobed four-step PSA process for separation of hydrogen from methane. Separate ROMs have been developed for each operating step with different POD modes for each of them. A significant reduction in the order of the number of states has been achieved. The reduced-order model has been successfully used to maximize hydrogen recovery by manipulating operating pressures, step times and feed and regeneration velocities, while meeting product purity and tight bounds on these parameters. Current results indicate the proposed ROM methodology as a promising surrogate modeling technique for cost-effective optimization purposes.« less

Time and frequency domain analysis of sampled data controllers via mixed operation equations

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1981-01-01

Specification of the mathematical equations required to define the dynamic response of a linear continuous plant, subject to sampled data control, is complicated by the fact that the digital components of the control system cannot be modeled via linear ordinary differential equations. This complication can be overcome by introducing two new mathematical operations; namely, the operation of zero order hold and digial delay. It is shown that by direct utilization of these operations, a set of linear mixed operation equations can be written and used to define the dynamic response characteristics of the controlled system. It also is shown how these linear mixed operation equations lead, in an automatable manner, directly to a set of finite difference equations which are in a format compatible with follow on time and frequency domain analysis methods.

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.

Next-to-leading order predictions for WW + jet production

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

Campbell, John M.; Miller, David J.; Robens, Tania

2015-07-28

In this study we report on a next-to-leading order calculation of WW + jet production at hadron colliders, with subsequent leptonic decays of the W bosons included. The calculation of the one-loop contributions is performed using generalized unitarity methods in order to derive analytic expressions for the relevant amplitudes. These amplitudes have been implemented in the parton-level Monte Carlo generator mcfm, which we use to provide a complete next-to-leading order calculation. Predictions for total cross sections, as well as differential distributions for several key observables, are computed both for the LHC operating at 14 TeV as well as for amore » possible future 100 TeV proton-proton collider.« less

Diffusion weighted imaging for the differentiation of breast tumors: From apparent diffusion coefficient to high order diffusion tensor imaging.

PubMed

Teruel, Jose R; Goa, Pål E; Sjøbakk, Torill E; Østlie, Agnes; Fjøsne, Hans E; Bathen, Tone F

2016-05-01

To compare "standard" diffusion weighted imaging, and diffusion tensor imaging (DTI) of 2(nd) and 4(th) -order for the differentiation of malignant and benign breast lesions. Seventy-one patients were imaged at 3 Tesla with a 16-channel breast coil. A diffusion weighted MRI sequence including b = 0 and b = 700 in 30 directions was obtained for all patients. The image data were fitted to three different diffusion models: isotropic model - apparent diffusion coefficient (ADC), 2(nd) -order tensor model (the standard model used for DTI) and a 4(th) -order tensor model, with increased degrees of freedom to describe anisotropy. The ability of the fitted parameters in the different models to differentiate between malignant and benign tumors was analyzed. Seventy-two breast lesions were analyzed, out of which 38 corresponded to malignant and 34 to benign tumors. ADC (using any model) presented the highest discriminative ability of malignant from benign tumors with a receiver operating characteristic area under the curve (AUC) of 0.968, and sensitivity and specificity of 94.1% and 94.7% respectively for a 1.33 × 10(-3) mm(2) /s cutoff. Anisotropy measurements presented high statistical significance between malignant and benign tumors (P < 0.001), but with lower discriminative ability of malignant from benign tumors than ADC (AUC of 0.896 and 0.897 for fractional anisotropy and generalized anisotropy respectively). Statistical significant difference was found between generalized anisotropy and fractional anisotropy for cancers (P < 0.001) but not for benign lesions (P = 0.87). While anisotropy parameters have the potential to provide additional value for breast applications as demonstrated in this study, ADC exhibited the highest differentiation power between malignant and benign breast tumors. © 2015 Wiley Periodicals, Inc.

A modification of \\mathsf {WKB} method for fractional differential operators of Schrödinger's type

NASA Astrophysics Data System (ADS)

Sayevand, K.; Pichaghchi, K.

2017-09-01

In this paper, we were concerned with the description of the singularly perturbed differential equations within the scope of fractional calculus. However, we shall note that one of the main methods used to solve these problems is the so-called WKB method. We should mention that this was not achievable via the existing fractional derivative definitions, because they do not obey the chain rule. In order to accommodate the WKB to the scope of fractional derivative, we proposed a relatively new derivative called the local fractional derivative. By use of properties of local fractional derivative, we extend the WKB method in the scope of the fractional differential equation. By means of this extension, the WKB analysis based on the Borel resummation, for fractional differential operators of WKB type are investigated. The convergence and the Mittag-Leffler stability of the proposed approach is proven. The obtained results are in excellent agreement with the existing ones in open literature and it is shown that the present approach is very effective and accurate. Furthermore, we are mainly interested to construct the solution of fractional Schrödinger equation in the Mittag-Leffler form and how it leads naturally to this semi-classical approximation namely modified WKB.

Harry Mergler with His Modified Differential Analyzer

NASA Image and Video Library

1951-06-21

Harry Mergler stands at the control board of a differential analyzer in the new Instrument Research Laboratory at the National Advisory Committee for Aeronautics (NACA) Lewis Flight Propulsion Laboratory. The differential analyzer was a multi-variable analog computation machine devised in 1931 by Massachusetts Institute of Technology researcher and future NACA Committee member Vannevar Bush. The mechanical device could solve computations up to the sixth order, but had to be rewired before each new computation. Mergler modified Bush’s differential analyzer in the late 1940s to calculate droplet trajectories for Lewis’ icing research program. In four days Mergler’s machine could calculate what previously required weeks. NACA Lewis built the Instrument Research Laboratory in 1950 and 1951 to house the large analog computer equipment. The two-story structure also provided offices for the Mechanical Computational Analysis, and Flow Physics sections of the Physics Division. The division had previously operated from the lab’s hangar because of its icing research and flight operations activities. Mergler joined the Instrument Research Section of the Physics Division in 1948 after earning an undergraduate degree in Physics from the Case Institute of Technology. Mergler’s focus was on the synthesis of analog computers with the machine tools used to create compressor and turbine blades for jet engines.

Maglev Train Signal Processing Architecture Based on Nonlinear Discrete Tracking Differentiator.

PubMed

Wang, Zhiqiang; Li, Xiaolong; Xie, Yunde; Long, Zhiqiang

2018-05-24

In a maglev train levitation system, signal processing plays an important role for the reason that some sensor signals are prone to be corrupted by noise due to the harsh installation and operation environment of sensors and some signals cannot be acquired directly via sensors. Based on these concerns, an architecture based on a new type of nonlinear second-order discrete tracking differentiator is proposed. The function of this signal processing architecture includes filtering signal noise and acquiring needed signals for levitation purposes. The proposed tracking differentiator possesses the advantages of quick convergence, no fluttering, and simple calculation. Tracking differentiator's frequency characteristics at different parameter values are studied in this paper. The performance of this new type of tracking differentiator is tested in a MATLAB simulation and this tracking-differentiator is implemented in Very-High-Speed Integrated Circuit Hardware Description Language (VHDL). In the end, experiments are conducted separately on a test board and a maglev train model. Simulation and experiment results show that the performance of this novel signal processing architecture can fulfill the real system requirement.

Validation of the Rotorcraft Flight Simulation Program (C81) Using Operational Loads Survey Flight Test Data.

DTIC Science & Technology

1980-07-01

implementing a first- order differential equation for the horsepower-available equation, patterned after the model in the hybrid-computer, version of C81...aircraft, so XMR(36) through XMR(40) were set to 0.0. The main rotor differential nacelle flat plate drag area was estimated to be due to two components...312040 000.N N0 133800030000S0000 00joo SI00 Vj . . . 0 Cf0 4~~~ e% &U0 000000 0 C 0 U - 0000.’ N1E Moo i6fo I u04000000 00O 0o I00000000000000000000 1

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

NASA Astrophysics Data System (ADS)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

A semigroup approach to the strong ergodic theorem of the multistate stable population process.

PubMed

Inaba, H

1988-01-01

"In this paper we first formulate the dynamics of multistate stable population processes as a partial differential equation. Next, we rewrite this equation as an abstract differential equation in a Banach space, and solve it by using the theory of strongly continuous semigroups of bounded linear operators. Subsequently, we investigate the asymptotic behavior of this semigroup to show the strong ergodic theorem which states that there exists a stable distribution independent of the initial distribution. Finally, we introduce the dual problem in order to obtain a logical definition for the reproductive value and we discuss its applications." (SUMMARY IN FRE) excerpt

Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces

NASA Astrophysics Data System (ADS)

Mantile, Andrea; Posilicano, Andrea; Sini, Mourad

2016-07-01

The theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic differential operator on Rn with linear boundary conditions on (a relatively open part of) a compact hypersurface. Our approach allows to obtain Kreĭn-like resolvent formulae where the reference operator coincides with the ;free; operator with domain H2 (Rn); this provides an useful tool for the scattering problem from a hypersurface. Concrete examples of this construction are developed in connection with the standard boundary conditions, Dirichlet, Neumann, Robin, δ and δ‧-type, assigned either on a (n - 1) dimensional compact boundary Γ = ∂ Ω or on a relatively open part Σ ⊂ Γ. Schatten-von Neumann estimates for the difference of the powers of resolvents of the free and the perturbed operators are also proven; these give existence and completeness of the wave operators of the associated scattering systems.

Advanced Control Systems for Aircraft Powerplants

DTIC Science & Technology

1980-02-01

production of high- integrity software. 1.0 INTRODUCTION Work on full-authority digital control for gas turbines was started at Rolls- Royce Limited... INTRODUCTION In order to fully understand the operation of the Secondary Power System Control Unit - abbreviated SPSCU - we must first take a close look at...Only Memory EPROM -- Erasable Read Only Memory PLA -- Power Lever Angle LVDT -- Linear Variable Differential Transformer INTRODUCTION Preliminary design

High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices

NASA Astrophysics Data System (ADS)

Dunham, Benjamin Z.

This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common linear algebra functions--most notably third-party sparse solvers and decomposition routines, in addition to basic matrix arithmetic operations and power series--without changing data-type or modifying code line by line; this allows differentiation across sequences of arbitrarily many such functions with minimal implementation effort. NMD works by enlarging the matrices and vectors passed to the routines, replacing each original scalar with a matrix block augmented by derivative data; these blocks are constructed with special sparsity structures, termed "stencils," each designed to be isomorphic to a particular multidimensional hypercomplex algebra. The algebras are in turn designed such that Taylor expansions of hypercomplex function evaluations are finite in length and thus exactly track derivatives without approximation error. Although this use of the method in the "forward mode" is unique in its own right, it is also possible to apply it to existing implementations of the (first-order) discrete adjoint method to find high-order derivatives with lowered cost complexity; for example, for a problem with N inputs and an adjoint solver whose cost is independent of N--i.e., O(1)--the N x N Hessian can be found in O(N) time, which is comparable to existing second-order adjoint methods that require far more problem-specific implementation effort. Higher derivatives are likewise less expensive--e.g., a N x N x N rank-three tensor can be found in O(N2). Alternatively, a Hessian-vector product can be found in O(1) time, which may open up many matrix-based simulations to a range of existing optimization or surrogate modeling approaches. As a final corollary in parallel to the NMD-adjoint hybrid method, the existing complex-step differentiation (CD) technique is also shown to be capable of finding the Hessian-vector product. All variants are implemented on a stochastic diffusion problem and compared in-depth with various cost and accuracy metrics.

Cohomology and deformation of 𝔞𝔣𝔣(1|1) acting on differential operators

NASA Astrophysics Data System (ADS)

Basdouri, Khaled; Omri, Salem

We consider the 𝔞𝔣𝔣(1|1)-module structure on the spaces of differential operators acting on the spaces of weighted densities. We compute the second differential cohomology of the Lie superalgebra 𝔞𝔣𝔣(1|1) with coefficients in differential operators acting on the spaces of weighted densities. We classify formal deformations of the 𝔞𝔣𝔣(1|1)-module structure on the superspaces of symbols of differential operators. We prove that any formal deformation of a given infinitesimal deformation of this structure is equivalent to its infinitesimal part. This work is the simplest superization of a result by Basdouri [Deformation of 𝔞𝔣𝔣(1)-modules of pseudo-differential operators and symbols, J. Pseudo-differ. Oper. Appl. 7(2) (2016) 157-179] and application of work by Basdouri et al. [First cohomology of 𝔞𝔣𝔣(1) and 𝔞𝔣𝔣(1|1) acting on linear differential operators, Int. J. Geom. Methods Mod. Phys. 13(1) (2016)].

GPC: General Polygon Clipper library

NASA Astrophysics Data System (ADS)

Murta, Alan

2015-12-01

The University of Manchester GPC library is a flexible and highly robust polygon set operations library for use with C, C#, Delphi, Java, Perl, Python, Haskell, Lua, VB.Net and other applications. It supports difference, intersection, exclusive-or and union clip operations, and polygons may be comprised of multiple disjoint contours. Contour vertices may be given in any order - clockwise or anticlockwise, and contours may be convex, concave or self-intersecting, and may be nested (i.e. polygons may have holes). Output may take the form of either polygon contours or tristrips, and hole and external contours are differentiated in the result.

A physically based connection between fractional calculus and fractal geometry

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

Butera, Salvatore, E-mail: sg.butera@gmail.com; Di Paola, Mario, E-mail: mario.dipaola@unipa.it

2014-11-15

We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalousmore » dimension of such geometry, as well as to the model used to describe the physics involved. By linearizing the non linear dependence of the response of the system at hand to a proper forcing action then, exploiting the Boltzmann superposition principle, a fractional differential equation is found, describing the dynamics of the system itself. The order of such equation is again related to the anomalous dimension of the underlying geometry.« less

High-order space charge effects using automatic differentiation

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

Reusch, M.F.; Bruhwiler, D.L.

1997-02-01

The Northrop Grumman Topkark code has been upgraded to Fortran 90, making use of operator overloading, so the same code can be used to either track an array of particles or construct a Taylor map representation of the accelerator lattice. We review beam optics and beam dynamics simulations conducted with TOPKARK in the past and we present a new method for modeling space charge forces to high-order with automatic differentiation. This method generates an accurate, high-order, 6-D Taylor map of the phase space variable trajectories for a bunched, high-current beam. The spatial distribution is modeled as the product of amore » Taylor Series times a Gaussian. The variables in the argument of the Gaussian are normalized to the respective second moments of the distribution. This form allows for accurate representation of a wide range of realistic distributions, including any asymmetries, and allows for rapid calculation of the space charge fields with free space boundary conditions. An example problem is presented to illustrate our approach. {copyright} {ital 1997 American Institute of Physics.}« less

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.

Elastic-wave-mode separation in TTI media with inverse-distance weighted interpolation involving position shading

NASA Astrophysics Data System (ADS)

Wang, Jian; Meng, Xiaohong; Zheng, Wanqiu

2017-10-01

The elastic-wave reverse-time migration of inhomogeneous anisotropic media is becoming the hotspot of research today. In order to ensure the accuracy of the migration, it is necessary to separate the wave mode into P-wave and S-wave before migration. For inhomogeneous media, the Kelvin-Christoffel equation can be solved in the wave-number domain by using the anisotropic parameters of the mesh nodes, and the polarization vector of the P-wave and S-wave at each node can be calculated and transformed into the space domain to obtain the quasi-differential operators. However, this method is computationally expensive, especially for the process of quasi-differential operators. In order to reduce the computational complexity, the wave-mode separation of mixed domain can be realized on the basis of a reference model in the wave-number domain. But conventional interpolation methods and reference model selection methods reduce the separation accuracy. In order to further improve the separation effect, this paper introduces an inverse-distance interpolation method involving position shading and uses the reference model selection method of random points scheme. This method adds the spatial weight coefficient K, which reflects the orientation of the reference point on the conventional IDW algorithm, and the interpolation process takes into account the combined effects of the distance and azimuth of the reference points. Numerical simulation shows that the proposed method can separate the wave mode more accurately using fewer reference models and has better practical value.

Compact tunable silicon photonic differential-equation solver for general linear time-invariant systems.

PubMed

Wu, Jiayang; Cao, Pan; Hu, Xiaofeng; Jiang, Xinhong; Pan, Ting; Yang, Yuxing; Qiu, Ciyuan; Tremblay, Christine; Su, Yikai

2014-10-20

We propose and experimentally demonstrate an all-optical temporal differential-equation solver that can be used to solve ordinary differential equations (ODEs) characterizing general linear time-invariant (LTI) systems. The photonic device implemented by an add-drop microring resonator (MRR) with two tunable interferometric couplers is monolithically integrated on a silicon-on-insulator (SOI) wafer with a compact footprint of ~60 μm × 120 μm. By thermally tuning the phase shifts along the bus arms of the two interferometric couplers, the proposed device is capable of solving first-order ODEs with two variable coefficients. The operation principle is theoretically analyzed, and system testing of solving ODE with tunable coefficients is carried out for 10-Gb/s optical Gaussian-like pulses. The experimental results verify the effectiveness of the fabricated device as a tunable photonic ODE solver.

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.

On the Definition of Surface Potentials for Finite-Difference Operators

NASA Technical Reports Server (NTRS)

Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

For a class of linear constant-coefficient finite-difference operators of the second order, we introduce the concepts similar to those of conventional single- and double-layer potentials for differential operators. The discrete potentials are defined completely independently of any notion related to the approximation of the continuous potentials on the grid. We rather use all approach based on differentiating, and then inverting the differentiation of a function with surface discontinuity of a particular kind, which is the most general way of introducing surface potentials in the theory of distributions. The resulting finite-difference "surface" potentials appear to be solutions of the corresponding continuous potentials. Primarily, this pertains to the possibility of representing a given solution to the homogeneous equation on the domain as a variety of surface potentials, with the density defined on the domain's boundary. At the same time the discrete surface potentials can be interpreted as one specific realization of the generalized potentials of Calderon's type, and consequently, their approximation properties can be studied independently in the framework of the difference potentials method by Ryaben'kii. The motivation for introducing and analyzing the discrete surface potentials was provided by the problems of active shielding and control of sound, in which the aforementioned source terms that drive the potentials are interpreted as the acoustic control sources that cancel out the unwanted noise on a predetermined region of interest.

Second order upwind Lagrangian particle method for Euler equations

DOE PAGES

Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin

2016-06-01

A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less

Second order upwind Lagrangian particle method for Euler equations

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

Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin

A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less

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.

Lagrange formula for differential operators on a tree-graph and the resolvents of well-posed restrictions of operator

NASA Astrophysics Data System (ADS)

Koshkarbayev, Nurbol; Kanguzhin, Baltabek

2017-09-01

In this paper we study the question on the full description of well-posed restrictions of given maximal differential operator on a tree-graph. Lagrange formula for differential operator on a tree with Kirchhoff conditions at its internal vertices is presented.

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

NASA Technical Reports Server (NTRS)

Klimas, A. J.; Sandri, G.; Scudder, J. D.; Howell, D. R.

1976-01-01

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained.

Solutions to an advanced functional partial differential equation of the pantograph type

PubMed Central

Zaidi, Ali A.; Van Brunt, B.; Wake, G. C.

2015-01-01

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained. PMID:26345391

Solutions to an advanced functional partial differential equation of the pantograph type.

PubMed

Zaidi, Ali A; Van Brunt, B; Wake, G C

2015-07-08

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained.

A three operator split-step method covering a larger set of non-linear partial differential equations

NASA Astrophysics Data System (ADS)

Zia, Haider

2017-06-01

This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

On the growth of solutions of a class of higher order linear differential equations with coefficients having the same order

NASA Astrophysics Data System (ADS)

Tu, Jin; Yi, Cai-Feng

2008-04-01

In this paper, the authors investigate the growth of solutions of a class of higher order linear differential equationsf(k)+Ak-1f(k-1)+...+A0f=0 when most coefficients in the above equations have the same order with each other, and obtain some results which improve previous results due to K.H. Kwon [K.H. Kwon, Nonexistence of finite order solutions of certain second order linear differential equations, Kodai Math. J. 19 (1996) 378-387] and ZE-X. Chen [Z.-X. Chen, The growth of solutions of the differential equation f''+e-zf'+Q(z)f=0, Sci. China Ser. A 31 (2001) 775-784 (in Chinese); ZE-X. Chen, On the hyper order of solutions of higher order differential equations, Chinese Ann. Math. Ser. B 24 (2003) 501-508 (in Chinese); Z.-X. Chen, On the growth of solutions of a class of higher order differential equations, Acta Math. Sci. Ser. B 24 (2004) 52-60 (in Chinese); Z.-X. Chen, C.-C. Yang, Quantitative estimations on the zeros and growth of entire solutions of linear differential equations, Complex Var. 42 (2000) 119-133].

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

Operation bandwidth optimization of photonic differentiators.

PubMed

Yan, Siqi; Zhang, Yong; Dong, Jianji; Zheng, Aoling; Liao, Shasha; Zhou, Hailong; Wu, Zhao; Xia, Jinsong; Zhang, Xinliang

2015-07-27

We theoretically investigate the operation bandwidth limitation of the photonic differentiator including the upper limitation, which is restrained by the device operation bandwidth and the lower limitation, which is restrained by the energy efficiency (EE) and detecting noise level. Taking the silicon photonic crystal L3 nano-cavity (PCN) as an example, for the first time, we experimentally demonstrate that the lower limitation of the operation bandwidth does exist and differentiators with different bandwidths have significantly different acceptable pulse width range of input signals, which are consistent to the theoretical prediction. Furthermore, we put forward a novel photonic differentiator scheme employing cascaded PCNs with different Q factors, which is likely to expand the operation bandwidth range of photonic differentiator dramatically.

Design of an all-optical fractional-order differentiator with terahertz bandwidth based on a fiber Bragg grating in transmission.

PubMed

Liu, Xin; Shu, Xuewen

2017-08-20

All-optical fractional-order temporal differentiators with bandwidths reaching terahertz (THz) values are demonstrated with transmissive fiber Bragg gratings. Since the designed fractional-order differentiator is a minimum phase function, the reflective phase of the designed function can be chosen arbitrarily. As examples, we first design several 0.5th-order differentiators with bandwidths reaching the THz range for comparison. The reflective phases of the 0.5th-order differentiators are chosen to be linear phase, quadratic phase, cubic phase, and biquadratic phase, respectively. We find that both the maximum coupling coefficient and the spatial resolution of the designed grating increase when the reflective phase varies from quadratic function to cubic function to biquadratic function. Furthermore, when the reflective phase is chosen to be a quadratic function, the obtained grating coupling coefficient and period are more likely to be achieved in practice. Then we design fractional-order differentiators with different orders when the reflective phase is chosen to be a quadratic function. We see that when the designed order of the differentiator increases, the obtained maximum coupling coefficient also increases while the oscillation of the coupling coefficient decreases. Finally, we give the numerical performance of the designed 0.5th-order differentiator by showing its temporal response and calculating its cross-correlation coefficient.

C1,1 regularity for degenerate elliptic obstacle problems

NASA Astrophysics Data System (ADS)

Daskalopoulos, Panagiota; Feehan, Paul M. N.

2016-03-01

The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic partial differential operator, where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to the obstacle problem for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset. With the aid of weighted Sobolev spaces and weighted Hölder spaces, we establish the optimal C 1 , 1 regularity (up to the boundary of the half-plane) for solutions to obstacle problems for the elliptic Heston operator when the obstacle functions are sufficiently smooth.

The quantum n-body problem in dimension d ⩾ n – 1: ground state

NASA Astrophysics Data System (ADS)

Miller, Willard, Jr.; Turbiner, Alexander V.; Escobar-Ruiz, M. A.

2018-05-01

We employ generalized Euler coordinates for the n body system in dimensional space, which consists of the centre-of-mass vector, relative (mutual) mass-independent distances r ij and angles as remaining coordinates. We prove that the kinetic energy of the quantum n-body problem for can be written as the sum of three terms: (i) kinetic energy of centre-of-mass, (ii) the second order differential operator which depends on relative distances alone and (iii) the differential operator which annihilates any angle-independent function. The operator has a large reflection symmetry group and in variables is an algebraic operator, which can be written in terms of generators of the hidden algebra . Thus, makes sense of the Hamiltonian of a quantum Euler–Arnold top in a constant magnetic field. It is conjectured that for any n, the similarity-transformed is the Laplace–Beltrami operator plus (effective) potential; thus, it describes a -dimensional quantum particle in curved space. This was verified for . After de-quantization the similarity-transformed becomes the Hamiltonian of the classical top with variable tensor of inertia in an external potential. This approach allows a reduction of the dn-dimensional spectral problem to a -dimensional spectral problem if the eigenfunctions depend only on relative distances. We prove that the ground state function of the n body problem depends on relative distances alone.

Automated feature detection and identification in digital point-ordered signals

DOEpatents

Oppenlander, Jane E.; Loomis, Kent C.; Brudnoy, David M.; Levy, Arthur J.

1998-01-01

A computer-based automated method to detect and identify features in digital point-ordered signals. The method is used for processing of non-destructive test signals, such as eddy current signals obtained from calibration standards. The signals are first automatically processed to remove noise and to determine a baseline. Next, features are detected in the signals using mathematical morphology filters. Finally, verification of the features is made using an expert system of pattern recognition methods and geometric criteria. The method has the advantage that standard features can be, located without prior knowledge of the number or sequence of the features. Further advantages are that standard features can be differentiated from irrelevant signal features such as noise, and detected features are automatically verified by parameters extracted from the signals. The method proceeds fully automatically without initial operator set-up and without subjective operator feature judgement.

Power spectrum oscillations from Planck-suppressed operators in effective field theory motivated monodromy inflation

NASA Astrophysics Data System (ADS)

Price, Layne C.

2015-11-01

We consider a phenomenological model of inflation where the inflaton is the phase of a complex scalar field Φ . Planck-suppressed operators of O (f5/Mpl) modify the geometry of the vev ⟨Φ ⟩ at first order in the decay constant f , which adds a first-order periodic term to the definition of the canonically normalized inflaton ϕ . This correction to the inflaton induces a fixed number of extra oscillatory terms in the potential V ˜θp. We derive the same result in a toy scenario where the vacuum ⟨Φ ⟩ is an ellipse with an arbitrarily large eccentricity. These extra oscillations change the form of the power spectrum as a function of scale k and provide a possible mechanism for differentiating effective field theory motivated inflation from models where the angular shift symmetry is a gauge symmetry.

Local terahertz microspectroscopy with λ/100 spatial resolution.

PubMed

Glotin, F; Ortega, J-M; Prazeres, R

2013-12-15

We have extended the spectral range of a differential method of infrared microspectroscopy in order to operate in the terahertz spectral region. We show on samples of graphite embedded in a matrix of polymers that the spatial resolution is practically independent of the wavelength and is at least λ/100. This method aims at performing "chemical mapping" of various objects since it is sensitive only to the imaginary part of the index of refraction.

Decompression Sickness, Extravehicular Activities, and Nitrogen Induced Osmosis: Brian Hills Revisited

DTIC Science & Technology

2001-06-01

hypobares ou hyperbares ] To order the complete compilation report, use: ADA395680 The component part is provided here to allow users access to individually...report: TITLE: Operational Medical Issues in Hypo-and Hyperbaric Conditions [les Questions medicales a caractere oprationel liees aux conditions...Hypo- and Hyperbaric Conditions ", held in Toronto, Canada, 16-19 October 2000, and published in RTO MP-062. 45-2 upon the local pressure differential

Representation of solution for fully nonlocal diffusion equations with deviation time variable

NASA Astrophysics Data System (ADS)

Drin, I. I.; Drin, S. S.; Drin, Ya. M.

2018-01-01

We prove the solvability of the Cauchy problem for a nonlocal heat equation which is of fractional order both in space and time. The representation formula for classical solutions for time- and space- fractional partial differential operator Dat + a2 (-Δ) γ/2 (0 <= α <= 1, γ ɛ (0, 2]) and deviation time variable is given in terms of the Fox H-function, using the step by step method.

Error modeling for differential GPS. M.S. Thesis - MIT, 12 May 1995

NASA Technical Reports Server (NTRS)

Blerman, Gregory S.

1995-01-01

Differential Global Positioning System (DGPS) positioning is used to accurately locate a GPS receiver based upon the well-known position of a reference site. In utilizing this technique, several error sources contribute to position inaccuracy. This thesis investigates the error in DGPS operation and attempts to develop a statistical model for the behavior of this error. The model for DGPS error is developed using GPS data collected by Draper Laboratory. The Marquardt method for nonlinear curve-fitting is used to find the parameters of a first order Markov process that models the average errors from the collected data. The results show that a first order Markov process can be used to model the DGPS error as a function of baseline distance and time delay. The model's time correlation constant is 3847.1 seconds (1.07 hours) for the mean square error. The distance correlation constant is 122.8 kilometers. The total process variance for the DGPS model is 3.73 sq meters.

Universal block diagram based modeling and simulation schemes for fractional-order control systems.

PubMed

Bai, Lu; Xue, Dingyü

2017-05-08

Universal block diagram based schemes are proposed for modeling and simulating the fractional-order control systems in this paper. A fractional operator block in Simulink is designed to evaluate the fractional-order derivative and integral. Based on the block, the fractional-order control systems with zero initial conditions can be modeled conveniently. For modeling the system with nonzero initial conditions, the auxiliary signal is constructed in the compensation scheme. Since the compensation scheme is very complicated, therefore the integrator chain scheme is further proposed to simplify the modeling procedures. The accuracy and effectiveness of the schemes are assessed in the examples, the computation results testify the block diagram scheme is efficient for all Caputo fractional-order ordinary differential equations (FODEs) of any complexity, including the implicit Caputo FODEs. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Sexy splicing: regulatory interplays governing sex determination from Drosophila to mammals.

PubMed

Lalli, Enzo; Ohe, Kenji; Latorre, Elisa; Bianchi, Marco E; Sassone-Corsi, Paolo

2003-02-01

A remarkable array of strategies is used to produce sexual differentiation in different species. Complex gene hierarchies govern sex determination pathways, as exemplified by the classic D. melanogaster paradigm, where an interplay of transcriptional, splicing and translational mechanisms operate. Molecular studies support the hypothesis that genetic sex determination pathways evolved in reverse order, from downstream to upstream genes, in the cascade. The recent identification of a role for the key regulatory factors SRY and WT1(+KTS) in pre-mRNA splicing indicates that important steps in the mammalian sex determination process are likely to operate at the post-transcriptional level.

Testing the Equivalence Principle in an Einstein Elevator: Detector Dynamics and Gravity Perturbations

NASA Technical Reports Server (NTRS)

Hubbard, Dorthy (Technical Monitor); Lorenzini, E. C.; Shapiro, I. I.; Cosmo, M. L.; Ashenberg, J.; Parzianello, G.; Iafolla, V.; Nozzoli, S.

2003-01-01

We discuss specific, recent advances in the analysis of an experiment to test the Equivalence Principle (EP) in free fall. A differential accelerometer detector with two proof masses of different materials free falls inside an evacuated capsule previously released from a stratospheric balloon. The detector spins slowly about its horizontal axis during the fall. An EP violation signal (if present) will manifest itself at the rotational frequency of the detector. The detector operates in a quiet environment as it slowly moves with respect to the co-moving capsule. There are, however, gravitational and dynamical noise contributions that need to be evaluated in order to define key requirements for this experiment. Specifically, higher-order mass moments of the capsule contribute errors to the differential acceleration output with components at the spin frequency which need to be minimized. The dynamics of the free falling detector (in its present design) has been simulated in order to estimate the tolerable errors at release which, in turn, define the release mechanism requirements. Moreover, the study of the higher-order mass moments for a worst-case position of the detector package relative to the cryostat has led to the definition of requirements on the shape and size of the proof masses.

Order, Disorder, Death: Lessons from a Superorganism

PubMed Central

Amdam, Gro V.; Seehuu, Siri-Christine

2008-01-01

Animal models contribute to the understanding of molecular mechanism of cancer, revealing complex roles of altered cellular-signaling networks and deficient surveillance systems. Analogous pathologies are documented in an unconventional model organism that receives attention in research on systems theory, evolution, and aging. The honeybee (Apis mellifera) colony is an advanced integrative unit, a “superorganism” in which order is controlled via complex signaling cascades and surveillance schemes. A facultatively sterile caste, the workers, regulates patterns of growth, differentiation, homeostasis, and death. Workers differentiate into temporal phenotypes in response to dynamic social cues; chemosensory signals that can translate into dramatic physiological responses, including programmed cell death. Temporal worker forms function together, and effectively identify and terminate abnormal colony members ranging from embryos to adults. As long as this regulatory system is operational at a colony level, the unit survives and propagates. However, if the worker phenotypes that collectively govern order become too few or change into malignant forms that bypass control mechanisms to replicate aberrantly; order is replaced by disorder that ultimately leads to the destruction of the society. In this chapter we describe fundamental properties of honeybee social organization, and explore conditions that lead to states of disorder. Our hope is that this chapter will be an inspirational source for ongoing and future work in the field of cancer research. PMID:16860655

Fractional calculus in bioengineering, part 3.

PubMed

Magin, Richard L

2004-01-01

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub-threshold nerve propagation. By expanding the range of mathematical operations to include fractional calculus, we can develop new and potentially useful functional relationships for modeling complex biological systems in a direct and rigorous manner. In Part 2 of this review (Crit Rev Biomed Eng 2004; 32(1):105-193), fractional calculus was applied to problems in nerve stimulation, dielectric relaxation, and viscoelastic materials by extending the governing differential equations to include fractional order terms. In this third and final installment, we consider distributed systems that represent shear stress in fluids, heat transfer in uniform one-dimensional media, and subthreshold nerve depolarization. Classic electrochemical analysis and impedance spectroscopy are also reviewed from the perspective of fractional calculus, and selected examples from recent studies in neuroscience, bioelectricity, and tissue biomechanics are analyzed to illustrate the vitality of the field.

The Lichnerowicz-Weitzenboeck formula and superconductivity

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

Vargas-Paredes, Alfredo A.; Doria, Mauro M.; Neto, Jose Abdala Helayeel

2013-01-15

We derive the Lichnerowicz-Weitzenboeck formula for the two-component order parameter superconductor, which provides a twofold view of the kinetic energy of the superconductor. For the one component order parameter superconductor we review the connection between the Lichnerowicz-Weitzenboeck formula and the Ginzburg-Landau theory. For the two-component case we claim that this formula opens a venue to describe inhomogeneous superconducting states intertwined by spin correlations and charged dislocation. In this case the Lichnerowicz-Weitzenboeck formula displays local rotational and electromagnetic gauge symmetry (SU(2) Circled-Times U(1)) and relies on local commuting momentum and spin operators. The order parameter lives in a space with curvaturemore » and torsion described by Elie Cartan geometrical formalism. The Lichnerowickz-Weitzenboeck formula leads to first order differential equations that are a three-dimensional version of the Seiberg-Witten equations.« less

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.

A round trip from Caldirola to Bateman systems

NASA Astrophysics Data System (ADS)

Guerrero, J.; López-Ruiz, F. F.; Aldaya, V.; Cossío, F.

2011-03-01

For the quantum Caldirola-Kanai Hamiltonian, describing a quantum damped harmonic oscillator, a couple of constant of motion operators generating the Heisenberg algebra can be found. The inclusion in this algebra, in a unitary manner, of the standard time evolution generator , which is not a constant of motion, requires a non-trivial extension of this basic algebra and the physical system itself, which now includes a new dual particle. This enlarged algebra, when exponentiated, leads to a group, named the Bateman group, which admits unitary representations with support in the Hilbert space of functions satisfying the Schrodinger equation associated with the quantum Bateman Hamiltonian, either as a second order differential operator as well as a first order one. The classical Bateman Hamiltonian describes a dual system of a damped (losing energy) particle and a dual (gaining energy) particle. The classical Bateman system has a solution submanifold containing the trajectories of the original system as a submanifold. When restricted to this submanifold, the Bateman dual classical Hamiltonian leads to the Caldirola-Kanai Hamiltonian for a single damped particle. This construction can also be done at the quantum level, and the Caldirola-Kanai Hamiltonian operator can be derived from the Bateman Hamiltonian operator when appropriate constraints are imposed.

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

Choi, Cheong R.

The structural changes of kinetic Alfvén solitary waves (KASWs) due to higher-order terms are investigated. While the first-order differential equation for KASWs provides the dispersion relation for kinetic Alfvén waves, the second-order differential equation describes the structural changes of the solitary waves due to higher-order nonlinearity. The reductive perturbation method is used to obtain the second-order and third-order partial differential equations; then, Kodama and Taniuti's technique [J. Phys. Soc. Jpn. 45, 298 (1978)] is applied in order to remove the secularities in the third-order differential equations and derive a linear second-order inhomogeneous differential equation. The solution to this new second-ordermore » equation indicates that, as the amplitude increases, the hump-type Korteweg-de Vries solution is concentrated more around the center position of the soliton and that dip-type structures form near the two edges of the soliton. This result has a close relationship with the interpretation of the complex KASW structures observed in space with satellites.« less

Stability analysis for acoustic wave propagation in tilted TI media by finite differences

NASA Astrophysics Data System (ADS)

Bakker, Peter M.; Duveneck, Eric

2011-05-01

Several papers in recent years have reported instabilities in P-wave modelling, based on an acoustic approximation, for inhomogeneous transversely isotropic media with tilted symmetry axis (TTI media). In particular, instabilities tend to occur if the axis of symmetry varies rapidly in combination with strong contrasts of medium parameters, which is typically the case at the foot of a steeply dipping salt flank. In a recent paper, we have proposed and demonstrated a P-wave modelling approach for TTI media, based on rotated stress and strain tensors, in which the wave equations reduce to a coupled set of two second-order partial differential equations for two scalar stress components: a normal component along the variable axis of symmetry and a lateral component of stress in the plane perpendicular to that axis. Spatially constant density is assumed in this approach. A numerical discretization scheme was proposed which uses discrete second-derivative operators for the non-mixed second-order derivatives in the wave equations, and combined first-derivative operators for the mixed second-order derivatives. This paper provides a complete and rigorous stability analysis, assuming a uniformly sampled grid. Although the spatial discretization operator for the TTI acoustic wave equation is not self-adjoint, this operator still defines a complete basis of eigenfunctions of the solution space, provided that the solution space is somewhat restricted at locations where the medium is elliptically anisotropic. First, a stability analysis is given for a discretization scheme, which is purely based on first-derivative operators. It is shown that the coefficients of the central difference operators should satisfy certain conditions. In view of numerical artefacts, such a discretization scheme is not attractive, and the non-mixed second-order derivatives of the wave equation are discretized directly by second-derivative operators. It is shown that this modification preserves stability, provided that the central difference operators of the second-order derivatives dominate over the twice applied operators of the first-order derivatives. In practice, it turns out that this is almost the case. Stability of the desired discretization scheme is enforced by slightly weighting down the mixed second-order derivatives in the wave equation. This has a minor, practically negligible, effect on the kinematics of wave propagation. Finally, it is shown that non-reflecting boundary conditions, enforced by applying a taper at the boundaries of the grid, do not harm the stability of the discretization scheme.

Differential Resonant Ring YIG Tuned Oscillator

NASA Technical Reports Server (NTRS)

Parrott, Ronald A.

2010-01-01

A differential SiGe oscillator circuit uses a resonant ring-oscillator topology in order to electronically tune the oscillator over multi-octave bandwidths. The oscillator s tuning is extremely linear, because the oscillator s frequency depends on the magnetic tuning of a YIG sphere, whose resonant frequency is equal to a fundamental constant times the DC magnetic field. This extremely simple circuit topology uses two coupling loops connecting a differential pair of SiGe bipolar transistors into a feedback configuration using a YIG tuned filter creating a closed-loop ring oscillator. SiGe device technology is used for this oscillator in order to keep the transistor s 1/f noise to an absolute minimum in order to achieve minimum RF phase noise. The single-end resonant ring oscillator currently has an advantage in fewer parts, but when the oscillation frequency is greater than 16 GHz, the package s parasitic behavior couples energy to the sphere and causes holes and poor phase noise performance. This is because the coupling to the YIG is extremely low, so that the oscillator operates at near the unloaded Q. With the differential resonant ring oscillator, the oscillation currents are just in the YIG coupling mechanisms. The phase noise is even better, and the physical size can be reduced to permit monolithic microwave integrated circuit oscillators. This invention is a YIG tuned oscillator circuit making use of a differential topology to simultaneously achieve an extremely broadband electronic tuning range and ultra-low phase noise. As a natural result of its differential circuit topology, all reactive elements, such as tuning stubs, which limit tuning bandwidth by contributing excessive open loop phase shift, have been eliminated. The differential oscillator s open-loop phase shift is associated with completely non-dispersive circuit elements such as the physical angle of the coupling loops, a differential loop crossover, and the high-frequency phase shift of the n-p-n transistors. At the input of the oscillator s feedback loop is a pair of differentially connected n-p-n SiGe transistors that provides extremely high gain, and because they are bulk-effect devices, extremely low 1/f noise (leading to ultralow RF phase noise). The 1/f corner frequency for n-p-n SiGe transistors is approximately 500 Hz. The RF energy from the transistor s collector output is connected directly to the top-coupling loop (the excitation loop) of a single-sphere YIG tuned filter. A uniform magnetic field to bias the YIG must be at a right angle to any vector associated with an RF current in a coupling loop in order for the precession to interact with the RF currents.

Reduced-order model for dynamic optimization of pressure swing adsorption processes

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

Agarwal, A.; Biegler, L.; Zitney, S.

2007-01-01

Over the past decades, pressure swing adsorption (PSA) processes have been widely used as energy-efficient gas and liquid separation techniques, especially for high purity hydrogen purification from refinery gases. The separation processes are based on solid-gas equilibrium and operate under periodic transient conditions. Models for PSA processes are therefore multiple instances of partial differential equations (PDEs) in time and space with periodic boundary conditions that link the processing steps together. The solution of this coupled stiff PDE system is governed by steep concentrations and temperature fronts moving with time. As a result, the optimization of such systems for either designmore » or operation represents a significant computational challenge to current differential algebraic equation (DAE) optimization techniques and nonlinear programming algorithms. Model reduction is one approach to generate cost-efficient low-order models which can be used as surrogate models in the optimization problems. The study develops a reduced-order model (ROM) based on proper orthogonal decomposition (POD), which is a low-dimensional approximation to a dynamic PDE-based model. Initially, a representative ensemble of solutions of the dynamic PDE system is constructed by solving a higher-order discretization of the model using the method of lines, a two-stage approach that discretizes the PDEs in space and then integrates the resulting DAEs over time. Next, the ROM method applies the Karhunen-Loeve expansion to derive a small set of empirical eigenfunctions (POD modes) which are used as basis functions within a Galerkin's projection framework to derive a low-order DAE system that accurately describes the dominant dynamics of the PDE system. The proposed method leads to a DAE system of significantly lower order, thus replacing the one obtained from spatial discretization before and making optimization problem computationally-efficient. The method has been applied to the dynamic coupled PDE-based model of a two-bed four-step PSA process for separation of hydrogen from methane. Separate ROMs have been developed for each operating step with different POD modes for each of them. A significant reduction in the order of the number of states has been achieved. The gas-phase mole fraction, solid-state loading and temperature profiles from the low-order ROM and from the high-order simulations have been compared. Moreover, the profiles for a different set of inputs and parameter values fed to the same ROM were compared with the accurate profiles from the high-order simulations. Current results indicate the proposed ROM methodology as a promising surrogate modeling technique for cost-effective optimization purposes. Moreover, deviations from the ROM for different set of inputs and parameters suggest that a recalibration of the model is required for the optimization studies. Results for these will also be presented with the aforementioned results.« less

Boolean linear differential operators on elementary cellular automata

NASA Astrophysics Data System (ADS)

Martín Del Rey, Ángel

2014-12-01

In this paper, the notion of boolean linear differential operator (BLDO) on elementary cellular automata (ECA) is introduced and some of their more important properties are studied. Special attention is paid to those differential operators whose coefficients are the ECA with rule numbers 90 and 150.

Reverse Transcription Quantitative Polymerase Chain Reaction for Detection of and Differentiation Between RNA and DNA of HIV-1-Based Lentiviral Vectors.

PubMed

Pavlovic, Melanie; Koehler, Nina; Anton, Martina; Dinkelmeier, Anna; Haase, Maren; Stellberger, Thorsten; Busch, Ulrich; Baiker, Armin E

2017-08-01

The purpose of the described method is the detection of and differentiation between RNA and DNA of human immunodeficiency virus (HIV)-derived lentiviral vectors (LV) in cell culture supernatants and swab samples. For the analytical surveillance of genetic engineering, operations methods for the detection of the HIV-1-based LV generations are required. Furthermore, for research issues, it is important to prove the absence of LV particles for downgrading experimental settings in terms of the biosafety level. Here, a quantitative polymerase chain reaction method targeting the long terminal repeat U5 subunit and the start sequence of the packaging signal ψ is described. Numerous controls are included in order to monitor the technical procedure.

Supplementary motor area as key structure for domain-general sequence processing: A unified account.

PubMed

Cona, Giorgia; Semenza, Carlo

2017-01-01

The Supplementary Motor Area (SMA) is considered as an anatomically and functionally heterogeneous region and is implicated in several functions. We propose that SMA plays a crucial role in domain-general sequence processes, contributing to the integration of sequential elements into higher-order representations regardless of the nature of such elements (e.g., motor, temporal, spatial, numerical, linguistic, etc.). This review emphasizes the domain-general involvement of the SMA, as this region has been found to support sequence operations in a variety of cognitive domains that, albeit different, share an inherent sequence processing. These include action, time and spatial processing, numerical cognition, music and language processing, and working memory. In this light, we reviewed and synthesized recent neuroimaging, stimulation and electrophysiological studies in order to compare and reconcile the distinct sources of data by proposing a unifying account for the role of the SMA. We also discussed the differential contribution of the pre-SMA and SMA-proper in sequence operations, and possible neural mechanisms by which such operations are executed. Copyright © 2016 Elsevier Ltd. All rights reserved.

Friedrichs systems in a Hilbert space framework: Solvability and multiplicity

NASA Astrophysics Data System (ADS)

Antonić, N.; Erceg, M.; Michelangeli, A.

2017-12-01

The Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antonić and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide sufficient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples.

Investigation into the risk perceptions of investors in the securities of nuclear-dependent electric utilities

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

Spudeck, R.E.

1983-01-01

Two weeks prior to the Three Mile Island accident, March 15, 1979, the Nuclear Regulatory Commission ordered five operating nuclear plants shut down in order to reexamine safety standards in these plants. Reports in the popular and trade press during this time suggested that these events, particularly the accident at Three Mile Island, caused investors in the securities of electric utilities that had nuclear-generation facilities to revise their risk perceptions. This study was designed to examine the impact of both the Nuclear Regulatory Commission order and the accident at Three Mile Island on investor risk perceptions. Selected categories of electricmore » utilities were chosen to examine any differential risk effects resulting from these events. An asset pricing model devoid of many of the restrictive assumptions of more familiar models was used to model investor behavior. The findings suggest that the events described did cause investors to revise upward their perceptions of systematic risk regarding different categories of electric utilities. More specifically, those electric utilities that were operating nuclear plants in 1979 experienced the largest and most sustained increase in systematic risk. However, electric utilities that in 1979 had no operating nuclear plants, but had planned and committed funds for nuclear plants in the future, also experienced increases in systematic risk.« less

Refractive index of He in the region 920-1910 A

NASA Technical Reports Server (NTRS)

Huber, M. C. E.; Tondello, G.

1974-01-01

The refractive index of He has been determined in the region 920-1910 A by measurements of wavelength shifts in a 3-m spectrograph alternately filled with He and evacuated. Differential pumping systems were used to allow operation of the light source at conveniently low pressures. Several plates were measured and analyzed in order to reduce statistical errors. The results at 919 A agree with the theory within 1%, i.e., less than the experimental error.

Massively Parallel Rogue Cell Detection Using Serial Time-Encoded Amplified Microscopy of Inertially Ordered Cells in High-Throughput Flow

DTIC Science & Technology

2012-08-01

techniques and STEAM imager. It couples the high-speed capability of the STEAM imager and differential phase contrast imaging of DIC / Nomarski microscopy...On 10 TPE chips, we obtained 9 homogenous and strong bonds, the failed bond being due to operator error and presence of air bubbles in the TPE...instruments, structural dynamics, and microelectromechanical systems (MEMS) via laser-scanning surface vibrometry , and observation of biomechanical motility

Computer simulation of space station computer steered high gain antenna

NASA Technical Reports Server (NTRS)

Beach, S. W.

1973-01-01

The mathematical modeling and programming of a complete simulation program for a space station computer-steered high gain antenna are described. The program provides for reading input data cards, numerically integrating up to 50 first order differential equations, and monitoring up to 48 variables on printed output and on plots. The program system consists of a high gain antenna, an antenna gimbal control system, an on board computer, and the environment in which all are to operate.

Lithographically-Scribed Planar Holographic Optical CDMA Devices and Systems

DTIC Science & Technology

2007-02-15

operate with quite high refractive index contrast (order 0.5). Thin -filn filter devices are viewed as relatively low in chromatic dispersion. We have...stack consists of planar interfaces between materials of refractive index n, and n,. Let An = In2 - nil and n = (n, - n1)/2. The planar interfaces are... index ). It may be desirable to have a relatively large refractive index differential when diffractive elements are formed from cladding material at a

Riemann-Liouville Fractional Calculus of Certain Finite Class of Classical Orthogonal Polynomials

NASA Astrophysics Data System (ADS)

Malik, Pradeep; Swaminathan, A.

2010-11-01

In this work we consider certain class of classical orthogonal polynomials defined on the positive real line. These polynomials have their weight function related to the probability density function of F distribution and are finite in number up to orthogonality. We generalize these polynomials for fractional order by considering the Riemann-Liouville type operator on these polynomials. Various properties like explicit representation in terms of hypergeometric functions, differential equations, recurrence relations are derived.

Influence of Strain on Thermal Conductivity of Silicon Nitride Thin Films

DTIC Science & Technology

2012-03-02

free path of amorphous materials is of the same order as the structural disorder [46], rendering thermal conductivity size independent. Here, the phases...16] Manninen A J, Leivo M M and Pekola J P 1997 Refrigeration of a dielectric membrane by superconductor /insulator/ normal-metal/insulator... superconductor tunneling Appl. Phys. Lett. 70 1885–7 [17] Olson E A et al 2003 The design and operation of a MEMS differential scanning nanocalorimeter for high

FAST TRACK COMMUNICATION: On the Liouvillian solution of second-order linear differential equations and algebraic invariant curves

NASA Astrophysics Data System (ADS)

Man, Yiu-Kwong

2010-10-01

In this communication, we present a method for computing the Liouvillian solution of second-order linear differential equations via algebraic invariant curves. The main idea is to integrate Kovacic's results on second-order linear differential equations with the Prelle-Singer method for computing first integrals of differential equations. Some examples on using this approach are provided.

Large liquid rocket engine transient performance simulation system

NASA Technical Reports Server (NTRS)

Mason, J. R.; Southwick, R. D.

1991-01-01

A simulation system, ROCETS, was designed and developed to allow cost-effective computer predictions of liquid rocket engine transient performance. The system allows a user to generate a simulation of any rocket engine configuration using component modules stored in a library through high-level input commands. The system library currently contains 24 component modules, 57 sub-modules and maps, and 33 system routines and utilities. FORTRAN models from other sources can be operated in the system upon inclusion of interface information on comment cards. Operation of the simulation is simplified for the user by run, execution, and output processors. The simulation system makes available steady-state trim balance, transient operation, and linear partial generation. The system utilizes a modern equation solver for efficient operation of the simulations. Transient integration methods include integral and differential forms for the trapezoidal, first order Gear, and second order Gear corrector equations. A detailed technology test bed engine (TTBE) model was generated to be used as the acceptance test of the simulation system. The general level of model detail was that reflected in the Space Shuttle Main Engine DTM. The model successfully obtained steady-state balance in main stage operation and simulated throttle transients, including engine starts and shutdown. A NASA FORTRAN control model was obtained, ROCETS interface installed in comment cards, and operated with the TTBE model in closed-loop transient mode.

Lagrangian particle method for compressible fluid dynamics

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Wang, Xingyu; Chen, Hsin-Chiang

2018-06-01

A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface/multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremal points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free interfaces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order. The method is generalizable to coupled hyperbolic-elliptic systems. Numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.

Harmonic component detection: Optimized Spectral Kurtosis for operational modal analysis

NASA Astrophysics Data System (ADS)

Dion, J.-L.; Tawfiq, I.; Chevallier, G.

2012-01-01

This work is a contribution in the field of Operational Modal Analysis to identify the modal parameters of mechanical structures using only measured responses. The study deals with structural responses coupled with harmonic components amplitude and frequency modulated in a short range, a common combination for mechanical systems with engines and other rotating machines in operation. These harmonic components generate misleading data interpreted erroneously by the classical methods used in OMA. The present work attempts to differentiate maxima in spectra stemming from harmonic components and structural modes. The detection method proposed is based on the so-called Optimized Spectral Kurtosis and compared with others definitions of Spectral Kurtosis described in the literature. After a parametric study of the method, a critical study is performed on numerical simulations and then on an experimental structure in operation in order to assess the method's performance.

Some properties for integro-differential operator defined by a fractional formal.

PubMed

Abdulnaby, Zainab E; Ibrahim, Rabha W; Kılıçman, Adem

2016-01-01

Recently, the study of the fractional formal (operators, polynomials and classes of special functions) has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator [Formula: see text] defined by a fractional formal (fractional differential operator) and study some its geometric properties by employing it in new subclasses of analytic univalent functions.

Given a one-step numerical scheme, on which ordinary differential equations is it exact?

NASA Astrophysics Data System (ADS)

Villatoro, Francisco R.

2009-01-01

A necessary condition for a (non-autonomous) ordinary differential equation to be exactly solved by a one-step, finite difference method is that the principal term of its local truncation error be null. A procedure to determine some ordinary differential equations exactly solved by a given numerical scheme is developed. Examples of differential equations exactly solved by the explicit Euler, implicit Euler, trapezoidal rule, second-order Taylor, third-order Taylor, van Niekerk's second-order rational, and van Niekerk's third-order rational methods are presented.

Efficient spectral-Galerkin algorithms for direct solution for second-order differential equations using Jacobi polynomials

NASA Astrophysics Data System (ADS)

Doha, E.; Bhrawy, A.

2006-06-01

It is well known that spectral methods (tau, Galerkin, collocation) have a condition number of ( is the number of retained modes of polynomial approximations). This paper presents some efficient spectral algorithms, which have a condition number of , based on the Jacobi?Galerkin methods of second-order elliptic equations in one and two space variables. The key to the efficiency of these algorithms is to construct appropriate base functions, which lead to systems with specially structured matrices that can be efficiently inverted. The complexities of the algorithms are a small multiple of operations for a -dimensional domain with unknowns, while the convergence rates of the algorithms are exponentials with smooth solutions.

Performing differential operation with a silver dendritic metasurface at visible wavelengths.

PubMed

Chen, Huan; An, Di; Li, Zhenchun; Zhao, Xiaopeng

2017-10-30

We design a reflective silver dendritic metasurface that can perform differential operation at visible wavelengths. The metasurface consists of an upper layer of silver dendritic structures, a silica spacer, and a lower layer of silver film. Simulation results show that the metasurface can realize differential operation in red, yellow, and green bands. Such a functionality is readily extended to infrared and communication wavelengths. The metasurface samples that respond to green and red bands are prepared by using the electrochemical deposition method, and their differential operation properties are proved through tests. Silver dendritic metasurfaces that can conduct the mathematical operation in visible light pave the way for realizing miniaturized, integratable all-optical information processing systems. Their differentiation functionality, which is used for real-time ultra-fast edge detection, image contrast enhancement, hidden object detection, and other practical applications, has a great development potential.

Differential Calculus on h-Deformed Spaces

NASA Astrophysics Data System (ADS)

Herlemont, Basile; Ogievetsky, Oleg

2017-10-01

We construct the rings of generalized differential operators on the h-deformed vector space of gl-type. In contrast to the q-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ring of h-deformed differential operators {Diff}_{h},σ(n) is labeled by a rational function σ in n variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system and describe some properties of the rings {Diff}_{h},σ(n).

Conformally Invariant Powers of the Laplacian, Q-Curvature, and Tractor Calculus

NASA Astrophysics Data System (ADS)

Gover, A. Rod; Peterson, Lawrence J.

We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS operators due to C.R. Graham et alia. These differential operators have leading part a power of the Laplacian. Conformal tractor calculus is the natural induced bundle calculus associated to the conformal Cartan connection. Applications discussed include standard formulae for these operators in terms of the Levi-Civita connection and its curvature and a direct definition and formula for T. Branson's so-called Q-curvature (which integrates to a global conformal invariant) as well as generalisations of the operators and the Q-curvature. Among examples, the operators of order 4, 6 and 8 and the related Q-curvatures are treated explicitly. The algorithm exploits the ambient metric construction of Fefferman and Graham and includes a procedure for converting the ambient curvature and its covariant derivatives into tractor calculus expressions. This is partly based on [12], where the relationship of the normal standard tractor bundle to the ambient construction is described.

Modeling Ability Differentiation in the Second-Order Factor Model

ERIC Educational Resources Information Center

Molenaar, Dylan; Dolan, Conor V.; van der Maas, Han L. J.

2011-01-01

In this article we present factor models to test for ability differentiation. Ability differentiation predicts that the size of IQ subtest correlations decreases as a function of the general intelligence factor. In the Schmid-Leiman decomposition of the second-order factor model, we model differentiation by introducing heteroscedastic residuals,…

A new medical image segmentation model based on fractional order differentiation and level set

NASA Astrophysics Data System (ADS)

Chen, Bo; Huang, Shan; Xie, Feifei; Li, Lihong; Chen, Wensheng; Liang, Zhengrong

2018-03-01

Segmenting medical images is still a challenging task for both traditional local and global methods because the image intensity inhomogeneous. In this paper, two contributions are made: (i) on the one hand, a new hybrid model is proposed for medical image segmentation, which is built based on fractional order differentiation, level set description and curve evolution; and (ii) on the other hand, three popular definitions of Fourier-domain, Grünwald-Letnikov (G-L) and Riemann-Liouville (R-L) fractional order differentiation are investigated and compared through experimental results. Because of the merits of enhancing high frequency features of images and preserving low frequency features of images in a nonlinear manner by the fractional order differentiation definitions, one fractional order differentiation definition is used in our hybrid model to perform segmentation of inhomogeneous images. The proposed hybrid model also integrates fractional order differentiation, fractional order gradient magnitude and difference image information. The widely-used dice similarity coefficient metric is employed to evaluate quantitatively the segmentation results. Firstly, experimental results demonstrated that a slight difference exists among the three expressions of Fourier-domain, G-L, RL fractional order differentiation. This outcome supports our selection of one of the three definitions in our hybrid model. Secondly, further experiments were performed for comparison between our hybrid segmentation model and other existing segmentation models. A noticeable gain was seen by our hybrid model in segmenting intensity inhomogeneous images.

Biological strategy for the fabrication of highly ordered aragonite helices: the microstructure of the cavolinioidean gastropods

PubMed Central

Checa, Antonio G.; Macías-Sánchez, Elena; Ramírez-Rico, Joaquín

2016-01-01

The Cavolinioidea are planktonic gastropods which construct their shells with the so-called aragonitic helical fibrous microstructure, consisting of a highly ordered arrangement of helically coiled interlocking continuous crystalline aragonite fibres. Our study reveals that, despite the high and continuous degree of interlocking between fibres, every fibre has a differentiated organic-rich thin external band, which is never invaded by neighbouring fibres. In this way, fibres avoid extinction. These intra-fibre organic-rich bands appear on the growth surface of the shell as minuscule elevations, which have to be secreted differentially by the outer mantle cells. We propose that, as the shell thickens during mineralization, fibre secretion proceeds by a mechanism of contact recognition and displacement of the tips along circular trajectories by the cells of the outer mantle surface. Given the sizes of the tips, this mechanism has to operate at the subcellular level. Accordingly, the fabrication of the helical microstructure is under strict biological control. This mechanism of fibre-by-fibre fabrication by the mantle cells is unlike that any other shell microstructure. PMID:27181457

Operant Variability: A Conceptual Analysis

ERIC Educational Resources Information Center

Barba, Lourenco de Souza

2012-01-01

Some researchers claim that variability is an operant dimension of behavior. The present paper reviews the concept of operant behavior and emphasizes that differentiation is the behavioral process that demonstrates an operant relation. Differentiation is conceived as change in the overlap between two probability distributions: the distribution of…

Enhanced differential evolution to combine optical mouse sensor with image structural patches for robust endoscopic navigation.

PubMed

Luo, Xiongbiao; Jayarathne, Uditha L; McLeod, A Jonathan; Mori, Kensaku

2014-01-01

Endoscopic navigation generally integrates different modalities of sensory information in order to continuously locate an endoscope relative to suspicious tissues in the body during interventions. Current electromagnetic tracking techniques for endoscopic navigation have limited accuracy due to tissue deformation and magnetic field distortion. To avoid these limitations and improve the endoscopic localization accuracy, this paper proposes a new endoscopic navigation framework that uses an optical mouse sensor to measure the endoscope movements along its viewing direction. We then enhance the differential evolution algorithm by modifying its mutation operation. Based on the enhanced differential evolution method, these movement measurements and image structural patches in endoscopic videos are fused to accurately determine the endoscope position. An evaluation on a dynamic phantom demonstrated that our method provides a more accurate navigation framework. Compared to state-of-the-art methods, it improved the navigation accuracy from 2.4 to 1.6 mm and reduced the processing time from 2.8 to 0.9 seconds.

Stability of elastic bending and torsion of uniform cantilever rotor blades in hover with variable structural coupling

NASA Technical Reports Server (NTRS)

Hodges, D. H., Roberta.

1976-01-01

The stability of elastic flap bending, lead-lag bending, and torsion of uniform, untwisted, cantilever rotor blades without chordwise offsets between the elastic, mass, tension, and areodynamic center axes is investigated for the hovering flight condition. The equations of motion are obtained by simplifying the general, nonlinear, partial differential equations of motion of an elastic rotating cantilever blade. The equations are adapted for a linearized stability analysis in the hovering flight condition by prescribing aerodynamic forces, applying Galerkin's method, and linearizing the resulting ordinary differential equations about the equilibrium operating condition. The aerodynamic forces are obtained from strip theory based on a quasi-steady approximation of two-dimensional unsteady airfoil theory. Six coupled mode shapes, calculated from free vibration about the equilibrium operating condition, are used in the linearized stability analysis. The study emphasizes the effects of two types of structural coupling that strongly influence the stability of hingeless rotor blades. The first structural coupling is the linear coupling between flap and lead-lag bending of the rotor blade. The second structural coupling is a nonlinear coupling between flap bending, lead-lag bending, and torsion deflections. Results are obtained for a wide variety of hingeless rotor configurations and operating conditions in order to provide a reasonably complete picture of hingeless rotor blade stability characteristics.

Mixed mimetic spectral element method for Stokes flow: A pointwise divergence-free solution

NASA Astrophysics Data System (ADS)

Kreeft, Jasper; Gerritsma, Marc

2013-05-01

In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in Kreeft et al. [51] is a higher-order method for curvilinear quadrilaterals and hexahedrals. Fundamental is the underlying structure of oriented geometric objects, the relation between these objects through the boundary operator and how this defines the exterior derivative, representing the grad, curl and div, through the generalized Stokes theorem. The mimetic method presented here uses the language of differential k-forms with k-cochains as their discrete counterpart, and the relations between them in terms of the mimetic operators: reduction, reconstruction and projection. The reconstruction consists of the recently developed mimetic spectral interpolation functions. The most important result of the mimetic framework is the commutation between differentiation at the continuous level with that on the finite dimensional and discrete level. As a result operators like gradient, curl and divergence are discretized exactly. For Stokes flow, this implies a pointwise divergence-free solution. This is confirmed using a set of test cases on both Cartesian and curvilinear meshes. It will be shown that the method converges optimally for all admissible boundary conditions.

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.

Multigrid treatment of implicit continuum diffusion

NASA Astrophysics Data System (ADS)

Francisquez, Manaure; Zhu, Ben; Rogers, Barrett

2017-10-01

Implicit treatment of diffusive terms of various differential orders common in continuum mechanics modeling, such as computational fluid dynamics, is investigated with spectral and multigrid algorithms in non-periodic 2D domains. In doubly periodic time dependent problems these terms can be efficiently and implicitly handled by spectral methods, but in non-periodic systems solved with distributed memory parallel computing and 2D domain decomposition, this efficiency is lost for large numbers of processors. We built and present here a multigrid algorithm for these types of problems which outperforms a spectral solution that employs the highly optimized FFTW library. This multigrid algorithm is not only suitable for high performance computing but may also be able to efficiently treat implicit diffusion of arbitrary order by introducing auxiliary equations of lower order. We test these solvers for fourth and sixth order diffusion with idealized harmonic test functions as well as a turbulent 2D magnetohydrodynamic simulation. It is also shown that an anisotropic operator without cross-terms can improve model accuracy and speed, and we examine the impact that the various diffusion operators have on the energy, the enstrophy, and the qualitative aspect of a simulation. This work was supported by DOE-SC-0010508. This research used resources of the National Energy Research Scientific Computing Center (NERSC).

7 CFR 1126.51 - Class I differential and price.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Class I differential and price. 1126.51 Section 1126.51... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE SOUTHWEST MARKETING AREA Order Regulating Handling Class Prices § 1126.51 Class I differential and price. The Class I differential shall be the...

7 CFR 1131.51 - Class I differential and price.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Class I differential and price. 1131.51 Section 1131.51... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE ARIZONA MARKETING AREA Order Regulating Handling Class Prices § 1131.51 Class I differential and price. The Class I differential shall be the...

7 CFR 1126.51 - Class I differential and price.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Class I differential and price. 1126.51 Section 1126.51... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE SOUTHWEST MARKETING AREA Order Regulating Handling Class Prices § 1126.51 Class I differential and price. The Class I differential shall be the...

7 CFR 1033.51 - Class I differential and price.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Class I differential and price. 1033.51 Section 1033.51... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE MIDEAST MARKETING AREA Order Regulating Handling Class Prices § 1033.51 Class I differential and price. The Class I differential shall be the...

7 CFR 1030.51 - Class I differential and price.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Class I differential and price. 1030.51 Section 1030.51... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE UPPER MIDWEST MARKETING AREA Order Regulating Handling Class Prices § 1030.51 Class I differential and price. The Class I differential shall be...

7 CFR 1001.51 - Class I differential and price.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Class I differential and price. 1001.51 Section 1001.51... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE NORTHEAST MARKETING AREA Order Regulating Handling Class Prices § 1001.51 Class I differential and price. The Class I differential shall be the...

7 CFR 1030.51 - Class I differential and price.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Class I differential and price. 1030.51 Section 1030.51... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE UPPER MIDWEST MARKETING AREA Order Regulating Handling Class Prices § 1030.51 Class I differential and price. The Class I differential shall be...

7 CFR 1124.51 - Class I differential and price.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Class I differential and price. 1124.51 Section 1124.51... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE PACIFIC NORTHWEST MARKETING AREA Order Regulating Handling Class Prices § 1124.51 Class I differential and price. The Class I differential shall be...

7 CFR 1032.51 - Class I differential and price.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Class I differential and price. 1032.51 Section 1032.51... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE CENTRAL MARKETING AREA Order Regulating Handling Class Prices § 1032.51 Class I differential and price. The Class I differential shall be the...

7 CFR 1033.51 - Class I differential and price.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Class I differential and price. 1033.51 Section 1033.51... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE MIDEAST MARKETING AREA Order Regulating Handling Class Prices § 1033.51 Class I differential and price. The Class I differential shall be the...

7 CFR 1032.51 - Class I differential and price.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Class I differential and price. 1032.51 Section 1032.51... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE CENTRAL MARKETING AREA Order Regulating Handling Class Prices § 1032.51 Class I differential and price. The Class I differential shall be the...

7 CFR 1131.51 - Class I differential and price.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Class I differential and price. 1131.51 Section 1131.51... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE ARIZONA MARKETING AREA Order Regulating Handling Class Prices § 1131.51 Class I differential and price. The Class I differential shall be the...

7 CFR 1124.51 - Class I differential and price.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Class I differential and price. 1124.51 Section 1124.51... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE PACIFIC NORTHWEST MARKETING AREA Order Regulating Handling Class Prices § 1124.51 Class I differential and price. The Class I differential shall be...

7 CFR 1001.51 - Class I differential and price.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Class I differential and price. 1001.51 Section 1001.51... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE NORTHEAST MARKETING AREA Order Regulating Handling Class Prices § 1001.51 Class I differential and price. The Class I differential shall be the...

Informed Conjecturing of Solutions for Differential Equations in a Modeling Context

ERIC Educational Resources Information Center

Winkel, Brian

2015-01-01

We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…

Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

NASA Technical Reports Server (NTRS)

Lucia, David J.; Beran, Philip S.; Silva, Walter A.

2003-01-01

This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The out-come of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the uid. For this research, the structural modes are sine waves of varying frequency, and the Volterra-POD approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms which are impulsed as part of the uid model realization. Using this approach, structural and uid operators are coupled into a single aeroelastic operator. This coupling converts a free boundary uid problem into an initial value problem, while preserving the parameter (or parameters) of interest for sensitivity analysis. The approach is applied to an elastic panel in supersonic cross ow. The hybrid Volterra-POD approach provides a low-order uid model in state-space form. The linear uid model is tightly coupled with a nonlinear panel model using an implicit integration scheme. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed for this research using traditional uid and structural solvers.

Order out of Randomness: Self-Organization Processes in Astrophysics

NASA Astrophysics Data System (ADS)

Aschwanden, Markus J.; Scholkmann, Felix; Béthune, William; Schmutz, Werner; Abramenko, Valentina; Cheung, Mark C. M.; Müller, Daniel; Benz, Arnold; Chernov, Guennadi; Kritsuk, Alexei G.; Scargle, Jeffrey D.; Melatos, Andrew; Wagoner, Robert V.; Trimble, Virginia; Green, William H.

2018-03-01

Self-organization is a property of dissipative nonlinear processes that are governed by a global driving force and a local positive feedback mechanism, which creates regular geometric and/or temporal patterns, and decreases the entropy locally, in contrast to random processes. Here we investigate for the first time a comprehensive number of (17) self-organization processes that operate in planetary physics, solar physics, stellar physics, galactic physics, and cosmology. Self-organizing systems create spontaneous " order out of randomness", during the evolution from an initially disordered system to an ordered quasi-stationary system, mostly by quasi-periodic limit-cycle dynamics, but also by harmonic (mechanical or gyromagnetic) resonances. The global driving force can be due to gravity, electromagnetic forces, mechanical forces (e.g., rotation or differential rotation), thermal pressure, or acceleration of nonthermal particles, while the positive feedback mechanism is often an instability, such as the magneto-rotational (Balbus-Hawley) instability, the convective (Rayleigh-Bénard) instability, turbulence, vortex attraction, magnetic reconnection, plasma condensation, or a loss-cone instability. Physical models of astrophysical self-organization processes require hydrodynamic, magneto-hydrodynamic (MHD), plasma, or N-body simulations. Analytical formulations of self-organizing systems generally involve coupled differential equations with limit-cycle solutions of the Lotka-Volterra or Hopf-bifurcation type.

[Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (1)].

PubMed

Murase, Kenya

2014-01-01

Utilization of differential equations and methods for solving them in medical physics are presented. First, the basic concept and the kinds of differential equations were overviewed. Second, separable differential equations and well-known first-order and second-order differential equations were introduced, and the methods for solving them were described together with several examples. In the next issue, the symbolic and series expansion methods for solving differential equations will be mainly introduced.

A novel interval type-2 fractional order fuzzy PID controller: Design, performance evaluation, and its optimal time domain tuning.

PubMed

Kumar, Anupam; Kumar, Vijay

2017-05-01

In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Differential formulation of the gyrokinetic Landau operator

DOE PAGES

Hirvijoki, Eero; Brizard, Alain J.; Pfefferlé, David

2017-01-05

Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the so-called Landau representation, this work investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Finally, based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent.

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

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

Du, Qiang, E-mail: jyanghkbu@gmail.com; Yang, Jiang, E-mail: qd2125@columbia.edu

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simplemore » ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.« less

The application of NAVSTAR Differential GPS to civil helicopter operations

NASA Technical Reports Server (NTRS)

Beser, J.; Parkinson, B. W.

1981-01-01

Principles concerning the operation of the NAVSTAR Global Positioning Systems (GPS) are discussed. Selective availability issues concerning NAVSTAR GPS and differential GPS concepts are analyzed. Civil support and market potential for differential GPS are outlined. It is concluded that differential GPS provides a variation on the baseline GPS system, and gives an assured, uninterrupted level of accuracy for the civilian community.

True amplitude wave equation migration arising from true amplitude one-way wave equations

NASA Astrophysics Data System (ADS)

Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

2003-10-01

One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition to these newly defined wavefields in heterogeneous media leads to the Kirchhoff inversion formula for common-shot data when the one-way wavefields are replaced by their ray theoretic approximations. This extension enhances the original WEM method. The objective of that technique was a reflector map, only. The underlying theory did not address amplitude issues. Computer output obtained using numerically generated data confirms the accuracy of this inversion method. However, there are practical limitations. The observed data must be a solution of the wave equation. Therefore, the data over the entire survey area must be collected from a single common-shot experiment. Multi-experiment data, such as common-offset data, cannot be used with this method as currently formulated. Research on extending the method is ongoing at this time.

Position dependent mass Schroedinger equation and isospectral potentials: Intertwining operator approach

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

Midya, Bikashkali; Roy, B.; Roychoudhury, R.

2010-02-15

Here, we have studied first- and second-order intertwining approaches to generate isospectral partner potentials of position dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as second-order linear differential operator with position dependent coefficients, and the system of equations arising from the intertwining relationship is solved for the coefficients by taking an ansatz. A complete scheme for obtaining general solution is obtained, which is valid for any arbitrary potential and mass function. The proposed technique allows us to generate isospectral potentials with the following spectral modifications: (i) to add new bound state(s), (ii) to removemore » bound state(s), and (iii) to leave the spectrum unaffected. To explain our findings with the help of an illustration, we have used point canonical transformation to obtain the general solution of the position dependent mass Schrodinger equation corresponding to a potential and mass function. It is shown that our results are consistent with the formulation of type A N-fold supersymmetry [T. Tanaka, J. Phys. A 39, 219 (2006); A. Gonzalez-Lopez and T. Tanaka, J. Phys. A 39, 3715 (2006)] for the particular cases N=1 and N=2, respectively.« less

The theory of pseudo-differential operators on the noncommutative n-torus

NASA Astrophysics Data System (ADS)

Tao, J.

2018-02-01

The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct analogy with the theory of pseudo-differential operators on finite-dimensional real vector spaces, one may derive a similar pseudo-differential calculus on noncommutative n-tori, and with the development of this calculus came many results concerning the local differential geometry of noncommutative tori for n=2,4, as shown in the groundbreaking paper in which the Gauss-Bonnet theorem on the noncommutative two-torus is proved and later papers. Certain details of the proofs in the original derivation of the calculus were omitted, such as the evaluation of oscillatory integrals, so we make it the objective of this paper to fill in all the details. After reproving in more detail the formula for the symbol of the adjoint of a pseudo-differential operator and the formula for the symbol of a product of two pseudo-differential operators, we extend these results to finitely generated projective right modules over the noncommutative n-torus. Then we define the corresponding analog of Sobolev spaces and prove equivalents of the Sobolev and Rellich lemmas.

A highly linear fully integrated powerline filter for biopotential acquisition systems.

PubMed

Alzaher, Hussain A; Tasadduq, Noman; Mahnashi, Yaqub

2013-10-01

Powerline interference is one of the most dominant problems in detection and processing of biopotential signals. This work presents a new fully integrated notch filter exhibiting high linearity and low power consumption. High filter linearity is preserved utilizing active-RC approach while IC implementation is achieved through replacing passive resistors by R-2R ladders achieving area saving of approximately 120 times. The filter design is optimized for low power operation using an efficient circuit topology and an ultra-low power operational amplifier. Fully differential implementation of the proposed filter shows notch depth of 43 dB (78 dB for 4th-order) with THD of better than -70 dB while consuming about 150 nW from 1.5 V supply.

[Operative treatment strategies for multiple trauma patients : early total care versus damage control].

PubMed

Klüter, T; Lippross, S; Oestern, S; Weuster, M; Seekamp, A

2013-09-01

The treatment of multiple trauma patients is a great challenge for an interdisciplinary team. After preclinical care and subsequent treatment in the emergency room the order of the interventions is prioritized depending of the individual risk stratification. For planning the surgery management it is essential to distinguish between absolutely essential operations to prevent life-threatening situations for the patient and interventions with shiftable indications, depending on the general condition of the patient. All interventions need to be done without causing significant secondary damage to prohibit hyperinflammation and systemic inflammatory response syndrome. The challenge consists in determination of the appropriate treatment at the right point in time. In general the early primary intervention, early total care, is differentiated from the damage control concept.

Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading

NASA Astrophysics Data System (ADS)

Gholami, Raheb; Ansari, Reza

2018-02-01

This article presents an attempt to study the nonlinear resonance of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates excited by a uniformly distributed harmonic transverse load. To this purpose, first, the extended rule of mixture including the efficiency parameters is employed to approximately obtain the effective material properties of FG-CNTRC annular sector plates. Then, the focus is on presenting the weak form of discretized mathematical formulation of governing equations based on the variational differential quadrature (VDQ) method and Hamilton's principle. The geometric nonlinearity and shear deformation effects are considered based on the von Kármán assumptions and Reddy's third-order shear deformation plate theory, respectively. The discretization process is performed via the generalized differential quadrature (GDQ) method together with numerical differential and integral operators. Then, an efficient multi-step numerical scheme is used to obtain the nonlinear dynamic behavior of the FG-CNTRC annular sector plates near their primary resonance as the frequency-response curve. The accuracy of the present results is first verified and then a parametric study is presented to show the impacts of CNT volume fraction, CNT distribution pattern, geometry of annular sector plate and sector angle on the nonlinear frequency-response curve of FG-CNTRC annular sector plates with different edge supports.

Utilization of the Discrete Differential Evolution for Optimization in Multidimensional Point Clouds.

PubMed

Uher, Vojtěch; Gajdoš, Petr; Radecký, Michal; Snášel, Václav

2016-01-01

The Differential Evolution (DE) is a widely used bioinspired optimization algorithm developed by Storn and Price. It is popular for its simplicity and robustness. This algorithm was primarily designed for real-valued problems and continuous functions, but several modified versions optimizing both integer and discrete-valued problems have been developed. The discrete-coded DE has been mostly used for combinatorial problems in a set of enumerative variants. However, the DE has a great potential in the spatial data analysis and pattern recognition. This paper formulates the problem as a search of a combination of distinct vertices which meet the specified conditions. It proposes a novel approach called the Multidimensional Discrete Differential Evolution (MDDE) applying the principle of the discrete-coded DE in discrete point clouds (PCs). The paper examines the local searching abilities of the MDDE and its convergence to the global optimum in the PCs. The multidimensional discrete vertices cannot be simply ordered to get a convenient course of the discrete data, which is crucial for good convergence of a population. A novel mutation operator utilizing linear ordering of spatial data based on the space filling curves is introduced. The algorithm is tested on several spatial datasets and optimization problems. The experiments show that the MDDE is an efficient and fast method for discrete optimizations in the multidimensional point clouds.

Utilization of the Discrete Differential Evolution for Optimization in Multidimensional Point Clouds

PubMed Central

Radecký, Michal; Snášel, Václav

2016-01-01

The Differential Evolution (DE) is a widely used bioinspired optimization algorithm developed by Storn and Price. It is popular for its simplicity and robustness. This algorithm was primarily designed for real-valued problems and continuous functions, but several modified versions optimizing both integer and discrete-valued problems have been developed. The discrete-coded DE has been mostly used for combinatorial problems in a set of enumerative variants. However, the DE has a great potential in the spatial data analysis and pattern recognition. This paper formulates the problem as a search of a combination of distinct vertices which meet the specified conditions. It proposes a novel approach called the Multidimensional Discrete Differential Evolution (MDDE) applying the principle of the discrete-coded DE in discrete point clouds (PCs). The paper examines the local searching abilities of the MDDE and its convergence to the global optimum in the PCs. The multidimensional discrete vertices cannot be simply ordered to get a convenient course of the discrete data, which is crucial for good convergence of a population. A novel mutation operator utilizing linear ordering of spatial data based on the space filling curves is introduced. The algorithm is tested on several spatial datasets and optimization problems. The experiments show that the MDDE is an efficient and fast method for discrete optimizations in the multidimensional point clouds. PMID:27974884

Solving Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Krogh, F. T.

1987-01-01

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Differentiation of Low- and High-Grade Pediatric Brain Tumors with High b-Value Diffusion-weighted MR Imaging and a Fractional Order Calculus Model

PubMed Central

Sui, Yi; Wang, He; Liu, Guanzhong; Damen, Frederick W.; Wanamaker, Christian; Li, Yuhua

2015-01-01

Purpose To demonstrate that a new set of parameters (D, β, and μ) from a fractional order calculus (FROC) diffusion model can be used to improve the accuracy of MR imaging for differentiating among low- and high-grade pediatric brain tumors. Materials and Methods The institutional review board of the performing hospital approved this study, and written informed consent was obtained from the legal guardians of pediatric patients. Multi-b-value diffusion-weighted magnetic resonance (MR) imaging was performed in 67 pediatric patients with brain tumors. Diffusion coefficient D, fractional order parameter β (which correlates with tissue heterogeneity), and a microstructural quantity μ were calculated by fitting the multi-b-value diffusion-weighted images to an FROC model. D, β, and μ values were measured in solid tumor regions, as well as in normal-appearing gray matter as a control. These values were compared between the low- and high-grade tumor groups by using the Mann-Whitney U test. The performance of FROC parameters for differentiating among patient groups was evaluated with receiver operating characteristic (ROC) analysis. Results None of the FROC parameters exhibited significant differences in normal-appearing gray matter (P ≥ .24), but all showed a significant difference (P < .002) between low- (D, 1.53 μm2/msec ± 0.47; β, 0.87 ± 0.06; μ, 8.67 μm ± 0.95) and high-grade (D, 0.86 μm2/msec ± 0.23; β, 0.73 ± 0.06; μ, 7.8 μm ± 0.70) brain tumor groups. The combination of D and β produced the largest area under the ROC curve (0.962) in the ROC analysis compared with individual parameters (β, 0.943; D,0.910; and μ, 0.763), indicating an improved performance for tumor differentiation. Conclusion The FROC parameters can be used to differentiate between low- and high-grade pediatric brain tumor groups. The combination of FROC parameters or individual parameters may serve as in vivo, noninvasive, and quantitative imaging markers for classifying pediatric brain tumors. © RSNA, 2015 PMID:26035586

Differentiating in Number & Operations: A Guide for Ongoing Assessment, Grouping Students, Targeting Instruction, and Adjusting Levels of Cognitive Demand

ERIC Educational Resources Information Center

Taylor-Cox, Jennifer

2008-01-01

Differentiating is good teaching. As a math intervention tool, it's power packed. And as a math acceleration instrument it's unbeatable. And differentiation doesn't have to be difficult. Not with "Differentiation in Number & Operations and the Other Math Content Standards, PreK-Grade 2". The author's five-volume series shows you easy and effective…

Rail-to-rail differential input amplification stage with main and surrogate differential pairs

DOEpatents

Britton, Jr., Charles Lanier; Smith, Stephen Fulton

2007-03-06

An operational amplifier input stage provides a symmetrical rail-to-rail input common-mode voltage without turning off either pair of complementary differential input transistors. Secondary, or surrogate, transistor pairs assume the function of the complementary differential transistors. The circuit also maintains essentially constant transconductance, constant slew rate, and constant signal-path supply current as it provides rail-to-rail operation.

Lagrangian particle method for compressible fluid dynamics

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

Samulyak, Roman; Wang, Xingyu; Chen, Hsin -Chiang

A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multi-phase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremalmore » points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free inter-faces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order . The method is generalizable to coupled hyperbolic-elliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.« less

Lagrangian particle method for compressible fluid dynamics

DOE PAGES

Samulyak, Roman; Wang, Xingyu; Chen, Hsin -Chiang

2018-02-09

A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multi-phase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremalmore » points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free inter-faces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order . The method is generalizable to coupled hyperbolic-elliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.« less

Fractional domain varying-order differential denoising method

NASA Astrophysics Data System (ADS)

Zhang, Yan-Shan; Zhang, Feng; Li, Bing-Zhao; Tao, Ran

2014-10-01

Removal of noise is an important step in the image restoration process, and it remains a challenging problem in image processing. Denoising is a process used to remove the noise from the corrupted image, while retaining the edges and other detailed features as much as possible. Recently, denoising in the fractional domain is a hot research topic. The fractional-order anisotropic diffusion method can bring a less blocky effect and preserve edges in image denoising, a method that has received much interest in the literature. Based on this method, we propose a new method for image denoising, in which fractional-varying-order differential, rather than constant-order differential, is used. The theoretical analysis and experimental results show that compared with the state-of-the-art fractional-order anisotropic diffusion method, the proposed fractional-varying-order differential denoising model can preserve structure and texture well, while quickly removing noise, and yields good visual effects and better peak signal-to-noise ratio.

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

PubMed

Grima, Ramon

2011-11-01

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

High-operating temperature MWIR photon detectors based on type II InAs/GaSb superlattice

NASA Astrophysics Data System (ADS)

Razeghi, Manijeh; Nguyen, Binh-Minh; Delaunay, Pierre-Yves; Abdollahi Pour, Siamak; Huang, Edward Kwei-wei; Manukar, Paritosh; Bogdanov, Simeon; Chen, Guanxi

2010-01-01

Recent efforts have been paid to elevate the operating temperature of Type II InAs/GaSb superlattice Mid Infrared photon detectors. Optimized growth parameters and interface engineering technique enable high quality material with a quantum efficiency above 50%. Intensive study on device architecture and doping profile has resulted in almost one order of magnitude of improvement to the electrical performance and lifted up the 300K-background BLIP operation temperature to 166K. At 77K, the ~4.2 μm cut-off devices exhibit a differential resistance area product in excess of the measurement system limit (106 Ohm.cm2) and a detectivity of 3x1013cm.Hz1/2/W. High quality focal plane arrays were demonstrated with a noise equivalent temperature of 10mK at 77K. Uncooled camera is capable to capture hot objects such as soldering iron.

A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods

NASA Astrophysics Data System (ADS)

Syrakos, Alexandros; Varchanis, Stylianos; Dimakopoulos, Yannis; Goulas, Apostolos; Tsamopoulos, John

2017-12-01

Finite volume methods (FVMs) constitute a popular class of methods for the numerical simulation of fluid flows. Among the various components of these methods, the discretisation of the gradient operator has received less attention despite its fundamental importance with regards to the accuracy of the FVM. The most popular gradient schemes are the divergence theorem (DT) (or Green-Gauss) scheme and the least-squares (LS) scheme. Both are widely believed to be second-order accurate, but the present study shows that in fact the common variant of the DT gradient is second-order accurate only on structured meshes whereas it is zeroth-order accurate on general unstructured meshes, and the LS gradient is second-order and first-order accurate, respectively. This is explained through a theoretical analysis and is confirmed by numerical tests. The schemes are then used within a FVM to solve a simple diffusion equation on unstructured grids generated by several methods; the results reveal that the zeroth-order accuracy of the DT gradient is inherited by the FVM as a whole, and the discretisation error does not decrease with grid refinement. On the other hand, use of the LS gradient leads to second-order accurate results, as does the use of alternative, consistent, DT gradient schemes, including a new iterative scheme that makes the common DT gradient consistent at almost no extra cost. The numerical tests are performed using both an in-house code and the popular public domain partial differential equation solver OpenFOAM.

A Model Parameter Extraction Method for Dielectric Barrier Discharge Ozone Chamber using Differential Evolution

NASA Astrophysics Data System (ADS)

Amjad, M.; Salam, Z.; Ishaque, K.

2014-04-01

In order to design an efficient resonant power supply for ozone gas generator, it is necessary to accurately determine the parameters of the ozone chamber. In the conventional method, the information from Lissajous plot is used to estimate the values of these parameters. However, the experimental setup for this purpose can only predict the parameters at one operating frequency and there is no guarantee that it results in the highest ozone gas yield. This paper proposes a new approach to determine the parameters using a search and optimization technique known as Differential Evolution (DE). The desired objective function of DE is set at the resonance condition and the chamber parameter values can be searched regardless of experimental constraints. The chamber parameters obtained from the DE technique are validated by experiment.

Dunkl-Darboux differential-difference operators

NASA Astrophysics Data System (ADS)

Khekalo, S. P.

2017-02-01

Using a natural generalization, we construct and study analogues of Dunkl differential-difference operators on the line. These analogues turn out to be closely connected with the so-called Burchnall- Chaundy-Adler-Moser polynomials and, therefore, with Darboux transforms. We find the eigenfunctions of these operators.

Higher-order automatic differentiation of mathematical functions

NASA Astrophysics Data System (ADS)

Charpentier, Isabelle; Dal Cappello, Claude

2015-04-01

Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

Convergence of damped inertial dynamics governed by regularized maximally monotone operators

NASA Astrophysics Data System (ADS)

Attouch, Hedy; Cabot, Alexandre

2018-06-01

In a Hilbert space setting, we study the asymptotic behavior, as time t goes to infinity, of the trajectories of a second-order differential equation governed by the Yosida regularization of a maximally monotone operator with time-varying positive index λ (t). The dissipative and convergence properties are attached to the presence of a viscous damping term with positive coefficient γ (t). A suitable tuning of the parameters γ (t) and λ (t) makes it possible to prove the weak convergence of the trajectories towards zeros of the operator. When the operator is the subdifferential of a closed convex proper function, we estimate the rate of convergence of the values. These results are in line with the recent articles by Attouch-Cabot [3], and Attouch-Peypouquet [8]. In this last paper, the authors considered the case γ (t) = α/t, which is naturally linked to Nesterov's accelerated method. We unify, and often improve the results already present in the literature.

Simultaneous source and attenuation reconstruction in SPECT using ballistic and single scattering data

NASA Astrophysics Data System (ADS)

Courdurier, M.; Monard, F.; Osses, A.; Romero, F.

2015-09-01

In medical single-photon emission computed tomography (SPECT) imaging, we seek to simultaneously obtain the internal radioactive sources and the attenuation map using not only ballistic measurements but also first-order scattering measurements and assuming a very specific scattering regime. The problem is modeled using the radiative transfer equation by means of an explicit non-linear operator that gives the ballistic and scattering measurements as a function of the radioactive source and attenuation distributions. First, by differentiating this non-linear operator we obtain a linearized inverse problem. Then, under regularity hypothesis for the source distribution and attenuation map and considering small attenuations, we rigorously prove that the linear operator is invertible and we compute its inverse explicitly. This allows proof of local uniqueness for the non-linear inverse problem. Finally, using the previous inversion result for the linear operator, we propose a new type of iterative algorithm for simultaneous source and attenuation recovery for SPECT based on the Neumann series and a Newton-Raphson algorithm.

Virtual Human Role Players for Studying Social Factors in Organizational Decision Making

PubMed Central

Khooshabeh, Peter; Lucas, Gale

2018-01-01

The cyber domain of military operations presents many challenges. A unique element is the social dynamic between cyber operators and their leadership because of the novel subject matter expertise involved in conducting technical cyber tasks, so there will be situations where senior leaders might have much less domain knowledge or no experience at all relative to the warfighters who report to them. Nonetheless, it will be important for junior cyber operators to convey convincing information relevant to a mission in order to persuade or influence a leader to make informed decisions. The power dynamic will make it difficult for the junior cyber operator to successfully influence a higher ranking leader. Here we present a perspective with a sketch for research paradigm(s) to study how different factors (normative vs. informational social influence, degree of transparency, and perceived appropriateness of making suggestions) might interact with differential social power dynamics of individuals in cyber decision-making contexts. Finally, we contextualize this theoretical perspective for the research paradigms in viable training technologies. PMID:29545759

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).

A predictive universal fractional-order differential model of wall-turbulence

NASA Astrophysics Data System (ADS)

Song, Fangying; Karniadakis, George

2017-11-01

Fractional calculus has been around for centuries but its use in computational since and engineering has emerged only recently. Here we develop a relatively simple one-dimensional model for fully-developed wall-turbulence that involves a fractional operator with variable fractional order. We use available DNS data bases to ``learn'' the function that describes the fractional order, which has a high value at the wall and decays monotonically to an asymptotic value at the centerline. We show that this function is universal upon re-scaling and hence it can be used to predict the mean velocity profile at all Reynolds numbers. We demonstrate the accuracy of our universal fractional model for channel flow at high Reynolds number as well as for pipe flow and we obtain good agreement with the Princeton super-pipe data up to Reynolds numbers 35,000,000. This work was supported by an ARO MURI Number: W911NF-15-1-0562.

A Fourier spectral-discontinuous Galerkin method for time-dependent 3-D Schrödinger-Poisson equations with discontinuous potentials

NASA Astrophysics Data System (ADS)

Lu, Tiao; Cai, Wei

2008-10-01

In this paper, we propose a high order Fourier spectral-discontinuous Galerkin method for time-dependent Schrödinger-Poisson equations in 3-D spaces. The Fourier spectral Galerkin method is used for the two periodic transverse directions and a high order discontinuous Galerkin method for the longitudinal propagation direction. Such a combination results in a diagonal form for the differential operators along the transverse directions and a flexible method to handle the discontinuous potentials present in quantum heterojunction and supperlattice structures. As the derivative matrices are required for various time integration schemes such as the exponential time differencing and Crank Nicholson methods, explicit derivative matrices of the discontinuous Galerkin method of various orders are derived. Numerical results, using the proposed method with various time integration schemes, are provided to validate the method.

Conforming and nonconforming virtual element methods for elliptic problems

DOE PAGES

Cangiani, Andrea; Manzini, Gianmarco; Sutton, Oliver J.

2016-08-03

Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general second-order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and nonsymmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H 1- and L 2-error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.

Gas Chromatic Mass Spectrometer

NASA Technical Reports Server (NTRS)

Wey, Chowen

1995-01-01

Gas chromatograph/mass spectrometer (GC/MS) used to measure and identify combustion species present in trace concentration. Advanced extractive diagnostic method measures to parts per billion (PPB), as well as differentiates between different types of hydrocarbons. Applicable for petrochemical, waste incinerator, diesel transporation, and electric utility companies in accurately monitoring types of hydrocarbon emissions generated by fuel combustion, in order to meet stricter environmental requirements. Other potential applications include manufacturing processes requiring precise detection of toxic gaseous chemicals, biomedical applications requiring precise identification of accumulative gaseous species, and gas utility operations requiring high-sensitivity leak detection.

Conforming and nonconforming virtual element methods for elliptic problems

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

Cangiani, Andrea; Manzini, Gianmarco; Sutton, Oliver J.

Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general second-order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and nonsymmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H 1- and L 2-error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.

Symmetry analysis of the high-order equations for the description of the Fermi - Pasta - Ulam problem

NASA Astrophysics Data System (ADS)

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

2017-01-01

Recently some new nonlinear equations for the description of the Fermi - Pasta - Ulam problem have been derived. The main aim of this work is to use the symmetry test to investigate these equations. We consider equations for the description of the α and α + β Fermi - Pasta - Ulam model. We find the infinitesimal operators and Lie groups, admitted by the equations. Using the groups we find the self-similar variables as well as the reductions to the ordinary differential equations. Some exact solutions are also constructed.

Offset quadrature communications with decision-feedback carrier synchronization

NASA Technical Reports Server (NTRS)

Simon, M. K.; Smith, J. G.

1974-01-01

In order to accommodate a quadrature amplitude-shift-keyed (QASK) signal, Simon and Smith (1974) have modified the decision-feedback loop which tracks a quadrature phase-shift-keyed (QPSK). In the investigation reported approaches are considered to modify the loops in such a way that offset QASK signals can be tracked, giving attention to the special case of an offset QPSK. The development of the stochastic integro-differential equation of operation for a decision-feedback offset QASK loop is discussed along with the probability density function of the phase error process.

Scalable 96-well Plate Based iPSC Culture and Production Using a Robotic Liquid Handling System.

PubMed

Conway, Michael K; Gerger, Michael J; Balay, Erin E; O'Connell, Rachel; Hanson, Seth; Daily, Neil J; Wakatsuki, Tetsuro

2015-05-14

Continued advancement in pluripotent stem cell culture is closing the gap between bench and bedside for using these cells in regenerative medicine, drug discovery and safety testing. In order to produce stem cell derived biopharmaceutics and cells for tissue engineering and transplantation, a cost-effective cell-manufacturing technology is essential. Maintenance of pluripotency and stable performance of cells in downstream applications (e.g., cell differentiation) over time is paramount to large scale cell production. Yet that can be difficult to achieve especially if cells are cultured manually where the operator can introduce significant variability as well as be prohibitively expensive to scale-up. To enable high-throughput, large-scale stem cell production and remove operator influence novel stem cell culture protocols using a bench-top multi-channel liquid handling robot were developed that require minimal technician involvement or experience. With these protocols human induced pluripotent stem cells (iPSCs) were cultured in feeder-free conditions directly from a frozen stock and maintained in 96-well plates. Depending on cell line and desired scale-up rate, the operator can easily determine when to passage based on a series of images showing the optimal colony densities for splitting. Then the necessary reagents are prepared to perform a colony split to new plates without a centrifugation step. After 20 passages (~3 months), two iPSC lines maintained stable karyotypes, expressed stem cell markers, and differentiated into cardiomyocytes with high efficiency. The system can perform subsequent high-throughput screening of new differentiation protocols or genetic manipulation designed for 96-well plates. This technology will reduce the labor and technical burden to produce large numbers of identical stem cells for a myriad of applications.

Solar Array at Very High Temperatures: Ground Tests

NASA Technical Reports Server (NTRS)

Vayner, Boris

2016-01-01

Solar array design for any spacecraft is determined by the orbit parameters. For example, operational voltage for spacecraft in Low Earth Orbit (LEO) is limited by significant differential charging due to interactions with low temperature plasma. In order to avoid arcing in LEO, solar array is designed to generate electrical power at comparatively low voltages (below 100 V) or to operate at higher voltages with encapsulated of all suspected discharge locations. In Geosynchronous Orbit (GEO) differential charging is caused by energetic electrons that produce differential potential between coverglass and conductive spacecraft body in a kilovolt range. In such a case, weakly conductive layer over coverglass (ITO) is one of possible measures to eliminate dangerous discharges on array surface. Temperature variations for solar arrays in both orbits are measured and documented within the range of -150 C +110 C. This wide interval of operational temperatures is regularly reproduced in ground tests with radiative heating and cooling inside shroud with flowing liquid nitrogen. The requirements to solar array design and tests turn out to be more complicated when planned trajectory crosses these two orbits and goes closer to Sun. Conductive layer over coverglass causes sharp increase in parasitic current collected from LEO plasma, high temperature may cause cracks in encapsulating material (RTV), radiative heating of coupon in vacuum chamber becomes practically impossible above 150 C, conductivities of glass and adhesive go up with temperature that decrease array efficiency, and mechanical stresses grow up to critical magnitudes. A few test arrangements and respective results are presented in current paper. Coupons were tested against arcing in simulated LEO and GEO environments under elevated temperatures up to 200 C. The dependence of leakage current on temperature was measured, and electrostatic cleanness was verified for coupons with antireflection (AR) coating over ITO layer.

On computing Gröbner bases in rings of differential operators

NASA Astrophysics Data System (ADS)

Ma, Xiaodong; Sun, Yao; Wang, Dingkang

2011-05-01

Insa and Pauer presented a basic theory of Groebner basis for differential operators with coefficients in a commutative ring in 1998, and a criterion was proposed to determine if a set of differential operators is a Groebner basis. In this paper, we will give a new criterion such that Insa and Pauer's criterion could be concluded as a special case and one could compute the Groebner basis more efficiently by this new criterion.

Transformation matrices between non-linear and linear differential equations

NASA Technical Reports Server (NTRS)

Sartain, R. L.

1983-01-01

In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n matrices of real numbers were considered. The 2n x 2n matrix was used to transform the above matrix equation into the first order matrix equation X' = MX. Specially the matrix M and the conditions which will diagonalize or triangularize M were studied. Transformation matrices P and P sub -1 were used to accomplish this diagonalization or triangularization to return to the solution of the second order matrix differential equation system from the first order system.

7 CFR 1124.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Adjusted Class I differentials. 1124.52 Section 1124.52... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE PACIFIC NORTHWEST MARKETING AREA Order Regulating Handling Class Prices § 1124.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1030.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Adjusted Class I differentials. 1030.52 Section 1030.52... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE UPPER MIDWEST MARKETING AREA Order Regulating Handling Class Prices § 1030.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1124.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Adjusted Class I differentials. 1124.52 Section 1124.52... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE PACIFIC NORTHWEST MARKETING AREA Order Regulating Handling Class Prices § 1124.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1007.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Adjusted Class I differentials. 1007.52 Section 1007.52... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE SOUTHEAST MARKETING AREA Order Regulating Handling Class Prices § 1007.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1007.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Adjusted Class I differentials. 1007.52 Section 1007.52... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE SOUTHEAST MARKETING AREA Order Regulating Handling Class Prices § 1007.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1006.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Adjusted Class I differentials. 1006.52 Section 1006.52... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE FLORIDA MARKETING AREA Order Regulating Handling Class Prices § 1006.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1126.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Adjusted Class I differentials. 1126.52 Section 1126.52... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE SOUTHWEST MARKETING AREA Order Regulating Handling Class Prices § 1126.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1006.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Adjusted Class I differentials. 1006.52 Section 1006.52... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE FLORIDA MARKETING AREA Order Regulating Handling Class Prices § 1006.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1005.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Adjusted Class I differentials. 1005.52 Section 1005.52... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE APPALACHIAN MARKETING AREA Order Regulating Handling Class Prices § 1005.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1131.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Adjusted Class I differentials. 1131.52 Section 1131.52... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE ARIZONA MARKETING AREA Order Regulating Handling Class Prices § 1131.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1126.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Adjusted Class I differentials. 1126.52 Section 1126.52... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE SOUTHWEST MARKETING AREA Order Regulating Handling Class Prices § 1126.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1131.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Adjusted Class I differentials. 1131.52 Section 1131.52... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE ARIZONA MARKETING AREA Order Regulating Handling Class Prices § 1131.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1001.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Adjusted Class I differentials. 1001.52 Section 1001.52... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE NORTHEAST MARKETING AREA Order Regulating Handling Class Prices § 1001.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1032.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Adjusted Class I differentials. 1032.52 Section 1032.52... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE CENTRAL MARKETING AREA Order Regulating Handling Class Prices § 1032.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1033.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Adjusted Class I differentials. 1033.52 Section 1033.52... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE MIDEAST MARKETING AREA Order Regulating Handling Class Prices § 1033.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1033.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Adjusted Class I differentials. 1033.52 Section 1033.52... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE MIDEAST MARKETING AREA Order Regulating Handling Class Prices § 1033.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1005.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Adjusted Class I differentials. 1005.52 Section 1005.52... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE APPALACHIAN MARKETING AREA Order Regulating Handling Class Prices § 1005.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1030.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Adjusted Class I differentials. 1030.52 Section 1030.52... Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE UPPER MIDWEST MARKETING AREA Order Regulating Handling Class Prices § 1030.52 Adjusted Class I differentials. See § 1000.52. ...

7 CFR 1032.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 9 2014-01-01 2013-01-01 true Adjusted Class I differentials. 1032.52 Section 1032.52... AGREEMENTS AND ORDERS; MILK), DEPARTMENT OF AGRICULTURE MILK IN THE CENTRAL MARKETING AREA Order Regulating Handling Class Prices § 1032.52 Adjusted Class I differentials. See § 1000.52. ...

Low-Power Differential SRAM design for SOC Based on the 25-um Technology

NASA Astrophysics Data System (ADS)

Godugunuri, Sivaprasad; Dara, Naveen; Sambasiva Nayak, R.; Nayeemuddin, Md; Singh, Yadu, Dr.; Veda, R. N. S. Sunil

2017-08-01

In recent, the SOC styles area unit the vast complicated styles in VLSI these SOC styles having important low-power operations problems, to comprehend this we tend to enforced low-power SRAM. However these SRAM Architectures critically affects the entire power of SOC and competitive space. To beat the higher than disadvantages, during this paper, a low-power differential SRAM design is planned. The differential SRAM design stores multiple bits within the same cell, operates at minimum in operation low-tension and space per bit. The differential SRAM design designed supported the 25-um technology using Tanner-EDA Tool.

Super-Laplacians and their symmetries

NASA Astrophysics Data System (ADS)

Howe, P. S.; Lindström, U.

2017-05-01

A super-Laplacian is a set of differential operators in superspace whose highestdimensional component is given by the spacetime Laplacian. Symmetries of super-Laplacians are given by linear differential operators of arbitrary finite degree and are determined by superconformal Killing tensors. We investigate these in flat superspaces. The differential operators determining the symmetries give rise to algebras which can be identified in many cases with the tensor algebras of the relevant superconformal Lie algebras modulo certain ideals. They have applications to Higher Spin theories.

Recent advances in high-order WENO finite volume methods for compressible multiphase flows

NASA Astrophysics Data System (ADS)

Dumbser, Michael

2013-10-01

We present two new families of better than second order accurate Godunov-type finite volume methods for the solution of nonlinear hyperbolic partial differential equations with nonconservative products. One family is based on a high order Arbitrary-Lagrangian-Eulerian (ALE) formulation on moving meshes, which allows to resolve the material contact wave in a very sharp way when the mesh is moved at the speed of the material interface. The other family of methods is based on a high order Adaptive Mesh Refinement (AMR) strategy, where the mesh can be strongly refined in the vicinity of the material interface. Both classes of schemes have several building blocks in common, in particular: a high order WENO reconstruction operator to obtain high order of accuracy in space; the use of an element-local space-time Galerkin predictor step which evolves the reconstruction polynomials in time and that allows to reach high order of accuracy in time in one single step; the use of a path-conservative approach to treat the nonconservative terms of the PDE. We show applications of both methods to the Baer-Nunziato model for compressible multiphase flows.

Real options valuation and optimization of energy assets

NASA Astrophysics Data System (ADS)

Thompson, Matthew

In this thesis we present algorithms for the valuation and optimal operation of natural gas storage facilities, hydro-electric power plants and thermal power generators in competitive markets. Real options theory is used to derive nonlinear partial-integro-differential equations (PIDEs) for the valuation and optimal operating strategies of all types of facilities. The equations are designed to incorporate a wide class of spot price models that can exhibit the same time-dependent, mean-reverting dynamics and price spikes as those observed in most energy markets. Particular attention is paid to the operational characteristics of real energy assets. For natural gas storage facilities these characteristics include: working gas capacities, variable deliverability and injection rates and cycling limitations. For thermal power plants relevant operational characteristics include variable start-up times and costs, control response time lags, minimum generating levels, nonlinear output functions, structural limitations on ramp rates, and minimum up/down time restrictions. For hydro-electric units, head effects and environmental constraints are addressed. We illustrate the models with numerical examples of a gas storage facility, a hydro-electric pump storage facility and a thermal power plant. This PIDE framework is the first in the literature to achieve second order accuracy in characterizing the operating states of hydro-electric and hydro-thermal power plants. The continuous state space representation derived in this thesis can therefore achieve far greater realism in terms of operating state specification than any other method in the literature to date. This thesis is also the first and only to allow for any continuous time jump diffusion processes in order to account for price spikes.

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

An AES chip with DPA resistance using hardware-based random order execution

NASA Astrophysics Data System (ADS)

Bo, Yu; Xiangyu, Li; Cong, Chen; Yihe, Sun; Liji, Wu; Xiangmin, Zhang

2012-06-01

This paper presents an AES (advanced encryption standard) chip that combats differential power analysis (DPA) side-channel attack through hardware-based random order execution. Both decryption and encryption procedures of an AES are implemented on the chip. A fine-grained dataflow architecture is proposed, which dynamically exploits intrinsic byte-level independence in the algorithm. A novel circuit called an HMF (Hold-Match-Fetch) unit is proposed for random control, which randomly sets execution orders for concurrent operations. The AES chip was manufactured in SMIC 0.18 μm technology. The average energy for encrypting one group of plain texts (128 bits secrete keys) is 19 nJ. The core area is 0.43 mm2. A sophisticated experimental setup was built to test the DPA resistance. Measurement-based experimental results show that one byte of a secret key cannot be disclosed from our chip under random mode after 64000 power traces were used in the DPA attack. Compared with the corresponding fixed order execution, the hardware based random order execution is improved by at least 21 times the DPA resistance.

Newton's method: A link between continuous and discrete solutions of nonlinear problems

NASA Technical Reports Server (NTRS)

Thurston, G. A.

1980-01-01

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Hermitian Hamiltonian equivalent to a given non-Hermitian one: manifestation of spectral singularity.

PubMed

Samsonov, Boris F

2013-04-28

One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the eigenfunctions of a Hermitian Hamiltonian equivalent to the given non-Hermitian one is found. As a result, the corresponding scattering matrix and cross section are given explicitly. It is demonstrated that the possible presence of a spectral singularity in the spectrum of the non-Hermitian Hamiltonian may be detected as a resonance in the scattering cross section of its Hermitian counterpart. Nevertheless, just at the singular point, the equivalent Hermitian Hamiltonian becomes undetermined.

Hawking from Catalan

DOE PAGES

Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.; ...

2016-05-12

The Virasoro algebra determines all ‘graviton’ matrix elements in AdS 3/CFT 2. We study the explicit exchange of any number of Virasoro gravitons between heavy and light CFT 2 operators at large central charge. These graviton exchanges can be written in terms of new on-shell tree diagrams, organized in a perturbative expansion in h H/c, the heavy operator dimension divided by the central charge. The Virasoro vacuum conformal block, which is the sum of all the tree diagrams, obeys a differential recursion relation generalizing that of the Catalan numbers. Here, we use this recursion relation to sum the on-shell diagramsmore » to all orders, computing the Virasoro vacuum block. Extrapolating to large h H/c determines the Hawking temperature of a BTZ black hole in dual AdS 3 theories.« less

Hawking from Catalan

NASA Astrophysics Data System (ADS)

Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.; Wang, Junpu

2016-05-01

The Virasoro algebra determines all `graviton' matrix elements in AdS3/CFT2. We study the explicit exchange of any number of Virasoro gravitons between heavy and light CFT2 operators at large central charge. These graviton exchanges can be written in terms of new on-shell tree diagrams, organized in a perturbative expansion in h H /c, the heavy operator dimension divided by the central charge. The Virasoro vacuum conformal block, which is the sum of all the tree diagrams, obeys a differential recursion relation generalizing that of the Catalan numbers. We use this recursion relation to sum the on-shell diagrams to all orders, computing the Virasoro vacuum block. Extrapolating to large h H /c determines the Hawking temperature of a BTZ black hole in dual AdS3 theories.

Modeling of thin-walled structures interacting with acoustic media as constrained two-dimensional continua

NASA Astrophysics Data System (ADS)

Rabinskiy, L. N.; Zhavoronok, S. I.

2018-04-01

The transient interaction of acoustic media and elastic shells is considered on the basis of the transition function approach. The three-dimensional hyperbolic initial boundary-value problem is reduced to a two-dimensional problem of shell theory with integral operators approximating the acoustic medium effect on the shell dynamics. The kernels of these integral operators are determined by the elementary solution of the problem of acoustic waves diffraction at a rigid obstacle with the same boundary shape as the wetted shell surface. The closed-form elementary solution for arbitrary convex obstacles can be obtained at the initial interaction stages on the background of the so-called “thin layer hypothesis”. Thus, the shell–wave interaction model defined by integro-differential dynamic equations with analytically determined kernels of integral operators becomes hence two-dimensional but nonlocal in time. On the other hand, the initial interaction stage results in localized dynamic loadings and consequently in complex strain and stress states that require higher-order shell theories. Here the modified theory of I.N.Vekua–A.A.Amosov-type is formulated in terms of analytical continuum dynamics. The shell model is constructed on a two-dimensional manifold within a set of field variables, Lagrangian density, and constraint equations following from the boundary conditions “shifted” from the shell faces to its base surface. Such an approach allows one to construct consistent low-order shell models within a unified formal hierarchy. The equations of the N th-order shell theory are singularly perturbed and contain second-order partial derivatives with respect to time and surface coordinates whereas the numerical integration of systems of first-order equations is more efficient. Such systems can be obtained as Hamilton–de Donder–Weyl-type equations for the Lagrangian dynamical system. The Hamiltonian formulation of the elementary N th-order shell theory is here briefly described.

The Local Brewery: A Project for Use in Differential Equations Courses

ERIC Educational Resources Information Center

Starling, James K.; Povich, Timothy J.; Findlay, Michael

2016-01-01

We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer. The project aims to expose the students to the modeling process by creating and solving a mathematical model and effectively communicating their…

Method translation and full metadata transfer from thermal to differential flow modulated comprehensive two dimensional gas chromatography: Profiling of suspected fragrance allergens.

PubMed

Cordero, Chiara; Rubiolo, Patrizia; Reichenbach, Stephen E; Carretta, Andrea; Cobelli, Luigi; Giardina, Matthew; Bicchi, Carlo

2017-01-13

The possibility to transfer methods from thermal to differential-flow modulated comprehensive two-dimensional gas chromatographic (GC×GC) platforms is of high interest to improve GC×GC flexibility and increase the compatibility of results from different platforms. The principles of method translation are here applied to an original method, developed for a loop-type thermal modulated GC×GC-MS/FID system, suitable for quali-quantitative screening of suspected fragrance allergens. The analysis conditions were translated to a reverse-injection differential flow modulated platform (GC×2GC-MS/FID) with a dual-parallel secondary column and dual detection. The experimental results, for a model mixture of suspected volatile allergens and for raw fragrance mixtures of different composition, confirmed the feasibility of translating methods by preserving 1 D elution order, as well as the relative alignment of resulting 2D peak patterns. A correct translation produced several benefits including an effective transfer of metadata (compound names, MS fragmentation pattern, response factors) by automatic template transformation and matching from the original/reference method to its translated counterpart. The correct translation provided: (a) 2D pattern repeatability, (b) MS fragmentation pattern reliability for identity confirmation, and (c) comparable response factors and quantitation accuracy within a concentration range of three orders of magnitude. The adoption of a narrow bore (i.e. 0.1mm d c ) first-dimension column to operate under close-to-optimal conditions with the differential-flow modulation GC×GC platform was also advantageous in halving the total analysis under the translated conditions. Copyright © 2016 Elsevier B.V. All rights reserved.

Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms.

PubMed

Chowdury, A; Kedziora, D J; Ankiewicz, A; Akhmediev, N

2014-09-01

We present the fifth-order equation of the nonlinear Schrödinger hierarchy. This integrable partial differential equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrödinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.

Enhanced perceptual functioning in autism: an update, and eight principles of autistic perception.

PubMed

Mottron, Laurent; Dawson, Michelle; Soulières, Isabelle; Hubert, Benedicte; Burack, Jake

2006-01-01

We propose an "Enhanced Perceptual Functioning" model encompassing the main differences between autistic and non-autistic social and non-social perceptual processing: locally oriented visual and auditory perception, enhanced low-level discrimination, use of a more posterior network in "complex" visual tasks, enhanced perception of first order static stimuli, diminished perception of complex movement, autonomy of low-level information processing toward higher-order operations, and differential relation between perception and general intelligence. Increased perceptual expertise may be implicated in the choice of special ability in savant autistics, and in the variability of apparent presentations within PDD (autism with and without typical speech, Asperger syndrome) in non-savant autistics. The overfunctioning of brain regions typically involved in primary perceptual functions may explain the autistic perceptual endophenotype.

Hessian-based norm regularization for image restoration with biomedical applications.

PubMed

Lefkimmiatis, Stamatios; Bourquard, Aurélien; Unser, Michael

2012-03-01

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second-order differential operators. Specifically, we derive second-order regularizers that involve matrix norms of the Hessian operator. The definition of these functionals is based on an alternative interpretation of TV that relies on mixed norms of directional derivatives. We show that the resulting regularizers retain some of the most favorable properties of TV, i.e., convexity, homogeneity, rotation, and translation invariance, while dealing effectively with the staircase effect. We further develop an efficient minimization scheme for the corresponding objective functions. The proposed algorithm is of the iteratively reweighted least-square type and results from a majorization-minimization approach. It relies on a problem-specific preconditioned conjugate gradient method, which makes the overall minimization scheme very attractive since it can be applied effectively to large images in a reasonable computational time. We validate the overall proposed regularization framework through deblurring experiments under additive Gaussian noise on standard and biomedical images.

Polyphenols Determination in Olive Oil Samples Based on a Thick Film Voltammetric Sensor and a Tyrosinase Biosensor

NASA Astrophysics Data System (ADS)

Capannesi, Cecilia; Palchetti, Ilaria; Mascini, Marco

2000-12-01

The aim of the present work was to compare different techniques to evaluate the variation with the storage time and storage conditions in the phenolic content of an extra-virgin olive oil. A disposable screen-printed sensor (SPE) was coupled with differential pulse voltammetry (DPV) to determine the phenolic fractions after extraction with glycine buffer; DPV parameters were chosen in order to study oxidation peak of oleuropein, that was used as reference compound. Moreover a tyrosinase based biosensor operating in organic solvent (hexane) was assembled, using an amperometric oxygen probe as transducer. Calibration curves were realised in flow injection analysis (F.I.A.) using phenol as substrate. Both of these methods are easy to operate, require no extraction (biosensor) or a rapid extraction procedure (SPE), and the analysis time is short (min.). The results obtained with these two innovative procedures were compared with classical spectrophotometric assay using the Folin-Ciocalteau reagent. Other extra-virgin olive oil quality parameters were investigated with classical methods in order to better define the alteration process and results are reported.

Are two hands (from different people) better than one? Mode effects and differential transfer between manual coordination modes.

PubMed

Gorman, Jamie C; Crites, Michael J

2013-08-01

We report an experiment in which we investigated differential transfer between unimanual (one-handed), bimanual (two-handed), and intermanual (different peoples' hands) coordination modes. People perform some manual tasks faster than others ("mode effects"). However, little is known about transfer between coordination modes. To investigate differential transfer, we draw hypotheses from two perspectives--information based and constraint based--of bimanual and interpersonal coordination and skill acquisition. Participants drove a teleoperated rover around a circular path in sets of two 2-min trials using two of the different coordination modes. Speed and variability of the rover's path were measured. Order of coordination modes was manipulated to examine differential transfer and mode effects. Differential transfer analyses revealed patterns of positive transfer from simpler (localized spatiotemporal constraints) to more complex (distributed spatiotemporal constraints) coordination modes paired with negative transfer in the opposite direction. Mode effects indicated that intermanual performance was significantly faster than unimanual performance, and bimanual performance was intermediate. Importantly, all of these effects disappeared with practice. The observed patterns of differential transfer between coordination modes may be better accounted for by a constraint-based explanation of differential transfer than by an information-based one. Mode effects may be attributable to anticipatory movements based on dyads' access to mutual visual information. Although people may be faster using more-complex coordination modes, when operators transition between modes, they may be more effective transitioning from simpler (e.g., bimanual) to more complex (e.g., intermanual) modes than vice versa. However, this difference may be critical only for novel or rarely practiced tasks.

Concerted spatial-frequency and polarization-phase filtering of laser images of polycrystalline networks of blood plasma smears

NASA Astrophysics Data System (ADS)

Ushenko, Yu A.

2012-11-01

The complex technique of concerted polarization-phase and spatial-frequency filtering of blood plasma laser images is suggested. The possibility of obtaining the coordinate distributions of phases of linearly and circularly birefringent protein networks of blood plasma separately is presented. The statistical (moments of the first to fourth orders) and scale self-similar (logarithmic dependences of power spectra) structure of phase maps of different types of birefringence of blood plasma of two groups of patients-healthy people (donors) and those suffering from rectal cancer-is investigated. The diagnostically sensitive parameters of a pathological change of the birefringence of blood plasma polycrystalline networks are determined. The effectiveness of this technique for detecting change in birefringence in the smears of other biological fluids in diagnosing the appearance of cholelithiasis (bile), operative differentiation of the acute and gangrenous appendicitis (exudate), and differentiation of inflammatory diseases of joints (synovial fluid) is shown.

Parameter identification for nonlinear aerodynamic systems

NASA Technical Reports Server (NTRS)

Pearson, Allan E.

1990-01-01

Parameter identification for nonlinear aerodynamic systems is examined. It is presumed that the underlying model can be arranged into an input/output (I/O) differential operator equation of a generic form. The algorithm estimation is especially efficient since the equation error can be integrated exactly given any I/O pair to obtain an algebraic function of the parameters. The algorithm for parameter identification was extended to the order determination problem for linear differential system. The degeneracy in a least squares estimate caused by feedback was addressed. A method of frequency analysis for determining the transfer function G(j omega) from transient I/O data was formulated using complex valued Fourier based modulating functions in contrast with the trigonometric modulating functions for the parameter estimation problem. A simulation result of applying the algorithm is given under noise-free conditions for a system with a low pass transfer function.

Development of a Differential Optical Absorption Spectroscopy System Using HighLuminance LED for Measurement of NO2

NASA Astrophysics Data System (ADS)

Fukuchi, Tetsuo; Nayuki, Takuya; Mori, Hideto; Goto, Naohiko; Fujii, Takashi; Nemoto, Koshichi

A differential optical absorption spectroscopy (DOAS) system for measurement of atmospheric NO2 was developed. The system uses a battery-operated, high luminance LED and a fiber-coupled spectrometer, and is portable. Laboratory experiments using a gas cell of length 0.22 m with varying NO2 concentrations were performed to evaluate the sensitivity of the DOAS system. The DOAS measurement results are in agreement with NO2 concentrations obtained simultaneously by a FT-IR (Fourier Transform Infrared) system for NO2 concentrations down to 20 ppm. Experiments with an optical path length of 93 m were also performed, and NO2 concentrations down to 0.20 ppm were measured. Since measurement of atmospheric NO2, which is in the order of several tens of ppb, requires optical path lengths of several hundred m, system improvements to improve the signal detection are necessary.

Rasch modeling to assess Albanian and South African learners' preferences for real-life situations to be used in mathematics: a pilot study.

PubMed

Kacerja, Suela; Julie, Cyril; Hadjerrouit, Said

2013-01-01

This paper reports on an investigation on the real-life situations students in grades 8 and 9 in South Africa and Albania prefer to use in Mathematics. The functioning of the instrument used to assess the order of preference learners from both countries have for contextual situations is assessed using Rasch modeling techniques. For both the cohorts, the data fit the Rasch model. The differential item functioning (DIF) analysis rendered 3 items operating differentially for the two cohorts. Explanations for these differences are provided in terms of differences in experiences learners in the two countries have related to some of the contextual situations. Implications for interpretation of international comparative tests are offered, as are the possibilities for the cross-country development of curriculum materials related to contexts that learners prefer to use in Mathematics.

Natural differential operations on manifolds: an algebraic approach

NASA Astrophysics Data System (ADS)

Katsylo, P. I.; Timashev, D. A.

2008-10-01

Natural algebraic differential operations on geometric quantities on smooth manifolds are considered. A method for the investigation and classification of such operations is described, the method of IT-reduction. With it the investigation of natural operations reduces to the analysis of rational maps between k-jet spaces, which are equivariant with respect to certain algebraic groups. On the basis of the method of IT-reduction a finite generation theorem is proved: for tensor bundles \\mathscr{V},\\mathscr{W}\\to M all the natural differential operations D\\colon\\Gamma(\\mathscr{V})\\to\\Gamma(\\mathscr{W}) of degree at most d can be algebraically constructed from some finite set of such operations. Conceptual proofs of known results on the classification of natural linear operations on arbitrary and symplectic manifolds are presented. A non-existence theorem is proved for natural deformation quantizations on Poisson manifolds and symplectic manifolds.Bibliography: 21 titles.

Concurrent Schedules of Positive and Negative Reinforcement: Differential-Impact and Differential-Outcomes Hypotheses

ERIC Educational Resources Information Center

Magoon, Michael A.; Critchfield, Thomas S.

2008-01-01

Considerable evidence from outside of operant psychology suggests that aversive events exert greater influence over behavior than equal-sized positive-reinforcement events. Operant theory is largely moot on this point, and most operant research is uninformative because of a scaling problem that prevents aversive events and those based on positive…

Genetic algorithm with maximum-minimum crossover (GA-MMC) applied in optimization of radiation pattern control of phased-array radars for rocket tracking systems.

PubMed

Silva, Leonardo W T; Barros, Vitor F; Silva, Sandro G

2014-08-18

In launching operations, Rocket Tracking Systems (RTS) process the trajectory data obtained by radar sensors. In order to improve functionality and maintenance, radars can be upgraded by replacing antennas with parabolic reflectors (PRs) with phased arrays (PAs). These arrays enable the electronic control of the radiation pattern by adjusting the signal supplied to each radiating element. However, in projects of phased array radars (PARs), the modeling of the problem is subject to various combinations of excitation signals producing a complex optimization problem. In this case, it is possible to calculate the problem solutions with optimization methods such as genetic algorithms (GAs). For this, the Genetic Algorithm with Maximum-Minimum Crossover (GA-MMC) method was developed to control the radiation pattern of PAs. The GA-MMC uses a reconfigurable algorithm with multiple objectives, differentiated coding and a new crossover genetic operator. This operator has a different approach from the conventional one, because it performs the crossover of the fittest individuals with the least fit individuals in order to enhance the genetic diversity. Thus, GA-MMC was successful in more than 90% of the tests for each application, increased the fitness of the final population by more than 20% and reduced the premature convergence.

Genetic Algorithm with Maximum-Minimum Crossover (GA-MMC) Applied in Optimization of Radiation Pattern Control of Phased-Array Radars for Rocket Tracking Systems

PubMed Central

Silva, Leonardo W. T.; Barros, Vitor F.; Silva, Sandro G.

2014-01-01

In launching operations, Rocket Tracking Systems (RTS) process the trajectory data obtained by radar sensors. In order to improve functionality and maintenance, radars can be upgraded by replacing antennas with parabolic reflectors (PRs) with phased arrays (PAs). These arrays enable the electronic control of the radiation pattern by adjusting the signal supplied to each radiating element. However, in projects of phased array radars (PARs), the modeling of the problem is subject to various combinations of excitation signals producing a complex optimization problem. In this case, it is possible to calculate the problem solutions with optimization methods such as genetic algorithms (GAs). For this, the Genetic Algorithm with Maximum-Minimum Crossover (GA-MMC) method was developed to control the radiation pattern of PAs. The GA-MMC uses a reconfigurable algorithm with multiple objectives, differentiated coding and a new crossover genetic operator. This operator has a different approach from the conventional one, because it performs the crossover of the fittest individuals with the least fit individuals in order to enhance the genetic diversity. Thus, GA-MMC was successful in more than 90% of the tests for each application, increased the fitness of the final population by more than 20% and reduced the premature convergence. PMID:25196013

On differential operators generating iterative systems of linear ODEs of maximal symmetry algebra

NASA Astrophysics Data System (ADS)

Ndogmo, J. C.

2017-06-01

Although every iterative scalar linear ordinary differential equation is of maximal symmetry algebra, the situation is different and far more complex for systems of linear ordinary differential equations, and an iterative system of linear equations need not be of maximal symmetry algebra. We illustrate these facts by examples and derive families of vector differential operators whose iterations are all linear systems of equations of maximal symmetry algebra. Some consequences of these results are also discussed.

All-optical temporal fractional order differentiator using an in-fiber ellipsoidal air-microcavity

NASA Astrophysics Data System (ADS)

Zhang, Lihong; Sun, Shuqian; Li, Ming; Zhu, Ninghua

2017-12-01

An all-optical temporal fractional order differentiator with ultrabroad bandwidth (~1.6 THz) and extremely simple fabrication is proposed and experimentally demonstrated based on an in-fiber ellipsoidal air-microcavity. The ellipsoidal air-microcavity is fabricated by splicing a single mode fiber (SMF) and a photonic crystal fiber (PCF) together using a simple arc-discharging technology. By changing the arc-discharging times, the propagation loss can be adjusted and then the differentiation order is tuned. A nearly Gaussian-like optical pulse with 3 dB bandwidth of 8 nm is launched into the differentiator and a 0.65 order differentiation of the input pulse is achieved with a processing error of 2.55%. Project supported by the the National Natural Science Foundation of China (Nos. 61522509, 61377002, 61535012), the National High-Tech Research & Development Program of China (No. SS2015AA011002), and the Beijing Natural Science Foundation (No. 4152052). Ming Li was supported in part by the Thousand Young Talent Program.

Varieties of operator manipulation. [for solving differential equations and calculating finite differences

NASA Technical Reports Server (NTRS)

Doohovskoy, A.

1977-01-01

A change in MACSYMA syntax is proposed to accommodate the operator manipulators necessary to implement direct and indirect methods for the solution of differential equations, calculus of finite differences, and the fractional calculus, as well as their modern counterparts. To illustrate the benefits and convenience of this syntax extension, an example is given to show how MACSYMA's pattern-matching capability can be used to implement a particular set of operator identities which can then be used to obtain exact solutions to nonlinear differential equations.

Numerical integration of ordinary differential equations of various orders

NASA Technical Reports Server (NTRS)

Gear, C. W.

1969-01-01

Report describes techniques for the numerical integration of differential equations of various orders. Modified multistep predictor-corrector methods for general initial-value problems are discussed and new methods are introduced.

315mJ, 2-micrometers Double-Pulsed Coherent Differential Absorption Lidar Transmitter for Atmospheric CO2 Sensing

NASA Technical Reports Server (NTRS)

Yu, Jirong; Trieu, Bo; Bai, Yingxin; Koch, Grady; Chen, Songsheng; Petzar, Paul; Singh, Upendra N.; Kavaya, Michael J.; Beyon, Jeffrey

2010-01-01

The design of a double pulsed, injection seeded, 2-micrometer compact coherent Differential absorption Lidar (DIAL) transmitter for CO2 sensing is presented. This system is hardened for ground and airborne applications. The design architecture includes three continuous wave lasers which provide controlled on and off line seeding, injection seeded power oscillator and a single amplifier operating in double pass configuration. As the derivative a coherent Doppler wind lidar, this instrument has the added benefit of providing wind information. The active laser material used for this application is a Ho: Tm:YLF crystal operates at the eye-safe wavelength. The 3-meter long folded ring resonator produces energy of 130-mJ (90/40) with a temporal pulse length around 220 nanoseconds and 530 nanosecond pulses for on and off lines respectively. The separation between the two pulses is on the order of 200 microseconds. The line width is in the order of 2.5MHz and the beam quality has an M(sup 2) of 1.1 times diffraction limited beam. A final output energy for a pair of both on and off pulses as high as 315 mJ (190/125) at a repetition rate of 10 Hz is achieved. The operating temperature is set around 20 C for the pump diode lasers and 10 C for the rod. Since the laser design has to meet high-energy as well as high beam quality requirements, close attention is paid to the laser head design to avoid thermal distortion in the rod. A side-pumped configuration is used and heat is removed uniformly by passing coolant through a tube slightly larger than the rod to reduce thermal gradient. This paper also discusses the advantage of using a long upper laser level life time laser crystal for DIAL application. In addition issues related to injection seeding with two different frequencies to achieve a transform limited line width will be presented.

Partial differential equation transform — Variational formulation and Fourier analysis

PubMed Central

Wang, Yang; Wei, Guo-Wei; Yang, Siyang

2011-01-01

Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systematically provide intrinsic mode functions (IMFs) of signals and images. Due to their tunable time-frequency localization and perfect reconstruction, the operation of MoDEEs is called a PDE transform. By appropriate selection of PDE transform parameters, we can tune IMFs into trends, edges, textures, noise etc., which can be further utilized in the secondary processing for various purposes. This work introduces the variational formulation, performs the Fourier analysis, and conducts biomedical and biological applications of the proposed PDE transform. The variational formulation offers an algorithm to incorporate two image functions and two sets of low-pass PDE operators in the total energy functional. Two low-pass PDE operators have different signs, leading to energy disparity, while a coupling term, acting as a relative fidelity of two image functions, is introduced to reduce the disparity of two energy components. We construct variational PDE transforms by using Euler-Lagrange equation and artificial time propagation. Fourier analysis of a simplified PDE transform is presented to shed light on the filter properties of high order PDE transforms. Such an analysis also offers insight on the parameter selection of the PDE transform. The proposed PDE transform algorithm is validated by numerous benchmark tests. In one selected challenging example, we illustrate the ability of PDE transform to separate two adjacent frequencies of sin(x) and sin(1.1x). Such an ability is due to PDE transform’s controllable frequency localization obtained by adjusting the order of PDEs. The frequency selection is achieved either by diffusion coefficients or by propagation time. Finally, we explore a large number of practical applications to further demonstrate the utility of proposed PDE transform. PMID:22207904

Process and domain specificity in regions engaged for face processing: an fMRI study of perceptual differentiation.

PubMed

Collins, Heather R; Zhu, Xun; Bhatt, Ramesh S; Clark, Jonathan D; Joseph, Jane E

2012-12-01

The degree to which face-specific brain regions are specialized for different kinds of perceptual processing is debated. This study parametrically varied demands on featural, first-order configural, or second-order configural processing of faces and houses in a perceptual matching task to determine the extent to which the process of perceptual differentiation was selective for faces regardless of processing type (domain-specific account), specialized for specific types of perceptual processing regardless of category (process-specific account), engaged in category-optimized processing (i.e., configural face processing or featural house processing), or reflected generalized perceptual differentiation (i.e., differentiation that crosses category and processing type boundaries). ROIs were identified in a separate localizer run or with a similarity regressor in the face-matching runs. The predominant principle accounting for fMRI signal modulation in most regions was generalized perceptual differentiation. Nearly all regions showed perceptual differentiation for both faces and houses for more than one processing type, even if the region was identified as face-preferential in the localizer run. Consistent with process specificity, some regions showed perceptual differentiation for first-order processing of faces and houses (right fusiform face area and occipito-temporal cortex and right lateral occipital complex), but not for featural or second-order processing. Somewhat consistent with domain specificity, the right inferior frontal gyrus showed perceptual differentiation only for faces in the featural matching task. The present findings demonstrate that the majority of regions involved in perceptual differentiation of faces are also involved in differentiation of other visually homogenous categories.

Process- and Domain-Specificity in Regions Engaged for Face Processing: An fMRI Study of Perceptual Differentiation

PubMed Central

Collins, Heather R.; Zhu, Xun; Bhatt, Ramesh S.; Clark, Jonathan D.; Joseph, Jane E.

2015-01-01

The degree to which face-specific brain regions are specialized for different kinds of perceptual processing is debated. The present study parametrically varied demands on featural, first-order configural or second-order configural processing of faces and houses in a perceptual matching task to determine the extent to which the process of perceptual differentiation was selective for faces regardless of processing type (domain-specific account), specialized for specific types of perceptual processing regardless of category (process-specific account), engaged in category-optimized processing (i.e., configural face processing or featural house processing) or reflected generalized perceptual differentiation (i.e. differentiation that crosses category and processing type boundaries). Regions of interest were identified in a separate localizer run or with a similarity regressor in the face-matching runs. The predominant principle accounting for fMRI signal modulation in most regions was generalized perceptual differentiation. Nearly all regions showed perceptual differentiation for both faces and houses for more than one processing type, even if the region was identified as face-preferential in the localizer run. Consistent with process-specificity, some regions showed perceptual differentiation for first-order processing of faces and houses (right fusiform face area and occipito-temporal cortex, and right lateral occipital complex), but not for featural or second-order processing. Somewhat consistent with domain-specificity, the right inferior frontal gyrus showed perceptual differentiation only for faces in the featural matching task. The present findings demonstrate that the majority of regions involved in perceptual differentiation of faces are also involved in differentiation of other visually homogenous categories. PMID:22849402

A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras

NASA Astrophysics Data System (ADS)

Alshammari, Fahad; Isaac, Phillip S.; Marquette, Ian

2018-02-01

We introduce a search algorithm that utilises differential operator realisations to find polynomial Casimir operators of Lie algebras. To demonstrate the algorithm, we look at two classes of examples: (1) the model filiform Lie algebras and (2) the Schrödinger Lie algebras. We find that an abstract form of dimensional analysis assists us in our algorithm, and greatly reduces the complexity of the problem.

A fourth-order box method for solving the boundary layer equations

NASA Technical Reports Server (NTRS)

Wornom, S. F.

1977-01-01

A fourth order box method for calculating high accuracy numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations is presented. The method is the natural extension of the second order Keller Box scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary layer equations. Numerical results for high accuracy test cases show the method to be significantly faster than other higher order and second order methods.

Oscillation theorems for second order nonlinear forced differential equations.

PubMed

Salhin, Ambarka A; Din, Ummul Khair Salma; Ahmad, Rokiah Rozita; Noorani, Mohd Salmi Md

2014-01-01

In this paper, a class of second order forced nonlinear differential equation is considered and several new oscillation theorems are obtained. Our results generalize and improve those known ones in the literature.

Rings of h-deformed differential operators

NASA Astrophysics Data System (ADS)

Ogievetsky, O. V.; Herlemont, B.

2017-08-01

We describe the center of the ring Diff h ( n) of h- deformed differential operators of type A. We establish an isomorphism between certain localizations of Diff h ( n) and the Weyl algebra W n , extended by n indeterminates.

The shear-Hall instability in newborn neutron stars

NASA Astrophysics Data System (ADS)

Kondić, T.; Rüdiger, G.; Hollerbach, R.

2011-11-01

Aims: In the first few minutes of a newborn neutron star's life the Hall effect and differential rotation may both be important. We demonstrate that these two ingredients are sufficient for generating a "shear-Hall instability" and for studying its excitation conditions, growth rates, and characteristic magnetic field patterns. Methods: We numerically solve the induction equation in a spherical shell, with a kinematically prescribed differential rotation profile Ω(s), where s is the cylindrical radius. The Hall term is linearized about an imposed uniform axial field. The linear stability of individual azimuthal modes, both axisymmetric and non-axisymmetric, is then investigated. Results: For the shear-Hall instability to occur, the axial field must be parallel to the rotation axis if Ω(s) decreases outward, whereas if Ω(s) increases outward it must be anti-parallel. The instability draws its energy from the differential rotation, and occurs on the short rotational timescale rather than on the much longer Hall timescale. It operates most efficiently if the Hall time is comparable to the diffusion time. Depending on the precise field strengths B0, either axisymmetric or non-axisymmetric modes may be the most unstable. Conclusions: Even if the differential rotation in newborn neutron stars is quenched within minutes, the shear-Hall instability may nevertheless amplify any seed magnetic fields by many orders of magnitude.

Integrated Kerr comb-based reconfigurable transversal differentiator for microwave photonic signal processing

NASA Astrophysics Data System (ADS)

Xu, Xingyuan; Wu, Jiayang; Shoeiby, Mehrdad; Nguyen, Thach G.; Chu, Sai T.; Little, Brent E.; Morandotti, Roberto; Mitchell, Arnan; Moss, David J.

2018-01-01

An arbitrary-order intensity differentiator for high-order microwave signal differentiation is proposed and experimentally demonstrated on a versatile transversal microwave photonic signal processing platform based on integrated Kerr combs. With a CMOS-compatible nonlinear micro-ring resonator, high quality Kerr combs with broad bandwidth and large frequency spacings are generated, enabling a larger number of taps and an increased Nyquist zone. By programming and shaping individual comb lines' power, calculated tap weights are realized, thus achieving a versatile microwave photonic signal processing platform. Arbitrary-order intensity differentiation is demonstrated on the platform. The RF responses are experimentally characterized, and systems demonstrations for Gaussian input signals are also performed.

Human factors in operations design

NASA Technical Reports Server (NTRS)

Chafin, R. L.

1982-01-01

The manner in which organizations develop their organizational structure is considered, taking into account an example in which the environment changes for an older organization. In such cases, it would be preferable to have some theoretical foundation on which to base the restructuring of the organization to meet new environmental needs. A description is given of a theoretic foundation based on the principles of Differentiation/Integration and Procedural/Knowledge based operations. The organizational design principle of Differentiation and Integration has been presented by Lawrence and Lorsch (1969). The differentiation/integration processes are related to the organizational structures presented in studies concerning NASA Deep Space Network (DSN) operations. The principles presented provide valuable tools for analyzing operations organization.

Temporal correlation measurements of pulsed dual CO2 lidar returns. [for atmospheric pollution detection

NASA Technical Reports Server (NTRS)

Menyuk, N.; Killinger, D. K.

1981-01-01

A pulsed dual-laser direct-detection differential-absorption lidar DIAL system, operating near 10.6 microns, is used to measure the temporal correlation and statistical properties of backscattered returns from specular and diffuse topographic targets. Results show that atmospheric-turbulence fluctuations can effectively be frozen for pulse separation times on the order of 1-3 msec or less. The diffuse target returns, however, yielded a much lower correlation than that obtained with the specular targets; this being due to uncorrelated system noise effects and different statistics for the two types of target returns.

Icing research tunnel rotating bar calibration measurement system

NASA Technical Reports Server (NTRS)

Gibson, Theresa L.; Dearmon, John M.

1993-01-01

In order to measure icing patterns across a test section of the Icing Research Tunnel, an automated rotating bar measurement system was developed at the NASA Lewis Research Center. In comparison with the previously used manual measurement system, this system provides a number of improvements: increased accuracy and repeatability, increased number of data points, reduced tunnel operating time, and improved documentation. The automated system uses a linear variable differential transformer (LVDT) to measure ice accretion. This instrument is driven along the bar by means of an intelligent stepper motor which also controls data recording. This paper describes the rotating bar calibration measurement system.

A regularity result for fixed points, with applications to linear response

NASA Astrophysics Data System (ADS)

Sedro, Julien

2018-04-01

In this paper, we show a series of abstract results on fixed point regularity with respect to a parameter. They are based on a Taylor development taking into account a loss of regularity phenomenon, typically occurring for composition operators acting on spaces of functions with finite regularity. We generalize this approach to higher order differentiability, through the notion of an n-graded family. We then give applications to the fixed point of a nonlinear map, and to linear response in the context of (uniformly) expanding dynamics (theorem 3 and corollary 2), in the spirit of Gouëzel-Liverani.

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.

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

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

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

1997-11-01

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

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.

DIFFERENTIAL ANALYZER

DOEpatents

Sorensen, E.G.; Gordon, C.M.

1959-02-10

Improvements in analog eomputing machines of the class capable of evaluating differential equations, commonly termed differential analyzers, are described. In general form, the analyzer embodies a plurality of basic computer mechanisms for performing integration, multiplication, and addition, and means for directing the result of any one operation to another computer mechanism performing a further operation. In the device, numerical quantities are represented by the rotation of shafts, or the electrical equivalent of shafts.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Resource planning and scheduling of payload for satellite with particle swarm optimization

NASA Astrophysics Data System (ADS)

Li, Jian; Wang, Cheng

2007-11-01

The resource planning and scheduling technology of payload is a key technology to realize an automated control for earth observing satellite with limited resources on satellite, which is implemented to arrange the works states of various payloads to carry out missions by optimizing the scheme of the resources. The scheduling task is a difficult constraint optimization problem with various and mutative requests and constraints. Based on the analysis of the satellite's functions and the payload's resource constraints, a proactive planning and scheduling strategy based on the availability of consumable and replenishable resources in time-order is introduced along with dividing the planning and scheduling period to several pieces. A particle swarm optimization algorithm is proposed to address the problem with an adaptive mutation operator selection, where the swarm is divided into groups with different probabilities to employ various mutation operators viz., differential evolution, Gaussian and random mutation operators. The probabilities are adjusted adaptively by comparing the effectiveness of the groups to select a proper operator. The simulation results have shown the feasibility and effectiveness of the method.

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Hou, Gene W.

1994-01-01

The straightforward automatic-differentiation and the hand-differentiated incremental iterative methods are interwoven to produce a hybrid scheme that captures some of the strengths of each strategy. With this compromise, discrete aerodynamic sensitivity derivatives are calculated with the efficient incremental iterative solution algorithm of the original flow code. Moreover, the principal advantage of automatic differentiation is retained (i.e., all complicated source code for the derivative calculations is constructed quickly with accuracy). The basic equations for second-order sensitivity derivatives are presented; four methods are compared. Each scheme requires that large systems are solved first for the first-order derivatives and, in all but one method, for the first-order adjoint variables. Of these latter three schemes, two require no solutions of large systems thereafter. For the other two for which additional systems are solved, the equations and solution procedures are analogous to those for the first order derivatives. From a practical viewpoint, implementation of the second-order methods is feasible only with software tools such as automatic differentiation, because of the extreme complexity and large number of terms. First- and second-order sensitivities are calculated accurately for two airfoil problems, including a turbulent flow example; both geometric-shape and flow-condition design variables are considered. Several methods are tested; results are compared on the basis of accuracy, computational time, and computer memory. For first-order derivatives, the hybrid incremental iterative scheme obtained with automatic differentiation is competitive with the best hand-differentiated method; for six independent variables, it is at least two to four times faster than central finite differences and requires only 60 percent more memory than the original code; the performance is expected to improve further in the future.

On the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_1^\\alpha ({T^N})

NASA Astrophysics Data System (ADS)

Ahmedov, Anvarjon; Materneh, Ehab; Zainuddin, Hishamuddin

2017-09-01

The relevance of waves in quantum mechanics naturally implies that the decomposition of arbitrary wave packets in terms of monochromatic waves plays an important role in applications of the theory. When eigenfunction expansions does not converge, then the expansions of the functions with certain smoothness should be considered. Such functions gained prominence primarily through their application in quantum mechanics. In this work we study the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_p^α ({T^N}), related to the self-adjoint extension of the Laplace operator in torus TN . The sufficient conditions for summability is obtained using the modified Poisson formula. Isomorphism properties of the elliptic differential operators is applied in order to obtain estimation for the Fourier series of the functions from the classes of Liouville L_p^α .

Finding higher order Darboux polynomials for a family of rational first order ordinary differential equations

NASA Astrophysics Data System (ADS)

Avellar, J.; Claudino, A. L. G. C.; Duarte, L. G. S.; da Mota, L. A. C. P.

2015-10-01

For the Darbouxian methods we are studying here, in order to solve first order rational ordinary differential equations (1ODEs), the most costly (computationally) step is the finding of the needed Darboux polynomials. This can be so grave that it can render the whole approach unpractical. Hereby we introduce a simple heuristics to speed up this process for a class of 1ODEs.

Hopf-algebraic structure of combinatorial objects and differential operators

NASA Technical Reports Server (NTRS)

Grossman, Robert; Larson, Richard G.

1989-01-01

A Hopf-algebraic structure on a vector space which has as basis a family of trees is described. Some applications of this structure to combinatorics and to differential operators are surveyed. Some possible future directions for this work are indicated.

Deployment strategy for battery energy storage system in distribution network based on voltage violation regulation

NASA Astrophysics Data System (ADS)

Wu, H.; Zhou, L.; Xu, T.; Fang, W. L.; He, W. G.; Liu, H. M.

2017-11-01

In order to improve the situation of voltage violation caused by the grid-connection of photovoltaic (PV) system in a distribution network, a bi-level programming model is proposed for battery energy storage system (BESS) deployment. The objective function of inner level programming is to minimize voltage violation, with the power of PV and BESS as the variables. The objective function of outer level programming is to minimize the comprehensive function originated from inner layer programming and all the BESS operating parameters, with the capacity and rated power of BESS as the variables. The differential evolution (DE) algorithm is applied to solve the model. Based on distribution network operation scenarios with photovoltaic generation under multiple alternative output modes, the simulation results of IEEE 33-bus system prove that the deployment strategy of BESS proposed in this paper is well adapted to voltage violation regulation invariable distribution network operation scenarios. It contributes to regulating voltage violation in distribution network, as well as to improve the utilization of PV systems.

Operator splitting method for simulation of dynamic flows in natural gas pipeline networks

DOE PAGES

Dyachenko, Sergey A.; Zlotnik, Anatoly; Korotkevich, Alexander O.; ...

2017-09-19

Here, we develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for mass flow and pressure on a metric graph, where turbulent losses of momentum are modeled by phenomenological Darcy-Weisbach friction. Mass flow balance is maintained through the boundary conditions at the network nodes, where natural gas is injected or withdrawn from the system. Gas flow through the network is controlled by compressors boosting pressure at the inlet of the adjoint pipe. Our operator splitting numerical scheme ismore » unconditionally stable and it is second order accurate in space and time. The scheme is explicit, and it is formulated to work with general networks with loops. We test the scheme over range of regimes and network configurations, also comparing its performance with performance of two other state of the art implicit schemes.« less

Simulations of incompressible Navier Stokes equations on curved surfaces using discrete exterior calculus

NASA Astrophysics Data System (ADS)

Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil

2015-11-01

We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.

New Hardware for Tethered Balloons,

DTIC Science & Technology

1980-01-01

package contained a differential- pressure switch , and a command receiver. Long wires extended up to the gas valves to actuate them, and a long tube was...similar in appear- ance to the former valve, but does contain batteries, an aneroid- operated switch, and a differential- pressure switch . Design is such...that either the aneroid-operated switch or the differential- pressure switch can be easily removed for checking Or setting in the laboratory. Likewise the

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

Connell, Patrick; Frolov, Valeri P.; Kubiznak, David

We obtain and study the equations describing the parallel transport of orthonormal frames along geodesics in a spacetime admitting a nondegenerate, principal, conformal Killing-Yano tensor h. We demonstrate that the operator F, obtained by a projection of h to a subspace orthogonal to the velocity, has in a generic case eigenspaces of dimension not greater than 2. Each of these eigenspaces is independently parallel propagated. This allows one to reduce the parallel transport equations to a set of first order, ordinary, differential equations for the angles of rotation in the 2D eigenspaces. General analysis is illustrated by studying the equationsmore » of the parallel transport in the Kerr-NUT-(A)dS metrics. Examples of three-, four-, and five-dimensional Kerr-NUT-(A)dS are considered, and it is shown that the obtained first order equations can be solved by a separation of variables.« less

Whole-Lesion Apparent Diffusion Coefficient-Based Entropy-Related Parameters for Characterizing Cervical Cancers: Initial Findings.

PubMed

Guan, Yue; Li, Weifeng; Jiang, Zhuoran; Chen, Ying; Liu, Song; He, Jian; Zhou, Zhengyang; Ge, Yun

2016-12-01

This study aimed to develop whole-lesion apparent diffusion coefficient (ADC)-based entropy-related parameters of cervical cancer to preliminarily assess intratumoral heterogeneity of this lesion in comparison to adjacent normal cervical tissues. A total of 51 women (mean age, 49 years) with cervical cancers confirmed by biopsy underwent 3-T pelvic diffusion-weighted magnetic resonance imaging with b values of 0 and 800 s/mm 2 prospectively. ADC-based entropy-related parameters including first-order entropy and second-order entropies were derived from the whole tumor volume as well as adjacent normal cervical tissues. Intraclass correlation coefficient, Wilcoxon test with Bonferroni correction, Kruskal-Wallis test, and receiver operating characteristic curve were used for statistical analysis. All the parameters showed excellent interobserver agreement (all intraclass correlation coefficients  > 0.900). Entropy, entropy(H) 0 , entropy(H) 45 , entropy(H) 90 , entropy(H) 135 , and entropy(H) mean were significantly higher, whereas entropy(H) range and entropy(H) std were significantly lower in cervical cancers compared to adjacent normal cervical tissues (all P <.0001). Kruskal-Wallis test showed that there were no significant differences among the values of various second-order entropies including entropy(H) 0, entropy(H) 45 , entropy(H) 90 , entropy(H) 135 , and entropy(H) mean. All second-order entropies had larger area under the receiver operating characteristic curve than first-order entropy in differentiating cervical cancers from adjacent normal cervical tissues. Further, entropy(H) 45 , entropy(H) 90 , entropy(H) 135 , and entropy(H) mean had the same largest area under the receiver operating characteristic curve of 0.867. Whole-lesion ADC-based entropy-related parameters of cervical cancers were developed successfully, which showed initial potential in characterizing intratumoral heterogeneity in comparison to adjacent normal cervical tissues. Copyright © 2016 The Association of University Radiologists. Published by Elsevier Inc. All rights reserved.

Variations in the Solution of Linear First-Order Differential Equations. Classroom Notes

ERIC Educational Resources Information Center

Seaman, Brian; Osler, Thomas J.

2004-01-01

A special project which can be given to students of ordinary differential equations is described in detail. Students create new differential equations by changing the dependent variable in the familiar linear first-order equation (dv/dx)+p(x)v=q(x) by means of a substitution v=f(y). The student then creates a table of the new equations and…

A numerical solution for a variable-order reaction-diffusion model by using fractional derivatives with non-local and non-singular kernel

NASA Astrophysics Data System (ADS)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.

2018-02-01

A reaction-diffusion system can be represented by the Gray-Scott model. The reaction-diffusion dynamic is described by a pair of time and space dependent Partial Differential Equations (PDEs). In this paper, a generalization of the Gray-Scott model by using variable-order fractional differential equations is proposed. The variable-orders were set as smooth functions bounded in (0 , 1 ] and, specifically, the Liouville-Caputo and the Atangana-Baleanu-Caputo fractional derivatives were used to express the time differentiation. In order to find a numerical solution of the proposed model, the finite difference method together with the Adams method were applied. The simulations results showed the chaotic behavior of the proposed model when different variable-orders are applied.

Relativistic differential-difference momentum operators and noncommutative differential calculus

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

Mir-Kasimov, R. M., E-mail: mirkr@theor.jinr.ru

2013-09-15

The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics (QM) in the Relativistic Configuration Space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated as the independent term of the total Hamiltonian. This relativistic kinetic energy term is not distinguishing in form from its nonrelativistic counterpart. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generating function for the matrix elements of the unitary irrepsmore » of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS.« less

Synchronization of chaotic systems involving fractional operators of Liouville-Caputo type with variable-order

NASA Astrophysics Data System (ADS)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.; Valtierra-Rodríguez, M.

2017-12-01

In this paper, we propose a state-observer-based approach to synchronize variable-order fractional (VOF) chaotic systems. In particular, this work is focused on complete synchronization with a so-called unidirectional master-slave topology. The master is described by a dynamical system in state-space representation whereas the slave is described by a state observer. The slave is composed of a master copy and a correction term which in turn is constituted of an estimation error and an appropriate gain that assures the synchronization. The differential equations of the VOF chaotic system are described by the Liouville-Caputo and Atangana-Baleanu-Caputo derivatives. Numerical simulations involving the synchronization of Rössler oscillators, Chua's systems and multi-scrolls are studied. The simulations show that different chaotic behaviors can be obtained if different smooths functions defined in the interval (0 , 1 ] are used as the variable order of the fractional derivatives. Furthermore, simulations show that the VOF chaotic systems can be synchronized.

Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Radhakrishnan, Krishnan; Hindmarsh, Alan C.

1993-01-01

LSODE, the Livermore Solver for Ordinary Differential Equations, is a package of FORTRAN subroutines designed for the numerical solution of the initial value problem for a system of ordinary differential equations. It is particularly well suited for 'stiff' differential systems, for which the backward differentiation formula method of orders 1 to 5 is provided. The code includes the Adams-Moulton method of orders 1 to 12, so it can be used for nonstiff problems as well. In addition, the user can easily switch methods to increase computational efficiency for problems that change character. For both methods a variety of corrector iteration techniques is included in the code. Also, to minimize computational work, both the step size and method order are varied dynamically. This report presents complete descriptions of the code and integration methods, including their implementation. It also provides a detailed guide to the use of the code, as well as an illustrative example problem.

Multigrid methods for differential equations with highly oscillatory coefficients

NASA Technical Reports Server (NTRS)

Engquist, Bjorn; Luo, Erding

1993-01-01

New coarse grid multigrid operators for problems with highly oscillatory coefficients are developed. These types of operators are necessary when the characters of the differential equations on coarser grids or longer wavelengths are different from that on the fine grid. Elliptic problems for composite materials and different classes of hyperbolic problems are practical examples. The new coarse grid operators can be constructed directly based on the homogenized differential operators or hierarchically computed from the finest grid. Convergence analysis based on the homogenization theory is given for elliptic problems with periodic coefficients and some hyperbolic problems. These are classes of equations for which there exists a fairly complete theory for the interaction between shorter and longer wavelengths in the problems. Numerical examples are presented.

A dimension reduction method for flood compensation operation of multi-reservoir system

NASA Astrophysics Data System (ADS)

Jia, B.; Wu, S.; Fan, Z.

2017-12-01

Multiple reservoirs cooperation compensation operations coping with uncontrolled flood play vital role in real-time flood mitigation. This paper come up with a reservoir flood compensation operation index (ResFCOI), which formed by elements of flood control storage, flood inflow volume, flood transmission time and cooperation operations period, then establish a flood cooperation compensation operations model of multi-reservoir system, according to the ResFCOI to determine a computational order of each reservoir, and lastly the differential evolution algorithm is implemented for computing single reservoir flood compensation optimization in turn, so that a dimension reduction method is formed to reduce computational complexity. Shiguan River Basin with two large reservoirs and an extensive uncontrolled flood area, is used as a case study, results show that (a) reservoirs' flood discharges and the uncontrolled flood are superimposed at Jiangjiaji Station, while the formed flood peak flow is as small as possible; (b) cooperation compensation operations slightly increase in usage of flood storage capacity in reservoirs, when comparing to rule-based operations; (c) it takes 50 seconds in average when computing a cooperation compensation operations scheme. The dimension reduction method to guide flood compensation operations of multi-reservoir system, can make each reservoir adjust its flood discharge strategy dynamically according to the uncontrolled flood magnitude and pattern, so as to mitigate the downstream flood disaster.

hp-Adaptive time integration based on the BDF for viscous flows

NASA Astrophysics Data System (ADS)

Hay, A.; Etienne, S.; Pelletier, D.; Garon, A.

2015-06-01

This paper presents a procedure based on the Backward Differentiation Formulas of order 1 to 5 to obtain efficient time integration of the incompressible Navier-Stokes equations. The adaptive algorithm performs both stepsize and order selections to control respectively the solution accuracy and the computational efficiency of the time integration process. The stepsize selection (h-adaptivity) is based on a local error estimate and an error controller to guarantee that the numerical solution accuracy is within a user prescribed tolerance. The order selection (p-adaptivity) relies on the idea that low-accuracy solutions can be computed efficiently by low order time integrators while accurate solutions require high order time integrators to keep computational time low. The selection is based on a stability test that detects growing numerical noise and deems a method of order p stable if there is no method of lower order that delivers the same solution accuracy for a larger stepsize. Hence, it guarantees both that (1) the used method of integration operates inside of its stability region and (2) the time integration procedure is computationally efficient. The proposed time integration procedure also features a time-step rejection and quarantine mechanisms, a modified Newton method with a predictor and dense output techniques to compute solution at off-step points.

Synopsis and Recommendations of the TSC Workshop on Differential Operation of NAVSTAR GPS

DOT National Transportation Integrated Search

1983-10-01

A workshop on Differential Operation of NAVSTAR GPS was held on June 9-10, 1983, at the Department of Transportation's Transportation Systems Center in Cambridge, Massachesetts. The primary purpose of the workship was to inititate the development of ...

The second-order differential phase contrast and its retrieval for imaging with x-ray Talbot interferometry.

PubMed

Yang, Yi; Tang, Xiangyang

2012-12-01

The x-ray differential phase contrast imaging implemented with the Talbot interferometry has recently been reported to be capable of providing tomographic images corresponding to attenuation-contrast, phase-contrast, and dark-field contrast, simultaneously, from a single set of projection data. The authors believe that, along with small-angle x-ray scattering, the second-order phase derivative Φ(") (s)(x) plays a role in the generation of dark-field contrast. In this paper, the authors derive the analytic formulae to characterize the contribution made by the second-order phase derivative to the dark-field contrast (namely, second-order differential phase contrast) and validate them via computer simulation study. By proposing a practical retrieval method, the authors investigate the potential of second-order differential phase contrast imaging for extensive applications. The theoretical derivation starts at assuming that the refractive index decrement of an object can be decomposed into δ = δ(s) + δ(f), where δ(f) corresponds to the object's fine structures and manifests itself in the dark-field contrast via small-angle scattering. Based on the paraxial Fresnel-Kirchhoff theory, the analytic formulae to characterize the contribution made by δ(s), which corresponds to the object's smooth structures, to the dark-field contrast are derived. Through computer simulation with specially designed numerical phantoms, an x-ray differential phase contrast imaging system implemented with the Talbot interferometry is utilized to evaluate and validate the derived formulae. The same imaging system is also utilized to evaluate and verify the capability of the proposed method to retrieve the second-order differential phase contrast for imaging, as well as its robustness over the dimension of detector cell and the number of steps in grating shifting. Both analytic formulae and computer simulations show that, in addition to small-angle scattering, the contrast generated by the second-order derivative is magnified substantially by the ratio of detector cell dimension over grating period, which plays a significant role in dark-field imaging implemented with the Talbot interferometry. The analytic formulae derived in this work to characterize the second-order differential phase contrast in the dark-field imaging implemented with the Talbot interferometry are of significance, which may initiate more activities in the research and development of x-ray differential phase contrast imaging for extensive preclinical and eventually clinical applications.

The Differential Effect of Sustained Operations on Psychomotor Skills of Helicopter Pilots.

PubMed

McMahon, Terry W; Newman, David G

2018-06-01

Flying a helicopter is a complex psychomotor skill requiring constant control inputs from pilots. A deterioration in psychomotor performance of a helicopter pilot may be detrimental to operational safety. The aim of this study was to test the hypothesis that psychomotor performance deteriorates over time during sustained operations and that the effect is more pronounced in the feet than the hands. The subjects were helicopter pilots conducting sustained multicrew offshore flight operations in a demanding environment. The remote flight operations involved constant workload in hot environmental conditions with complex operational tasking. Over a period of 6 d 10 helicopter pilots were tested. At the completion of daily flying duties, a helicopter-specific screen-based compensatory tracking task measuring tracking accuracy (over a 5-min period) tested both hands and feet. Data were compared over time and tested for statistical significance for both deterioration and differential effect. A statistically significant deterioration of psychomotor performance was evident in the pilots over time for both hands and feet. There was also a statistically significant differential effect between the hands and the feet in terms of tracking accuracy. The hands recorded a 22.6% decrease in tracking accuracy, while the feet recorded a 39.9% decrease in tracking accuracy. The differential effect may be due to prioritization of limb movement by the motor cortex due to factors such as workload-induced cognitive fatigue. This may result in a greater reduction in performance in the feet than the hands, posing a significant risk to operational safety.McMahon TW, Newman DG. The differential effect of sustained operations on psychomotor skills of helicopter pilots. Aerosp Med Hum Perform. 2018; 89(6):496-502.

Operational method of solution of linear non-integer ordinary and partial differential equations.

PubMed

Zhukovsky, K V

2016-01-01

We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black-Scholes-like equations etc. are demonstrated by the operational technique.

Cryogenic instrumentation for ITER magnets

NASA Astrophysics Data System (ADS)

Poncet, J.-M.; Manzagol, J.; Attard, A.; André, J.; Bizel-Bizellot, L.; Bonnay, P.; Ercolani, E.; Luchier, N.; Girard, A.; Clayton, N.; Devred, A.; Huygen, S.; Journeaux, J.-Y.

2017-02-01

Accurate measurements of the helium flowrate and of the temperature of the ITER magnets is of fundamental importance to make sure that the magnets operate under well controlled and reliable conditions, and to allow suitable helium flow distribution in the magnets through the helium piping. Therefore, the temperature and flow rate measurements shall be reliable and accurate. In this paper, we present the thermometric chains as well as the venturi flow meters installed in the ITER magnets and their helium piping. The presented thermometric block design is based on the design developed by CERN for the LHC, which has been further optimized via thermal simulations carried out by CEA. The electronic part of the thermometric chain was entirely developed by the CEA and will be presented in detail: it is based on a lock-in measurement and small signal amplification, and also provides a web interface and software to an industrial PLC. This measuring device provides a reliable, accurate, electromagnetically immune, and fast (up to 100 Hz bandwidth) system for resistive temperature sensors between a few ohms to 100 kΩ. The flowmeters (venturi type) which make up part of the helium mass flow measurement chain have been completely designed, and manufacturing is on-going. The behaviour of the helium gas has been studied in detailed thanks to ANSYS CFX software in order to obtain the same differential pressure for all types of flowmeters. Measurement uncertainties have been estimated and the influence of input parameters has been studied. Mechanical calculations have been performed to guarantee the mechanical strength of the venturis required for pressure equipment operating in nuclear environment. In order to complete the helium mass flow measurement chain, different technologies of absolute and differential pressure sensors have been tested in an applied magnetic field to identify equipment compatible with the ITER environment.

Design and Fabrication of a Differential Electrostatic Accelerometer for Space-Station Testing of the Equivalence Principle.

PubMed

Han, Fengtian; Liu, Tianyi; Li, Linlin; Wu, Qiuping

2016-08-10

The differential electrostatic space accelerometer is an equivalence principle (EP) experiment instrument proposed to operate onboard China's space station in the 2020s. It is designed to compare the spin-spin interaction between two rotating extended bodies and the Earth to a precision of 10(-12), which is five orders of magnitude better than terrestrial experiment results to date. To achieve the targeted test accuracy, the sensitive space accelerometer will use the very soft space environment provided by a quasi-drag-free floating capsule and long-time observation of the free-fall mass motion for integration of the measurements over 20 orbits. In this work, we describe the design and capability of the differential accelerometer to test weak space acceleration. Modeling and simulation results of the electrostatic suspension and electrostatic motor are presented based on attainable space microgravity condition. Noise evaluation shows that the electrostatic actuation and residual non-gravitational acceleration are two major noise sources. The evaluated differential acceleration noise is 1.01 × 10(-9) m/s²/Hz(1/2) at the NEP signal frequency of 0.182 mHz, by neglecting small acceleration disturbances. The preliminary work on development of the first instrument prototype is introduced for on-ground technological assessments. This development has already confirmed several crucial fabrication processes and measurement techniques and it will open the way to the construction of the final differential space accelerometer.

Design and Fabrication of a Differential Electrostatic Accelerometer for Space-Station Testing of the Equivalence Principle

PubMed Central

Han, Fengtian; Liu, Tianyi; Li, Linlin; Wu, Qiuping

2016-01-01

The differential electrostatic space accelerometer is an equivalence principle (EP) experiment instrument proposed to operate onboard China’s space station in the 2020s. It is designed to compare the spin-spin interaction between two rotating extended bodies and the Earth to a precision of 10−12, which is five orders of magnitude better than terrestrial experiment results to date. To achieve the targeted test accuracy, the sensitive space accelerometer will use the very soft space environment provided by a quasi-drag-free floating capsule and long-time observation of the free-fall mass motion for integration of the measurements over 20 orbits. In this work, we describe the design and capability of the differential accelerometer to test weak space acceleration. Modeling and simulation results of the electrostatic suspension and electrostatic motor are presented based on attainable space microgravity condition. Noise evaluation shows that the electrostatic actuation and residual non-gravitational acceleration are two major noise sources. The evaluated differential acceleration noise is 1.01 × 10−9 m/s2/Hz1/2 at the NEP signal frequency of 0.182 mHz, by neglecting small acceleration disturbances. The preliminary work on development of the first instrument prototype is introduced for on-ground technological assessments. This development has already confirmed several crucial fabrication processes and measurement techniques and it will open the way to the construction of the final differential space accelerometer. PMID:27517927

Delay differential equations via the matrix Lambert W function and bifurcation analysis: application to machine tool chatter.

PubMed

Yi, Sun; Nelson, Patrick W; Ulsoy, A Galip

2007-04-01

In a turning process modeled using delay differential equations (DDEs), we investigate the stability of the regenerative machine tool chatter problem. An approach using the matrix Lambert W function for the analytical solution to systems of delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. The Lambert W function, known to be useful for solving scalar first-order DDEs, has recently been extended to a matrix Lambert W function approach to solve systems of DDEs. The essential advantages of the matrix Lambert W approach are not only the similarity to the concept of the state transition matrix in lin ear ordinary differential equations, enabling its use for general classes of linear delay differential equations, but also the observation that we need only the principal branch among an infinite number of roots to determine the stability of a system of DDEs. The bifurcation method combined with Sturm sequences provides an algorithm for determining the stability of DDEs without restrictive geometric analysis. With this approach, one can obtain the critical values of delay, which determine the stability of a system and hence the preferred operating spindle speed without chatter. We apply both the matrix Lambert W function and the bifurcation analysis approach to the problem of chatter stability in turning, and compare the results obtained to existing methods. The two new approaches show excellent accuracy and certain other advantages, when compared to traditional graphical, computational and approximate methods.

Existence of a coupled system of fractional differential equations

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

Ibrahim, Rabha W.; Siri, Zailan

2015-10-22

We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator.

Operator pencil passing through a given operator

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

Biggs, A., E-mail: khudian@manchester.ac.uk, E-mail: adam.biggs@student.manchester.ac.uk; Khudaverdian, H. M., E-mail: khudian@manchester.ac.uk, E-mail: adam.biggs@student.manchester.ac.uk

Let Δ be a linear differential operator acting on the space of densities of a given weight λ{sub 0} on a manifold M. One can consider a pencil of operators Π-circumflex(Δ)=(Δ{sub λ}) passing through the operator Δ such that any Δ{sub λ} is a linear differential operator acting on densities of weight λ. This pencil can be identified with a linear differential operator Δ-circumflex acting on the algebra of densities of all weights. The existence of an invariant scalar product in the algebra of densities implies a natural decomposition of operators, i.e., pencils of self-adjoint and anti-self-adjoint operators. We studymore » lifting maps that are on one hand equivariant with respect to divergenceless vector fields, and, on the other hand, with values in self-adjoint or anti-self-adjoint operators. In particular, we analyze the relation between these two concepts, and apply it to the study of diff (M)-equivariant liftings. Finally, we briefly consider the case of liftings equivariant with respect to the algebra of projective transformations and describe all regular self-adjoint and anti-self-adjoint liftings. Our constructions can be considered as a generalisation of equivariant quantisation.« less

A conformal mapping based fractional order approach for sub-optimal tuning of PID controllers with guaranteed dominant pole placement

NASA Astrophysics Data System (ADS)

Saha, Suman; Das, Saptarshi; Das, Shantanu; Gupta, Amitava

2012-09-01

A novel conformal mapping based fractional order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second order systems. The conventional pole placement tuning via Linear Quadratic Regulator (LQR) method is extended for open loop oscillatory systems as well. The locations of the open loop zeros of a fractional order PID (FOPID or PIλDμ) controller have been approximated in this paper vis-à-vis a LQR tuned conventional integer order PID controller, to achieve equivalent integer order PID control system. This approach eases the implementation of analog/digital realization of a FOPID controller with its integer order counterpart along with the advantages of fractional order controller preserved. It is shown here in the paper that decrease in the integro-differential operators of the FOPID/PIλDμ controller pushes the open loop zeros of the equivalent PID controller towards greater damping regions which gives a trajectory of the controller zeros and dominant closed loop poles. This trajectory is termed as "M-curve". This phenomena is used to design a two-stage tuning algorithm which reduces the existing PID controller's effort in a significant manner compared to that with a single stage LQR based pole placement method at a desired closed loop damping and frequency.

On the spline-based wavelet differentiation matrix

NASA Technical Reports Server (NTRS)

Jameson, Leland

1993-01-01

The differentiation matrix for a spline-based wavelet basis is constructed. Given an n-th order spline basis it is proved that the differentiation matrix is accurate of order 2n + 2 when periodic boundary conditions are assumed. This high accuracy, or superconvergence, is lost when the boundary conditions are no longer periodic. Furthermore, it is shown that spline-based bases generate a class of compact finite difference schemes.

Polytomous Differential Item Functioning and Violations of Ordering of the Expected Latent Trait by the Raw Score

ERIC Educational Resources Information Center

DeMars, Christine E.

2008-01-01

The graded response (GR) and generalized partial credit (GPC) models do not imply that examinees ordered by raw observed score will necessarily be ordered on the expected value of the latent trait (OEL). Factors were manipulated to assess whether increased violations of OEL also produced increased Type I error rates in differential item…

Numerical analysis for distributed-order differential equations

NASA Astrophysics Data System (ADS)

Diethelm, Kai; Ford, Neville J.

2009-03-01

In this paper we present and analyse a numerical method for the solution of a distributed-order differential equation of the general form where m is a positive real number and where the derivative is taken to be a fractional derivative of Caputo type of order r. We give a convergence theory for our method and conclude with some numerical examples.

A Multilevel Algorithm for the Solution of Second Order Elliptic Differential Equations on Sparse Grids

NASA Technical Reports Server (NTRS)

Pflaum, Christoph

1996-01-01

A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles. Suitable discretizations provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order Omicron(1) for the multilevel algorithm.

New physics in the visible final states of B → D(*) τν

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

Ligeti, Zoltan; Papucci, Michele; Robinson, Dean J.

We derive compact expressions for the helicity amplitudes of the many-body B → D (*) (→ DY)τ(→ Xν)ν decays, specifically for X = ℓν or π and Y = π or γ. We include contributions from all ten possible new physics four-Fermi operators with arbitrary couplings. Our results capture interference effects in the full phase space of the visible τ and D * decay products which are missed in analyses that treat the τ or D * or both as stable. The τ interference effects are sizable, formally of order m τ/m B for the standard model, and may bemore » of order unity in the presence of new physics. Treating interference correctly is essential when considering kinematic distributions of the τ or D * decay products, and when including experimentally unavoidable phase space cuts. Our amplitude-level results also allow for efficient exploration of new physics effects in the fully differential phase space, by enabling experiments to perform such studies on fully simulated Monte Carlo datasets via efficient event reweighing. As an example, we explore a class of new physics interactions that can fit the observed R(D (*) ) ratios, and show that analyses including more differential kinematic information can provide greater discriminating power for new physics, than single kinematic variables alone.« less

New physics in the visible final states of B → D(*) τν

DOE PAGES

Ligeti, Zoltan; Papucci, Michele; Robinson, Dean J.

2017-01-18

We derive compact expressions for the helicity amplitudes of the many-body B → D (*) (→ DY)τ(→ Xν)ν decays, specifically for X = ℓν or π and Y = π or γ. We include contributions from all ten possible new physics four-Fermi operators with arbitrary couplings. Our results capture interference effects in the full phase space of the visible τ and D * decay products which are missed in analyses that treat the τ or D * or both as stable. The τ interference effects are sizable, formally of order m τ/m B for the standard model, and may bemore » of order unity in the presence of new physics. Treating interference correctly is essential when considering kinematic distributions of the τ or D * decay products, and when including experimentally unavoidable phase space cuts. Our amplitude-level results also allow for efficient exploration of new physics effects in the fully differential phase space, by enabling experiments to perform such studies on fully simulated Monte Carlo datasets via efficient event reweighing. As an example, we explore a class of new physics interactions that can fit the observed R(D (*) ) ratios, and show that analyses including more differential kinematic information can provide greater discriminating power for new physics, than single kinematic variables alone.« less

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.

On the nonlinear stability of the unsteady, viscous flow of an incompressible fluid in a curved pipe

NASA Technical Reports Server (NTRS)

Shortis, Trudi A.; Hall, Philip

1995-01-01

The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined.

State-to-state reaction dynamics of 18O+32O2 studied by a time-dependent quantum wavepacket method

NASA Astrophysics Data System (ADS)

Xie, Wenbo; Liu, Lan; Sun, Zhigang; Guo, Hua; Dawes, Richard

2015-02-01

The title isotope exchange reaction was studied by converged time-dependent wave packet calculations, where an efficient 4th order split operator was applied to propagate the initial wave packet. State-to-state differential and integral cross sections up to the collision energy of 0.35 eV were obtained with 32O2 in the hypothetical j0 = 0 state. It is discovered that the differential cross sections are largely forward biased in the studied collision energy range, due to the fact that there is a considerable part of the reaction occurring with large impact parameter and short lifetime relative to the rotational period of the intermediate complex. The oscillations of the forward scattering amplitude as a function of collision energy, which result from coherent contribution of adjacent resonances, may be a sensitive probe for examining the quality of the underlying potential energy surface. A good agreement between the theoretical and recent experimental integral and differential cross sections at collision energy of 7.3 kcal/mol is obtained. However, the theoretical results predict slightly too much forward scattering and colder rotational distributions than the experimental observations at collision energy of 5.7 kcal/mol.

Spaces of differential forms and maps with controlled distortion

NASA Astrophysics Data System (ADS)

Vodop'yanov, Sergei K.

2010-09-01

We study necessary and sufficient conditions for an approximately differentiable map f\\colon M\\to M' between Riemannian manifolds to induce a bounded transfer operator of differential forms with respect to the norms of Lebesgue spaces. As a corollary, we see that every homeomorphism f\\colon M\\to M' of class \\operatorname{ACL}(M) whose transfer operator of differential forms with norm in L_p is an isomorphism must necessarily be either quasi-conformal or quasi-isometric. We give some applications of our results to the study of the functoriality of cohomology in Lebesgue spaces.

Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael

2016-02-01

One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.

On shifted Jacobi spectral method for high-order multi-point boundary value problems

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Hafez, R. M.

2012-10-01

This paper reports a spectral tau method for numerically solving multi-point boundary value problems (BVPs) of linear high-order ordinary differential equations. The construction of the shifted Jacobi tau approximation is based on conventional differentiation. This use of differentiation allows the imposition of the governing equation at the whole set of grid points and the straight forward implementation of multiple boundary conditions. Extension of the tau method for high-order multi-point BVPs with variable coefficients is treated using the shifted Jacobi Gauss-Lobatto quadrature. Shifted Jacobi collocation method is developed for solving nonlinear high-order multi-point BVPs. The performance of the proposed methods is investigated by considering several examples. Accurate results and high convergence rates are achieved.

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.

Solar Array at Very High Temperatures: Ground Tests

NASA Technical Reports Server (NTRS)

Vayner, Boris

2016-01-01

Solar array design for any spacecraft is determined by the orbit parameters. For example, operational voltage for spacecraft in Low Earth Orbit (LEO) is limited by significant differential charging due to interactions with low temperature plasma. In order to avoid arcing in LEO, solar array is designed to generate electrical power at comparatively low voltages (below 100 volts) or to operate at higher voltages with encapsulation of all suspected discharge locations. In Geosynchronous Orbit (GEO) differential charging is caused by energetic electrons that produce differential potential between the coverglass and the conductive spacecraft body in a kilovolt range. In such a case, the weakly conductive layer over coverglass, indium tin oxide (ITO) is one of the possible measures to eliminate dangerous discharges on array surface. Temperature variations for solar arrays in both orbits are measured and documented within the range of minus150 degrees Centigrade to plus 1100 degrees Centigrade. This wide interval of operational temperatures is regularly reproduced in ground tests with radiative heating and cooling inside a shroud with flowing liquid nitrogen. The requirements to solar array design and tests turn out to be more complicated when planned trajectory crosses these two orbits and goes closer to the Sun. The conductive layer over coverglass causes a sharp increase in parasitic current collected from LEO plasma, high temperature may cause cracks in encapsulating (Room Temperature Vulcanizing (RTV) material; radiative heating of a coupon in vacuum chamber becomes practically impossible above 1500 degrees Centigrade; conductivities of glass and adhesive go up with temperature that decrease array efficiency; and mechanical stresses grow up to critical magnitudes. A few test arrangements and respective results are presented in current paper. Coupons were tested against arcing in simulated LEO and GEO environments under elevated temperatures up to 2000 degrees Centigrade. The dependence of leakage current on temperature was measured, and electrostatic cleanness was verified for coupons with antireflection (AR) coating over the indium tin oxide (ITO) layer.

A New Color Image Encryption Scheme Using CML and a Fractional-Order Chaotic System

PubMed Central

Wu, Xiangjun; Li, Yang; Kurths, Jürgen

2015-01-01

The chaos-based image cryptosystems have been widely investigated in recent years to provide real-time encryption and transmission. In this paper, a novel color image encryption algorithm by using coupled-map lattices (CML) and a fractional-order chaotic system is proposed to enhance the security and robustness of the encryption algorithms with a permutation-diffusion structure. To make the encryption procedure more confusing and complex, an image division-shuffling process is put forward, where the plain-image is first divided into four sub-images, and then the position of the pixels in the whole image is shuffled. In order to generate initial conditions and parameters of two chaotic systems, a 280-bit long external secret key is employed. The key space analysis, various statistical analysis, information entropy analysis, differential analysis and key sensitivity analysis are introduced to test the security of the new image encryption algorithm. The cryptosystem speed is analyzed and tested as well. Experimental results confirm that, in comparison to other image encryption schemes, the new algorithm has higher security and is fast for practical image encryption. Moreover, an extensive tolerance analysis of some common image processing operations such as noise adding, cropping, JPEG compression, rotation, brightening and darkening, has been performed on the proposed image encryption technique. Corresponding results reveal that the proposed image encryption method has good robustness against some image processing operations and geometric attacks. PMID:25826602

Nonlinear dynamic simulation of single- and multi-spool core engines

NASA Technical Reports Server (NTRS)

Schobeiri, T.; Lippke, C.; Abouelkheir, M.

1993-01-01

In this paper a new computational method for accurate simulation of the nonlinear dynamic behavior of single- and multi-spool core engines, turbofan engines, and power generation gas turbine engines is presented. In order to perform the simulation, a modularly structured computer code has been developed which includes individual mathematical modules representing various engine components. The generic structure of the code enables the dynamic simulation of arbitrary engine configurations ranging from single-spool thrust generation to multi-spool thrust/power generation engines under adverse dynamic operating conditions. For precise simulation of turbine and compressor components, row-by-row calculation procedures were implemented that account for the specific turbine and compressor cascade and blade geometry and characteristics. The dynamic behavior of the subject engine is calculated by solving a number of systems of partial differential equations, which describe the unsteady behavior of the individual components. In order to ensure the capability, accuracy, robustness, and reliability of the code, comprehensive critical performance assessment and validation tests were performed. As representatives, three different transient cases with single- and multi-spool thrust and power generation engines were simulated. The transient cases range from operating with a prescribed fuel schedule, to extreme load changes, to generator and turbine shut down.

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.

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.

Saturation behavior: a general relationship described by a simple second-order differential equation.

PubMed

Kepner, Gordon R

2010-04-13

The numerous natural phenomena that exhibit saturation behavior, e.g., ligand binding and enzyme kinetics, have been approached, to date, via empirical and particular analyses. This paper presents a mechanism-free, and assumption-free, second-order differential equation, designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation, based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches. For the general saturation curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving factor for the basic saturation behavior is the probability of the interactive site being free, which is described quantitatively. Solving the equation relates the variables in terms of the two empirical constants common to all these phenomena, the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the active site and its dependence on the calculable probability the interactive site is free. These results are illustrated using specific cases, including ligand binding and enzyme kinetics. This leads to a revised understanding of how to interpret the empirical constants, in terms of the variables pertinent to the phenomenon under study. The second-order differential equation revealed the basic underlying relations that describe these saturation phenomena, and the basic mathematical properties of the standard experimental data plot. It was shown how to integrate this differential equation, and define the common basic properties of these phenomena. The results regarding the importance of the slope and the new perspectives on the empirical constants governing the behavior of these phenomena led to an alternative perspective on saturation behavior kinetics. Their essential commonality was revealed by this analysis, based on the second-order differential equation.

Scilab software package for the study of dynamical systems

NASA Astrophysics Data System (ADS)

Bordeianu, C. C.; Beşliu, C.; Jipa, Al.; Felea, D.; Grossu, I. V.

2008-05-01

This work presents a new software package for the study of chaotic flows and maps. The codes were written using Scilab, a software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. It was found that Scilab provides various functions for ordinary differential equation solving, Fast Fourier Transform, autocorrelation, and excellent 2D and 3D graphical capabilities. The chaotic behaviors of the nonlinear dynamics systems were analyzed using phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropy. Various well known examples are implemented, with the capability of the users inserting their own ODE. Program summaryProgram title: Chaos Catalogue identifier: AEAP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 885 No. of bytes in distributed program, including test data, etc.: 5925 Distribution format: tar.gz Programming language: Scilab 3.1.1 Computer: PC-compatible running Scilab on MS Windows or Linux Operating system: Windows XP, Linux RAM: below 100 Megabytes Classification: 6.2 Nature of problem: Any physical model containing linear or nonlinear ordinary differential equations (ODE). Solution method: Numerical solving of ordinary differential equations. The chaotic behavior of the nonlinear dynamical system is analyzed using Poincaré sections, phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropies. Restrictions: The package routines are normally able to handle ODE systems of high orders (up to order twelve and possibly higher), depending on the nature of the problem. Running time: 10 to 20 seconds for problems that do not involve Lyapunov exponents calculation; 60 to 1000 seconds for problems that involve high orders ODE and Lyapunov exponents calculation.

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.

Analyzing Lie symmetry and constructing conservation laws for time-fractional Benny-Lin equation

NASA Astrophysics Data System (ADS)

Rashidi, Saeede; Hejazi, S. Reza

This paper investigates the invariance properties of the time fractional Benny-Lin equation with Riemann-Liouville and Caputo derivatives. This equation can be reduced to the Kawahara equation, fifth-order Kdv equation, the Kuramoto-Sivashinsky equation and Navier-Stokes equation. By using the Lie group analysis method of fractional differential equations (FDEs), we derive Lie symmetries for the Benny-Lin equation. Conservation laws for this equation are obtained with the aid of the concept of nonlinear self-adjointness and the fractional generalization of the Noether’s operators. Furthermore, by means of the invariant subspace method, exact solutions of the equation are also constructed.

RF current sensor

DOEpatents

Moore, James A.; Sparks, Dennis O.

1998-11-10

An RF sensor having a novel current sensing probe and a voltage sensing probe to measure voltage and current. The current sensor is disposed in a transmission line to link all of the flux generated by the flowing current in order to obtain an accurate measurement. The voltage sensor is a flat plate which operates as a capacitive plate to sense voltage on a center conductor of the transmission line, in which the measured voltage is obtained across a resistance leg of a R-C differentiator circuit formed by the characteristic impedance of a connecting transmission line and a capacitance of the plate, which is positioned proximal to the center conductor.

A novel continuous fractional sliding mode control

NASA Astrophysics Data System (ADS)

Muñoz-Vázquez, A. J.; Parra-Vega, V.; Sánchez-Orta, A.

2017-10-01

A new fractional-order controller is proposed, whose novelty is twofold: (i) it withstands a class of continuous but not necessarily differentiable disturbances as well as uncertainties and unmodelled dynamics, and (ii) based on a principle of dynamic memory resetting of the differintegral operator, it is enforced an invariant sliding mode in finite time. Both (i) and (ii) account for exponential convergence of tracking errors, where such principle is instrumental to demonstrate the closed-loop stability, robustness and a sustained sliding motion, as well as that high frequencies are filtered out from the control signal. The proposed methodology is illustrated with a representative simulation study.

Direct magnetocaloric characterization and simulation of thermomagnetic cycles

NASA Astrophysics Data System (ADS)

Porcari, G.; Buzzi, M.; Cugini, F.; Pellicelli, R.; Pernechele, C.; Caron, L.; Brück, E.; Solzi, M.

2013-07-01

An experimental setup for the direct measurement of the magnetocaloric effect capable of simulating high frequency magnetothermal cycles on laboratory-scale samples is described. The study of the magnetocaloric properties of working materials under operative conditions is fundamental for the development of innovative devices. Frequency and time dependent characterization can provide essential information on intrinsic features such as magnetic field induced fatigue in materials undergoing first order magnetic phase transitions. A full characterization of the adiabatic temperature change performed for a sample of Gadolinium across its Curie transition shows the good agreement between our results and literature data and in-field differential scanning calorimetry.

Local convertibility of the ground state of the perturbed toric code

NASA Astrophysics Data System (ADS)

Santra, Siddhartha; Hamma, Alioscia; Cincio, Lukasz; Subasi, Yigit; Zanardi, Paolo; Amico, Luigi

2014-12-01

We present analytical and numerical studies of the behavior of the α -Renyi entropies in the toric code in presence of several types of perturbations aimed at studying the simulability of these perturbations to the parent Hamiltonian using local operations and classical communications (LOCC)—a property called local convertibility. In particular, the derivatives, with respect to the perturbation parameter, present different signs for different values of α within the topological phase. From the information-theoretic point of view, this means that such ground states cannot be continuously deformed within the topological phase by means of catalyst assisted local operations and classical communications (LOCC). Such LOCC differential convertibility is on the other hand always possible in the trivial disordered phase. The non-LOCC convertibility is remarkable because it can be computed on a system whose size is independent of correlation length. This method can therefore constitute an experimentally feasible witness of topological order.

The 1.5 post-Newtonian radiative quadrupole moment in the context of a nonlocal field theory of gravity

NASA Astrophysics Data System (ADS)

Dirkes, Alain

2018-04-01

We recently suggested a nonlocal modification of Einstein’s field equations in which Newton’s constant G was promoted to a covariant differential operator G_Λ(\\Box_g) . The latter contains two independent contributions which operate respectively in the infrared (IR) and ultraviolet (UV) energy regimes. In the light of the recent direct gravitational radiation measurements we aim to determine the UV-modified 1.5 post-Newtonian radiative quadrupole moment of a generic n-body system. We eventually use these preliminary results in the context of a binary system and observe that in the limit vanishing UV parameters we precisely recover the corresponding general relativistic results. Moreover we notice that the leading order deviation of the UV-modified radiative quadrupole moment numerically coincides with findings obtained in the framework of calculations performed previously in the context of the perihelion precession of Mercury.

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

Dyachenko, Sergey A.; Zlotnik, Anatoly; Korotkevich, Alexander O.

Here, we develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for mass flow and pressure on a metric graph, where turbulent losses of momentum are modeled by phenomenological Darcy-Weisbach friction. Mass flow balance is maintained through the boundary conditions at the network nodes, where natural gas is injected or withdrawn from the system. Gas flow through the network is controlled by compressors boosting pressure at the inlet of the adjoint pipe. Our operator splitting numerical scheme ismore » unconditionally stable and it is second order accurate in space and time. The scheme is explicit, and it is formulated to work with general networks with loops. We test the scheme over range of regimes and network configurations, also comparing its performance with performance of two other state of the art implicit schemes.« less

Teaching children with autism spectrum disorders to mand for the removal of stimuli that prevent access to preferred items.

PubMed

Shillingsburg, M Alice; Powell, Nicole M; Bowen, Crystal N

2013-01-01

Mand training is often a primary focus in early language instruction and typically includes mands that are positively reinforced. However, mands maintained by negative reinforcement are also important skills to teach. These include mands to escape aversive demands or unwanted items. Another type of negatively reinforced mand important to teach involves the removal of a stimulus that prevents access to a preferred activity. We taught 5 participants diagnosed with autism spectrum disorders to mand for the removal of a stimulus in order to access a preferred item that had been blocked. An evaluation was conducted to determine if participants responded differentially when the establishing operations for the preferred item were present versus absent. All participants learned to mand for the removal of the stimulus exclusively under conditions when the establishing operation was present.

A self-organizing Lagrangian particle method for adaptive-resolution advection-diffusion simulations

NASA Astrophysics Data System (ADS)

Reboux, Sylvain; Schrader, Birte; Sbalzarini, Ivo F.

2012-05-01

We present a novel adaptive-resolution particle method for continuous parabolic problems. In this method, particles self-organize in order to adapt to local resolution requirements. This is achieved by pseudo forces that are designed so as to guarantee that the solution is always well sampled and that no holes or clusters develop in the particle distribution. The particle sizes are locally adapted to the length scale of the solution. Differential operators are consistently evaluated on the evolving set of irregularly distributed particles of varying sizes using discretization-corrected operators. The method does not rely on any global transforms or mapping functions. After presenting the method and its error analysis, we demonstrate its capabilities and limitations on a set of two- and three-dimensional benchmark problems. These include advection-diffusion, the Burgers equation, the Buckley-Leverett five-spot problem, and curvature-driven level-set surface refinement.

Integrated all-optical logic discriminators based on plasmonic bandgap engineering

PubMed Central

Lu, Cuicui; Hu, Xiaoyong; Yang, Hong; Gong, Qihuang

2013-01-01

Optical computing uses photons as information carriers, opening up the possibility for ultrahigh-speed and ultrawide-band information processing. Integrated all-optical logic devices are indispensible core components of optical computing systems. However, up to now, little experimental progress has been made in nanoscale all-optical logic discriminators, which have the function of discriminating and encoding incident light signals according to wavelength. Here, we report a strategy to realize a nanoscale all-optical logic discriminator based on plasmonic bandgap engineering in a planar plasmonic microstructure. Light signals falling within different operating wavelength ranges are differentiated and endowed with different logic state encodings. Compared with values previously reported, the operating bandwidth is enlarged by one order of magnitude. Also the SPP light source is integrated with the logic device while retaining its ultracompact size. This opens up a way to construct on-chip all-optical information processors and artificial intelligence systems. PMID:24071647

ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

NASA Astrophysics Data System (ADS)

Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

2018-04-01

In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

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 .

Homological Order in Three and Four dimensions: Wilson Algebra, Entanglement Entropy and Twist Defects

NASA Astrophysics Data System (ADS)

Roy, Abhishek; Chen, Xiao; Teo, Jeffrey

2013-03-01

We investigate homological orders in two, three and four dimensions by studying Zk toric code models on simplicial, cellular or in general differential complexes. The ground state degeneracy is obtained from Wilson loop and surface operators, and the homological intersection form. We compute these for a series of closed 3 and 4 dimensional manifolds and study the projective representations of mapping class groups (modular transformations). Braiding statistics between point and string excitations in (3+1)-dimensions or between dual string excitations in (4+1)-dimensions are topologically determined by the higher dimensional linking number, and can be understood by an effective topological field theory. An algorithm for calculating entanglemnent entropy of any bipartition of closed manifolds is presented, and its topological signature is completely characterized homologically. Extrinsic twist defects (or disclinations) are studied in 2,3 and 4 dimensions and are shown to carry exotic fusion and braiding properties. Simons Fellowship

Status of the Short-Pulse X-ray Project at the Advanced Photon Source

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

Nassiri, A; Berenc, T G; Borland, M

2012-07-01

The Advanced Photon Source Upgrade (APS-U) Project at Argonne will include generation of short-pulse x-rays based on Zholents deflecting cavity scheme. We have chosen superconducting (SC) cavities in order to have a continuous train of crabbed bunches and flexibility of operating modes. In collaboration with Jefferson Laboratory, we are prototyping and testing a number of single-cell deflecting cavities and associated auxiliary systems with promising initial results. In collaboration with Lawrence Berkeley National Laboratory, we are working to develop state-of-the-art timing, synchronization, and differential rf phase stability systems that are required for SPX. Collaboration with Advanced Computations Department at Stanford Linearmore » Accelerator Center is looking into simulations of complex, multi-cavity geometries with lower- and higher-order modes waveguide dampers using ACE3P. This contribution provides the current R&D status of the SPX project.« less

Limit Theorems and Their Relation to Solute Transport in Simulated Fractured Media

NASA Astrophysics Data System (ADS)

Reeves, D. M.; Benson, D. A.; Meerschaert, M. M.

2003-12-01

Solute particles that travel through fracture networks are subject to wide velocity variations along a restricted set of directions. This may result in super-Fickian dispersion along a few primary scaling directions. The fractional advection-dispersion equation (FADE), a modification of the original advection-dispersion equation in which a fractional derivative replaces the integer-order dispersion term, has the ability to model rapid, non-Gaussian solute transport. The FADE assumes that solute particle motions converge to either α -stable or operator stable densities, which are modeled by spatial fractional derivatives. In multiple dimensions, the multi-fractional dispersion derivative dictates the order and weight of differentiation in all directions, which correspond to the statistics of large particle motions in all directions. This study numerically investigates the presence of super- Fickian solute transport through simulated two-dimensional fracture networks. An ensemble of networks is gen

Conformal anomaly of generalized form factors and finite loop integrals

NASA Astrophysics Data System (ADS)

Chicherin, Dmitry; Sokatchev, Emery

2018-04-01

We reveal a new mechanism of conformal symmetry breaking at Born level. It occurs in generalized form factors with several local operators and an on-shell state of massless particles. The effect is due to hidden singularities on collinear configurations of the momenta. This conformal anomaly is different from the holomorphic anomaly of amplitudes. We present a number of examples in four and six dimensions. We find an application of the new conformal anomaly to finite loop momentum integrals with one or more massless legs. The collinear region around a massless leg creates a contact anomaly, made visible by the loop integration. The anomalous conformal Ward identity for an ℓ-loop integral is a 2nd-order differential equation whose right-hand side is an (ℓ - 1)-loop integral. It could serve as a new useful tool to find/test analytic expressions for conformal integrals. We illustrate this point with several examples of known integrals. We propose a new differential equation for the four-dimensional scalar double box.

The diagnostic capability of laser induced fluorescence in the characterization of excised breast tissues

NASA Astrophysics Data System (ADS)

Galmed, A. H.; Elshemey, Wael M.

2017-08-01

Differentiating between normal, benign and malignant excised breast tissues is one of the major worldwide challenges that need a quantitative, fast and reliable technique in order to avoid personal errors in diagnosis. Laser induced fluorescence (LIF) is a promising technique that has been applied for the characterization of biological tissues including breast tissue. Unfortunately, only few studies have adopted a quantitative approach that can be directly applied for breast tissue characterization. This work provides a quantitative means for such characterization via introduction of several LIF characterization parameters and determining the diagnostic accuracy of each parameter in the differentiation between normal, benign and malignant excised breast tissues. Extensive analysis on 41 lyophilized breast samples using scatter diagrams, cut-off values, diagnostic indices and receiver operating characteristic (ROC) curves, shows that some spectral parameters (peak height and area under the peak) are superior for characterization of normal, benign and malignant breast tissues with high sensitivity (up to 0.91), specificity (up to 0.91) and accuracy ranking (highly accurate).

Theoretical and experimental characterization of the DUal-BAse transistor (DUBAT)

NASA Astrophysics Data System (ADS)

Wu, Chung-Yu; Wu, Ching-Yuan

1980-11-01

A new A-type integrated voltage controlled differential negative resistance device using an extra effective base region to form a lateral pnp (npn) bipolar transistor beside the original base region of a vertical npn (pnp) bipolar junction transistor, and so called the DUal BAse Transistor (DUBAT), is studied both experimentally and theoretically, The DUBAT has three terminals and is fully comparible with the existing bipolar integrated circuits technologies. Based upon the equivalent circuit of the DUBAT, a simple first-order analytical theory is developed, and important device parameters, such as: the I-V characteristic, the differential negative resistance, and the peak and valley points, are also characterized. One of the proposed integrated structures of the DUBAT, which is similar in structure to I 2L but with similar high density and a normally operated vertical npn transistor, has been successfully fabricated and studied. Comparisons between the experimental data and theoretical analyses are made, and show in satisfactory agreements.

Simultaneous Voltammetric Detection of Carbaryl and Paraquat Pesticides on Graphene-Modified Boron-Doped Diamond Electrode

PubMed Central

Pop, Aniela; Manea, Florica; Flueras, Adriana; Schoonman, Joop

2017-01-01

Monitoring of pesticide residues in food, beverages, and the environment requires fast, versatile, and sensitive analyzing methods. Direct electrochemical detection of pesticides could represent an efficient solution. Adequate electrode material, electrochemical technique, and optimal operation parameters define the detection method for practical application. In this study, cyclic voltammetric and differential pulse voltammetric techniques were used in order to individually and simultaneously detect two pesticides, i.e., carbaryl (CR) and paraquat (PQ), from an acetate buffer solution and also from natural apple juice. A graphene-modified boron-doped diamond electrode, denoted BDDGR, was obtained and successfully applied in the simultaneous detection of CR and PQ pesticides, using the differential pulse voltammetric technique with remarkable electroanalytical parameters in terms of sensitivity: 33.27 μA μM−1 cm−2 for CR and 31.83 μA μM−1 cm−2 for PQ. These outstanding results obtained in the acetate buffer supporting electrolyte allowed us to simultaneously detect the targeted pesticides in natural apple juice. PMID:28878151

Artificial neural network methods in quantum mechanics

NASA Astrophysics Data System (ADS)

Lagaris, I. E.; Likas, A.; Fotiadis, D. I.

1997-08-01

In a previous article we have shown how one can employ Artificial Neural Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigenvalue problems for differential and integrodifferential operators, using ANNs. We start by considering the Schrödinger equation for the Morse potential that has an analytically known solution, to test the accuracy of the method. We then proceed with the Schrödinger and the Dirac equations for a muonic atom, as well as with a nonlocal Schrödinger integrodifferential equation that models the n + α system in the framework of the resonating group method. In two dimensions we consider the well-studied Henon-Heiles Hamiltonian and in three dimensions the model problem of three coupled anharmonic oscillators. The method in all of the treated cases proved to be highly accurate, robust and efficient. Hence it is a promising tool for tackling problems of higher complexity and dimensionality.

Automating the parallel processing of fluid and structural dynamics calculations

NASA Technical Reports Server (NTRS)

Arpasi, Dale J.; Cole, Gary L.

1987-01-01

The NASA Lewis Research Center is actively involved in the development of expert system technology to assist users in applying parallel processing to computational fluid and structural dynamic analysis. The goal of this effort is to eliminate the necessity for the physical scientist to become a computer scientist in order to effectively use the computer as a research tool. Programming and operating software utilities have previously been developed to solve systems of ordinary nonlinear differential equations on parallel scalar processors. Current efforts are aimed at extending these capabilities to systems of partial differential equations, that describe the complex behavior of fluids and structures within aerospace propulsion systems. This paper presents some important considerations in the redesign, in particular, the need for algorithms and software utilities that can automatically identify data flow patterns in the application program and partition and allocate calculations to the parallel processors. A library-oriented multiprocessing concept for integrating the hardware and software functions is described.

7 CFR 1001.52 - Adjusted Class I differentials.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 9 2010-01-01 2009-01-01 true Adjusted Class I differentials. 1001.52 Section 1001.52 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing Agreements and Orders; Milk), DEPARTMENT OF AGRICULTURE MILK IN THE NORTHEAST MARKETING AREA Order Regulating...

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...

(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.

All-optical 1st- and 2nd-order differential equation solvers with large tuning ranges using Fabry-Pérot semiconductor optical amplifiers.

PubMed

Chen, Kaisheng; Hou, Jie; Huang, Zhuyang; Cao, Tong; Zhang, Jihua; Yu, Yuan; Zhang, Xinliang

2015-02-09

We experimentally demonstrate an all-optical temporal computation scheme for solving 1st- and 2nd-order linear ordinary differential equations (ODEs) with tunable constant coefficients by using Fabry-Pérot semiconductor optical amplifiers (FP-SOAs). By changing the injection currents of FP-SOAs, the constant coefficients of the differential equations are practically tuned. A quite large constant coefficient tunable range from 0.0026/ps to 0.085/ps is achieved for the 1st-order differential equation. Moreover, the constant coefficient p of the 2nd-order ODE solver can be continuously tuned from 0.0216/ps to 0.158/ps, correspondingly with the constant coefficient q varying from 0.0000494/ps(2) to 0.006205/ps(2). Additionally, a theoretical model that combining the carrier density rate equation of the semiconductor optical amplifier (SOA) with the transfer function of the Fabry-Pérot (FP) cavity is exploited to analyze the solving processes. For both 1st- and 2nd-order solvers, excellent agreements between the numerical simulations and the experimental results are obtained. The FP-SOAs based all-optical differential-equation solvers can be easily integrated with other optical components based on InP/InGaAsP materials, such as laser, modulator, photodetector and waveguide, which can motivate the realization of the complicated optical computing on a single integrated chip.

[DIFFERENTIATED TACTICS OF VIDEOTHORACOSCOPIC DIAGNOSIS OF THE PLEURAL EXUDATE SYNDROME].

PubMed

Ivashchenko, V E; Kalabukha, I A; Mayetnyi, E M

2016-04-01

Differentiated tactics of diagnostic videothoracoscopy (VTHS) in a pleural exudate syndrome, which ought to be treated with hydrothorax elimination and artificial pneumothorax creation, was proposed. Further roentgenological investigation permits to create a plan for the operation conduction and a certain anesthesia application. Criteria for the operation planning and the anesthesiological support choice were elaborated. Results of VTHS conduction in 261 patients in Department of Thoracic Surgery were analyzed. The differentiated tactics for the VTHS performance application have had saved the patients from the unnecessary endotracheal narcosis conduction, and reduced a pharmacological load on a patient, as well as a rate of contraindications for the operation usage and the stationary treatment duration.

Algorithms For Integrating Nonlinear Differential Equations

NASA Technical Reports Server (NTRS)

Freed, A. D.; Walker, K. P.

1994-01-01

Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

The explicit computation of integration algorithms and first integrals for ordinary differential equations with polynomials coefficients using trees

NASA Technical Reports Server (NTRS)

Crouch, P. E.; Grossman, Robert

1992-01-01

This note is concerned with the explicit symbolic computation of expressions involving differential operators and their actions on functions. The derivation of specialized numerical algorithms, the explicit symbolic computation of integrals of motion, and the explicit computation of normal forms for nonlinear systems all require such computations. More precisely, if R = k(x(sub 1),...,x(sub N)), where k = R or C, F denotes a differential operator with coefficients from R, and g member of R, we describe data structures and algorithms for efficiently computing g. The basic idea is to impose a multiplicative structure on the vector space with basis the set of finite rooted trees and whose nodes are labeled with the coefficients of the differential operators. Cancellations of two trees with r + 1 nodes translates into cancellation of O(N(exp r)) expressions involving the coefficient functions and their derivatives.

Medium-Frequency Data Link for Differential NAVSTAR/GPS Broadcasts

DOT National Transportation Integrated Search

1986-06-01

Differential GPS must communicate differential corrections to civilian users of the Global Positioning System. Modulation of existing marine radiobeacons can provide the needed communication link for DGPS, provided the operation of existing radiobeac...

Attempts at a numerical realisation of stochastic differential equations containing Preisach operator

NASA Astrophysics Data System (ADS)

McCarthy, S.; Rachinskii, D.

2011-01-01

We describe two Euler type numerical schemes obtained by discretisation of a stochastic differential equation which contains the Preisach memory operator. Equations of this type are of interest in areas such as macroeconomics and terrestrial hydrology where deterministic models containing the Preisach operator have been developed but do not fully encapsulate stochastic aspects of the area. A simple price dynamics model is presented as one motivating example for our studies. Some numerical evidence is given that the two numerical schemes converge to the same limit as the time step decreases. We show that the Preisach term introduces a damping effect which increases on the parts of the trajectory demonstrating a stronger upwards or downwards trend. The results are preliminary to a broader programme of research of stochastic differential equations with the Preisach hysteresis operator.

Histogram analysis of apparent diffusion coefficient maps for the differentiation between lymphoma and metastatic lymph nodes of squamous cell carcinoma in head and neck region.

PubMed

Wang, Yan-Jun; Xu, Xiao-Quan; Hu, Hao; Su, Guo-Yi; Shen, Jie; Shi, Hai-Bin; Wu, Fei-Yun

2018-06-01

Background To clarify the nature of cervical malignant lymphadenopathy is highly important for the diagnosis and differential diagnosis of head and neck tumors. Purpose To investigate the role of first-order apparent diffusion coefficient (ADC) histogram analysis for differentiating lymphoma from metastatic lymph nodes of squamous cell carcinoma (SCC) in the head and neck region. Material and Methods Diffusion-weighted imaging (DWI) data of 67 patients (lymphoma, n = 20; SCC, n = 47) with malignant lymphadenopathy were retrospectively analyzed. The SCC group was divided into nasopharyngeal SCC and non-nasopharyngeal SCC groups. The ADC histogram features (ADC 10 , ADC 25 , ADC mean , ADC median , ADC 75 , ADC 90 , skewness, and kurtosis) were derived and then compared by independent-samples t-test and one-way analysis of variance test, respectively. Receiver operating characteristic curve analyses were employed to investigate diagnostic performance of the significant parameters. Results Lymphoma showed significantly lower ADC mean , ADC median , ADC 75 , and ADC 90 than SCC (all P < 0.05). Setting ADC 90  = 0.719 × 10 -3  mm 2 /s as the threshold value, optimal diagnostic performance was achieved (area under the curve [AUC] = 0.719, sensitivity = 95.7%, specificity = 50.0%). Subgroup analyses showed no significant difference between lymphoma and NPC (all P > 0.05). Lymphoma showed significantly lower ADC 25 , ADC mean , ADC median , ADC 75 , and ADC 90 than non-nasopharyngeal SCC (all P < 0.05). Optimal diagnostic performance (AUC = 0.847, sensitivity = 86.7%, specificity = 80.0%) could be achieved when setting ADC 90  = 0.943 × 10 -3  mm 2 /s as the threshold value. Conclusion Given its limitations, our study has shown that first-order ADC histogram analysis is capable of differentiating lymphoma from metastatic lymph nodes of SCC, especially those of non-nasopharyngeal SCC.

Numerical modeling of exciton-polariton Bose-Einstein condensate in a microcavity

NASA Astrophysics Data System (ADS)

Voronych, Oksana; Buraczewski, Adam; Matuszewski, Michał; Stobińska, Magdalena

2017-06-01

A novel, optimized numerical method of modeling of an exciton-polariton superfluid in a semiconductor microcavity was proposed. Exciton-polaritons are spin-carrying quasiparticles formed from photons strongly coupled to excitons. They possess unique properties, interesting from the point of view of fundamental research as well as numerous potential applications. However, their numerical modeling is challenging due to the structure of nonlinear differential equations describing their evolution. In this paper, we propose to solve the equations with a modified Runge-Kutta method of 4th order, further optimized for efficient computations. The algorithms were implemented in form of C++ programs fitted for parallel environments and utilizing vector instructions. The programs form the EPCGP suite which has been used for theoretical investigation of exciton-polaritons. Catalogue identifier: AFBQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: BSD-3 No. of lines in distributed program, including test data, etc.: 2157 No. of bytes in distributed program, including test data, etc.: 498994 Distribution format: tar.gz Programming language: C++ with OpenMP extensions (main numerical program), Python (helper scripts). Computer: Modern PC (tested on AMD and Intel processors), HP BL2x220. Operating system: Unix/Linux and Windows. Has the code been vectorized or parallelized?: Yes (OpenMP) RAM: 200 MB for single run Classification: 7, 7.7. Nature of problem: An exciton-polariton superfluid is a novel, interesting physical system allowing investigation of high temperature Bose-Einstein condensation of exciton-polaritons-quasiparticles carrying spin. They have brought a lot of attention due to their unique properties and potential applications in polariton-based optoelectronic integrated circuits. This is an out-of-equilibrium quantum system confined within a semiconductor microcavity. It is described by a set of nonlinear differential equations similar in spirit to the Gross-Pitaevskii (GP) equation, but their unique properties do not allow standard GP solving frameworks to be utilized. Finding an accurate and efficient numerical algorithm as well as development of optimized numerical software is necessary for effective theoretical investigation of exciton-polaritons. Solution method: A Runge-Kutta method of 4th order was employed to solve the set of differential equations describing exciton-polariton superfluids. The method was fitted for the exciton-polariton equations and further optimized. The C++ programs utilize OpenMP extensions and vector operations in order to fully utilize the computer hardware. Running time: 6h for 100 ps evolution, depending on the values of parameters

Solving ay'' + by' + cy = 0 with a Simple Product Rule Approach

ERIC Educational Resources Information Center

Tolle, John

2011-01-01

When elementary ordinary differential equations (ODEs) of first and second order are included in the calculus curriculum, second-order linear constant coefficient ODEs are typically solved by a method more appropriate to differential equations courses. This method involves the characteristic equation and its roots, complex-valued solutions, and…

Generalization of the Bernoulli ODE

ERIC Educational Resources Information Center

Azevedo, Douglas; Valentino, Michele C.

2017-01-01

In this note, we propose a generalization of the famous Bernoulli differential equation by introducing a class of nonlinear first-order ordinary differential equations (ODEs). We provide a family of solutions for this introduced class of ODEs and also we present some examples in order to illustrate the applications of our result.

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).

Monitoring of Emissions From a Refinery Tank Farm Using a Combination of Optical Remote Sensing Techniques

NASA Astrophysics Data System (ADS)

Polidori, A.; Tisopulos, L.; Pikelnaya, O.; Mellqvist, J.; Samuelsson, J.; Marianne, E.; Robinson, R. A.; Innocenti, F.; Finlayson, A.; Hashmonay, R.

2016-12-01

Despite great advances in reducing air pollution, the South Coast Air Basin (SCAB) still faces challenges to attain federal health standards for air quality. Refineries are large sources of ozone precursors and, hence contribute to the air quality problems of the region. Additionally, petrochemical facilities are also sources of other hazardous air pollutants (HAP) that adversely affect human health, for example aromatic hydrocarbons. In order to assure safe operation, decrease air pollution and minimize population exposure to HAP the South Coast Air Quality Management District (SCAQMD) has a number of regulations for petrochemical facilities. However, significant uncertainties still exist in emission estimates and traditional monitoring techniques often do not allow for real-time emission monitoring. In the fall of 2015 the SCAQMD, Fluxsense Inc., the National Physical Laboratory (NPL), and Atmosfir Optics Ltd. conducted a measurement study to characterize and quantify gaseous emissions from the tank farm of one of the largest oil refineries in the SCAB. Fluxsense used a vehicle equipped with Solar Occultation Flux (SOF), Differential Optical Absorption Spectroscopy (DOAS), and Extractive Fourier Transform Infrared (FTIR) spectroscopy instruments. Concurrently, NPL operated their Differential Absorption Lidar (DIAL) system. Both research groups quantified emissions from the entire tank farm and identified fugitive emission sources within the farm. At the same time, Atmosfir operated an Open Path FTIR (OP-FTIR) spectrometer along the fenceline of the tank farm. During this presentation we will discuss the results of the emission measurements from the tank farm of the petrochemical facility. Emission rates resulting from measurements by different ORS methods will be compared and discussed in detail.

Variable Order and Distributed Order Fractional Operators

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

2002-01-01

Many physical processes appear to exhibit fractional order behavior that may vary with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. This paper develops the concept of variable and distributed order fractional operators. Definitions based on the Riemann-Liouville definitions are introduced and behavior of the operators is studied. Several time domain definitions that assign different arguments to the order q in the Riemann-Liouville definition are introduced. For each of these definitions various characteristics are determined. These include: time invariance of the operator, operator initialization, physical realization, linearity, operational transforms. and memory characteristics of the defining kernels. A measure (m2) for memory retentiveness of the order history is introduced. A generalized linear argument for the order q allows the concept of "tailored" variable order fractional operators whose a, memory may be chosen for a particular application. Memory retentiveness (m2) and order dynamic behavior are investigated and applications are shown. The concept of distributed order operators where the order of the time based operator depends on an additional independent (spatial) variable is also forwarded. Several definitions and their Laplace transforms are developed, analysis methods with these operators are demonstrated, and examples shown. Finally operators of multivariable and distributed order are defined in their various applications are outlined.

Modeling Differentiation of Cognitive Abilities within the Higher-Order Factor Model Using Moderated Factor Analysis

ERIC Educational Resources Information Center

Molenaar, Dylan; Dolan, Conor V.; Wicherts, Jelte M.; van der Maas, Han L. J.

2010-01-01

The general differentiation hypothesis states that the strength of the correlations among a set of IQ subtests varies with a given variable. Instances of the general differentiation hypothesis that have been considered in the literature include age and ability differentiation. Traditionally, the differentiation effect is attributed to the varying…

Differentiated Storytelling: From Focused Observation to Strategic Teaching

ERIC Educational Resources Information Center

Abilock, Debbie, Ed.

2008-01-01

Differentiated teaching focuses on the student--the varying needs, interests and abilities in the classroom--in order to design curriculum which results in student understanding through application. Some differentiation implementations are little more than tweaks, but if one is ambitious, differentiation modifications can require substantial time…

Characteristic operator functions for quantum input-plant-output models and coherent control

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

Gough, John E.

We introduce the characteristic operator as the generalization of the usual concept of a transfer function of linear input-plant-output systems to arbitrary quantum nonlinear Markovian input-output models. This is intended as a tool in the characterization of quantum feedback control systems that fits in with the general theory of networks. The definition exploits the linearity of noise differentials in both the plant Heisenberg equations of motion and the differential form of the input-output relations. Mathematically, the characteristic operator is a matrix of dimension equal to the number of outputs times the number of inputs (which must coincide), but with entriesmore » that are operators of the plant system. In this sense, the characteristic operator retains details of the effective plant dynamical structure and is an essentially quantum object. We illustrate the relevance to model reduction and simplification definition by showing that the convergence of the characteristic operator in adiabatic elimination limit models requires the same conditions and assumptions appearing in the work on limit quantum stochastic differential theorems of Bouten and Silberfarb [Commun. Math. Phys. 283, 491-505 (2008)]. This approach also shows in a natural way that the limit coefficients of the quantum stochastic differential equations in adiabatic elimination problems arise algebraically as Schur complements and amounts to a model reduction where the fast degrees of freedom are decoupled from the slow ones and eliminated.« less

A trust-region algorithm for the optimization of PSA processes using reduced-order modeling

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

Agarwal, A.; Biegler, L.; Zitney, S.

2009-01-01

The last few decades have seen a considerable increase in the applications of adsorptive gas separation technologies, such as pressure swing adsorption (PSA); the applications range from bulk separations to trace contaminant removal. PSA processes are based on solid-gas equilibrium and operate under periodic transient conditions [1]. Bed models for these processes are therefore defined by coupled nonlinear partial differential and algebraic equations (PDAEs) distributed in space and time with periodic boundary conditions that connect the processing steps together and high nonlinearities arising from non-isothermal effects and nonlinear adsorption isotherms. As a result, the optimization of such systems for eithermore » design or operation represents a significant computational challenge to current nonlinear programming algorithms. Model reduction is a powerful methodology that permits systematic generation of cost-efficient low-order representations of large-scale systems that result from discretization of such PDAEs. In particular, low-dimensional approximations can be obtained from reduced order modeling (ROM) techniques based on proper orthogonal decomposition (POD) and can be used as surrogate models in the optimization problems. In this approach, a representative ensemble of solutions of the dynamic PDAE system is constructed by solving a higher-order discretization of the model using the method of lines, followed by the application of Karhunen-Loeve expansion to derive a small set of empirical eigenfunctions (POD modes). These modes are used as basis functions within a Galerkin's projection framework to derive a low-order DAE system that accurately describes the dominant dynamics of the PDAE system. This approach leads to a DAE system of significantly lower order, thus replacing the one obtained from spatial discretization before and making optimization problem computationally efficient [2]. The ROM methodology has been successfully applied to a 2-bed 4-step PSA process used for separating a hydrogen-methane mixture in [3]. The reduced order model developed was successfully used to optimize this process to maximize hydrogen recovery within a trust-region. We extend this approach in this work to develop a rigorous trust-region algorithm for ROM-based optimization of PSA processes. The trust-region update rules and sufficient decrease condition for the objective is used to determine the size of the trust-region. Based on the decrease in the objective function and error in the ROM, a ROM updation strategy is designed [4, 5]. The inequalities and bounds are handled in the algorithm using exact penalty formulation, and a non-smooth trust-region algorithm by Conn et al. [6] is used to handle non-differentiability. To ensure that the first order consistency condition is met and the optimum obtained from ROM-based optimization corresponds to the optimum of the original problem, a scaling function, such as one proposed by Alexandrov et al. [7], is incorporated in the objective function. Such error control mechanism is also capable of handling numerical inconsistencies such as unphysical oscillations in the state variable profiles. The proposed methodology is applied to optimize a PSA process to concentrate CO{sub 2} from a nitrogen-carbon dioxide mixture. As in [3], separate ROMs are developed for each operating step with different POD modes for each state variable. Numerical results will be presented for optimization case studies which involve maximizing CO{sub 2} recovery, feed throughput or minimizing overall power consumption.« less

Interval oscillation criteria for second-order forced impulsive delay differential equations with damping term.

PubMed

Thandapani, Ethiraju; Kannan, Manju; Pinelas, Sandra

2016-01-01

In this paper, we present some sufficient conditions for the oscillation of all solutions of a second order forced impulsive delay differential equation with damping term. Three factors-impulse, delay and damping that affect the interval qualitative properties of solutions of equations are taken into account together. The results obtained in this paper extend and generalize some of the the known results for forced impulsive differential equations. An example is provided to illustrate the main result.

Differentiating constitutional thinness from anorexia nervosa in DSM 5 era.

PubMed

Estour, Bruno; Marouani, Nesrine; Sigaud, Torrance; Lang, François; Fakra, Eric; Ling, Yiin; Diamondé, Aurélie; Minnion, James S; Galusca, Bogdan; Germain, Natacha

2017-10-01

Constitutional thinness (CT) is an underweight state characterized by normal menstruations and no change in feeding behaviour. Thinness is the only resemblance between Anorexia Nervosa (AN) and CT. Removal of amenorrhea from the new DSM 5 definition of AN might result in misdiagnosis between these two populations. The objective of this study was to compare CT, AN and Control subjects in terms of biological, anthropometric, and psychological markers in order to better distinguish AN from CT subjects. Body composition, nutritional markers, pituitary hormones, bone markers and psychological scores were evaluated in three groups of young women: fifty-six CT, forty restrictive-type AN and fifty-four Control subjects. For every marker, a receiver Operator Characteristics (ROC) curve was calculated to evaluate the accuracy of differentiation between AN and CT groups. For most studied parameters, CT subjects were similar to Controls but dramatically different from AN subjects. DEBQ Restrained Eating subscale score was identified by ROC data analysis as the only psychological parameter tested to successfully differentiate AN from CT. Free-T3 and Leptin were shown to be powerful markers to differentiate AN and CT populations as they were highly specific and sensitive ones. The exclusive use of psychological testing criteria is not always sufficient to differentiate AN and CT patients. Minimally, additional testing of Free T3 levels, which is cheap and widely accessible for general practitioners, should be completed to avoid misdiagnosis which could result in the implementation of ineffective treatment plans and social stigmatization for CT women. Copyright © 2017 Elsevier Ltd. All rights reserved.

FPGA-based distributed computing microarchitecture for complex physical dynamics investigation.

PubMed

Borgese, Gianluca; Pace, Calogero; Pantano, Pietro; Bilotta, Eleonora

2013-09-01

In this paper, we present a distributed computing system, called DCMARK, aimed at solving partial differential equations at the basis of many investigation fields, such as solid state physics, nuclear physics, and plasma physics. This distributed architecture is based on the cellular neural network paradigm, which allows us to divide the differential equation system solving into many parallel integration operations to be executed by a custom multiprocessor system. We push the number of processors to the limit of one processor for each equation. In order to test the present idea, we choose to implement DCMARK on a single FPGA, designing the single processor in order to minimize its hardware requirements and to obtain a large number of easily interconnected processors. This approach is particularly suited to study the properties of 1-, 2- and 3-D locally interconnected dynamical systems. In order to test the computing platform, we implement a 200 cells, Korteweg-de Vries (KdV) equation solver and perform a comparison between simulations conducted on a high performance PC and on our system. Since our distributed architecture takes a constant computing time to solve the equation system, independently of the number of dynamical elements (cells) of the CNN array, it allows us to reduce the elaboration time more than other similar systems in the literature. To ensure a high level of reconfigurability, we design a compact system on programmable chip managed by a softcore processor, which controls the fast data/control communication between our system and a PC Host. An intuitively graphical user interface allows us to change the calculation parameters and plot the results.

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.

A neuro approach to solve fuzzy Riccati differential equations

NASA Astrophysics Data System (ADS)

Shahrir, Mohammad Shazri; Kumaresan, N.; Kamali, M. Z. M.; Ratnavelu, Kurunathan

2015-10-01

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

A neuro approach to solve fuzzy Riccati differential equations

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

Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com; Telekom Malaysia, R&D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor; Kumaresan, N., E-mail: drnk2008@gmail.com

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

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.

Dimensional analysis yields the general second-order differential equation underlying many natural phenomena: the mathematical properties of a phenomenon's data plot then specify a unique differential equation for it.

PubMed

Kepner, Gordon R

2014-08-27

This study uses dimensional analysis to derive the general second-order differential equation that underlies numerous physical and natural phenomena described by common mathematical functions. It eschews assumptions about empirical constants and mechanisms. It relies only on the data plot's mathematical properties to provide the conditions and constraints needed to specify a second-order differential equation that is free of empirical constants for each phenomenon. A practical example of each function is analyzed using the general form of the underlying differential equation and the observable unique mathematical properties of each data plot, including boundary conditions. This yields a differential equation that describes the relationship among the physical variables governing the phenomenon's behavior. Complex phenomena such as the Standard Normal Distribution, the Logistic Growth Function, and Hill Ligand binding, which are characterized by data plots of distinctly different sigmoidal character, are readily analyzed by this approach. It provides an alternative, simple, unifying basis for analyzing each of these varied phenomena from a common perspective that ties them together and offers new insights into the appropriate empirical constants for describing each phenomenon.

A semi-analytical method for the computation of the Lyapunov exponents of fractional-order systems

NASA Astrophysics Data System (ADS)

Caponetto, Riccardo; Fazzino, Stefano

2013-01-01

Fractional-order differential equations are interesting for their applications in the construction of mathematical models in finance, materials science or diffusion. In this paper, an application of a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equation is employed for calculating Lyapunov exponents of fractional order systems. It is known that the Lyapunov exponents, first introduced by Oseledec, play a crucial role in characterizing the behaviour of dynamical systems. They can be used to analyze the sensitive dependence on initial conditions and the presence of chaotic attractors. The results reveal that the proposed method is very effective and simple and leads to accurate, approximately convergent solutions.

Source signature of volatile organic compounds from oil and natural gas operations in northeastern Colorado.

PubMed

Gilman, J B; Lerner, B M; Kuster, W C; de Gouw, J A

2013-02-05

An extensive set of volatile organic compounds (VOCs) was measured at the Boulder Atmospheric Observatory (BAO) in winter 2011 in order to investigate the composition and influence of VOC emissions from oil and natural gas (O&NG) operations in northeastern Colorado. BAO is 30 km north of Denver and is in the southwestern section of Wattenberg Field, one of Colorado's most productive O&NG fields. We compare VOC concentrations at BAO to those of other U.S. cities and summertime measurements at two additional sites in northeastern Colorado, as well as the composition of raw natural gas from Wattenberg Field. These comparisons show that (i) the VOC source signature associated with O&NG operations can be clearly differentiated from urban sources dominated by vehicular exhaust, and (ii) VOCs emitted from O&NG operations are evident at all three measurement sites in northeastern Colorado. At BAO, the reactivity of VOCs with the hydroxyl radical (OH) was dominated by C(2)-C(6) alkanes due to their remarkably large abundances (e.g., mean propane = 27.2 ppbv). Through statistical regression analysis, we estimate that on average 55 ± 18% of the VOC-OH reactivity was attributable to emissions from O&NG operations indicating that these emissions are a significant source of ozone precursors.

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.

A Real Time Differential GPS Tracking System for NASA Sounding Rockets

NASA Technical Reports Server (NTRS)

Bull, Barton; Bauer, Frank (Technical Monitor)

2000-01-01

Sounding rockets are suborbital launch vehicles capable of carrying scientific payloads to several hundred miles in altitude. These missions return a variety of scientific data including: chemical makeup and physical processes taking place in the atmosphere, natural radiation surrounding the Earth, data on the Sun, stars, galaxies and many other phenomena. In addition, sounding rockets provide a reasonably economical means of conducting engineering tests for instruments and devices to be used on satellites and other spacecraft prior to their use in these more expensive missions. Typically around thirty of these rockets are launched each year, from established ranges at Wallops Island, Virginia; Poker Flat Research Range, Alaska; White Sands Missile Range, New Mexico and from a number of ranges outside the United States. Many times launches are conducted from temporary launch ranges in remote parts of the world requiring considerable expense to transport and operate tracking radars. In order to support these missions, an inverse differential GPS system has been developed. The flight system consists of a small, inexpensive receiver, a preamplifier and a wrap-around antenna. A rugged, compact, portable ground station extracts GPS data from the raw payload telemetry stream, performs a real time differential solution and graphically displays the rocket's path relative to a predicted trajectory plot. In addition to generating a real time navigation solution, the system has been used for payload recovery, timing, data timetagging, precise tracking of multiple payloads and slaving of optical tracking systems for over the horizon acquisition. This paper discusses, in detail, the flight and ground hardware, as well as data processing and operational aspects of the system, and provides evidence of the system accuracy.

Rethinking pedagogy for second-order differential equations: a simplified approach to understanding well-posed problems

NASA Astrophysics Data System (ADS)

Tisdell, Christopher C.

2017-07-01

Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching 'well posedness' of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a first-order system of equations. We show that this excursion is unnecessary and present a direct approach regarding second- and higher-order problems that does not require an understanding of systems.

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

2014-01-01

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

Vulnerability of point-of-care test reagents and instruments to environmental stresses: implications for health professionals and developers.

PubMed

Louie, Richard F; Ferguson, William J; Curtis, Corbin M; Vy, John H; Kost, Gerald J

2014-03-01

Strategic integration of point-of-care (POC) diagnostic tools during crisis response can accelerate triage and improve management of victims. Timely differential diagnosis is essential wherever care is provided to rule out or rule in disease, expedite life-saving treatment, and improve utilization of limited resources. POC testing needs to be accurate in any environment in which it is used. Devices are exposed to potentially adverse storage and operating conditions, such as high/low temperature and humidity during emergencies and field rescues. Therefore, characterizing environmental conditions allows technology developers, operators, and responders to understand the broad operational requirements of test reagents, instruments, and equipment in order to improve the quality and delivery of care in complex emergencies, disasters, and austere environmental settings. This review aims to describe the effects of environmental stress on POC testing performance and its impact on decision-making, to describe how to study the effects, and to summarize ways to mitigate the effects of environmental stresses through good laboratory practice, development of robust reagents, and novel thermal packaging solutions.

The symbolic computation and automatic analysis of trajectories

NASA Technical Reports Server (NTRS)

Grossman, Robert

1991-01-01

Research was generally done on computation of trajectories of dynamical systems, especially control systems. Algorithms were further developed for rewriting expressions involving differential operators. The differential operators involved arise in the local analysis of nonlinear control systems. An initial design was completed of the system architecture for software to analyze nonlinear control systems using data base computing.

The Effect of Differential Motivation on IRT Linking

ERIC Educational Resources Information Center

Mittelhaëuser, Marie-Anne; Béguin, Anton A.; Sijtsma, Klaas

2015-01-01

The purpose of this study was to investigate whether simulated differential motivation between the stakes for operational tests and anchor items produces an invalid linking result if the Rasch model is used to link the operational tests. This was done for an external anchor design and a variation of a pretest design. The study also investigated…

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

De Geronimo, Gianluigi

Embodiments of comparator circuits are disclosed. A comparator circuit may include a differential input circuit, an output circuit, a positive feedback circuit operably coupled between the differential input circuit and the output circuit, and a hysteresis control circuit operably coupled with the positive feedback circuit. The hysteresis control circuit includes a switching device and a transistor. The comparator circuit provides sub-hysteresis discrimination and high speed discrimination.

Ferroelectric Field-Effect Transistor Differential Amplifier Circuit Analysis

NASA Technical Reports Server (NTRS)

Phillips, Thomas A.; MacLeod, Todd C.; Ho, Fat D.

2008-01-01

There has been considerable research investigating the Ferroelectric Field-Effect Transistor (FeFET) in memory circuits. However, very little research has been performed in applying the FeFET to analog circuits. This paper investigates the use of FeFETs in a common analog circuit, the differential amplifier. The two input Metal-Oxide-Semiconductor (MOS) transistors in a general MOS differential amplifier circuit are replaced with FeFETs. Resistors are used in place of the other three MOS transistors. The FeFET model used in the analysis has been previously reported and was based on experimental device data. Because of the FeFET hysteresis, the FeFET differential amplifier has four different operating modes depending on whether the FeFETs are positively or negatively polarized. The FeFET differential amplifier operation in the different modes was analyzed by calculating the amplifier voltage transfer and gain characteristics shown in figures 2 through 5. Comparisons were made between the FeFET differential amplifier and the standard MOS differential amplifier. Possible applications and benefits of the FeFET differential amplifier are discussed.

Dual exponential polynomials and linear differential equations

NASA Astrophysics Data System (ADS)

Wen, Zhi-Tao; Gundersen, Gary G.; Heittokangas, Janne

2018-01-01

We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.

The Effects of the Reverse Current Caused by the Series Compensation on the Current Differential Protection

PubMed Central

Tang, Cui; Yin, Xianggen; Qi, Xuanwei; Zhang, Zhe

2014-01-01

The series capacitor compensation is one of the key technologies in the EHV and UHV long distance power transmission lines. This paper analyzes the operation characteristics of the main protection combined with the engineering practice when the transmission line overcompensation due to the series compensation system is modified and analyzes the influence of the transition resistance and the system operation mode on the current differential protection. According to the simulation results, it presents countermeasure on improving the sensitivity of differential current protection. PMID:25247206

Note: cryogenic low-noise dc-coupled wideband differential amplifier based on SiGe heterojunction bipolar transistors.

PubMed

Beev, Nikolai; Kiviranta, Mikko

2012-06-01

Silicon-germanium heterojunction bipolar transistors can be used to construct low-noise cryogenic amplifiers. We present a dc-coupled differential amplifier capable of operating down to 10 K. In this temperature regime it has bandwidth of 15 MHz and noise temperature as low as 1.3 K. When operated at liquid nitrogen temperature of 77 K, the measured noise temperature is lower than 3 K. The amplifier is based on the commercially available transistors NESG3031 and operational amplifier OPA836 and is capable of standalone operation without any additional stages at room temperature.

Limited-memory adaptive snapshot selection for proper orthogonal decomposition

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

Oxberry, Geoffrey M.; Kostova-Vassilevska, Tanya; Arrighi, Bill

2015-04-02

Reduced order models are useful for accelerating simulations in many-query contexts, such as optimization, uncertainty quantification, and sensitivity analysis. However, offline training of reduced order models can have prohibitively expensive memory and floating-point operation costs in high-performance computing applications, where memory per core is limited. To overcome this limitation for proper orthogonal decomposition, we propose a novel adaptive selection method for snapshots in time that limits offline training costs by selecting snapshots according an error control mechanism similar to that found in adaptive time-stepping ordinary differential equation solvers. The error estimator used in this work is related to theory boundingmore » the approximation error in time of proper orthogonal decomposition-based reduced order models, and memory usage is minimized by computing the singular value decomposition using a single-pass incremental algorithm. Results for a viscous Burgers’ test problem demonstrate convergence in the limit as the algorithm error tolerances go to zero; in this limit, the full order model is recovered to within discretization error. The resulting method can be used on supercomputers to generate proper orthogonal decomposition-based reduced order models, or as a subroutine within hyperreduction algorithms that require taking snapshots in time, or within greedy algorithms for sampling parameter space.« less

Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations.

PubMed

Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

2015-12-01

The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

Bifurcation and chaos of a new discrete fractional-order logistic map

NASA Astrophysics Data System (ADS)

Ji, YuanDong; Lai, Li; Zhong, SuChuan; Zhang, Lu

2018-04-01

The fractional-order discrete maps with chaotic behaviors based on the theory of ;fractional difference; are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps.

On hyperbolicity and Gevrey well-posedness. Part two: Scalar or degenerate transitions

NASA Astrophysics Data System (ADS)

Morisse, Baptiste

2018-04-01

For first-order quasi-linear systems of partial differential equations, we formulate an assumption of a transition from initial hyperbolicity to ellipticity. This assumption bears on the principal symbol of the first-order operator. Under such an assumption, we prove a strong Hadamard instability for the associated Cauchy problem, namely an instantaneous defect of Hölder continuity of the flow from Gσ to L2, with 0 < σ <σ0, the limiting Gevrey index σ0 depending on the nature of the transition. We restrict here to scalar transitions, and non-scalar transitions in which the boundary of the hyperbolic zone satisfies a flatness condition. As in our previous work for initially elliptic Cauchy problems [B. Morisse, On hyperbolicity and Gevrey well-posedness. Part one: the elliptic case, arxiv:arXiv:1611.07225], the instability follows from a long-time Cauchy-Kovalevskaya construction for highly oscillating solutions. This extends recent work of N. Lerner, T. Nguyen, and B. Texier [The onset of instability in first-order systems, to appear in J. Eur. Math. Soc.].

The Use of an Electron Microchannel as a Self-Extracting and Focusing Plasma Cathode Electron Gun

NASA Astrophysics Data System (ADS)

Cornish, S.; Khachan, J.

2016-02-01

A new and simple type of electron gun is presented. Unlike conventional electron guns, which require a heated filament or extractor, accelerator and focusing electrodes, this gun uses the collimated electron microchannels of an inertial electrostatic confinement (IEC) discharge to achieve the same outcome. A cylindrical cathode is placed coaxially within a cylindrical anode to create the discharge. Collimated beams of electrons and fast neutrals emerge along the axis of the cylindrical cathode. This geometry isolates one of the microchannels that emerge in a negatively biased IEC grid. The internal operating pressure range of the gun is 35-190 mTorr. A small aperture separates the gun from the main vacuum chamber in order to achieve a pressure differential. The chamber was operated at pressures of 4-12 mTorr. The measured current produced by the gun was 0.1-3 mA (0.2-14 mA corrected measurement) for discharge currents of 1-45 mA and discharge voltages of 0.5-12 kV. The collimated electron beam emerges from the aperture into the vacuum chamber. The performance of the gun is unaffected by the pressure differential between the vacuum chamber and the gun. This allows the aperture to be removed and the chamber pressure to be equal to the gun pressure if required.

Fully differential Higgs boson pair production in association with a Z boson at next-to-next-to-leading order in QCD

NASA Astrophysics Data System (ADS)

Li, Hai Tao; Li, Chong Sheng; Wang, Jian

2018-04-01

We present a fully differential next-to-next-to-leading order QCD calculation of the Higgs pair production in association with a Z boson at hadron colliders, which is important for probing the trilinear Higgs self-coupling. The next-to-next-to-leading-order corrections enhance the next-to-leading order total cross sections by a factor of 1.2-1.5, depending on the collider energy, and change the shape of next-to-leading order kinematic distributions. We discuss how to determine the trilinear Higgs self-coupling using our results.

Fully differential Higgs boson pair production in association with a Z boson at next-to-next-to-leading order in QCD

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

Li, Hai Tao; Li, Chong Sheng; Wang, Jian

Here, we present a fully differential next-to-next-to-leading order QCD calculation of the Higgs pair production in association with a Z boson at hadron colliders, which is important for probing the trilinear Higgs self-coupling. The next-to-next-to-leading-order corrections enhance the next-to-leading order total cross sections by a factor of 1.2–1.5, depending on the collider energy, and change the shape of next-to-leading order kinematic distributions. We discuss how to determine the trilinear Higgs self-coupling using our results.

Fully differential Higgs boson pair production in association with a Z boson at next-to-next-to-leading order in QCD

DOE PAGES

Li, Hai Tao; Li, Chong Sheng; Wang, Jian

2018-04-23

Here, we present a fully differential next-to-next-to-leading order QCD calculation of the Higgs pair production in association with a Z boson at hadron colliders, which is important for probing the trilinear Higgs self-coupling. The next-to-next-to-leading-order corrections enhance the next-to-leading order total cross sections by a factor of 1.2–1.5, depending on the collider energy, and change the shape of next-to-leading order kinematic distributions. We discuss how to determine the trilinear Higgs self-coupling using our results.

Theoretical study of the incompressible Navier-Stokes equations by the least-squares method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Loh, Ching Y.; Povinelli, Louis A.

1994-01-01

Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis.

Estimating maneuvers for precise relative orbit determination using GPS

NASA Astrophysics Data System (ADS)

Allende-Alba, Gerardo; Montenbruck, Oliver; Ardaens, Jean-Sébastien; Wermuth, Martin; Hugentobler, Urs

2017-01-01

Precise relative orbit determination is an essential element for the generation of science products from distributed instrumentation of formation flying satellites in low Earth orbit. According to the mission profile, the required formation is typically maintained and/or controlled by executing maneuvers. In order to generate consistent and precise orbit products, a strategy for maneuver handling is mandatory in order to avoid discontinuities or precision degradation before, after and during maneuver execution. Precise orbit determination offers the possibility of maneuver estimation in an adjustment of single-satellite trajectories using GPS measurements. However, a consistent formulation of a precise relative orbit determination scheme requires the implementation of a maneuver estimation strategy which can be used, in addition, to improve the precision of maneuver estimates by drawing upon the use of differential GPS measurements. The present study introduces a method for precise relative orbit determination based on a reduced-dynamic batch processing of differential GPS pseudorange and carrier phase measurements, which includes maneuver estimation as part of the relative orbit adjustment. The proposed method has been validated using flight data from space missions with different rates of maneuvering activity, including the GRACE, TanDEM-X and PRISMA missions. The results show the feasibility of obtaining precise relative orbits without degradation in the vicinity of maneuvers as well as improved maneuver estimates that can be used for better maneuver planning in flight dynamics operations.

LOOP- SIMULATION OF THE AUTOMATIC FREQUENCY CONTROL SUBSYSTEM OF A DIFFERENTIAL MINIMUM SHIFT KEYING RECEIVER

NASA Technical Reports Server (NTRS)

Davarian, F.

1994-01-01

The LOOP computer program was written to simulate the Automatic Frequency Control (AFC) subsystem of a Differential Minimum Shift Keying (DMSK) receiver with a bit rate of 2400 baud. The AFC simulated by LOOP is a first order loop configuration with a first order R-C filter. NASA has been investigating the concept of mobile communications based on low-cost, low-power terminals linked via geostationary satellites. Studies have indicated that low bit rate transmission is suitable for this application, particularly from the frequency and power conservation point of view. A bit rate of 2400 BPS is attractive due to its applicability to the linear predictive coding of speech. Input to LOOP includes the following: 1) the initial frequency error; 2) the double-sided loop noise bandwidth; 3) the filter time constants; 4) the amount of intersymbol interference; and 5) the bit energy to noise spectral density. LOOP output includes: 1) the bit number and the frequency error of that bit; 2) the computed mean of the frequency error; and 3) the standard deviation of the frequency error. LOOP is written in MS SuperSoft FORTRAN 77 for interactive execution and has been implemented on an IBM PC operating under PC DOS with a memory requirement of approximately 40K of 8 bit bytes. This program was developed in 1986.

State-to-state reaction dynamics of {sup 18}O+{sup 32}O{sub 2} studied by a time-dependent quantum wavepacket method

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

Xie, Wenbo; Liu, Lan; Sun, Zhigang, E-mail: zsun@dicp.ac.cn

2015-02-14

The title isotope exchange reaction was studied by converged time-dependent wave packet calculations, where an efficient 4th order split operator was applied to propagate the initial wave packet. State-to-state differential and integral cross sections up to the collision energy of 0.35 eV were obtained with {sup 32}O{sub 2} in the hypothetical j{sub 0} = 0 state. It is discovered that the differential cross sections are largely forward biased in the studied collision energy range, due to the fact that there is a considerable part of the reaction occurring with large impact parameter and short lifetime relative to the rotational periodmore » of the intermediate complex. The oscillations of the forward scattering amplitude as a function of collision energy, which result from coherent contribution of adjacent resonances, may be a sensitive probe for examining the quality of the underlying potential energy surface. A good agreement between the theoretical and recent experimental integral and differential cross sections at collision energy of 7.3 kcal/mol is obtained. However, the theoretical results predict slightly too much forward scattering and colder rotational distributions than the experimental observations at collision energy of 5.7 kcal/mol.« less

Lithium Chloride can Induce Differentiation of Human Immortalized RenVm Cells into Dopaminergic Neurons.

PubMed

Soleimani, Mitra; Ghasemi, Nazem

2017-01-01

Stem cell-based therapy is a novel strategy for the treatment of neurodegenerative diseases. The transplantation of fully differentiated cells instead of stem cells in order to decrease serious adverse complications of stem cell therapy is a new idea. In this study, the effect of lithium chloride on dopaminergic differentiation of human immortalized RenVm cells was investigated in order to access a population of fully differentiated cells for transplantation in Parkinson disease. The immortalized RenVm cells were induced to dopaminergic differentiation using a neurobasal medium supplemented with N2 and different concentrations (1, 3, 6 mM ) of Lithium Chloride (LiCl) for 4, 8 and 12 days. The efficiency of dopaminergic differentiation was evaluated using immunocytochemistry and western blot techniques for tyrosine hydroxylase and β-catenin marker expression. Our results indicated that LiCl can promote dopaminergic differentiation of RenVm cells in a dose-dependent manner. It can be concluded that LiCl is able to facilitate dopaminergic differentiation of cultured cells by affecting Wnt-frizzled signaling pathway.

On analyticity of linear waves scattered by a layered medium

NASA Astrophysics Data System (ADS)

Nicholls, David P.

2017-10-01

The scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering. In this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of High-Order Perturbation of Surfaces methods for simulating such waves. More specifically, we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a multiply layered periodic structure in three dimensions. This result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of Operator Expansions, Field Expansions, and Transformed Field Expansions.

Surface Acoustic Wave Monitor for Deposition and Analysis of Ultra-Thin Films

NASA Technical Reports Server (NTRS)

Hines, Jacqueline H. (Inventor)

2015-01-01

A surface acoustic wave (SAW) based thin film deposition monitor device and system for monitoring the deposition of ultra-thin films and nanomaterials and the analysis thereof is characterized by acoustic wave device embodiments that include differential delay line device designs, and which can optionally have integral reference devices fabricated on the same substrate as the sensing device, or on a separate device in thermal contact with the film monitoring/analysis device, in order to provide inherently temperature compensated measurements. These deposition monitor and analysis devices can include inherent temperature compensation, higher sensitivity to surface interactions than quartz crystal microbalance (QCM) devices, and the ability to operate at extreme temperatures.

Capacitively coupled RF voltage probe having optimized flux linkage

DOEpatents

Moore, James A.; Sparks, Dennis O.

1999-02-02

An RF sensor having a novel current sensing probe and a voltage sensing probe to measure voltage and current. The current sensor is disposed in a transmission line to link all of the flux generated by the flowing current in order to obtain an accurate measurement. The voltage sensor is a flat plate which operates as a capacitive plate to sense voltage on a center conductor of the transmission line, in which the measured voltage is obtained across a resistance leg of a R-C differentiator circuit formed by the characteristic impedance of a connecting transmission line and a capacitance of the plate, which is positioned proximal to the center conductor.

Dynamics and Control of Constrained Multibody Systems modeled with Maggi's equation: Application to Differential Mobile Robots Part I

NASA Astrophysics Data System (ADS)

Amengonu, Yawo H.; Kakad, Yogendra P.

2014-07-01

Quasivelocity techniques such as Maggi's and Boltzmann-Hamel's equations eliminate Lagrange multipliers from the beginning as opposed to the Euler-Lagrange method where one has to solve for the n configuration variables and the multipliers as functions of time when there are m nonholonomic constraints. Maggi's equation produces n second-order differential equations of which (n-m) are derived using (n-m) independent quasivelocities and the time derivative of the m kinematic constraints which add the remaining m second order differential equations. This technique is applied to derive the dynamics of a differential mobile robot and a controller which takes into account these dynamics is developed.

Concurrent Schedules of Positive and Negative Reinforcement: Differential-Impact and Differential-Outcomes Hypotheses

PubMed Central

Magoon, Michael A; Critchfield, Thomas S

2008-01-01

Considerable evidence from outside of operant psychology suggests that aversive events exert greater influence over behavior than equal-sized positive-reinforcement events. Operant theory is largely moot on this point, and most operant research is uninformative because of a scaling problem that prevents aversive events and those based on positive reinforcement from being directly compared. In the present investigation, humans' mouse-click responses were maintained on similarly structured, concurrent schedules of positive (money gain) and negative (avoidance of money loss) reinforcement. Because gains and losses were of equal magnitude, according to the analytical conventions of the generalized matching law, bias (log b ≠ 0) would indicate differential impact by one type of consequence; however, no systematic bias was observed. Further research is needed to reconcile this outcome with apparently robust findings in other literatures of superior behavior control by aversive events. In an incidental finding, the linear function relating log behavior ratio and log reinforcement ratio was steeper for concurrent negative and positive reinforcement than for control conditions involving concurrent positive reinforcement. This may represent the first empirical confirmation of a free-operant differential-outcomes effect predicted by contingency-discriminability theories of choice. PMID:18683609

PLZT block data composers operated in differential phase mode. [lanthanum-modified lead zirconate titanate ceramic device for digital holographic memory

NASA Technical Reports Server (NTRS)

Drake, M. D.; Klingler, D. E.

1973-01-01

The use of PLZT ceramics with the 7/65/35 composition in block data composer (BDC) input devices for holographic memory systems has previously been described for operation in the strain biased, scattering, and edge effect modes. A new and promising mode of BDC operation is the differential phase mode in which each element of a matrix array BDC acts as a phase modulator. The phase modulation results from a phase difference in the optical path length between the electrically poled and depoled states of the PLZT. It is shown that a PLZT BDC can be used as a matrix-type phase modulator to record and process digital data by the differential phase mode in a holographic recording/processing system with readout contrast ratios of between 10:1 and 15:1. The differential phase mode has the advantages that strain bias is not required and that the thickness and strain variations in the PLZT are cancelled out.

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients.

PubMed

Boyko, Vyacheslav M; Popovych, Roman O; Shapoval, Nataliya M

2013-01-01

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients

PubMed Central

Boyko, Vyacheslav M.; Popovych, Roman O.; Shapoval, Nataliya M.

2013-01-01

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach. PMID:23564972

Keep Your Distance! Using Second-Order Ordinary Differential Equations to Model Traffic Flow

ERIC Educational Resources Information Center

McCartney, Mark

2004-01-01

A simple mathematical model for how vehicles follow each other along a stretch of road is presented. The resulting linear second-order differential equation with constant coefficients is solved and interpreted. The model can be used as an application of solution techniques taught at first-year undergraduate level and as a motivator to encourage…

Stability and square integrability of derivatives of solutions of nonlinear fourth order differential equations with delay.

PubMed

Korkmaz, Erdal

2017-01-01

In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov's second method. The results obtained essentially improve, include and complement the results in the literature.

A New Factorisation of a General Second Order Differential Equation

ERIC Educational Resources Information Center

Clegg, Janet

2006-01-01

A factorisation of a general second order ordinary differential equation is introduced from which the full solution to the equation can be obtained by performing two integrations. The method is compared with traditional methods for solving these type of equations. It is shown how the Green's function can be derived directly from the factorisation…

Fully Differential Vector-Boson-Fusion Higgs Production at Next-to-Next-to-Leading Order.

PubMed

Cacciari, Matteo; Dreyer, Frédéric A; Karlberg, Alexander; Salam, Gavin P; Zanderighi, Giulia

2015-08-21

We calculate the fully differential next-to-next-to-leading-order (NNLO) corrections to vector-boson fusion (VBF) Higgs boson production at proton colliders, in the limit in which there is no cross talk between the hadronic systems associated with the two protons. We achieve this using a new "projection-to-Born" method that combines an inclusive NNLO calculation in the structure-function approach and a suitably factorized next-to-leading-order VBF Higgs plus three-jet calculation, using appropriate Higgs plus two-parton counterevents. An earlier calculation of the fully inclusive cross section had found small NNLO corrections, at the 1% level. In contrast, the cross section after typical experimental VBF cuts receives NNLO contributions of about (5-6)%, while differential distributions show corrections of up to (10-12)% for some standard observables. The corrections are often outside the next-to-leading-order scale-uncertainty band.

Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

PubMed

Lorenzo, C F; Hartley, T T; Malti, R

2013-05-13

A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

Lie group classification of first-order delay ordinary differential equations

NASA Astrophysics Data System (ADS)

Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

2018-05-01

A group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs), which consists of linear DODEs and solution-independent delay relations, have infinite-dimensional symmetry algebras—as do nonlinear ones that are linearizable by an invertible transformation of variables. Genuinely nonlinear DODSs have symmetry algebras of dimension n, . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.

Multiple positive solutions to a coupled systems of nonlinear fractional differential equations.

PubMed

Shah, Kamal; Khan, Rahmat Ali

2016-01-01

In this article, we study existence, uniqueness and nonexistence of positive solution to a highly nonlinear coupled system of fractional order differential equations. Necessary and sufficient conditions for the existence and uniqueness of positive solution are developed by using Perov's fixed point theorem for the considered problem. Further, we also established sufficient conditions for existence of multiplicity results for positive solutions. Also, we developed some conditions under which the considered coupled system of fractional order differential equations has no positive solution. Appropriate examples are also provided which demonstrate our results.

(O8 , O8 ) contribution to B ¯→Xsγ γ at O (αs)

NASA Astrophysics Data System (ADS)

Asatrian, H. M.; Greub, C.; Kokulu, A.

2016-01-01

In this analysis, we present the contribution associated with the chromomagnetic dipole operator O8 to the double differential decay width d Γ /(d s1d s2) for the inclusive process B ¯→Xsγ γ . The kinematical variables s1 and s2 are defined as si=(pb-qi)2/mb2, where pb, q1, q2 are the momenta of b quark and two photons. This contribution (taken at tree level) is of order αs, like the recently calculated QCD corrections to the contribution of the operator O7. In order to regulate possible collinear singularities of one of the photons with the strange quark, we introduce a nonzero mass ms for the strange quark. Our results are obtained for exact ms, which we interpret as a constituent mass being varied between 400 and 600 MeV. Numerically it turns out that the effect of the (O8 , O8 ) contribution to the branching ratio of B ¯→Xsγ γ does not exceed +0.1 % for any kinematically allowed value of our physical cutoff parameter c , confirming the expected suppression of this contribution relative to the QCD corrections to d Γ77/(d s1d s2).

Recursive linearization of multibody dynamics equations of motion

NASA Technical Reports Server (NTRS)

Lin, Tsung-Chieh; Yae, K. Harold

1989-01-01

The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated.

A Solution to the Fundamental Linear Fractional Order Differential Equation

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

High-Order Methods for Computational Fluid Dynamics: A Brief Review of Compact Differential Formulations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Huynh, H. T.; Wang, Z. J.; Vincent, P. E.

2013-01-01

Popular high-order schemes with compact stencils for Computational Fluid Dynamics (CFD) include Discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV) methods. The recently proposed Flux Reconstruction (FR) approach or Correction Procedure using Reconstruction (CPR) is based on a differential formulation and provides a unifying framework for these high-order schemes. Here we present a brief review of recent developments for the FR/CPR schemes as well as some pacing items.

The performance of differential VLBI delay during interplanetary cruise

NASA Technical Reports Server (NTRS)

Moultrie, B.; Wolff, P. J.; Taylor, T. H.

1984-01-01

Project Voyager radio metric data are used to evaluate the orbit determination abilities of several data strategies during spacecraft interplanetary cruise. Benchmark performance is established with an operational data strategy of conventional coherent doppler, coherent range, and explicitly differenced range data from two intercontinental baselines to ameliorate the low declination singularity of the doppler data. Employing a Voyager operations trajectory as a reference, the performance of the operational data strategy is compared to the performances of data strategies using differential VLBI delay data (spacecraft delay minus quasar delay) in combinations with the aforementioned conventional data types. The comparison of strategy performances indicates that high accuracy cruise orbit determination can be achieved with a data strategy employing differential VLBI delay data, where the quantity of coherent radio metric data has been greatly reduced.

Electrophysiological evidence for differential processing of numerical quantity and order in humans.

PubMed

Turconi, Eva; Jemel, Boutheina; Rossion, Bruno; Seron, Xavier

2004-09-01

It is yet unclear whether the processing of number magnitude and order rely on common or different functional processes and neural substrates. On the one hand, recent neuroimaging studies show that quantity and order coding activate the same areas in the parietal and prefrontal cortices. On the other hand, evidence from developmental and neuropsychological studies suggest dissociated mechanisms for processing quantity and order information. To clarify this issue, the present study investigated the spatio-temporal course of quantity and order coding operations using event-related potentials (ERPs). Twenty-four subjects performed a quantity task (classifying numbers as smaller or larger than 15) and an order task on the same material (classifying numbers as coming before or after 15), as well as a control order task on letters (classifying letters as coming before or after M). Behavioral results showed a classical distance effect (decreasing reaction times [RTs] with increasing distance from the standard) for all tasks. In agreement with previous electrophysiological evidence, this effect was significant on a P2 parietal component for numerical material. However, the difference between processing numbers close or far from the target appeared earlier and was larger on the left hemisphere for quantity processing, while it was delayed and bilateral for order processing. There was also a significant distance effect in all tasks on parietal sites for the following P3 component elicited by numbers, but this effect was larger on prefrontal areas for the order judgment. In conclusion, both quantity and order show similar behavioral effects, but they are associated with different spatio-temporal courses in parietal and prefrontal cortices.

Mathematics for generative processes: Living and non-living systems

NASA Astrophysics Data System (ADS)

Giannantoni, Corrado

2006-05-01

The traditional Differential Calculus often shows its limits when describing living systems. These in fact present such a richness of characteristics that are, in the majority of cases, much wider than the description capabilities of the usual differential equations. Such an aspect became particularly evident during the research (completed in 2001) for an appropriate formulation of Odum's Maximum Em-Power Principle (proposed by the Author as a possible Fourth Thermodynamic Principle). In fact, in such a context, the particular non-conservative Algebra, adopted to account for both Quality and quantity of generative processes, suggested we introduce a faithfully corresponding concept of "derivative" (of both integer and fractional order) to describe dynamic conditions however variable. The new concept not only succeeded in pointing out the corresponding differential bases of all the rules of Emergy Algebra, but also represented the preferential guide in order to recognize the most profound physical nature of the basic processes which mostly characterize self-organizing Systems (co-production, co-injection, inter-action, feed-back, splits, etc.).From a mathematical point of view, the most important novelties introduced by such a new approach are: (i) the derivative of any integer or fractional order can be obtained independently from the evaluation of its lower order derivatives; (ii) the exponential function plays an extremely hinge role, much more marked than in the case of traditional differential equations; (iii) wide classes of differential equations, traditionally considered as being non-linear, become "intrinsically" linear when reconsidered in terms of "incipient" derivatives; (iv) their corresponding explicit solutions can be given in terms of new classes of functions (such as "binary" and "duet" functions); (v) every solution shows a sort of "persistence of form" when representing the product generated with respect to the agents of the generating process; (iv) and, at the same time, an intrinsic "genetic" ordinality which reflects the fact that any product "generated" is something more than the sum of the generating elements. Consequently all these properties enable us to follow the evolution of the "product" of any generative process from the very beginning, in its "rising", in its "incipient" act of being born. This is why the new "operator" introduced, specifically apt when describing the above-mentioned aspects, was termed as "incipient" (or "spring") derivative.In addition, even if the considered approach was suggested by the analysis of self-organizing living Systems, some specific examples of non-living Systems will also be mentioned. In fact, what is much more surprising is that such an approach is even more valid (than the traditional one) to describe non-living Systems too. In fact the resulting "drift" between traditional solutions and "incipient" solutions led us to reconsider the phenomenon of Mercury's precessions. The satisfactory agreement with the astronomical data suggested, as a consequential hypothesis, a different interpretation of its physical origin, substantially based on the Maximum Em-Power Principle.

Extending High-Order Flux Operators on Spherical Icosahedral Grids and Their Applications in the Framework of a Shallow Water Model

NASA Astrophysics Data System (ADS)

Zhang, Yi

2018-01-01

This study extends a set of unstructured third/fourth-order flux operators on spherical icosahedral grids from two perspectives. First, the fifth-order and sixth-order flux operators of this kind are further extended, and the nominally second-order to sixth-order operators are then compared based on the solid body rotation and deformational flow tests. Results show that increasing the nominal order generally leads to smaller absolute errors. Overall, the standard fifth-order scheme generates the smallest errors in limited and unlimited tests, although it does not enhance the convergence rate. Even-order operators show higher limiter sensitivity than the odd-order operators. Second, a triangular version of these high-order operators is repurposed for transporting the potential vorticity in a space-time-split shallow water framework. Results show that a class of nominally third-order upwind-biased operators generates better results than second-order and fourth-order counterparts. The increase of the potential enstrophy over time is suppressed owing to the damping effect. The grid-scale noise in the vorticity is largely alleviated, and the total energy remains conserved. Moreover, models using high-order operators show smaller numerical errors in the vorticity field because of a more accurate representation of the nonlinear Coriolis term. This improvement is especially evident in the Rossby-Haurwitz wave test, in which the fluid is highly rotating. Overall, high-order flux operators with higher damping coefficients, which essentially behave like the Anticipated Potential Vorticity Method, present better results.

Critical study of higher order numerical methods for solving the boundary-layer equations

NASA Technical Reports Server (NTRS)

Wornom, S. F.

1978-01-01

A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows.

Spectral analysis of difference and differential operators in weighted spaces

NASA Astrophysics Data System (ADS)

Bichegkuev, M. S.

2013-11-01

This paper is concerned with describing the spectrum of the difference operator \\displaystyle \\mathscr{K}\\colon l_\\alpha^p( Z,X)\\to l_\\alpha^p( Z......athscr{K}x)(n)=Bx(n-1), \\ \\ n\\in{Z}, \\ \\ x\\in l_\\alpha^p( Z,X), with a constant operator coefficient B, which is a bounded linear operator in a Banach space X. It is assumed that \\mathscr{K} acts in the weighted space l_\\alpha^p( Z,X), 1\\leq p\\leq \\infty, of two-sided sequences of vectors from X. The main results are obtained in terms of the spectrum \\sigma(B) of the operator coefficient B and properties of the weight function. Applications to the study of the spectrum of a differential operator with an unbounded operator coefficient (the generator of a strongly continuous semigroup of operators) in weighted function spaces are given. Bibliography: 23 titles.

Labeled trees and the efficient computation of derivations

NASA Technical Reports Server (NTRS)

Grossman, Robert; Larson, Richard G.

1989-01-01

The effective parallel symbolic computation of operators under composition is discussed. Examples include differential operators under composition and vector fields under the Lie bracket. Data structures consisting of formal linear combinations of rooted labeled trees are discussed. A multiplication on rooted labeled trees is defined, thereby making the set of these data structures into an associative algebra. An algebra homomorphism is defined from the original algebra of operators into this algebra of trees. An algebra homomorphism from the algebra of trees into the algebra of differential operators is then described. The cancellation which occurs when noncommuting operators are expressed in terms of commuting ones occurs naturally when the operators are represented using this data structure. This leads to an algorithm which, for operators which are derivations, speeds up the computation exponentially in the degree of the operator. It is shown that the algebra of trees leads naturally to a parallel version of the algorithm.

Multi-output differential technologies

NASA Astrophysics Data System (ADS)

Bidare, Srinivas R.

1997-01-01

A differential is a very old and proven mechanical device that allows a single input to be split into two outputs having equal torque irrespective of the output speeds. A standard differential is capable of providing only two outputs from a single input. A recently patented multi-output differential technology known as `Plural-Output Differential' allows a single input to be split into many outputs. This new technology is the outcome of a systematic study of complex gear trains (Bidare 1992). The unique feature of a differential (equal torque at different speeds) can be applied to simplify the construction and operation of many complex mechanical devices that require equal torque's or forces at multiple outputs. It is now possible to design a mechanical hand with three or more fingers with equal torque. Since these finger are powered via a differential they are `mechanically intelligent'. A prototype device is operational and has been used to demonstrate the utility and flexibility of the design. In this paper we shall review two devices that utilize the new technology resulting in increased performance, robustness with reduced complexity and cost.