Characterization of van der Waals type bimodal,- lambda,- meta- and spinodal phase transitions in liquid mixtures, solid suspensions and thin films.

PubMed

Rosenholm, Jarl B

2018-03-01

The perfect gas law is used as a reference when selecting state variables (P, V, T, n) needed to characterize ideal gases (vapors), liquids and solids. Van der Waals equation of state is used as a reference for models characterizing interactions in liquids, solids and their mixtures. Van der Waals loop introduces meta- and unstable states between the observed gas (vapor)-liquid P-V transitions at low T. These intermediate states are shown to appear also between liquid-liquid, liquid-solid and solid-solid phase transitions. First-order phase transitions are characterized by a sharp discontinuity of first-order partial derivatives (P, S, V) of Helmholtz and Gibbs free energies. Second-order partial derivatives (K T , B, C V , C P , E) consist of a static contribution relating to second-order phase transitions and a relaxation contribution representing the degree of first-order phase transitions. Bimodal (first-order) and spinodal (second-order) phase boundaries are used to separate stable phases from metastable and unstable phases. The boundaries are identified and quantified by partial derivatives of molar Gibbs free energy or chemical potentials with respect to P, S, V and composition (mole fractions). Molecules confined to spread Langmuir monolayers or adsorbed Gibbs monolayers are characterized by equation of state and adsorption isotherms relating to a two-dimensional van der Waals equation of state. The basic work of two-dimensional wetting (cohesion, adsorption, spreading, immersion), have to be adjusted by a horizontal surface pressure in the presence of adsorbed vapor layers. If the adsorption is extended to liquid films a vertical surface pressure (Π) may be added to account for the lateral interaction, thus restoring PV = ΠAh dependence of thin films. Van der Waals attraction, Coulomb repulsion and structural hydration forces contribute to the vertical surface pressure. A van der Waals type coexistence of ordered (dispersed) and disordered (aggregated) phases is shown to exist when liquid vapor is confined in capillaries (condensation-liquefaction-evaporation and flux). This pheno-menon can be experimentally illustrated with suspended nano-sized particles (flocculation-coagulation-peptisation of colloidal sols) being confined in sample holders of varying size. The self-assembled aggregates represent critical self-similar equilibrium structures corres-ponding to rate determining complexes in kinetics. Overall, a self-consistent thermodynamic framework is established for the characterization of two- and three-dimensional phase separations in one-, two- and three-component systems. Copyright © 2018 Elsevier B.V. All rights reserved.

Asymptotic derivation of nonlocal plate models from three-dimensional stress gradient elasticity

NASA Astrophysics Data System (ADS)

Hache, F.; Challamel, N.; Elishakoff, I.

2018-01-01

This paper deals with the asymptotic derivation of thin and thick nonlocal plate models at different orders from three-dimensional stress gradient elasticity, through the power series expansions of the displacements in the thickness ratio of the plate. Three nonlocal asymptotic approaches are considered: a partial nonlocality following the thickness of the plate, a partial nonlocality following the two directions of the plates and a full nonlocality (following all the directions). The three asymptotic approaches lead at the zeroth order to a nonlocal Kirchhoff-Love plate model, but differ in the expression of the length scale. The nonlocal asymptotic models coincide at this order with the stress gradient Kirchhoff-Love plate model, only when the nonlocality is following the two directions of the plate and expressed through a nabla operator. This asymptotic model also yields the nonlocal truncated Uflyand-Mindlin plate model at the second order. However, the two other asymptotic models lead to equations that differ from the current existing nonlocal engineering models (stress gradient engineering plate models). The natural frequencies for an all-edges simply supported plate are obtained for each model. It shows that the models provide similar results for low orders of frequencies or small thickness ratio or nonlocal lengths. Moreover, only the asymptotic model with a partial nonlocality following the two directions of the plates is consistent with a stress gradient plate model, whatever the geometry of the plate.

Fast gravity, gravity partials, normalized gravity, gravity gradient torque and magnetic field: Derivation, code and data

NASA Technical Reports Server (NTRS)

Gottlieb, Robert G.

1993-01-01

Derivation of first and second partials of the gravitational potential is given in both normalized and unnormalized form. Two different recursion formulas are considered. Derivation of a general gravity gradient torque algorithm which uses the second partial of the gravitational potential is given. Derivation of the geomagnetic field vector is given in a form that closely mimics the gravitational algorithm. Ada code for all algorithms that precomputes all possible data is given. Test cases comparing the new algorithms with previous data are given, as well as speed comparisons showing the relative efficiencies of the new algorithms.

Causal dissipation for the relativistic dynamics of ideal gases

NASA Astrophysics Data System (ADS)

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

Causal dissipation for the relativistic dynamics of ideal gases

PubMed Central

2017-01-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier–Stokes equations. PMID:28588397

Causal dissipation for the relativistic dynamics of ideal gases.

PubMed

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

(U) Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses Using Ray-Tracing

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

Favorite, Jeffrey A.

The Second-Level Adjoint Sensitivity System (2nd-LASS) that yields the second-order sensitivities of a response of uncollided particles with respect to isotope densities, cross sections, and source emission rates is derived in Refs. 1 and 2. In Ref. 2, we solved problems for the uncollided leakage from a homogeneous sphere and a multiregion cylinder using the PARTISN multigroup discrete-ordinates code. In this memo, we derive solutions of the 2nd-LASS for the particular case when the response is a flux or partial current density computed at a single point on the boundary, and the inner products are computed using ray-tracing. Both themore » PARTISN approach and the ray-tracing approach are implemented in a computer code, SENSPG. The next section of this report presents the equations of the 1st- and 2nd-LASS for uncollided particles and the first- and second-order sensitivities that use the solutions of the 1st- and 2nd-LASS. Section III presents solutions of the 1st- and 2nd-LASS equations for the case of ray-tracing from a detector point. Section IV presents specific solutions of the 2nd-LASS and derives the ray-trace form of the inner products needed for second-order sensitivities. Numerical results for the total leakage from a homogeneous sphere are presented in Sec. V and for the leakage from one side of a two-region slab in Sec. VI. Section VII is a summary and conclusions.« less

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

NASA Astrophysics Data System (ADS)

Bazow, Dennis; Heinz, Ulrich; Strickland, Michael

2014-11-01

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

TaylUR 3, a multivariate arbitrary-order automatic differentiation package for Fortran 95

NASA Astrophysics Data System (ADS)

von Hippel, G. M.

2010-03-01

This new version of TaylUR is based on a completely new core, which now is able to compute the numerical values of all of a complex-valued function's partial derivatives up to an arbitrary order, including mixed partial derivatives. New version program summaryProgram title: TaylUR Catalogue identifier: ADXR_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXR_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPLv2 No. of lines in distributed program, including test data, etc.: 6750 No. of bytes in distributed program, including test data, etc.: 19 162 Distribution format: tar.gz Programming language: Fortran 95 Computer: Any computer with a conforming Fortran 95 compiler Operating system: Any system with a conforming Fortran 95 compiler Classification: 4.12, 4.14 Catalogue identifier of previous version: ADXR_v2_0 Journal reference of previous version: Comput. Phys. Comm. 176 (2007) 710 Does the new version supersede the previous version?: Yes Nature of problem: Problems that require potentially high orders of partial derivatives with respect to several variables or derivatives of complex-valued functions, such as e.g. momentum or mass expansions of Feynman diagrams in perturbative QFT, and which previous versions of this TaylUR [1,2] cannot handle due to their lack of support for mixed partial derivatives. Solution method: Arithmetic operators and Fortran intrinsics are overloaded to act correctly on objects of a defined type taylor, which encodes a function along with its first few partial derivatives with respect to the user-defined independent variables. Derivatives of products and composite functions are computed using multivariate forms [3] of Leibniz's rule D(fg)=∑{ν!}/{μ!(μ-ν)!}DfDg where ν=(ν,…,ν), |ν|=∑j=1dν, ν!=∏j=1dν!, Df=∂f/(∂x⋯∂x), and μ<ν iff either |μ|<|ν| or |μ|=|ν|,μ=ν,…,μ=ν,μ<ν for some k∈{0,…,d-1}, and of Fàa di Bruno's formula D(f○g)=∑p=1|ν|(f○g)∑s=1|ν|∑,…,k;λ,…,λ)}ν!/(∏j=1sk!λ!)(g)k where the sum is over {(k,…,k;λ,…,λ)∈Z:k>0,0<λ<⋯<λ, ∑i=1sk=p,∑i=1skλ=ν}. An indexed storage system is used to store the higher-order derivative tensors in a one-dimensional array. The relevant indices (k,…,k;λ,…,λ) and the weights occurring in the sums in Leibniz's and Fàa di Bruno's formula are precomputed at startup and stored in static arrays for later use. Reasons for new version: The earlier version lacked support for mixed partial derivatives, but a number of projects of interest required them. Summary of revisions: The internal representation of a taylor object has changed to a one-dimensional array which contains the partial derivatives in ascending order, and in lexicographic order of the corresponding multiindex within the same order. The necessary mappings between multiindices and indices into the taylor objects' internal array are computed at startup. To support the change to a genuinely multivariate taylor type, the DERIVATIVE function is now implemented via an interface that accepts both the older format derivative(f,mu,n)=∂μnf and also a new format derivative(f,mu(:))=Df that allows access to mixed partial derivatives. Another related extension to the functionality of the module is the HESSIAN function that returns the Hessian matrix of second derivatives of its argument. Since the calculation of all mixed partial derivatives can be very costly, and in many cases only some subset is actually needed, a masking facility has been added. Calling the subroutine DEACTIVATE_DERIVATIVE with a multiindex as an argument will deactivate the calculation of the partial derivative belonging to that multiindex, and of all partial derivatives it can feed into. Similarly, calling the subroutine ACTIVATE_DERIVATIVE will activate the calculation of the partial derivative belonging to its argument, and of all partial derivatives that can feed into it. Moreover, it is possible to turn off the computation of mixed derivatives altogether by setting Diagonal_taylors to .TRUE.. It should be noted that any change of Diagonal_taylors or Taylor_order invalidates all existing taylor objects. To aid the better integration of TaylUR into the HPSrc library [4], routines SET_DERIVATIVE and SET_ALL_DERIVATIVES are provided as a means of manually constructing a taylor object with given derivatives. Restrictions: Memory and CPU time constraints may restrict the number of variables and Taylor expansion order that can be achieved. Loss of numerical accuracy due to cancellation may become an issue at very high orders. Unusual features: These are the same as in previous versions, but are enumerated again here for clarity. The complex conjugation operation assumes all independent variables to be real. The functions REAL and AIMAG do not convert to real type, but return a result of type taylor (with the real/imaginary part of each derivative taken) instead. The user-defined functions VALUE, REALVALUE and IMAGVALUE, which return the value of a taylor object as a complex number, and the real and imaginary part of this value, respectively, as a real number are also provided. Fortran 95 intrinsics that are defined only for arguments of real type ( ACOS, AINT, ANINT, ASIN, ATAN, ATAN2, CEILING, DIM, FLOOR, INT, LOG10, MAX, MAXLOC, MAXVAL, MIN, MINLOC, MINVAL, MOD, MODULO, NINT, SIGN) will silently take the real part of taylor-valued arguments unless the module variable Real_args_warn is set to .TRUE., in which case they will return a quiet NaN value (if supported by the compiler) when called with a taylor argument whose imaginary part exceeds the module variable Real_args_tol. In those cases where the derivative of a function becomes undefined at certain points (as for ABS, AINT, ANINT, MAX, MIN, MOD, and MODULO), while the value is well defined, the derivative fields will be filled with quiet NaN values (if supported by the compiler). Additional comments: This version of TaylUR is released under the second version of the GNU General Public License (GPLv2). Therefore anyone is free to use or modify the code for their own calculations. As part of the licensing, it is requested that any publications including results from the use of TaylUR or any modification derived from it cite Refs. [1,2] as well as this paper. Finally, users are also requested to communicate to the author details of such publications, as well as of any bugs found or of required or useful modifications made or desired by them. Running time: The running time of TaylUR operations grows rapidly with both the number of variables and the Taylor expansion order. Judicious use of the masking facility to drop unneeded higher derivatives can lead to significant accelerations, as can activation of the Diagonal_taylors variable whenever mixed partial derivatives are not needed. Acknowledgments: The author thanks Alistair Hart for helpful comments and suggestions. This work is supported by the Deutsche Forschungsgemeinschaft in the SFB/TR 09. References:G.M. von Hippel, TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95, Comput. Phys. Comm. 174 (2006) 569. G.M. von Hippel, New version announcement for TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95, Comput. Phys. Comm. 176 (2007) 710. G.M. Constantine, T.H. Savits, A multivariate Faa di Bruno formula with applications, Trans. Amer. Math. Soc. 348 (2) (1996) 503. A. Hart, G.M. von Hippel, R.R. Horgan, E.H. Müller, Automated generation of lattice QCD Feynman rules, Comput. Phys. Comm. 180 (2009) 2698, doi:10.1016/j.cpc.2009.04.021, arXiv:0904.0375.

An investigation of using an RQP based method to calculate parameter sensitivity derivatives

NASA Technical Reports Server (NTRS)

Beltracchi, Todd J.; Gabriele, Gary A.

1989-01-01

Estimation of the sensitivity of problem functions with respect to problem variables forms the basis for many of our modern day algorithms for engineering optimization. The most common application of problem sensitivities has been in the calculation of objective function and constraint partial derivatives for determining search directions and optimality conditions. A second form of sensitivity analysis, parameter sensitivity, has also become an important topic in recent years. By parameter sensitivity, researchers refer to the estimation of changes in the modeling functions and current design point due to small changes in the fixed parameters of the formulation. Methods for calculating these derivatives have been proposed by several authors (Armacost and Fiacco 1974, Sobieski et al 1981, Schmit and Chang 1984, and Vanderplaats and Yoshida 1985). Two drawbacks to estimating parameter sensitivities by current methods have been: (1) the need for second order information about the Lagrangian at the current point, and (2) the estimates assume no change in the active set of constraints. The first of these two problems is addressed here and a new algorithm is proposed that does not require explicit calculation of second order information.

Auto-Bäcklund transformations for a matrix partial differential equation

NASA Astrophysics Data System (ADS)

Gordoa, P. R.; Pickering, A.

2018-07-01

We derive auto-Bäcklund transformations, analogous to those of the matrix second Painlevé equation, for a matrix partial differential equation. We also then use these auto-Bäcklund transformations to derive matrix equations involving shifts in a discrete variable, a process analogous to the use of the auto-Bäcklund transformations of the matrix second Painlevé equation to derive a discrete matrix first Painlevé equation. The equations thus derived then include amongst other examples a semidiscrete matrix equation which can be considered to be an extension of this discrete matrix first Painlevé equation. The application of this technique to the auto-Bäcklund transformations of the scalar case of our partial differential equation has not been considered before, and so the results obtained here in this scalar case are also new. Other equations obtained here using this technique include a scalar semidiscrete equation which arises in the case of the second Painlevé equation, and which does not seem to have been thus derived previously.

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.

Gyrokinetic equations and full f solution method based on Dirac's constrained Hamiltonian and inverse Kruskal iteration

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

Heikkinen, J. A.; Nora, M.

2011-02-15

Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J= as one of the averaging coordinates in phase space, provides an alternative to the standard gyrokinetics. Within second order in gyrokinetic parameter, the new equations do not show explicit ponderomotivelike or polarizationlike terms. Pullback of particle information with an iterated gyrophase and field dependent gyroradius function from the gyrocenter position defined by gyroaveraged coordinates allowsmore » direct numerical integration of the gyrokinetic equations in particle simulation of the field and particles with full distribution function. As an example, gyrokinetic systems with polarization drift either present or absent in the equations of motion are considered.« less

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.

Theoretical predictions of latitude dependencies in the solar wind

NASA Technical Reports Server (NTRS)

Winge, C. R., Jr.; Coleman, P. J., Jr.

1974-01-01

Results are presented which were obtained with the Winge-Coleman model for theoretical predictions of latitudinal dependencies in the solar wind. A first-order expansion is described which allows analysis of first-order latitudinal variations in the coronal boundary conditions and results in a second-order partial differential equation for the perturbation stream function. Latitudinal dependencies are analytically separated out in the form of Legendre polynomials and their derivative, and are reduced to the solution of radial differential equations. This analysis is shown to supply an estimate of how large the coronal variation in latitude must be to produce an 11 km/sec/deg gradient in the radial velocity of the solar wind, assuming steady-state processes.

Beam wander and M2-factor of partially coherent electromagnetic hollow Gaussian beam propagating through non-Kolmogorov turbulence

NASA Astrophysics Data System (ADS)

Xu, Yonggen; Tian, Huanhuan; Dan, Youquan; Feng, Hao; Wang, Shijian

2017-04-01

Propagation formulae for M2-factor and beam wander of partially coherent electromagnetic hollow Gaussian (PCEHG) beam in non-Kolmogorov turbulence are derived based on the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function. Our results indicate that the normalized M2-factors of PCEHG beam with larger beam order, waist width, inner scale of turbulence, the generalized exponent parameter, and smaller transverse coherent widths, outer scale of turbulence, the generalized structure parameter are less affected by the turbulence. The root mean square beam wander and relative beam wander are more obvious for PCEHG beam with smaller beam order, larger inner and outer scales of turbulence, exponent parameter, transverse coherent widths, and the generalized structure parameter. What is more, the beam wander properties of PCEHG beam in non-Kolmogorov turbulence are very different from M2-factor and spreading properties of beam in turbulence.

Unconditionally stable, second-order accurate schemes for solid state phase transformations driven by mechano-chemical spinodal decomposition

DOE PAGES

Sagiyama, Koki; Rudraraju, Shiva; Garikipati, Krishna

2016-09-13

Here, we consider solid state phase transformations that are caused by free energy densities with domains of non-convexity in strain-composition space; we refer to the non-convex domains as mechano-chemical spinodals. The non-convexity with respect to composition and strain causes segregation into phases with different crystal structures. We work on an existing model that couples the classical Cahn-Hilliard model with Toupin’s theory of gradient elasticity at finite strains. Both systems are represented by fourth-order, nonlinear, partial differential equations. The goal of this work is to develop unconditionally stable, second-order accurate time-integration schemes, motivated by the need to carry out large scalemore » computations of dynamically evolving microstructures in three dimensions. We also introduce reduced formulations naturally derived from these proposed schemes for faster computations that are still second-order accurate. Although our method is developed and analyzed here for a specific class of mechano-chemical problems, one can readily apply the same method to develop unconditionally stable, second-order accurate schemes for any problems for which free energy density functions are multivariate polynomials of solution components and component gradients. Apart from an analysis and construction of methods, we present a suite of numerical results that demonstrate the schemes in action.« less

The Artificial Hamiltonian, First Integrals, and Closed-Form Solutions of Dynamical Systems for Epidemics

NASA Astrophysics Data System (ADS)

Naz, Rehana; Naeem, Imran

2018-03-01

The non-standard Hamiltonian system, also referred to as a partial Hamiltonian system in the literature, of the form {\\dot q^i} = {partial H}/{partial {p_i}},\\dot p^i = - {partial H}/{partial {q_i}} + {Γ ^i}(t,{q^i},{p_i}) appears widely in economics, physics, mechanics, and other fields. The non-standard (partial) Hamiltonian systems arise from physical Hamiltonian structures as well as from artificial Hamiltonian structures. We introduce the term `artificial Hamiltonian' for the Hamiltonian of a model having no physical structure. We provide here explicitly the notion of an artificial Hamiltonian for dynamical systems of ordinary differential equations (ODEs). Also, we show that every system of second-order ODEs can be expressed as a non-standard (partial) Hamiltonian system of first-order ODEs by introducing an artificial Hamiltonian. This notion of an artificial Hamiltonian gives a new way to solve dynamical systems of first-order ODEs and systems of second-order ODEs that can be expressed as a non-standard (partial) Hamiltonian system by using the known techniques applicable to the non-standard Hamiltonian systems. We employ the proposed notion to solve dynamical systems of first-order ODEs arising in epidemics.

DFTB3: Extension of the self-consistent-charge density-functional tight-binding method (SCC-DFTB).

PubMed

Gaus, Michael; Cui, Qiang; Elstner, Marcus

2012-04-10

The self-consistent-charge density-functional tight-binding method (SCC-DFTB) is an approximate quantum chemical method derived from density functional theory (DFT) based on a second-order expansion of the DFT total energy around a reference density. In the present study we combine earlier extensions and improve them consistently with, first, an improved Coulomb interaction between atomic partial charges, and second, the complete third-order expansion of the DFT total energy. These modifications lead us to the next generation of the DFTB methodology called DFTB3, which substantially improves the description of charged systems containing elements C, H, N, O, and P, especially regarding hydrogen binding energies and proton affinities. As a result, DFTB3 is particularly applicable to biomolecular systems. Remaining challenges and possible solutions are also briefly discussed.

Fast computation of derivative based sensitivities of PSHA models via algorithmic differentiation

NASA Astrophysics Data System (ADS)

Leövey, Hernan; Molkenthin, Christian; Scherbaum, Frank; Griewank, Andreas; Kuehn, Nicolas; Stafford, Peter

2015-04-01

Probabilistic seismic hazard analysis (PSHA) is the preferred tool for estimation of potential ground-shaking hazard due to future earthquakes at a site of interest. A modern PSHA represents a complex framework which combines different models with possible many inputs. Sensitivity analysis is a valuable tool for quantifying changes of a model output as inputs are perturbed, identifying critical input parameters and obtaining insight in the model behavior. Differential sensitivity analysis relies on calculating first-order partial derivatives of the model output with respect to its inputs. Moreover, derivative based global sensitivity measures (Sobol' & Kucherenko '09) can be practically used to detect non-essential inputs of the models, thus restricting the focus of attention to a possible much smaller set of inputs. Nevertheless, obtaining first-order partial derivatives of complex models with traditional approaches can be very challenging, and usually increases the computation complexity linearly with the number of inputs appearing in the models. In this study we show how Algorithmic Differentiation (AD) tools can be used in a complex framework such as PSHA to successfully estimate derivative based sensitivities, as is the case in various other domains such as meteorology or aerodynamics, without no significant increase in the computation complexity required for the original computations. First we demonstrate the feasibility of the AD methodology by comparing AD derived sensitivities to analytically derived sensitivities for a basic case of PSHA using a simple ground-motion prediction equation. In a second step, we derive sensitivities via AD for a more complex PSHA study using a ground motion attenuation relation based on a stochastic method to simulate strong motion. The presented approach is general enough to accommodate more advanced PSHA studies of higher complexity.

Ghost-Free Theory with Third-Order Time Derivatives

NASA Astrophysics Data System (ADS)

Motohashi, Hayato; Suyama, Teruaki; Yamaguchi, Masahide

2018-06-01

As the first step to extend our understanding of higher-derivative theories, within the framework of analytic mechanics of point particles, we construct a ghost-free theory involving third-order time derivatives in Lagrangian. While eliminating linear momentum terms in the Hamiltonian is necessary and sufficient to kill the ghosts associated with higher derivatives for Lagrangian with at most second-order derivatives, we find that this is necessary but not sufficient for the Lagrangian with higher than second-order derivatives. We clarify a set of ghost-free conditions under which we show that the Hamiltonian is bounded, and that equations of motion are reducible into a second-order system.

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.

Hyperbolic Method for Dispersive PDEs: Same High-Order of Accuracy for Solution, Gradient, and Hessian

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Ricchiuto, Mario; Nishikawa, Hiroaki

2016-01-01

In this paper, we introduce a new hyperbolic first-order system for general dispersive partial differential equations (PDEs). We then extend the proposed system to general advection-diffusion-dispersion PDEs. We apply the fourth-order RD scheme of Ref. 1 to the proposed hyperbolic system, and solve time-dependent dispersive equations, including the classical two-soliton KdV and a dispersive shock case. We demonstrate that the predicted results, including the gradient and Hessian (second derivative), are in a very good agreement with the exact solutions. We then show that the RD scheme applied to the proposed system accurately captures dispersive shocks without numerical oscillations. We also verify that the solution, gradient and Hessian are predicted with equal order of accuracy.

A computer model for the recombination zone of a microwave-plasma electrothermal rocket

NASA Technical Reports Server (NTRS)

Filpus, John W.; Hawley, Martin C.

1987-01-01

As part of a study of the microwave-plasma electrothermal rocket, a computer model of the flow regime below the plasma has been developed. A second-order model, including axial dispersion of energy and material and boundary conditions at infinite length, was developed to partially reproduce the absence of mass-flow rate dependence that was seen in experimental temperature profiles. To solve the equations of the model, a search technique was developed to find the initial derivatives. On integrating with a trial set of initial derivatives, the values and their derivatives were checked to judge whether the values were likely to attain values outside the practical regime, and hence, the boundary conditions at infinity were likely to be violated. Results are presented and directions for further development are suggested.

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.

Action principle for Coulomb collisions in plasmas

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

Hirvijoki, Eero

In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.

Action principle for Coulomb collisions in plasmas

DOE PAGES

Hirvijoki, Eero

2016-09-14

In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.

Connectivity of Photosystem II Is the Physical Basis of Retrapping in Photosynthetic Thermoluminescence

PubMed Central

Tyystjärvi, Esa; Rantamäki, Susanne; Tyystjärvi, Joonas

2009-01-01

Energy transfer between photosystem II (PSII) centers is known from previous fluorescence studies. We have studied the theoretical consequences of energetic connectivity of PSII centers on photosynthetic thermoluminescence (TL) and predict that connectivity affects the TL Q band. First, connectivity is expected to make the Q band wider and more symmetric than an ideal first-order TL band. Second, the presence of closed PSII centers in an energetically connected group of PSII centers is expected to lower the probability that an exciton originating in a recombination reaction becomes retrapped. The latter effect would shift the Q band toward lower temperature, and the shift would be greater the higher the percentage of closed PSII centers at the beginning of the measurement. These effects can be generalized as second-order effects, as they make the Q band resemble the second-order TL bands obtained from semiconducting solids. We applied the connected-units model of chlorophyll fluorescence to derive equations for quantifying the second-order effects in TL. To test the effect of the initial proportion of closed reaction centers, we measured the Q band with different intensities of the excitation flash and found that the peak position changed by 2.5°C toward higher temperature when the flash intensity was lowered from saturating to 0.39% of saturating. The result shows that energy transfer between reaction centers of PSII forms the physical basis of retrapping in photosynthetic TL. The second-order effects partially explain the deviation of the form of the Q band from ideal first-order TL. PMID:19413979

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

NASA Astrophysics Data System (ADS)

Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

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

Optimum sensitivity derivatives of objective functions in nonlinear programming

NASA Technical Reports Server (NTRS)

Barthelemy, J.-F. M.; Sobieszczanski-Sobieski, J.

1983-01-01

The feasibility of eliminating second derivatives from the input of optimum sensitivity analyses of optimization problems is demonstrated. This elimination restricts the sensitivity analysis to the first-order sensitivity derivatives of the objective function. It is also shown that when a complete first-order sensitivity analysis is performed, second-order sensitivity derivatives of the objective function are available at little additional cost. An expression is derived whose application to linear programming is presented.

Geochemical and Nd-Sr-Pb isotope characteristics of synorogenic lower crust-derived granodiorites (Central Damara orogen, Namibia)

NASA Astrophysics Data System (ADS)

Simon, I.; Jung, S.; Romer, R. L.; Garbe-Schönberg, D.; Berndt, J.

2017-03-01

The 547 ± 7 Ma old Achas intrusion (Damara orogen, Namibia) includes magnesian, metaluminous to slightly peraluminous, calcic to calc-alkalic granodiorites and ferroan, metaluminous to slightly peraluminous, calc-alkalic to alkali-calcic leucogranites. For the granodiorites, major and trace element variations show weak if any evidence for fractional crystallization whereas some leucogranites are highly fractionated. Both, granodiorites and leucogranites are isotopically evolved (granodiorites: εNdinit: - 12.4 to - 20.5; TDM: 2.4-1.9; leucogranites: εNdinit: - 12.1 to - 20.6, TDM: 2.5-2.0), show similar Pb isotopic compositions, and may be derived from late Archean to Paleoproterozoic crustal source rocks. Comparison with melting experiments and simple partial melting modeling indicate that the granodiorites may be derived by extensive melting (> 40%) at 900-950 °C under water-undersaturated conditions (< 5 wt.% H2O) of felsic gneisses. Al-Ti and zircon saturation thermometry of the most primitive granodiorite sample yielded temperatures of ca. 930 °C and ca. 800 °C. In contrast to other lower crust-derived granodiorites and granites of the Central Damara orogen, the composition of the magma source is considered the first-order cause of the compositional diversity of the Achas granite. Second-order processes such as fractional crystallization at least for the granodiorites were minor and evidence for coupled assimilation-fractional crystallization processes is lacking. The most likely petrogenetic model involves high temperature partial melting of a Paleoproterozoic felsic source in the lower crust ca. 10-20 Ma before the first peak of regional high-temperature metamorphism. Underplating of the lower crust by magmas derived from the lithospheric mantle may have provided the heat for melting of the basement to produce anhydrous granodioritic melts.

Degenerate limit thermodynamics beyond leading order for models of dense matter

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

Constantinou, Constantinos, E-mail: c.constantinou@fz-juelich.de; Muccioli, Brian, E-mail: bm956810@ohio.edu; Prakash, Madappa, E-mail: prakash@ohio.edu

2015-12-15

Analytical formulas for next-to-leading order temperature corrections to the thermal state variables of interacting nucleons in bulk matter are derived in the degenerate limit. The formalism developed is applicable to a wide class of non-relativistic and relativistic models of hot and dense matter currently used in nuclear physics and astrophysics (supernovae, proto-neutron stars and neutron star mergers) as well as in condensed matter physics. We consider the general case of arbitrary dimensionality of momentum space and an arbitrary degree of relativity (for relativistic models). For non-relativistic zero-range interactions, knowledge of the Landau effective mass suffices to compute next-to-leading order effects,more » but for finite-range interactions, momentum derivatives of the Landau effective mass function up to second order are required. Results from our analytical formulas are compared with the exact results for zero- and finite-range potential and relativistic mean-field theoretical models. In all cases, inclusion of next-to-leading order temperature effects substantially extends the ranges of partial degeneracy for which the analytical treatment remains valid. Effects of many-body correlations that deserve further investigation are highlighted.« less

A compact and realistic cerebral cortical layout derived from prewhitened resting-state fMRI time series: Cherniak's adjacency rule, size law, and metamodule grouping upheld

PubMed Central

Lewis, Scott M.; Christova, Peka; Jerde, Trenton A.; Georgopoulos, Apostolos P.

2012-01-01

We used hierarchical tree clustering to derive a functional organizational chart of 52 human cortical areas (26 per hemisphere) from zero-lag correlations calculated between single-voxel, prewhitened, resting-state BOLD fMRI time series in 18 subjects. No special “resting-state networks” were identified. There were four major features in the resulting tree (dendrogram). First, there was a strong clustering of homotopic, left-right hemispheric areas. Second, cortical areas were concatenated in multiple, partially overlapping clusters. Third, the arrangement of the areas revealed a layout that closely resembled the actual layout of the cerebral cortex, namely an orderly progression from anterior to posterior. And fourth, the layout of the cortical areas in the tree conformed to principles of efficient, compact layout of components proposed by Cherniak. Since the tree was derived on the basis of the strength of neural correlations, these results document an orderly relation between functional interactions and layout, i.e., between structure and function. PMID:22973198

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

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

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

Physical activity measured by physical activity monitoring system correlates with glucose trends reconstructed from continuous glucose monitoring.

PubMed

Zecchin, Chiara; Facchinetti, Andrea; Sparacino, Giovanni; Dalla Man, Chiara; Manohar, Chinmay; Levine, James A; Basu, Ananda; Kudva, Yogish C; Cobelli, Claudio

2013-10-01

In type 1 diabetes mellitus (T1DM), physical activity (PA) lowers the risk of cardiovascular complications but hinders the achievement of optimal glycemic control, transiently boosting insulin action and increasing hypoglycemia risk. Quantitative investigation of relationships between PA-related signals and glucose dynamics, tracked using, for example, continuous glucose monitoring (CGM) sensors, have been barely explored. In the clinic, 20 control and 19 T1DM subjects were studied for 4 consecutive days. They underwent low-intensity PA sessions daily. PA was tracked by the PA monitoring system (PAMS), a system comprising accelerometers and inclinometers. Variations on glucose dynamics were tracked estimating first- and second-order time derivatives of glucose concentration from CGM via Bayesian smoothing. Short-time effects of PA on glucose dynamics were quantified through the partial correlation function in the interval (0, 60 min) after starting PA. Correlation of PA with glucose time derivatives is evident. In T1DM, the negative correlation with the first-order glucose time derivative is maximal (absolute value) after 15 min of PA, whereas the positive correlation is maximal after 40-45 min. The negative correlation between the second-order time derivative and PA is maximal after 5 min, whereas the positive correlation is maximal after 35-40 min. Control subjects provided similar results but with positive and negative correlation peaks anticipated of 5 min. Quantitative information on correlation between mild PA and short-term glucose dynamics was obtained. This represents a preliminary important step toward incorporation of PA information in more realistic physiological models of the glucose-insulin system usable in T1DM simulators, in development of closed-loop artificial pancreas control algorithms, and in CGM-based prediction algorithms for generation of hypoglycemic alerts.

Isometric Non-Rigid Shape-from-Motion with Riemannian Geometry Solved in Linear Time.

PubMed

Parashar, Shaifali; Pizarro, Daniel; Bartoli, Adrien

2017-10-06

We study Isometric Non-Rigid Shape-from-Motion (Iso-NRSfM): given multiple intrinsically calibrated monocular images, we want to reconstruct the time-varying 3D shape of a thin-shell object undergoing isometric deformations. We show that Iso-NRSfM is solvable from local warps, the inter-image geometric transformations. We propose a new theoretical framework based on the Riemmanian manifold to represent the unknown 3D surfaces as embeddings of the camera's retinal plane. This allows us to use the manifold's metric tensor and Christoffel Symbol (CS) fields. These are expressed in terms of the first and second order derivatives of the inverse-depth of the 3D surfaces, which are the unknowns for Iso-NRSfM. We prove that the metric tensor and the CS are related across images by simple rules depending only on the warps. This forms a set of important theoretical results. We show that current solvers cannot solve for the first and second order derivatives of the inverse-depth simultaneously. We thus propose an iterative solution in two steps. 1) We solve for the first order derivatives assuming that the second order derivatives are known. We initialise the second order derivatives to zero, which is an infinitesimal planarity assumption. We derive a system of two cubics in two variables for each image pair. The sum-of-squares of these polynomials is independent of the number of images and can be solved globally, forming a well-posed problem for N ≥ 3 images. 2) We solve for the second order derivatives by initialising the first order derivatives from the previous step. We solve a linear system of 4N-4 equations in three variables. We iterate until the first order derivatives converge. The solution for the first order derivatives gives the surfaces' normal fields which we integrate to recover the 3D surfaces. The proposed method outperforms existing work in terms of accuracy and computation cost on synthetic and real datasets.

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 classification of scalar evolution equations with non-constant separant

NASA Astrophysics Data System (ADS)

Hümeyra Bilge, Ayşe; Mizrahi, Eti

2017-01-01

The ‘separant’ of the evolution equation u t   =  F, where F is some differentiable function of the derivatives of u up to order m, is the partial derivative \\partial F/\\partial {{u}m}, where {{u}m}={{\\partial}m}u/\\partial {{x}m} . As an integrability test, we use the formal symmetry method of Mikhailov-Shabat-Sokolov, which is based on the existence of a recursion operator as a formal series. The solvability of its coefficients in the class of local functions gives a sequence of conservation laws, called the ‘conserved densities’ {ρ(i)}, i=-1,1,2,3,\\ldots . We apply this method to the classification of scalar evolution equations of orders 3≤slant m≤slant 15 , for which {ρ(-1)}={≤ft[\\partial F/\\partial {{u}m}\\right]}-1/m} and {{ρ(1)} are non-trivial, i.e. they are not total derivatives and {ρ(-1)} is not linear in its highest order derivative. We obtain the ‘top level’ parts of these equations and their ‘top dependencies’ with respect to the ‘level grading’, that we defined in a previous paper, as a grading on the algebra of polynomials generated by the derivatives u b+i , over the ring of {{C}∞} functions of u,{{u}1},\\ldots,{{u}b} . In this setting b and i are called ‘base’ and ‘level’, respectively. We solve the conserved density conditions to show that if {ρ(-1)} depends on u,{{u}1},\\ldots,{{u}b}, then, these equations are level homogeneous polynomials in {{u}b+i},\\ldots,{{u}m} , i≥slant 1 . Furthermore, we prove that if {ρ(3)} is non-trivial, then {ρ(-1)}={≤ft(α ub2+β {{u}b}+γ \\right)}1/2} , with b≤slant 3 while if {{ρ(3)} is trivial, then {ρ(-1)}={≤ft(λ {{u}b}+μ \\right)}1/3} , where b≤slant 5 and α, β, γ, λ and μ are functions of u,\\ldots,{{u}b-1} . We show that the equations that we obtain form commuting flows and we construct their recursion operators that are respectively of orders 2 and 6 for non-trivial and trivial {{ρ(3)} respectively. Omitting lower order dependencies, we show that equations with non-trivial {ρ(3)} and b  =  3 are symmetries of the ‘essentially non-linear third order equation’ for trivial {ρ(3)} , the equations with b  =  5 are symmetries of a non-quasilinear fifth order equation obtained in previous work, while for b  =  3, 4 they are symmetries of quasilinear fifth order equations.

Peripheral Refraction, Peripheral Eye Length, and Retinal Shape in Myopia.

PubMed

Verkicharla, Pavan K; Suheimat, Marwan; Schmid, Katrina L; Atchison, David A

2016-09-01

To investigate how peripheral refraction and peripheral eye length are related to retinal shape. Relative peripheral refraction (RPR) and relative peripheral eye length (RPEL) were determined in 36 young adults (M +0.75D to -5.25D) along horizontal and vertical visual field meridians out to ±35° and ±30°, respectively. Retinal shape was determined in terms of vertex radius of curvature Rv, asphericity Q, and equivalent radius of curvature REq using a partial coherence interferometry method involving peripheral eye lengths and model eye raytracing. Second-order polynomial fits were applied to RPR and RPEL as functions of visual field position. Linear regressions were determined for the fits' second order coefficients and for retinal shape estimates as functions of central spherical refraction. Linear regressions investigated relationships of RPR and RPEL with retinal shape estimates. Peripheral refraction, peripheral eye lengths, and retinal shapes were significantly affected by meridian and refraction. More positive (hyperopic) relative peripheral refraction, more negative RPELs, and steeper retinas were found along the horizontal than along the vertical meridian and in myopes than in emmetropes. RPR and RPEL, as represented by their second-order fit coefficients, correlated significantly with retinal shape represented by REq. Effects of meridian and refraction on RPR and RPEL patterns are consistent with effects on retinal shape. Patterns derived from one of these predict the others: more positive (hyperopic) RPR predicts more negative RPEL and steeper retinas, more negative RPEL predicts more positive relative peripheral refraction and steeper retinas, and steeper retinas derived from peripheral eye lengths predict more positive RPR.

Weighted interior penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows

NASA Astrophysics Data System (ADS)

Di Pietro, Daniele A.; Marche, Fabien

2018-02-01

In this paper, we further investigate the use of a fully discontinuous Finite Element discrete formulation for the study of shallow water free surface flows in the fully nonlinear and weakly dispersive flow regime. We consider a decoupling strategy in which we approximate the solutions of the classical shallow water equations supplemented with a source term globally accounting for the non-hydrostatic effects. This source term can be computed through the resolution of elliptic second-order linear sub-problems, which only involve second order partial derivatives in space. We then introduce an associated Symmetric Weighted Internal Penalty discrete bilinear form, allowing to deal with the discontinuous nature of the elliptic problem's coefficients in a stable and consistent way. Similar discrete formulations are also introduced for several recent optimized fully nonlinear and weakly dispersive models. These formulations are validated again several benchmarks involving h-convergence, p-convergence and comparisons with experimental data, showing optimal convergence properties.

Second Order Boltzmann-Gibbs Principle for Polynomial Functions and Applications

NASA Astrophysics Data System (ADS)

Gonçalves, Patrícia; Jara, Milton; Simon, Marielle

2017-01-01

In this paper we give a new proof of the second order Boltzmann-Gibbs principle introduced in Gonçalves and Jara (Arch Ration Mech Anal 212(2):597-644, 2014). The proof does not impose the knowledge on the spectral gap inequality for the underlying model and it relies on a proper decomposition of the antisymmetric part of the current of the system in terms of polynomial functions. In addition, we fully derive the convergence of the equilibrium fluctuations towards (1) a trivial process in case of super-diffusive systems, (2) an Ornstein-Uhlenbeck process or the unique energy solution of the stochastic Burgers equation, as defined in Gubinelli and Jara (SPDEs Anal Comput (1):325-350, 2013) and Gubinelli and Perkowski (Arxiv:1508.07764, 2015), in case of weakly asymmetric diffusive systems. Examples and applications are presented for weakly and partial asymmetric exclusion processes, weakly asymmetric speed change exclusion processes and hamiltonian systems with exponential interactions.

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras

PubMed Central

Gazizov, R. K.

2017-01-01

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures. PMID:28265184

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras.

PubMed

Gainetdinova, A A; Gazizov, R K

2017-01-01

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.

Explanation-based generalization of partially ordered plans

NASA Technical Reports Server (NTRS)

Kambhampati, Subbarao; Kedar, Smadar

1991-01-01

Most previous work in analytic generalization of plans dealt with totally ordered plans. These methods cannot be directly applied to generalizing partially ordered plans, since they do not capture all interactions among plan operators for all total orders of such plans. We introduce a new method for generalizing partially ordered plans. This method is based on providing explanation-based generalization (EBG) with explanations which systematically capture the interactions among plan operators for all the total orders of a partially-ordered plan. The explanations are based on the Modal Truth Criterion which states the necessary and sufficient conditions for ensuring the truth of a proposition at any point in a plan, for a class of partially ordered plans. The generalizations obtained by this method guarantee successful and interaction-free execution of any total order of the generalized plan. In addition, the systematic derivation of the generalization algorithms from the Modal Truth Criterion obviates the need for carrying out a separate formal proof of correctness of the EBG algorithms.

Semi-abelian Z-theory: NLSM+ ϕ 3 from the open string

NASA Astrophysics Data System (ADS)

Carrasco, John Joseph M.; Mafra, Carlos R.; Schlotterer, Oliver

2017-08-01

We continue our investigation of Z-theory, the second double-copy component of open-string tree-level interactions besides super-Yang-Mills (sYM). We show that the amplitudes of the extended non-linear sigma model (NLSM) recently considered by Cachazo, Cha, and Mizera are reproduced by the leading α '-order of Z-theory amplitudes in the semi-abelian case. The extension refers to a coupling of NLSM pions to bi-adjoint scalars, and the semi-abelian case involves to a partial symmetrization over one of the color orderings that characterize the Z-theory amplitudes. Alternatively, the partial symmetrization corresponds to a mixed interaction among abelian and non-abelian states in the underlying open-superstring amplitude. We simplify these permutation sums via monodromy relations which greatly increase the efficiency in extracting the α '-expansion of these amplitudes. Their α '-corrections encode higher-derivative interactions between NLSM pions and bi-colored scalars all of which obey the duality between color and kinematics. Through double-copy, these results can be used to generate the predictions of supersymmetric Dirac-Born-Infeld-Volkov-Akulov theory coupled with sYM as well as a complete tower of higher-order α '-corrections.

Analytic calculations of anharmonic infrared and Raman vibrational spectra

PubMed Central

Louant, Orian; Ruud, Kenneth

2016-01-01

Using a recently developed recursive scheme for the calculation of high-order geometric derivatives of frequency-dependent molecular properties [Ringholm et al., J. Comp. Chem., 2014, 35, 622], we present the first analytic calculations of anharmonic infrared (IR) and Raman spectra including anharmonicity both in the vibrational frequencies and in the IR and Raman intensities. In the case of anharmonic corrections to the Raman intensities, this involves the calculation of fifth-order energy derivatives—that is, the third-order geometric derivatives of the frequency-dependent polarizability. The approach is applicable to both Hartree–Fock and Kohn–Sham density functional theory. Using generalized vibrational perturbation theory to second order, we have calculated the anharmonic infrared and Raman spectra of the non- and partially deuterated isotopomers of nitromethane, where the inclusion of anharmonic effects introduces combination and overtone bands that are observed in the experimental spectra. For the major features of the spectra, the inclusion of anharmonicities in the calculation of the vibrational frequencies is more important than anharmonic effects in the calculated infrared and Raman intensities. Using methanimine as a trial system, we demonstrate that the analytic approach avoids errors in the calculated spectra that may arise if numerical differentiation schemes are used. PMID:26784673

Second-order singular pertubative theory for gravitational lenses

NASA Astrophysics Data System (ADS)

Alard, C.

2018-03-01

The extension of the singular perturbative approach to the second order is presented in this paper. The general expansion to the second order is derived. The second-order expansion is considered as a small correction to the first-order expansion. Using this approach, it is demonstrated that in practice the second-order expansion is reducible to a first order expansion via a re-definition of the first-order pertubative fields. Even if in usual applications the second-order correction is small the reducibility of the second-order expansion to the first-order expansion indicates a potential degeneracy issue. In general, this degeneracy is hard to break. A useful and simple second-order approximation is the thin source approximation, which offers a direct estimation of the correction. The practical application of the corrections derived in this paper is illustrated by using an elliptical NFW lens model. The second-order pertubative expansion provides a noticeable improvement, even for the simplest case of thin source approximation. To conclude, it is clear that for accurate modelization of gravitational lenses using the perturbative method the second-order perturbative expansion should be considered. In particular, an evaluation of the degeneracy due to the second-order term should be performed, for which the thin source approximation is particularly useful.

Self-energy of an impurity in an ideal Fermi gas to second order in the interaction strength

NASA Astrophysics Data System (ADS)

Trefzger, Christian; Castin, Yvan

2014-09-01

We study in three dimensions the problem of a spatially homogeneous zero-temperature ideal Fermi gas of spin-polarized particles of mass m perturbed by the presence of a single distinguishable impurity of mass M. The interaction between the impurity and the fermions involves only the partial s wave through the scattering length a and has negligible range b compared to the inverse Fermi wave number 1/kF of the gas. Through the interactions with the Fermi gas the impurity gives birth to a quasiparticle, which will be here a Fermi polaron (or more precisely a monomeron). We consider the general case of an impurity moving with wave vector K ≠0: Then the quasiparticle acquires a finite lifetime in its initial momentum channel because it can radiate particle-hole pairs in the Fermi sea. A description of the system using a variational approach, based on a finite number of particle-hole excitations of the Fermi sea, then becomes inappropriate around K =0. We rely thus upon perturbation theory, where the small and negative parameter kFa→0- excludes any branches other than the monomeronic one in the ground state (as, e.g., the dimeronic one), and allows us a systematic study of the system. We calculate the impurity self-energy Σ(2)(K,ω) up to second order included in a. Remarkably, we obtain an analytical explicit expression for Σ(2)(K,ω), allowing us to study its derivatives in the plane (K,ω). These present interesting singularities, which in general appear in the third-order derivatives ∂3Σ(2)(K,ω). In the special case of equal masses, M =m, singularities appear already in the physically more accessible second-order derivatives ∂2Σ(2)(K,ω); using a self-consistent heuristic approach based on Σ(2) we then regularize the divergence of the second-order derivative ∂K2ΔE(K) of the complex energy of the quasiparticle found in Trefzger and Castin [Europhys. Lett. 104, 50005 (2013), 10.1209/0295-5075/104/50005] at K =kF, and we predict an interesting scaling law in the neighborhood of K =kF. As a by product of our theory we have access to all moments of the momentum of the particle-hole pair emitted by the impurity while damping its motion in the Fermi sea at the level of Fermi's golden rule.

Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere.

PubMed

Dan, Youquan; Zhang, Bin

2008-09-29

The Wigner distribution function (WDF) has been used to study the beam propagation factor (M(2)-factor) for partially coherent flat-topped (PCFT) beams with circular symmetry in a turbulent atmosphere. Based on the extended Huygens-Fresnel principle and the definition of the WDF, an expression for the WDF of PCFT beams in turbulence has been given. By use of the second-order moments of the WDF, the analytical formulas for the root-mean-square (rms) spatial width, the rms angular width, and the M(2)-factor of PCFT beams in turbulence have been derived, which can be applied to cases of different spatial power spectra of the refractive index fluctuations. The rms angular width and the M(2)-factor of PCFT beams in turbulence have been discussed with numerical examples. It can be shown that the M(2)-factor of PCFT beams in turbulence depends on the beam order, degree of global coherence of the source, waist width, wavelength, spatial power spectrum of the refractive index fluctuations, and propagation distance.

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.

Second-order variational equations for N-body simulations

NASA Astrophysics Data System (ADS)

Rein, Hanno; Tamayo, Daniel

2016-07-01

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

Second-order reconstruction of the inflationary potential

NASA Technical Reports Server (NTRS)

Liddle, Andrew R.; Turner, Michael S.

1994-01-01

To first order in the deviation from scale invariance the inflationary potential and its first two derivatives can be expressed in terms of the spectral indices of the scalar and tensor perturbations, n and n(sub T), and their contributions to the variance of the quadrupole CBR temperature anisotropy, S and T. In addition, there is a 'consistency relation' between these quantities: n(sub T) = (-1/ 7)(T/S). We derive the second-order expressions for the inflationary potential and its first two derivatives and the first-order expression for its third derivative, in terms, of n, n(sub T), S, T, and dn/d ln gamma. We also obtain the second-order consistency relation, n(sub T) = (-1/7)(T/S)(1 + 0.11(T/S) + 0.15(n-1)). As an example we consider the exponential potential, the only known case where exact analytic solutions for the perturbation spectra exist. We reconstruct the potential via Taylor expansion (with coefficients calculated at both first and second order), and introduce the Pade approximate as a greatly improved alternative.

Stefan-Maxwell Relations and Heat Flux with Anisotropic Transport Coefficients for Ionized Gases in a Magnetic Field with Application to the Problem of Ambipolar Diffusion

NASA Astrophysics Data System (ADS)

Kolesnichenko, A. V.; Marov, M. Ya.

2018-01-01

The defining relations for the thermodynamic diffusion and heat fluxes in a multicomponent, partially ionized gas mixture in an external electromagnetic field have been obtained by the methods of the kinetic theory. Generalized Stefan-Maxwell relations and algebraic equations for anisotropic transport coefficients (the multicomponent diffusion, thermal diffusion, electric and thermoelectric conductivity coefficients as well as the thermal diffusion ratios) associated with diffusion-thermal processes have been derived. The defining second-order equations are derived by the Chapman-Enskog procedure using Sonine polynomial expansions. The modified Stefan-Maxwell relations are used for the description of ambipolar diffusion in the Earth's ionospheric plasma (in the F region) composed of electrons, ions of many species, and neutral particles in a strong electromagnetic field.

Achieving second order advantage with multi-way partial least squares and residual bi-linearization with total synchronous fluorescence data of monohydroxy-polycyclic aromatic hydrocarbons in urine samples.

PubMed

Calimag-Williams, Korina; Knobel, Gaston; Goicoechea, H C; Campiglia, A D

2014-02-06

An attractive approach to handle matrix interference in samples of unknown composition is to generate second- or higher-order data formats and process them with appropriate chemometric algorithms. Several strategies exist to generate high-order data in fluorescence spectroscopy, including wavelength time matrices, excitation-emission matrices and time-resolved excitation-emission matrices. This article tackles a different aspect of generating high-order fluorescence data as it focuses on total synchronous fluorescence spectroscopy. This approach refers to recording synchronous fluorescence spectra at various wavelength offsets. Analogous to the concept of an excitation-emission data format, total synchronous data arrays fit into the category of second-order data. The main difference between them is the non-bilinear behavior of synchronous fluorescence data. Synchronous spectral profiles change with the wavelength offset used for sample excitation. The work presented here reports the first application of total synchronous fluorescence spectroscopy to the analysis of monohydroxy-polycyclic aromatic hydrocarbons in urine samples of unknown composition. Matrix interference is appropriately handled by processing the data either with unfolded-partial least squares and multi-way partial least squares, both followed by residual bi-linearization. Copyright © 2013 Elsevier B.V. All rights reserved.

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.

Zernike expansion of derivatives and Laplacians of the Zernike circle polynomials.

PubMed

Janssen, A J E M

2014-07-01

The partial derivatives and Laplacians of the Zernike circle polynomials occur in various places in the literature on computational optics. In a number of cases, the expansion of these derivatives and Laplacians in the circle polynomials are required. For the first-order partial derivatives, analytic results are scattered in the literature. Results start as early as 1942 in Nijboer's thesis and continue until present day, with some emphasis on recursive computation schemes. A brief historic account of these results is given in the present paper. By choosing the unnormalized version of the circle polynomials, with exponential rather than trigonometric azimuthal dependence, and by a proper combination of the two partial derivatives, a concise form of the expressions emerges. This form is appropriate for the formulation and solution of a model wavefront sensing problem of reconstructing a wavefront on the level of its expansion coefficients from (measurements of the expansion coefficients of) the partial derivatives. It turns out that the least-squares estimation problem arising here decouples per azimuthal order m, and per m the generalized inverse solution assumes a concise analytic form so that singular value decompositions are avoided. The preferred version of the circle polynomials, with proper combination of the partial derivatives, also leads to a concise analytic result for the Zernike expansion of the Laplacian of the circle polynomials. From these expansions, the properties of the Laplacian as a mapping from the space of circle polynomials of maximal degree N, as required in the study of the Neumann problem associated with the transport-of-intensity equation, can be read off within a single glance. Furthermore, the inverse of the Laplacian on this space is shown to have a concise analytic form.

Approach for Input Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

NASA Technical Reports Server (NTRS)

Putko, Michele M.; Taylor, Arthur C., III; Newman, Perry A.; Green, Lawrence L.

2002-01-01

An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 3-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first- and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Extended Weyl invariance in a bimetric model and partial masslessness

NASA Astrophysics Data System (ADS)

Hassan, S. F.; Schmidt-May, Angnis; von Strauss, Mikael

2016-01-01

We revisit a particular ghost-free bimetric model which is related to both partial masslessness (PM) and conformal gravity. Linearly, the model propagates six instead of seven degrees of freedom not only around de Sitter but also around flat spacetime. Nonlinearly, the equations of motion can be recast in the form of expansions in powers of curvatures, and exhibit a remarkable amount of structure. In this form, the equations are shown to be invariant under scalar gauge transformations, at least up to six orders in derivatives, the lowest order term being a Weyl scaling of the metrics. The terms at two-derivative order reproduce the usual PM gauge transformations on de Sitter backgrounds. At the four-derivative order, a potential obstruction that could destroy the symmetry is shown to vanish. This in turn guarantees the gauge invariance to at least six-orders in derivatives. This is equivalent to adding up to ten-derivative corrections to conformal gravity. More generally, we outline a procedure for constructing the gauge transformations order by order as an expansion in derivatives and comment on the validity and limitations of the procedure. We also discuss recent arguments against the existence of a PM gauge symmetry in bimetric theory and show that, at least in their present form, they are evaded by the model considered here. Finally, we argue that a bimetric approach to PM theory is more promising than one based on the existence of a fundamental PM field.

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.

ppcor: An R Package for a Fast Calculation to Semi-partial Correlation Coefficients.

PubMed

Kim, Seongho

2015-11-01

Lack of a general matrix formula hampers implementation of the semi-partial correlation, also known as part correlation, to the higher-order coefficient. This is because the higher-order semi-partial correlation calculation using a recursive formula requires an enormous number of recursive calculations to obtain the correlation coefficients. To resolve this difficulty, we derive a general matrix formula of the semi-partial correlation for fast computation. The semi-partial correlations are then implemented on an R package ppcor along with the partial correlation. Owing to the general matrix formulas, users can readily calculate the coefficients of both partial and semi-partial correlations without computational burden. The package ppcor further provides users with the level of the statistical significance with its test statistic.

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

USGS Publications Warehouse

Lai, Chintu

1977-01-01

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

Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis

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

Plyushchay, Mikhail S., E-mail: mikhail.plyushchay@usach.cl

A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metamorphosis that associates quantum systems with the first-order supersymmetry to the systems with the second-order supercharges.

A novel second-order standard addition analytical method based on data processing with multidimensional partial least-squares and residual bilinearization.

PubMed

Lozano, Valeria A; Ibañez, Gabriela A; Olivieri, Alejandro C

2009-10-05

In the presence of analyte-background interactions and a significant background signal, both second-order multivariate calibration and standard addition are required for successful analyte quantitation achieving the second-order advantage. This report discusses a modified second-order standard addition method, in which the test data matrix is subtracted from the standard addition matrices, and quantitation proceeds via the classical external calibration procedure. It is shown that this novel data processing method allows one to apply not only parallel factor analysis (PARAFAC) and multivariate curve resolution-alternating least-squares (MCR-ALS), but also the recently introduced and more flexible partial least-squares (PLS) models coupled to residual bilinearization (RBL). In particular, the multidimensional variant N-PLS/RBL is shown to produce the best analytical results. The comparison is carried out with the aid of a set of simulated data, as well as two experimental data sets: one aimed at the determination of salicylate in human serum in the presence of naproxen as an additional interferent, and the second one devoted to the analysis of danofloxacin in human serum in the presence of salicylate.

High-order fractional partial differential equation transform for molecular surface construction.

PubMed

Hu, Langhua; Chen, Duan; Wei, Guo-Wei

2013-01-01

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.

Development and Application of Modern Optimal Controllers for a Membrane Structure Using Vector Second Order Form

NASA Astrophysics Data System (ADS)

Ferhat, Ipar

With increasing advancement in material science and computational power of current computers that allows us to analyze high dimensional systems, very light and large structures are being designed and built for aerospace applications. One example is a reflector of a space telescope that is made of membrane structures. These reflectors are light and foldable which makes the shipment easy and cheaper unlike traditional reflectors made of glass or other heavy materials. However, one of the disadvantages of membranes is that they are very sensitive to external changes, such as thermal load or maneuvering of the space telescope. These effects create vibrations that dramatically affect the performance of the reflector. To overcome vibrations in membranes, in this work, piezoelectric actuators are used to develop distributed controllers for membranes. These actuators generate bending effects to suppress the vibration. The actuators attached to a membrane are relatively thick which makes the system heterogeneous; thus, an analytical solution cannot be obtained to solve the partial differential equation of the system. Therefore, the Finite Element Model is applied to obtain an approximate solution for the membrane actuator system. Another difficulty that arises with very flexible large structures is the dimension of the discretized system. To obtain an accurate result, the system needs to be discretized using smaller segments which makes the dimension of the system very high. This issue will persist as long as the improving technology will allow increasingly complex and large systems to be designed and built. To deal with this difficulty, the analysis of the system and controller development to suppress the vibration are carried out using vector second order form as an alternative to vector first order form. In vector second order form, the number of equations that need to be solved are half of the number equations in vector first order form. Analyzing the system for control characteristics such as stability, controllability and observability is a key step that needs to be carried out before developing a controller. This analysis determines what kind of system is being modeled and the appropriate approach for controller development. Therefore, accuracy of the system analysis is very crucial. The results of the system analysis using vector second order form and vector first order form show the computational advantages of using vector second order form. Using similar concepts, LQR and LQG controllers, that are developed to suppress the vibration, are derived using vector second order form. To develop a controller using vector second order form, two different approaches are used. One is reducing the size of the Algebraic Riccati Equation to half by partitioning the solution matrix. The other approach is using the Hamiltonian method directly in vector second order form. Controllers are developed using both approaches and compared to each other. Some simple solutions for special cases are derived for vector second order form using the reduced Algebraic Riccati Equation. The advantages and drawbacks of both approaches are explained through examples. System analysis and controller applications are carried out for a square membrane system with four actuators. Two different systems with different actuator locations are analyzed. One system has the actuators at the corners of the membrane, the other has the actuators away from the corners. The structural and control effect of actuator locations are demonstrated with mode shapes and simulations. The results of the controller applications and the comparison of the vector first order form with the vector second order form demonstrate the efficacy of the controllers.

Geometerial description for a proposed aeroassist flight experiment vehicle

NASA Technical Reports Server (NTRS)

Cheatwood, F. M.; Dejarnette, F. J.; Hamilton, H. H., II

1986-01-01

One geometry currently under consideration for the Aeroassist Flight Experiment (AFE) vehicle is composed of several segments of simple general conics: an ellipsoidal nose tangent to an elliptical cone and a base skirt with the base plane raked relative to the body axis. An analytic representation for the body coordinates and first and second partial derivatives of this configuration has been developed. Equations are given which define the body radius and partial derivatives for a prescribed axial and circumferential position on the vehicle. The results for a sample case are tabulated and presented graphically.

General Tricomi-Rassias problem and oblique derivative problem for generalized Chaplygin equations

NASA Astrophysics Data System (ADS)

Wen, Guochun; Chen, Dechang; Cheng, Xiuzhen

2007-09-01

Many authors have discussed the Tricomi problem for some second order equations of mixed type, which has important applications in gas dynamics. In particular, Bers proposed the Tricomi problem for Chaplygin equations in multiply connected domains [L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Wiley, New York, 1958]. And Rassias proposed the exterior Tricomi problem for mixed equations in a doubly connected domain and proved the uniqueness of solutions for the problem [J.M. Rassias, Lecture Notes on Mixed Type Partial Differential Equations, World Scientific, Singapore, 1990]. In the present paper, we discuss the general Tricomi-Rassias problem for generalized Chaplygin equations. This is one general oblique derivative problem that includes the exterior Tricomi problem as a special case. We first give the representation of solutions of the general Tricomi-Rassias problem, and then prove the uniqueness and existence of solutions for the problem by a new method. In this paper, we shall also discuss another general oblique derivative problem for generalized Chaplygin equations.

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 2: Derivations of second-order asymptotic boundary value solutions

NASA Technical Reports Server (NTRS)

Lancaster, J. E.

1973-01-01

Previously published asymptotic solutions for lunar and interplanetery trajectories have been modified and combined to formulate a general analytical solution to the problem of N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The complete derivation of the second-order solution, including the application of a regorous matching principle, is given. It is shown that the outer and inner expansions can be matched in a region of order mu to the alpha power, where 2/5 alpha 1/2, and mu (the moon/earth or planet/sun mass ratio) is much less than one. The second-order asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-Earth, and interplanetary solutions. Each is presented as an explicit analytical solution which does not require iterative steps to satisfy the boundary conditions. The complete derivation of each solution is shown, as well as instructions for numerical evaluation. For Vol. 1, see N73-27738.

Finite-SNR analysis for partial relaying cooperation with channel coding and opportunistic relay selection

NASA Astrophysics Data System (ADS)

Vu, Thang X.; Duhamel, Pierre; Chatzinotas, Symeon; Ottersten, Bjorn

2017-12-01

This work studies the performance of a cooperative network which consists of two channel-coded sources, multiple relays, and one destination. To achieve high spectral efficiency, we assume that a single time slot is dedicated to relaying. Conventional network-coded-based cooperation (NCC) selects the best relay which uses network coding to serve the two sources simultaneously. The bit error rate (BER) performance of NCC with channel coding, however, is still unknown. In this paper, we firstly study the BER of NCC via a closed-form expression and analytically show that NCC only achieves diversity of order two regardless of the number of available relays and the channel code. Secondly, we propose a novel partial relaying-based cooperation (PARC) scheme to improve the system diversity in the finite signal-to-noise ratio (SNR) regime. In particular, closed-form expressions for the system BER and diversity order of PARC are derived as a function of the operating SNR value and the minimum distance of the channel code. We analytically show that the proposed PARC achieves full (instantaneous) diversity order in the finite SNR regime, given that an appropriate channel code is used. Finally, numerical results verify our analysis and demonstrate a large SNR gain of PARC over NCC in the SNR region of interest.

Polymer Coatings Degradation Properties

DTIC Science & Technology

1985-02-01

undertaken 124). The Box-Jenkins approach first evaluates the partial auto -correlation function and determines the order of the moving average memory function...78 - Tables 15 and 16 show the resalit- f- a, the partial auto correlation plots. Second order moving .-. "ra ;;th -he appropriate lags were...coated films. Kaempf, Guenter; Papenroth, Wolfgang; Kunststoffe Date: 1982 Volume: 72 Number:7 Pages: 424-429 Parameters influencing the accelerated

Effects of the non-extensive parameter on the propagation of ion acoustic waves in five-component cometary plasma system

NASA Astrophysics Data System (ADS)

Mahmoud, Abeer A.

2018-01-01

Some important evolution nonlinear partial differential equations are derived using the reductive perturbation method for unmagnetized collisionless system of five component plasma. This plasma system is a multi-ion contains negatively and positively charged Oxygen ions (heavy ions), positive Hydrogen ions (lighter ions), hot electrons from solar origin and colder electrons from cometary origin. The positive Hydrogen ion and the two types of electrons obey q-non-extensive distributions. The derived equations have three types of ion acoustic waves, which are soliton waves, shock waves and kink waves. The effects of the non-extensive parameters for the hot electrons, the colder electrons and the Hydrogen ions on the propagation of the envelope waves are studied. The compressive and rarefactive shapes of the three envelope waves appear in this system for the first order of the power of the nonlinearity strength with different values of non-extensive parameters. For the second order, the strength of nonlinearity will increase and the compressive type of the envelope wave only appears.

Singularities in the lineshape of a second-order perturbed quadrupolar nucleus and their use in data fitting.

PubMed

Field, Timothy R; Bain, Alex D

2014-01-01

Even for large quadrupolar interactions, the powder spectrum of the central transition for a half-integral spin is relatively narrow, because it is unperturbed to first order. However, the second-order perturbation is still orientation dependent, so it generates a characteristic lineshape. This lineshape has both finite step discontinuities and singularities where the spectrum is infinite, in theory. The relative positions of these features are well-known and they play an important role in fitting experimental data. However, there has been relatively little discussion of how high the steps are, so we present explicit formulae for these heights. This gives a full characterization of the features in this lineshape which can lead to an analysis of the spectrum without the usual laborious powder average. The transition frequency, as a function of the orientation angles, shows critical points: maxima, minima and saddle points. The maxima and minima correspond to the step discontinuities and the saddle points generate the singularities. Near a maximum, the contours are ellipses, whose dimensions are determined by the second derivatives of the frequency with respect to the polar and azimuthal angles. The density of points is smooth as the contour levels move up and down, but then drops to zero when a maximum is passed, giving a step. The height of the step is determined by the Hessian matrix-the matrix of all partial second derivatives. The points near the poles and the saddle points require a more detailed analysis, but this can still be done analytically. The resulting formulae are then compared to numerical simulations of the lineshape. We expand this calculation to include a relatively simple case where there is chemical shielding anisotropy and use this to fit experimental (139)La spectra of La2O3. Copyright © 2014 Elsevier Inc. All rights reserved.

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Green, Lawrence L.; Newman, Perry A.; Putko, Michele M.

2001-01-01

An efficient incremental-iterative approach for differentiating advanced flow codes is successfully demonstrated on a 2D inviscid model problem. The method employs the reverse-mode capability of the automatic- differentiation software tool ADIFOR 3.0, and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straight-forward, black-box reverse- mode application of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-order aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoint) procedures; then, a very efficient non-iterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hessian matrices) of lift, wave-drag, and pitching-moment coefficients are calculated with respect to geometric- shape, angle-of-attack, and freestream Mach number

Fast Numerical Methods for Stochastic Partial Differential Equations

DTIC Science & Technology

2016-04-15

analysis we first derived a system of forward and backward SDEs (BSDEs) for (Xt, Qt, Zt){ dXs = b( Xs )dt+ σsdWs, Xt = x, t < s < T, (SDE) dQs = ZsdWs...g( Xs )QsdVs, QT = Φ(XT ). (BSDE) (6) Here Wt and Vt are two independent Brownian motions. The first equation in (6) is a forward SDE while the second...first order scheme for a general coupled system of forward-backward SDEs [1]: dXs = b( Xs )ds+ σ( Xs )dWs, t ≤ s ≤ T, dYs = +f(s, Xs , Ys)ds +g(s

Generic analysis of kinetically driven inflation

NASA Astrophysics Data System (ADS)

Saitou, Rio

2018-04-01

We perform a model-independent analysis of kinetically driven inflation (KDI) which (partially) includes generalized G-inflation and ghost inflation. We evaluate the background evolution splitting into the inflationary attractor and the perturbation around it. We also consider the quantum fluctuation of the scalar mode with a usual scaling and derive the spectral index, ignoring the contribution from the second-order products of slow-roll parameters. Using these formalisms, we find that within our generic framework the models of KDI which possess the shift symmetry of scalar field cannot create the quantum fluctuation consistent with the observation. Breaking the shift symmetry, we obtain a few essential conditions for viable models of KDI associated with the graceful exit.

Static shape control for flexible structures

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Scheid, R. E., Jr.

1986-01-01

An integrated methodology is described for defining static shape control laws for large flexible structures. The techniques include modeling, identifying and estimating the control laws of distributed systems characterized in terms of infinite dimensional state and parameter spaces. The models are expressed as interconnected elliptic partial differential equations governing a range of static loads, with the capability of analyzing electromagnetic fields around antenna systems. A second-order analysis is carried out for statistical errors, and model parameters are determined by maximizing an appropriate defined likelihood functional which adjusts the model to observational data. The parameter estimates are derived from the conditional mean of the observational data, resulting in a least squares superposition of shape functions obtained from the structural model.

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.

Approach for Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

NASA Technical Reports Server (NTRS)

Putko, Michele M.; Newman, Perry A.; Taylor, Arthur C., III; Green, Lawrence L.

2001-01-01

This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD (computational fluid dynamics) code. Given uncertainties in statistically independent, random, normally distributed input variables, a first- and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

High-order flux correction/finite difference schemes for strand grids

NASA Astrophysics Data System (ADS)

Katz, Aaron; Work, Dalon

2015-02-01

A novel high-order method combining unstructured flux correction along body surfaces and high-order finite differences normal to surfaces is formulated for unsteady viscous flows on strand grids. The flux correction algorithm is applied in each unstructured layer of the strand grid, and the layers are then coupled together via a source term containing derivatives in the strand direction. Strand-direction derivatives are approximated to high-order via summation-by-parts operators for first derivatives and second derivatives with variable coefficients. We show how this procedure allows for the proper truncation error canceling properties required for the flux correction scheme. The resulting scheme possesses third-order design accuracy, but often exhibits fourth-order accuracy when higher-order derivatives are employed in the strand direction, especially for highly viscous flows. We prove discrete conservation for the new scheme and time stability in the absence of the flux correction terms. Results in two dimensions are presented that demonstrate improvements in accuracy with minimal computational and algorithmic overhead over traditional second-order algorithms.

A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics

NASA Astrophysics Data System (ADS)

Boscheri, Walter; Dumbser, Michael; Loubère, Raphaël; Maire, Pierre-Henri

2018-04-01

In this paper we develop a conservative cell-centered Lagrangian finite volume scheme for the solution of the hydrodynamics equations on unstructured multidimensional grids. The method is derived from the Eucclhyd scheme discussed in [47,43,45]. It is second-order accurate in space and is combined with the a posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness and stability at shock waves. Second-order of accuracy in time is achieved via the ADER (Arbitrary high order schemes using DERivatives) approach. A large set of numerical test cases is proposed to assess the ability of the method to achieve effective second order of accuracy on smooth flows, maintaining an essentially non-oscillatory behavior on discontinuous profiles, general robustness ensuring physical admissibility of the numerical solution, and precision where appropriate.

Extending compile-time reverse mode and exploiting partial separability in ADIFOR

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

Bischof, C.H.; El-Khadiri, M.

1992-10-01

The numerical methods employed in the solution of many scientific computing problems require the computation of the gradient of a function f: R[sup n] [yields] R. ADIFOR is a source translator that, given a collection of subroutines to compute f, generates Fortran 77 code for computing the derivative of this function. Using the so-called torsion problem from the MINPACK-2 test collection as an example, this paper explores two issues in automatic differentiation: the efficient computation of derivatives for partial separable functions and the use of the compile-time reverse mode for the generation of derivatives. We show that orders of magnitudesmore » of improvement are possible when exploiting partial separability and maximizing use of the reverse mode.« less

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.

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

NASA Astrophysics Data System (ADS)

Shamseldeen, S.

2018-03-01

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

Development and validation of different methods manipulating zero order and first order spectra for determination of the partially overlapped mixture benazepril and amlodipine: A comparative study

NASA Astrophysics Data System (ADS)

Hemdan, A.

2016-07-01

Three simple, selective, and accurate spectrophotometric methods have been developed and then validated for the analysis of Benazepril (BENZ) and Amlodipine (AML) in bulk powder and pharmaceutical dosage form. The first method is the absorption factor (AF) for zero order and amplitude factor (P-F) for first order spectrum, where both BENZ and AML can be measured from their resolved zero order spectra at 238 nm or from their first order spectra at 253 nm. The second method is the constant multiplication coupled with constant subtraction (CM-CS) for zero order and successive derivative subtraction-constant multiplication (SDS-CM) for first order spectrum, where both BENZ and AML can be measured from their resolved zero order spectra at 240 nm and 238 nm, respectively, or from their first order spectra at 214 nm and 253 nm for Benazepril and Amlodipine respectively. The third method is the novel constant multiplication coupled with derivative zero crossing (CM-DZC) which is a stability indicating assay method for determination of Benazepril and Amlodipine in presence of the main degradation product of Benazepril which is Benazeprilate (BENZT). The three methods were validated as per the ICH guidelines and the standard curves were found to be linear in the range of 5-60 μg/mL for Benazepril and 5-30 for Amlodipine, with well accepted mean correlation coefficient for each analyte. The intra-day and inter-day precision and accuracy results were well within the acceptable limits.

Development and validation of different methods manipulating zero order and first order spectra for determination of the partially overlapped mixture benazepril and amlodipine: A comparative study.

PubMed

Hemdan, A

2016-07-05

Three simple, selective, and accurate spectrophotometric methods have been developed and then validated for the analysis of Benazepril (BENZ) and Amlodipine (AML) in bulk powder and pharmaceutical dosage form. The first method is the absorption factor (AF) for zero order and amplitude factor (P-F) for first order spectrum, where both BENZ and AML can be measured from their resolved zero order spectra at 238nm or from their first order spectra at 253nm. The second method is the constant multiplication coupled with constant subtraction (CM-CS) for zero order and successive derivative subtraction-constant multiplication (SDS-CM) for first order spectrum, where both BENZ and AML can be measured from their resolved zero order spectra at 240nm and 238nm, respectively, or from their first order spectra at 214nm and 253nm for Benazepril and Amlodipine respectively. The third method is the novel constant multiplication coupled with derivative zero crossing (CM-DZC) which is a stability indicating assay method for determination of Benazepril and Amlodipine in presence of the main degradation product of Benazepril which is Benazeprilate (BENZT). The three methods were validated as per the ICH guidelines and the standard curves were found to be linear in the range of 5-60μg/mL for Benazepril and 5-30 for Amlodipine, with well accepted mean correlation coefficient for each analyte. The intra-day and inter-day precision and accuracy results were well within the acceptable limits. Copyright © 2016 Elsevier B.V. All rights reserved.

M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere.

PubMed

Yuan, Yangsheng; Cai, Yangjian; Qu, Jun; Eyyuboğlu, Halil T; Baykal, Yahya; Korotkova, Olga

2009-09-28

Analytical formula is derived for the M(2)-factor of coherent and partially coherent dark hollow beams (DHB) in turbulent atmosphere based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function. Our numerical results show that the M(2)- factor of a DHB in turbulent atmosphere increases on propagation, which is much different from its invariant properties in free-space, and is mainly determined by the parameters of the beam and the atmosphere. The relative M(2)-factor of a DHB increases slower than that of Gaussian and flat-topped beams on propagation, which means a DHB is less affected by the atmospheric turbulence than Gaussian and flat-topped beams. Furthermore, the relative M(2)-factor of a DHB with lower coherence, longer wavelength and larger dark size is less affected by the atmospheric turbulence. Our results will be useful in long-distance free-space optical communications.

Classification of Fusarium-Infected Korean Hulled Barley Using Near-Infrared Reflectance Spectroscopy and Partial Least Squares Discriminant Analysis

PubMed Central

Lim, Jongguk; Kim, Giyoung; Mo, Changyeun; Oh, Kyoungmin; Yoo, Hyeonchae; Ham, Hyeonheui; Kim, Moon S.

2017-01-01

The purpose of this study is to use near-infrared reflectance (NIR) spectroscopy equipment to nondestructively and rapidly discriminate Fusarium-infected hulled barley. Both normal hulled barley and Fusarium-infected hulled barley were scanned by using a NIR spectrometer with a wavelength range of 1175 to 2170 nm. Multiple mathematical pretreatments were applied to the reflectance spectra obtained for Fusarium discrimination and the multivariate analysis method of partial least squares discriminant analysis (PLS-DA) was used for discriminant prediction. The PLS-DA prediction model developed by applying the second-order derivative pretreatment to the reflectance spectra obtained from the side of hulled barley without crease achieved 100% accuracy in discriminating the normal hulled barley and the Fusarium-infected hulled barley. These results demonstrated the feasibility of rapid discrimination of the Fusarium-infected hulled barley by combining multivariate analysis with the NIR spectroscopic technique, which is utilized as a nondestructive detection method. PMID:28974012

First- and second-order sensitivity analysis of linear and nonlinear structures

NASA Technical Reports Server (NTRS)

Haftka, R. T.; Mroz, Z.

1986-01-01

This paper employs the principle of virtual work to derive sensitivity derivatives of structural response with respect to stiffness parameters using both direct and adjoint approaches. The computations required are based on additional load conditions characterized by imposed initial strains, body forces, or surface tractions. As such, they are equally applicable to numerical or analytical solution techniques. The relative efficiency of various approaches for calculating first and second derivatives is assessed. It is shown that for the evaluation of second derivatives the most efficient approach is one that makes use of both the first-order sensitivities and adjoint vectors. Two example problems are used for demonstrating the various approaches.

On CAPM and Black-Scholes differing risk-return strategies

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.; Gunaratne, Gemunu H.

2003-11-01

In their path-finding 1973 paper, Black and Scholes presented two separate derivations of their famous option pricing partial differential equation. The second derivation was from the standpoint that was Black's original motivation, namely, the capital asset pricing model (CAPM). We show here, in contrast, that the option valuation is not uniquely determined; in particular, strategies based on the delta-hedge and CAPM provide different valuations of an option although both hedges are instantaneouly riskfree. Second, we show explicitly that CAPM is not, as economists claim, an equilibrium theory.

Second- and Higher-Order Virial Coefficients Derived from Equations of State for Real Gases

ERIC Educational Resources Information Center

Parkinson, William A.

2009-01-01

Derivation of the second- and higher-order virial coefficients for models of the gaseous state is demonstrated by employing a direct differential method and subsequent term-by-term comparison to power series expansions. This communication demonstrates the application of this technique to van der Waals representations of virial coefficients.…

High-order fractional partial differential equation transform for molecular surface construction

PubMed Central

Hu, Langhua; Chen, Duan; Wei, Guo-Wei

2013-01-01

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation. PMID:24364020

Fitting and Testing Conditional Multinormal Partial Credit Models

ERIC Educational Resources Information Center

Hessen, David J.

2012-01-01

A multinormal partial credit model for factor analysis of polytomously scored items with ordered response categories is derived using an extension of the Dutch Identity (Holland in "Psychometrika" 55:5-18, 1990). In the model, latent variables are assumed to have a multivariate normal distribution conditional on unweighted sums of item…

First and second order derivatives for optimizing parallel RF excitation waveforms.

PubMed

Majewski, Kurt; Ritter, Dieter

2015-09-01

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations. Copyright © 2015 Elsevier Inc. All rights reserved.

First and second order derivatives for optimizing parallel RF excitation waveforms

NASA Astrophysics Data System (ADS)

Majewski, Kurt; Ritter, Dieter

2015-09-01

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations.

On the complete and partial integrability of non-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Bountis, T. C.; Ramani, A.; Grammaticos, B.; Dorizzi, B.

1984-11-01

The methods of singularity analysis are applied to several third order non-Hamiltonian systems of physical significance including the Lotka-Volterra equations, the three-wave interaction and the Rikitake dynamo model. Complete integrability is defined and new completely integrable systems are discovered by means of the Painlevé property. In all these cases we obtain integrals, which reduce the equations either to a final quadrature or to an irreducible second order ordinary differential equation (ODE) solved by Painlevé transcendents. Relaxing the Painlevé property we find many partially integrable cases whose movable singularities are poles at leading order, with In( t- t0) terms entering at higher orders. In an Nth order, generalized Rössler model a precise relation is established between the partial fulfillment of the Painlevé conditions and the existence of N - 2 integrals of the motion.

Rapid Detection of Volatile Oil in Mentha haplocalyx by Near-Infrared Spectroscopy and Chemometrics.

PubMed

Yan, Hui; Guo, Cheng; Shao, Yang; Ouyang, Zhen

2017-01-01

Near-infrared spectroscopy combined with partial least squares regression (PLSR) and support vector machine (SVM) was applied for the rapid determination of chemical component of volatile oil content in Mentha haplocalyx . The effects of data pre-processing methods on the accuracy of the PLSR calibration models were investigated. The performance of the final model was evaluated according to the correlation coefficient ( R ) and root mean square error of prediction (RMSEP). For PLSR model, the best preprocessing method combination was first-order derivative, standard normal variate transformation (SNV), and mean centering, which had of 0.8805, of 0.8719, RMSEC of 0.091, and RMSEP of 0.097, respectively. The wave number variables linking to volatile oil are from 5500 to 4000 cm-1 by analyzing the loading weights and variable importance in projection (VIP) scores. For SVM model, six LVs (less than seven LVs in PLSR model) were adopted in model, and the result was better than PLSR model. The and were 0.9232 and 0.9202, respectively, with RMSEC and RMSEP of 0.084 and 0.082, respectively, which indicated that the predicted values were accurate and reliable. This work demonstrated that near infrared reflectance spectroscopy with chemometrics could be used to rapidly detect the main content volatile oil in M. haplocalyx . The quality of medicine directly links to clinical efficacy, thus, it is important to control the quality of Mentha haplocalyx . Near-infrared spectroscopy combined with partial least squares regression (PLSR) and support vector machine (SVM) was applied for the rapid determination of chemical component of volatile oil content in Mentha haplocalyx . For SVM model, 6 LVs (less than 7 LVs in PLSR model) were adopted in model, and the result was better than PLSR model. It demonstrated that near infrared reflectance spectroscopy with chemometrics could be used to rapidly detect the main content volatile oil in Mentha haplocalyx . Abbreviations used: 1 st der: First-order derivative; 2 nd der: Second-order derivative; LOO: Leave-one-out; LVs: Latent variables; MC: Mean centering, NIR: Near-infrared; NIRS: Near infrared spectroscopy; PCR: Principal component regression, PLSR: Partial least squares regression; RBF: Radial basis function; RMSEC: Root mean square error of cross validation, RMSEC: Root mean square error of calibration; RMSEP: Root mean square error of prediction; SNV: Standard normal variate transformation; SVM: Support vector machine; VIP: Variable Importance in projection.

Toward lattice fractional vector calculus

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-09-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

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...

Extending compile-time reverse mode and exploiting partial separability in ADIFOR. ADIFOR Working Note No. 7

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

Bischof, C.H.; El-Khadiri, M.

1992-10-01

The numerical methods employed in the solution of many scientific computing problems require the computation of the gradient of a function f: R{sup n} {yields} R. ADIFOR is a source translator that, given a collection of subroutines to compute f, generates Fortran 77 code for computing the derivative of this function. Using the so-called torsion problem from the MINPACK-2 test collection as an example, this paper explores two issues in automatic differentiation: the efficient computation of derivatives for partial separable functions and the use of the compile-time reverse mode for the generation of derivatives. We show that orders of magnitudesmore » of improvement are possible when exploiting partial separability and maximizing use of the reverse mode.« less

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Green, Lawrence L.; Newman, Perry A.; Putko, Michele M.

2003-01-01

An efficient incremental iterative approach for differentiating advanced flow codes is successfully demonstrated on a two-dimensional inviscid model problem. The method employs the reverse-mode capability of the automatic differentiation software tool ADIFOR 3.0 and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straightforward, black-box reverse-mode applicaiton of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-rder aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoinct) procedures; then, a very efficient noniterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hesian matrices) of lift, wave drag, and pitching-moment coefficients are calculated with respect to geometric shape, angle of attack, and freestream Mach number.

A differential equation for the Generalized Born radii.

PubMed

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2013-06-28

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

Photometry with FORS

NASA Astrophysics Data System (ADS)

Freudling, W.; Møller, P.; Patat, F.; Moehler, S.; Romaniello, M.; Jehin, E.; O'Brien, K.; Izzo, C.; Pompei, E.

Photometric calibration observations are routinely carried out with all ESO imaging cameras in every clear night. The nightly zeropoints derived from these observations are accurate to about 10%. Recently, we have started the FORS Absolute Photometry Project (FAP) to investigate, if and how percent-level absolute photometric accuracy can be achieved with FORS1, and how such photometric calibration can be offered to observers. We found that there are significant differences between the sky-flats and the true photometric response of the instrument which partially depend on the rotator angle. A second order correction to the sky-flat significantly improves the relative photometry within the field. We demonstrate the feasibility of percent level photometry and describe the calibrations necessary to achieve that level of accuracy.

A note on the velocity derivative flatness factor in decaying HIT

NASA Astrophysics Data System (ADS)

Djenidi, L.; Danaila, L.; Antonia, R. A.; Tang, S.

2017-05-01

We develop an analytical expression for the velocity derivative flatness factor, F, in decaying homogenous and isotropic turbulence (HIT) starting with the transport equation of the third-order moment of the velocity increment and assuming self-preservation. This expression, fully consistent with the Navier-Stokes equations, relates F to the product between the second-order pressure derivative (∂2p /∂x2) and second-order moment of the longitudinal velocity derivative ((∂u/∂x ) 2), highlighting the role the pressure plays in the scaling of the fourth-order moment of the longitudinal velocity derivative. It is also shown that F has an upper bound which follows the integral of k*4Ep*(k* ) where Ep and k are the pressure spectrum and the wavenumber, respectively (the symbol * represents the Kolmogorov normalization). Direct numerical simulations of forced HIT suggest that this integral converges toward a constant as the Reynolds number increases.

Second harmonic generation and crystal growth of new chalcone derivatives

NASA Astrophysics Data System (ADS)

Patil, P. S.; Dharmaprakash, S. M.; Ramakrishna, K.; Fun, Hoong-Kun; Sai Santosh Kumar, R.; Narayana Rao, D.

2007-05-01

We report on the synthesis, crystal structure and optical characterization of chalcone derivatives developed for second-order nonlinear optics. The investigation of a series of five chalcone derivatives with the second harmonic generation powder test according to Kurtz and Perry revealed that these chalcones show efficient second-order nonlinear activity. Among them, high-quality single crystals of 3-Br-4'-methoxychalcone (3BMC) were grown by solvent evaporation solution growth technique. Grown crystals were characterized by X-ray powder diffraction (XRD), laser damage threshold, UV-vis-NIR and refractive index measurement studies. Infrared spectroscopy, thermogravimetric analysis and differential thermal analysis measurements were performed to study the molecular vibration and thermal behavior of 3BMC crystal. Thermal analysis does not show any structural phase transition.

Improved explanation of human intelligence using cortical features with second order moments and regression.

PubMed

Park, Hyunjin; Yang, Jin-ju; Seo, Jongbum; Choi, Yu-yong; Lee, Kun-ho; Lee, Jong-min

2014-04-01

Cortical features derived from magnetic resonance imaging (MRI) provide important information to account for human intelligence. Cortical thickness, surface area, sulcal depth, and mean curvature were considered to explain human intelligence. One region of interest (ROI) of a cortical structure consisting of thousands of vertices contained thousands of measurements, and typically, one mean value (first order moment), was used to represent a chosen ROI, which led to a potentially significant loss of information. We proposed a technological improvement to account for human intelligence in which a second moment (variance) in addition to the mean value was adopted to represent a chosen ROI, so that the loss of information would be less severe. Two computed moments for the chosen ROIs were analyzed with partial least squares regression (PLSR). Cortical features for 78 adults were measured and analyzed in conjunction with the full-scale intelligence quotient (FSIQ). Our results showed that 45% of the variance of the FSIQ could be explained using the combination of four cortical features using two moments per chosen ROI. Our results showed improvement over using a mean value for each ROI, which explained 37% of the variance of FSIQ using the same set of cortical measurements. Our results suggest that using additional second order moments is potentially better than using mean values of chosen ROIs for regression analysis to account for human intelligence. Copyright © 2014 Elsevier Ltd. All rights reserved.

Diameter increase in second-growth Appalachian hardwood stands - a comparison of species

Treesearch

George R., Jr. Trimble

1967-01-01

A study of growth at d.b.h. among eight hardwood species after partial cutting in second-growth stands. Red oak grew fastest, followed in order by yellow-poplar, sugar maple, basswood, black cherry, white ash, beech, and chestnut oak.

A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation

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

Nash, Patrick L.

2008-01-10

Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation {delta}{sub perpendicular} {sup FDA} of 1/r ({partial_derivative})/({partial_derivative}r) r({partial_derivative})/({partial_derivative}r) that possesses an associated exact unitary representation of e{sup i/2{lambda}}{sup {delta}{sub perpendicular}{sup FDA}}. The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown tomore » be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium.« less

A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2017-12-01

In this manuscript, we consider an initial-boundary-value problem governed by a (1 + 1)-dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics. The model considers the presence of a spatial Laplacian of fractional order which is defined in terms of Riesz fractional derivatives, as well as the inclusion of a generic continuously differentiable potential. It is known that the undamped regime has an associated positive energy functional, and we show here that it is preserved throughout time under suitable boundary conditions. To approximate the solutions of this model, we propose a finite-difference discretization based on fractional centered differences. Some discrete quantities are proposed in this work to estimate the energy functional, and we show that the numerical method is capable of conserving the discrete energy under the same boundary conditions for which the continuous model is conservative. Moreover, we establish suitable computational constraints under which the discrete energy of the system is positive. The method is consistent of second order, and is both stable and convergent. The numerical simulations shown here illustrate the most important features of our numerical methodology.

Direct reconstruction of the two-dimensional pair distribution function in partially ordered systems with angular correlations.

PubMed

Zaluzhnyy, I A; Kurta, R P; Menushenkov, A P; Ostrovskii, B I; Vartanyants, I A

2016-09-01

An x-ray scattering approach to determine the two-dimensional (2D) pair distribution function (PDF) in partially ordered 2D systems is proposed. We derive relations between the structure factor and PDF that enable quantitative studies of positional and bond-orientational (BO) order in real space. We apply this approach in the x-ray study of a liquid crystal (LC) film undergoing the smectic-A-hexatic-B phase transition, to analyze the interplay between the positional and BO order during the temperature evolution of the LC film. We analyze the positional correlation length in different directions in real space.

Microstructure selection in thin-sample directional solidification of an Al-Cu alloy: In situ X-ray imaging and phase-field simulations

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

Clarke, A. J.; Tourret, D.; Song, Y.

We study microstructure selection during directional solidification of a thin metallic sample. We combine in situ X-ray radiography of a dilute Al-Cu alloy solidification experiments with three-dimensional phase-field simulations. We explore a range of temperature gradient G and growth velocity V and build a microstructure selection map for this alloy. We investigate the selection of the primary dendritic spacing Lambda and tip radius rho. While rho shows a good agreement between experimental measurements and dendrite growth theory, with rho similar to V-1/2, Lambda is observed to increase with V (partial derivative Lambda/partial derivative V > 0), in apparent disagreement withmore » classical scaling laws for primary dendritic spacing, which predict that partial derivative Lambda/partial derivative V <0. We show through simulations that this trend inversion for Lambda(V) is due to liquid convection in our experiments, despite the thin sample configuration. We use a classical diffusion boundary-layer approximation to semi-quantitatively incorporate the effect of liquid convection into phase-field simulations. This approximation is implemented by assuming complete solute mixing outside a purely diffusive zone of constant thickness that surrounds the solid-liquid interface. This simple method enables us to quantitatively match experimental measurements of the planar morphological instability threshold and primary spacings over an order of magnitude in V. We explain the observed inversion of partial derivative Lambda/partial derivative V by a combination of slow transient dynamics of microstructural homogenization and the influence of the sample thickness.« less

A higher order numerical method for time fractional partial differential equations with nonsmooth data

NASA Astrophysics Data System (ADS)

Xing, Yanyuan; Yan, Yubin

2018-03-01

Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 by directly approximating the integer-order derivative with some finite difference quotients in the definition of the Caputo fractional derivative, see also Lv and Xu [20] (2016), where k is the time step size. Under the assumption that the solution of the time fractional partial differential equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. However, in general the solution of the time fractional partial differential equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. In this paper, we first obtain a similar approximation scheme to the Riemann-Liouville fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 as in Gao et al. [11] (2014) by approximating the Hadamard finite-part integral with the piecewise quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 < α < 1 for any fixed tn > 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

Second-order sliding mode control with experimental application.

PubMed

Eker, Ilyas

2010-07-01

In this article, a second-order sliding mode control (2-SMC) is proposed for second-order uncertain plants using equivalent control approach to improve the performance of control systems. A Proportional + Integral + Derivative (PID) sliding surface is used for the sliding mode. The sliding mode control law is derived using direct Lyapunov stability approach and asymptotic stability is proved theoretically. The performance of the closed-loop system is analysed through an experimental application to an electromechanical plant to show the feasibility and effectiveness of the proposed second-order sliding mode control and factors involved in the design. The second-order plant parameters are experimentally determined using input-output measured data. The results of the experimental application are presented to make a quantitative comparison with the traditional (first-order) sliding mode control (SMC) and PID control. It is demonstrated that the proposed 2-SMC system improves the performance of the closed-loop system with better tracking specifications in the case of external disturbances, better behavior of the output and faster convergence of the sliding surface while maintaining the stability. 2010 ISA. Published by Elsevier Ltd. All rights reserved.

Second order perturbations of a macroscopic string: Covariant approach

NASA Astrophysics Data System (ADS)

Larsen, A. L.; Nicolaidis, A.

2001-06-01

Using a world-sheet covariant formalism, we derive the equations of motion for second order perturbations of a generic macroscopic string, thus generalizing previous results for first order perturbations. We give the explicit results for the first and second order perturbations of a contracting near-circular string; these results are relevant for the understanding of the possible outcome when a cosmic string contracts under its own tension, as discussed in a series of papers by Vilenkin and Garriga. In particular, second order perturbations are necessary for a consistent computation of the energy. We also quantize the perturbations and derive the mass formula up to second order in perturbations for an observer using world-sheet time τ. The high frequency modes give the standard Minkowski result while, interestingly enough, the Hamiltonian turns out to be nondiagonal in oscillators for low-frequency modes. Using an alternative definition of the vacuum, it is possible to diagonalize the Hamiltonian, and the standard string mass spectrum appears for all frequencies. We finally discuss how our results are also relevant for the problems concerning string-spreading near a black hole horizon, as originally discussed by Susskind.

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

PubMed

Einkemmer, Lukas; Ostermann, Alexander

2014-07-01

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

An almost symmetric Strang splitting scheme for nonlinear evolution equations☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2014-01-01

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

Second derivative in the model of classical binary system

NASA Astrophysics Data System (ADS)

Abubekerov, M. K.; Gostev, N. Yu.

2016-06-01

We have obtained an analytical expression for the second derivatives of the light curve with respect to geometric parameters in the model of eclipsing classical binary systems. These expressions are essentially efficient algorithm to calculate the numerical values of these second derivatives for all physical values of geometric parameters. Knowledge of the values of second derivatives of the light curve at some point provides additional information about asymptotical behaviour of the function near this point and can significantly improve the search for the best-fitting light curve through the use of second-order optimization method. We write the expression for the second derivatives in a form which is most compact and uniform for all values of the geometric parameters and so make it easy to write a computer program to calculate the values of these derivatives.

Conformal and covariant Z4 formulation of the Einstein equations: Strongly hyperbolic first-order reduction and solution with discontinuous Galerkin schemes

NASA Astrophysics Data System (ADS)

Dumbser, Michael; Guercilena, Federico; Köppel, Sven; Rezzolla, Luciano; Zanotti, Olindo

2018-04-01

We present a strongly hyperbolic first-order formulation of the Einstein equations based on the conformal and covariant Z4 system (CCZ4) with constraint-violation damping, which we refer to as FO-CCZ4. As CCZ4, this formulation combines the advantages of a conformal and traceless formulation, with the suppression of constraint violations given by the damping terms, but being first order in time and space, it is particularly suited for a discontinuous Galerkin (DG) implementation. The strongly hyperbolic first-order formulation has been obtained by making careful use of first and second-order ordering constraints. A proof of strong hyperbolicity is given for a selected choice of standard gauges via an analytical computation of the entire eigenstructure of the FO-CCZ4 system. The resulting governing partial differential equations system is written in nonconservative form and requires the evolution of 58 unknowns. A key feature of our formulation is that the first-order CCZ4 system decouples into a set of pure ordinary differential equations and a reduced hyperbolic system of partial differential equations that contains only linearly degenerate fields. We implement FO-CCZ4 in a high-order path-conservative arbitrary-high-order-method-using-derivatives (ADER)-DG scheme with adaptive mesh refinement and local time-stepping, supplemented with a third-order ADER-WENO subcell finite-volume limiter in order to deal with singularities arising with black holes. We validate the correctness of the formulation through a series of standard tests in vacuum, performed in one, two and three spatial dimensions, and also present preliminary results on the evolution of binary black-hole systems. To the best of our knowledge, these are the first successful three-dimensional simulations of moving punctures carried out with high-order DG schemes using a first-order formulation of the Einstein equations.

Distributed event-triggered consensus tracking of second-order multi-agent systems with a virtual leader

NASA Astrophysics Data System (ADS)

Jie, Cao; Zhi-Hai, Wu; Li, Peng

2016-05-01

This paper investigates the consensus tracking problems of second-order multi-agent systems with a virtual leader via event-triggered control. A novel distributed event-triggered transmission scheme is proposed, which is intermittently examined at constant sampling instants. Only partial neighbor information and local measurements are required for event detection. Then the corresponding event-triggered consensus tracking protocol is presented to guarantee second-order multi-agent systems to achieve consensus tracking. Numerical simulations are given to illustrate the effectiveness of the proposed strategy. Project supported by the National Natural Science Foundation of China (Grant Nos. 61203147, 61374047, and 61403168).

A macroscopic plasma Lagrangian and its application to wave interactions and resonances

NASA Technical Reports Server (NTRS)

Peng, Y. K. M.

1974-01-01

The derivation of a macroscopic plasma Lagrangian is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the Lagrangian is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a Lagrangian are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The Lagrangians for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma Lagrangian is shown to differ from the velocity-integrated low Lagrangian by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction.

A time correlation function theory describing static field enhanced third order optical effects at interfaces.

PubMed

Neipert, Christine; Space, Brian

2006-12-14

Sum vibrational frequency spectroscopy, a second order optical process, is interface specific in the dipole approximation. At charged interfaces, there exists a static field, and as a direct consequence, the experimentally detected signal is a combination of enhanced second and static field induced third order contributions. There is significant evidence in the literature of the importance/relative magnitude of this third order contribution, but no previous molecularly detailed approach existed to separately calculate the second and third order contributions. Thus, for the first time, a molecularly detailed time correlation function theory is derived here that allows for the second and third order contributions to sum frequency vibrational spectra to be individually determined. Further, a practical, molecular dynamics based, implementation procedure for the derived correlation functions that describe the third order phenomenon is also presented. This approach includes a novel generalization of point atomic polarizability models to calculate the hyperpolarizability of a molecular system. The full system hyperpolarizability appears in the time correlation functions responsible for third order contributions in the presence of a static field.

Dissipative hydrodynamics for multi-component systems

NASA Astrophysics Data System (ADS)

El, Andrej; Bouras, Ioannis; Wesp, Christian; Xu, Zhe; Greiner, Carsten

2012-11-01

Second-order dissipative hydrodynamic equations for each component of a multi-component system are derived using the entropy principle. Comparison of the solutions with kinetic transport results demonstrates validity of the obtained equations. We demonstrate how the shear viscosity of the total system can be calculated in terms of the involved cross-sections and partial densities. The presence of the inter-species interactions leads to a characteristic time dependence of the shear viscosity of the mixture, which also means that the shear viscosity of a mixture cannot be calculated using the Green-Kubo formalism the way it has been done recently. This finding is of interest for understanding of the shear viscosity of a quark-gluon plasma extracted from comparisons of hydrodynamic simulations with experimental results from RHIC and LHC.

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

NASA Astrophysics Data System (ADS)

Warminski, Jerzy

2018-01-01

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

Function Invariant and Parameter Scale-Free Transformation Methods

ERIC Educational Resources Information Center

Bentler, P. M.; Wingard, Joseph A.

1977-01-01

A scale-invariant simple structure function of previously studied function components for principal component analysis and factor analysis is defined. First and second partial derivatives are obtained, and Newton-Raphson iterations are utilized. The resulting solutions are locally optimal and subjectively pleasing. (Author/JKS)

Probe-Independent EEG Assessment of Mental Workload in Pilots

DTIC Science & Technology

2015-05-18

Teager Energy Operator - Frequency Modulated Component - z- score 10.94 17.46 10 Hurst Exponent - Discrete Second Order Derivative 7.02 17.06 D. Best...Teager Energy Operator– Frequency Modulated Component – Z-score 45. Line Length – Time Series 46. Line Length – Time Series – Z-score 47. Hurst Exponent ...Discrete Second Order Derivative 48. Hurst Exponent – Wavelet Based Adaptation 49. Hurst Exponent – Rescaled Range 50. Hurst Exponent – Discrete

Radiation-reaction force on a small charged body to second order

NASA Astrophysics Data System (ADS)

Moxon, Jordan; Flanagan, Éanna

2018-05-01

In classical electrodynamics, an accelerating charged body emits radiation and experiences a corresponding radiation-reaction force, or self-force. We extend to higher order in the total charge a previous rigorous derivation of the electromagnetic self-force in flat spacetime by Gralla, Harte, and Wald. The method introduced by Gralla, Harte, and Wald computes the self-force from the Maxwell field equations and conservation of stress-energy in a limit where the charge, size, and mass of the body go to zero, and it does not require regularization of a singular self-field. For our higher-order computation, an adjustment of the definition of the mass of the body is necessary to avoid including self-energy from the electromagnetic field sourced by the body in the distant past. We derive the evolution equations for the mass, spin, and center-of-mass position of the body through second order. We derive, for the first time, the second-order acceleration dependence of the evolution of the spin (self-torque), as well as a mixing between the extended body effects and the acceleration-dependent effects on the overall body motion.

Coherence of beam arrays propagating in the turbulent atmosphere

NASA Astrophysics Data System (ADS)

Charnotskii, Mikhail

2010-04-01

We analyze some recent publications addressing propagation of the partially coherent polarized beams and beam arrays in the turbulent atmosphere. We show that the published results are limited to the scalar propagation model, and are not particular to the beam polarization. Therefore these results are equally relevant for the scalar beam pairs and arrays discriminated by some parameters such as small frequency shift, time delay or geometry, but not necessary the polarization. We use the virtual incoherent source model to derive the general form of the mutual coherence function of the two Schell-type beams. We discuss some physical stochastic models that result in the creation of the Schell-type beams and beam arrays. New classes of the uniformly, nonuniformly and nonlocally coherent beam pairs emerge naturally from this analysis. Rigorous, Markov approximation-based, propagation model provides relatively simple analytic results for the second-order moments of the optical field of the partially-coherent individual beams and beam pairs. We examine the changes of the beam mutual coherence in the process of the free-space propagation and propagation through the turbulent atmosphere.

Theoretical study on the spectroscopic and third-order nonlinear optical properties of two-dimensional charge-transfer pyrazine derivatives

NASA Astrophysics Data System (ADS)

Li, Haipeng; Zhang, Yi; Bi, Zetong; Xu, Runfeng; Li, Mingxue; Shen, Xiaopeng; Tang, Gang; Han, Kui

2017-12-01

In this paper, density functional theory method was employed to study the electronic absorption spectrum and electronic static second hyperpolarisability of X-shaped pyrazine derivatives with two-dimensional charge-transfer structures. Computational results show that the push-pull electron abilities of the substituent groups and the length of the conjugated chains affect the electronic spectrum and static second hyperpolarisability of the pyrazine derivatives. As the push-pull electron abilities of the substituent groups or the length of the conjugated chains increases, the frontier molecular orbital energy gap decreases, resulting in increased second hyperpolarisability and redshift of the electronic absorption bands. The electronic absorption spectra of the pyrazine derivatives maintain good transparency in the blue light band. The electronic static second hyperpolarisability exhibits a linear relationship to the frontier molecular orbital energy gap. Particularly, increasing/decreasing the push-pull electron abilities of the substituent groups considerably affect the static second hyperpolarisability in long conjugated systems, which is important to the modulation of molecular organic nonlinear optical (NLO) properties. The studied pyrazine derivatives show large third-order NLO response and good transparency in the blue light band and are thus promising candidates as NLO materials for photonics applications.

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 hydrostatic flows in isentropic coordinates

NASA Astrophysics Data System (ADS)

Bokhove, Onno

2000-01-01

The hydrostatic primitive equations of motion which have been used in large-scale weather prediction and climate modelling over the last few decades are analysed with variational methods in an isentropic Eulerian framework. The use of material isentropic coordinates for the Eulerian hydrostatic equations is known to have distinct conceptual advantages since fluid motion is, under inviscid and statically stable circumstances, confined to take place on quasi-horizontal isentropic surfaces. First, an Eulerian isentropic Hamilton's principle, expressed in terms of fluid parcel variables, is therefore derived by transformation of a Lagrangian Hamilton's principle to an Eulerian one. This Eulerian principle explicitly describes the boundary dynamics of the time-dependent domain in terms of advection of boundary isentropes sB; these are the values the isentropes have at their intersection with the (lower) boundary. A partial Legendre transform for only the interior variables yields an Eulerian ‘action’ principle. Secondly, Noether's theorem is used to derive energy and potential vorticity conservation from the Eulerian Hamilton's principle. Thirdly, these conservation laws are used to derive a wave-activity invariant which is second-order in terms of small-amplitude disturbances relative to a resting or moving basic state. Linear stability criteria are derived but only for resting basic states. In mid-latitudes a time- scale separation between gravity and vortical modes occurs. Finally, this time-scale separation suggests that conservative geostrophic and ageostrophic approximations can be made to the Eulerian action principle for hydrostatic flows. Approximations to Eulerian variational principles may be more advantageous than approximations to Lagrangian ones because non-dimensionalization and scaling tend to be based on Eulerian estimates of the characteristic scales involved. These approximations to the stratified hydrostatic formulation extend previous approximations to the shallow- water equations. An explicit variational derivation is given of an isentropic version of Hoskins & Bretherton's model for atmospheric fronts.

Incremental online learning in high dimensions.

PubMed

Vijayakumar, Sethu; D'Souza, Aaron; Schaal, Stefan

2005-12-01

Locally weighted projection regression (LWPR) is a new algorithm for incremental nonlinear function approximation in high-dimensional spaces with redundant and irrelevant input dimensions. At its core, it employs nonparametric regression with locally linear models. In order to stay computationally efficient and numerically robust, each local model performs the regression analysis with a small number of univariate regressions in selected directions in input space in the spirit of partial least squares regression. We discuss when and how local learning techniques can successfully work in high-dimensional spaces and review the various techniques for local dimensionality reduction before finally deriving the LWPR algorithm. The properties of LWPR are that it (1) learns rapidly with second-order learning methods based on incremental training, (2) uses statistically sound stochastic leave-one-out cross validation for learning without the need to memorize training data, (3) adjusts its weighting kernels based on only local information in order to minimize the danger of negative interference of incremental learning, (4) has a computational complexity that is linear in the number of inputs, and (5) can deal with a large number of-possibly redundant-inputs, as shown in various empirical evaluations with up to 90 dimensional data sets. For a probabilistic interpretation, predictive variance and confidence intervals are derived. To our knowledge, LWPR is the first truly incremental spatially localized learning method that can successfully and efficiently operate in very high-dimensional spaces.

Global solutions in higher dimensions to a fourth-order parabolic equation modeling epitaxial thin-film growth

NASA Astrophysics Data System (ADS)

Winkler, Michael

2011-08-01

The initial-value problem for u_t=-Δ^2 u - μΔ u - λ Δ |nabla u|^2 + f(x)qquad qquad (star) is studied under the conditions {{partial/partialν} u={partial/partialν} Δ u=0} on the boundary of a bounded convex domain {Ω subset {{R}}^n} with smooth boundary. This problem arises in the modeling of the evolution of a thin surface when exposed to molecular beam epitaxy. Correspondingly the physically most relevant spatial setting is obtained when n = 2, but previous mathematical results appear to concentrate on the case n = 1. In this work, it is proved that when n ≤ 3, μ ≥ 0, λ > 0 and {f in L^infty(Ω)} satisfies {{int_Ω} f ge 0}, for each prescribed initial distribution {u_0 in L^infty(Ω)} fulfilling {{int_Ω} u_0 ge 0}, there exists at least one global weak solution {u in L^2_{loc}([0,infty); W^{1,2}(Ω))} satisfying {{int_Ω} u(\\cdot,t) ge 0} for a.e. t > 0, and moreover, it is shown that this solution can be obtained through a Rothe-type approximation scheme. Furthermore, under an additional smallness condition on μ and {\\|f\\|_{L^infty(Ω)}}, it is shown that there exists a bounded set {Ssubset L^1(Ω)} which is absorbing for {(star)} in the sense that for any such solution, we can pick T > 0 such that {e^{2λ u(\\cdot,t)}in S} for all t > T, provided that Ω is a ball and u 0 and f are radially symmetric with respect to x = 0. This partially extends similar absorption results known in the spatially one-dimensional case. The techniques applied to derive appropriate compactness properties via a priori estimates include straightforward testing procedures which lead to integral inequalities involving, for instance, the functional {{int_Ω} e^{2λ u}dx}, but also the use of a maximum principle for second-order elliptic equations.

Second-order discrete Kalman filtering equations for control-structure interaction simulations

NASA Technical Reports Server (NTRS)

Park, K. C.; Belvin, W. Keith; Alvin, Kenneth F.

1991-01-01

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

Three-dimensional seismic depth migration

NASA Astrophysics Data System (ADS)

Zhou, Hongbo

1998-12-01

One-pass 3-D modeling and migration for poststack seismic data may be implemented by replacing the traditional 45sp° one-way wave equation (a third-order partial differential equation) with a pair of second and first order partial differential equations. Except for an extra correction term, the resulting second order equation has a form similar to Claerbout's 15sp° one-way wave equation, which is known to have a nearly circular horizontal impulse response. In this approach, there is no need to compensate for splitting errors. Numerical tests on synthetic data show that this algorithm has the desirable attributes of being second-order in accuracy and economical to solve. A modification of the Crank-Nicholson implementation maintains stability. Absorbing boundary conditions play an important role in one-way wave extrapolations by reducing reflections at grid edges. Clayton and Engquist's 2-D absorbing boundary conditions for one-way wave extrapolation by depth-stepping in the frequency domain are extended to 3-D using paraxial approximations of the scalar wave equation. Internal consistency is retained by incorporating the interior extrapolation equation with the absorbing boundary conditions. Numerical schemes are designed to make the proposed absorbing boundary conditions both mathematically correct and efficient with negligible extra cost. Synthetic examples illustrate the effectiveness of the algorithm for extrapolation with the 3-D 45sp° one-way wave equation. Frequency-space domain Butterworth and Chebyshev dip filters are implemented. By regrouping the product terms in the filter transfer function into summations, a cascaded (serial) Butterworth dip filter can be made parallel. A parallel Chebyshev dip filter can be similarly obtained, and has the same form as the Butterworth filter; but has different coeffcients. One of the advantages of the Chebyshev filter is that it has a sharper transition zone than that of Butterworth filter of the same order. Both filters are incorporated into 3-D one-way frequency-space depth migration for evanescent energy removal and for phase compensation of splitting errors; a single filter achieves both goals. Synthetic examples illustrate the behavior of the parallel filters. For a given order of filter, the cost of the Butterworth and Chebyshev filters is the same. A Chebyshev filter is more effective for phase compensation than the Butterworth filter of the same order, at the expense of some wavenumber-dependent amplitude ripples. An analytical formula for geometrical spreading is derived for a horizontally layered transversely isotropic medium with a vertical symmetry axis. Under this expression, geometrical spreading can be determined only by the anisotropic parameters in the first layer, the traveltime derivatives, and source-receiver offset. An explicit, numerically feasible expression for geometrical spreading can be further obtained by considering some of the special cases of transverse isotropy, such as weak anisotropy or elliptic anisotropy. Therefore, with the techniques of non-hyerbolic moveout for transverse isotropic media, geometrical spreading can be calculated by using picked traveltimes of primary P-wave reflections without having to know the actual parameters in the deeper subsurface; no ray tracing is needed. Synthetic examples verify the algorithm and show that it is numerically feasible for calculation of geometrical spreading.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Numerical method based on the lattice Boltzmann model for the Fisher equation.

PubMed

Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng

2008-06-01

In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.

Incorporation of New Benzofulvene Derivatives Into Polymers to Give New NLO Materials

NASA Technical Reports Server (NTRS)

Bowens, Andrea D.; Bu, Xiu; Mintz, Eric A.; Zhang, Yue

1996-01-01

The need for fast electro-optic switches and modulators for optical communication, and laser frequency conversion has created a demand for new second-order non-linear optical materials. One approach to produce such materials is to align chromophores with large molecular hyperpolarizabilities in polymers. Recently fulvenes and benzofulvenes which contain electron donating groups have been shown to exhibit large second-order non-linear optical properties. The resonance structures shown below suggest that intramolecular charge transfer (ICT) should be favorable in omega - (hydroxyphenyl)benzofulvenes and even more favorable in omega-omega - (phenoxy)benzofulvenes because of the enhanced donor properties of the O group. This ICT should lead to enormously enhanced second-order hyperpolarizability. We have prepared all three new omega - (hydroxyphenyl)benzofulvenes by the condensation of indene with the appropriate hydroxyaryl aldehyde in MeOH or MeOH/H2O under base catalysis. In a similar fashion we have prepared substituted benzofulvenes with multipal donor groups. Preliminary studies show that some of our benzofulvene derivatives exhibit second order harmonic generation (SHG). Measurements were carried out by preparing host-guest polymers. The results of our work on benzofulvene derivatives in host-guest polymers when covalently bonded in the polymer will be described.

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

Propagation of partially coherent vector anomalous vortex beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Zhang, Xu; Wang, Haiyan; Tang, Lei

2018-01-01

A theoretical model is proposed to describe a partially coherent vector anomalous vortex(AV) beam. Based on the extended Huygens-Fresnel principle, analytical propagation formula for the proposed beams in turbulent atmosphere is derived. The spectral properties of the partially coherent vector AV beam are explored by using the unified theory of coherence and polarization in detail. It is interesting to find that the turbulence of atmosphere and the source parameter of the partially coherent vector AV beam( order, topological charge, coherence length, beam waist size etc) have significantly impacted the propagation properties of the partially coherent vector AV beam in turbulent atmosphere.

ACCURATE SOLUTION AND GRADIENT COMPUTATION FOR ELLIPTIC INTERFACE PROBLEMS WITH VARIABLE COEFFICIENTS

PubMed Central

LI, ZHILIN; JI, HAIFENG; CHEN, XIAOHONG

2016-01-01

A new augmented method is proposed for elliptic interface problems with a piecewise variable coefficient that has a finite jump across a smooth interface. The main motivation is not only to get a second order accurate solution but also a second order accurate gradient from each side of the interface. The key of the new method is to introduce the jump in the normal derivative of the solution as an augmented variable and re-write the interface problem as a new PDE that consists of a leading Laplacian operator plus lower order derivative terms near the interface. In this way, the leading second order derivatives jump relations are independent of the jump in the coefficient that appears only in the lower order terms after the scaling. An upwind type discretization is used for the finite difference discretization at the irregular grid points near or on the interface so that the resulting coefficient matrix is an M-matrix. A multi-grid solver is used to solve the linear system of equations and the GMRES iterative method is used to solve the augmented variable. Second order convergence for the solution and the gradient from each side of the interface has also been proved in this paper. Numerical examples for general elliptic interface problems have confirmed the theoretical analysis and efficiency of the new method. PMID:28983130

Sensitivity analysis of complex coupled systems extended to second and higher order derivatives

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw

1989-01-01

In design of engineering systems, the what if questions often arise such as: what will be the change of the aircraft payload, if the wing aspect ratio is incremented by 10 percent. Answers to such questions are commonly sought by incrementing the pertinent variable, and reevaluating the major disciplinary analyses involved. These analyses are contributed by engineering disciplines that are, usually, coupled, as are the aerodynamics, structures, and performance in the context of the question above. The what if questions can be answered precisely by computation of the derivatives. A method for calculation of the first derivatives has been developed previously. An algorithm is presented for calculation of the second and higher order derivatives.

Bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations

DOE PAGES

Azunre, P.

2016-09-21

Here in this paper, two novel techniques for bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations are developed. The first provides a theorem to construct interval bounds, while the second provides a theorem to construct lower bounds convex and upper bounds concave in the parameter. The convex/concave bounds can be significantly tighter than the interval bounds because of the wrapping effect suffered by interval analysis in dynamical systems. Both types of bounds are computationally cheap to construct, requiring solving auxiliary systems twice and four times larger than the original system, respectively. An illustrative numerical examplemore » of bound construction and use for deterministic global optimization within a simple serial branch-and-bound algorithm, implemented numerically using interval arithmetic and a generalization of McCormick's relaxation technique, is presented. Finally, problems within the important class of reaction-diffusion systems may be optimized with these tools.« less

Higher order alchemical derivatives from coupled perturbed self-consistent field theory.

PubMed

Lesiuk, Michał; Balawender, Robert; Zachara, Janusz

2012-01-21

We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals. © 2012 American Institute of Physics

(U) Analytic First and Second Derivatives of the Uncollided Leakage for a Homogeneous Sphere

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

Favorite, Jeffrey A.

2017-04-26

The second-order adjoint sensitivity analysis methodology (2nd-ASAM), developed by Cacuci, has been applied by Cacuci to derive second derivatives of a response with respect to input parameters for uncollided particles in an inhomogeneous transport problem. In this memo, we present an analytic benchmark for verifying the derivatives of the 2nd-ASAM. The problem is a homogeneous sphere, and the response is the uncollided total leakage. This memo does not repeat the formulas given in Ref. 2. We are preparing a journal article that will include the derivation of Ref. 2 and the benchmark of this memo.

Transfer function of radio over fiber multimode fiber optic links considering third-order dispersion.

PubMed

Capmany, J; Gasulla, Ivana

2007-08-20

Although a considerable number of multimode fiber (MMF) links operate in a wavelength region around 850 nm where chromatic dispersion of a given modal group mu is described adequately by the second derivative beta(mu) (2) of the propagation constant beta(mu)(omega), there is also an increasing interest in MMF links transmitting in the second spectral window (@1300nm) where this second derivative vanishes being thus necessary to consider the third derivative beta(mu) (3) in the evaluation of the transfer function of the multimode fiber link. We present in this paper, for the first time to our knowledge, an analytical model for the transfer function of a multimode fiber (MMF) optic link taken into account the impact of third-order dispersion. The model extends the operation of a previously reported one for second-order dispersion. Our results show that the performance of broadband radio over fiber transmission through middle-reach distances can be improved by working at the minimum-dispersion wavelength as long as low-linewidth lasers are employed.

Investigations on the stability, oscillation, and stress conditions of airplanes with tab control. Second partial report : application of the solutions obtained in the first partial report to tab-controlled airplanes.

NASA Technical Reports Server (NTRS)

Filzek, B

1949-01-01

The first partial report, FB 2000, contained a discussion of the derivation of the equations of motion and their solutions for a tab-controlled airplane; the results obtained there are now to be applied to the longitudinal motion of tab-controlled airplanes. In view of the abundance of structural factors and aerodynamic parameters, a general discussion of the problems is unfeasible. Thus it is demonstrated on the basis of examples what stability, oscillation, and stress conditions are to be expected for tab-controlled airplanes. (author)

Generalized energy and potential enstrophy conserving finite difference schemes for the shallow water equations

NASA Technical Reports Server (NTRS)

Abramopoulos, Frank

1988-01-01

The conditions under which finite difference schemes for the shallow water equations can conserve both total energy and potential enstrophy are considered. A method of deriving such schemes using operator formalism is developed. Several such schemes are derived for the A-, B- and C-grids. The derived schemes include second-order schemes and pseudo-fourth-order schemes. The simplest B-grid pseudo-fourth-order schemes are presented.

Universal algorithms and programs for calculating the motion parameters in the two-body problem

NASA Technical Reports Server (NTRS)

Bakhshiyan, B. T.; Sukhanov, A. A.

1979-01-01

The algorithms and FORTRAN programs for computing positions and velocities, orbital elements and first and second partial derivatives in the two-body problem are presented. The algorithms are applicable for any value of eccentricity and are convenient for computing various navigation parameters.

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

Mozrzymas, Marek; Horodecki, Michał; Studziński, Michał

We consider the structure of algebra of operators, acting in n-fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its regular representation, we derive basic properties of the algebra. In particular, we describe all irreducible representations of the algebra of partially transposed operators and derive expressions for matrix elements of the representations. It appears that there are two kinds of irreducible representations of the algebra. The first one is strictly connected with the representations of the group S(n − 1) induced by irreduciblemore » representations of the group S(n − 2). The second kind is structurally connected with irreducible representations of the group S(n − 1)« less

Brans-Dicke Galileon and the variational principle

NASA Astrophysics Data System (ADS)

Quiros, Israel; García-Salcedo, Ricardo; Gonzalez, Tame; Horta-Rangel, F. Antonio; Saavedra, Joel

2016-09-01

This paper is aimed at a (mostly) pedagogical exposition of the derivation of the motion equations of certain modifications of general relativity. Here we derive in all detail the motion equations in the Brans-Dicke theory with cubic self-interaction. This is a modification of the Brans-Dicke theory by the addition of a term in the Lagrangian which is non-linear in the derivatives of the scalar field: it contains second-order derivatives. This is the basis of the so-called Brans-Dicke Galileon. We pay special attention to the variational principle and to the algebraic details of the derivation. It is shown how higher order derivatives of the fields appearing in the intermediate computations cancel out leading to second order motion equations. The reader will find useful tips for the derivation of the field equations of modifications of general relativity such as the scalar-tensor theories and f(R) theories, by means of the (stationary action) variational principle. The content of this paper is particularly recommended to those graduate and postgraduate students who are interested in the study of the mentioned modifications of general relativity.

When Can Information from Ordinal Scale Variables Be Integrated?

ERIC Educational Resources Information Center

Kemp, Simon; Grace, Randolph C.

2010-01-01

Many theoretical constructs of interest to psychologists are multidimensional and derive from the integration of several input variables. We show that input variables that are measured on ordinal scales cannot be combined to produce a stable weakly ordered output variable that allows trading off the input variables. Instead a partial order is…

Generalized Israel junction conditions for a fourth-order brane world

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

Balcerzak, Adam; Dabrowski, Mariusz P.

2008-01-15

We discuss a general fourth-order theory of gravity on the brane. In general, the formulation of the junction conditions (except for Euler characteristics such as Gauss-Bonnet term) leads to the higher powers of the delta function and requires regularization. We suggest the way to avoid such a problem by imposing the metric and its first derivative to be regular at the brane, while the second derivative to have a kink, the third derivative of the metric to have a step function discontinuity, and no sooner as the fourth derivative of the metric to give the delta function contribution to themore » field equations. Alternatively, we discuss the reduction of the fourth-order gravity to the second-order theory by introducing an extra tensor field. We formulate the appropriate junction conditions on the brane. We prove the equivalence of both theories. In particular, we prove the equivalence of the junction conditions with different assumptions related to the continuity of the metric along the brane.« less

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

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Higher order relativistic galaxy number counts: dominating terms

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

Nielsen, Jeppe TrØst; Durrer, Ruth, E-mail: Jeppe.Trost@nbi.dk, E-mail: Ruth.Durrer@unige.ch

2017-03-01

We review the number counts to second order concentrating on the terms which dominate on sub horizon scales. We re-derive the result for these terms and compare it with the different versions found in the literature. We generalize our derivation to higher order terms, especially the third order number counts which are needed to compute the 1-loop contribution to the power spectrum.

A second-order shock-expansion method applicable to bodies of revolution near zero lift

NASA Technical Reports Server (NTRS)

1957-01-01

A second-order shock-expansion method applicable to bodies of revolution is developed by the use of the predictions of the generalized shock-expansion method in combination with characteristics theory. Equations defining the zero-lift pressure distributions and the normal-force and pitching-moment derivatives are derived. Comparisons with experimental results show that the method is applicable at values of the similarity parameter, the ratio of free-stream Mach number to nose fineness ratio, from about 0.4 to 2.

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.

A second order derivative scheme based on Bregman algorithm class

NASA Astrophysics Data System (ADS)

Campagna, Rosanna; Crisci, Serena; Cuomo, Salvatore; Galletti, Ardelio; Marcellino, Livia

2016-10-01

The algorithms based on the Bregman iterative regularization are known for efficiently solving convex constraint optimization problems. In this paper, we introduce a second order derivative scheme for the class of Bregman algorithms. Its properties of convergence and stability are investigated by means of numerical evidences. Moreover, we apply the proposed scheme to an isotropic Total Variation (TV) problem arising out of the Magnetic Resonance Image (MRI) denoising. Experimental results confirm that our algorithm has good performance in terms of denoising quality, effectiveness and robustness.

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.

High-resolution schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Harten, A.

1982-01-01

A class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws is presented. These highly nonlinear schemes are obtained by applying a nonoscillatory first order accurae scheme to an appropriately modified flux function. The so derived second order accurate schemes achieve high resolution while preserving the robustness of the original nonoscillatory first order accurate scheme.

Designing optimal universal pulses using second-order, large-scale, non-linear optimization

NASA Astrophysics Data System (ADS)

Anand, Christopher Kumar; Bain, Alex D.; Curtis, Andrew Thomas; Nie, Zhenghua

2012-06-01

Recently, RF pulse design using first-order and quasi-second-order pulses has been actively investigated. We present a full second-order design method capable of incorporating relaxation, inhomogeneity in B0 and B1. Our model is formulated as a generic optimization problem making it easy to incorporate diverse pulse sequence features. To tame the computational cost, we present a method of calculating second derivatives in at most a constant multiple of the first derivative calculation time, this is further accelerated by using symbolic solutions of the Bloch equations. We illustrate the relative merits and performance of quasi-Newton and full second-order optimization with a series of examples, showing that even a pulse already optimized using other methods can be visibly improved. To be useful in CPMG experiments, a universal refocusing pulse should be independent of the delay time and insensitive of the relaxation time and RF inhomogeneity. We design such a pulse and show that, using it, we can obtain reliable R2 measurements for offsets within ±γB1. Finally, we compare our optimal refocusing pulse with other published refocusing pulses by doing CPMG experiments.

Regional Recovery of the Disturbing Gravitational Potential from Satellite Observations of First-, Second- and Third-order Radial Derivatives of the Disturbing Gravitational Potential

NASA Astrophysics Data System (ADS)

Novak, P.; Pitonak, M.; Sprlak, M.

2015-12-01

Recently realized gravity-dedicated satellite missions allow for measuring values of scalar, vectorial (Gravity Recovery And Climate Experiment - GRACE) and second-order tensorial (Gravity field and steady-state Ocean Circulation Explorer - GOCE) parameters of the Earth's gravitational potential. Theoretical aspects related to using moving sensors for measuring elements of a third-order gravitational tensor are currently under investigation, e.g. the gravity-dedicated satellite mission OPTIMA (OPTical Interferometry for global Mass change detection from space) should measure third-order derivatives of the Earth's gravitational potential. This contribution investigates regional recovery of the disturbing gravitational potential on the Earth's surface from satellite observations of first-, second- and third-order radial derivatives of the disturbing gravitational potential. Synthetic measurements along a satellite orbit at the altitude of 250 km are synthetized from the global gravitational model EGM2008 and polluted by the Gaussian noise. The process of downward continuation is stabilized by the Tikhonov regularization. Estimated values of the disturbing gravitational potential are compared with the same quantity synthesized directly from EGM2008. Finally, this contribution also discusses merging a regional solution into a global field as a patchwork.

Possibilities of the regional gravity field recovery from first-, second- and third-order radial derivatives of the disturbing gravitational potential measured on moving platforms

NASA Astrophysics Data System (ADS)

Pitonak, Martin; Sprlak, Michal; Novak, Pavel; Tenzer, Robert

2016-04-01

Recently realized gravity-dedicated satellite missions allow for measuring values of scalar, vectorial (Gravity Recovery And Climate Experiment - GRACE) and second-order tensorial (Gravity field and steady-state Ocean Circulation Explorer - GOCE) parameters of the Earth's gravitational potential. Theoretical aspects related to using moving sensors for measuring elements of the third-order gravitational tensor are currently under investigation, e.g., the gravity field-dedicated satellite mission OPTIMA (OPTical Interferometry for global Mass change detection from space) should measure third-order derivatives of the Earth's gravitational potential. This contribution investigates regional recovery of the disturbing gravitational potential on the Earth's surface from satellite and aerial observations of the first-, second- and third-order radial derivatives of the disturbing gravitational potential. Synthetic measurements along a satellite orbit at the altitude of 250 km and along an aircraft track at the altitude of 10 km are synthetized from the global gravitational model EGM2008 and polluted by the Gaussian noise. The process of downward continuation is stabilized by the Tikhonov regularization. Estimated values of the disturbing gravitational potential are compared with the same quantity synthesized directly from EGM2008.

Second-order evaluations of orthogonal and symplectic Yangians

NASA Astrophysics Data System (ADS)

Karakhanyan, D. R.; Kirschner, R.

2017-08-01

Orthogonal or symplectic Yangians are defined by the Yang-Baxter RLL relation involving the fundamental R-matrix with the corresponding so( n) or sp(2 m) symmetry. We investigate the second-order solution conditions, where the expansion of L( u) in u -1 is truncated at the second power, and we derive the relations for the two nontrivial terms in L( u).

On the 4D generalized Proca action for an Abelian vector field

NASA Astrophysics Data System (ADS)

Allys, Erwan; Beltrán Almeida, Juan P.; Peter, Patrick; Rodríguez, Yeinzon

2016-09-01

We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated Stückelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the Stückelberg field describing the longitudinal mode, which is in agreement with the results of JCAP 05 (2014) 015 and Phys. Lett. B 757 (2016) 405 and complements those of JCAP 02 (2016) 004. We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field Aμ, the Faraday tensor Fμν and its Hodge dual tilde Fμν.

Application of the Finite Element Method in Atomic and Molecular Physics

NASA Technical Reports Server (NTRS)

Shertzer, Janine

2007-01-01

The finite element method (FEM) is a numerical algorithm for solving second order differential equations. It has been successfully used to solve many problems in atomic and molecular physics, including bound state and scattering calculations. To illustrate the diversity of the method, we present here details of two applications. First, we calculate the non-adiabatic dipole polarizability of Hi by directly solving the first and second order equations of perturbation theory with FEM. In the second application, we calculate the scattering amplitude for e-H scattering (without partial wave analysis) by reducing the Schrodinger equation to set of integro-differential equations, which are then solved with FEM.

A second-order 3D electromagnetics algorithm for curved interfaces between anisotropic dielectrics on a Yee mesh

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

Bauer, Carl A., E-mail: bauerca@colorado.ed; Werner, Gregory R.; Cary, John R.

A new frequency-domain electromagnetics algorithm is developed for simulating curved interfaces between anisotropic dielectrics embedded in a Yee mesh with second-order error in resonant frequencies. The algorithm is systematically derived using the finite integration formulation of Maxwell's equations on the Yee mesh. Second-order convergence of the error in resonant frequencies is achieved by guaranteeing first-order error on dielectric boundaries and second-order error in bulk (possibly anisotropic) regions. Convergence studies, conducted for an analytically solvable problem and for a photonic crystal of ellipsoids with anisotropic dielectric constant, both show second-order convergence of frequency error; the convergence is sufficiently smooth that Richardsonmore » extrapolation yields roughly third-order convergence. The convergence of electric fields near the dielectric interface for the analytic problem is also presented.« less

Diversity Order Analysis of Dual-Hop Relaying with Partial Relay Selection

NASA Astrophysics Data System (ADS)

Bao, Vo Nguyen Quoc; Kong, Hyung Yun

In this paper, we study the performance of dual hop relaying in which the best relay selected by partial relay selection will help the source-destination link to overcome the channel impairment. Specifically, closed-form expressions for outage probability, symbol error probability and achievable diversity gain are derived using the statistical characteristic of the signal-to-noise ratio. Numerical investigation shows that the system achieves diversity of two regardless of relay number and also confirms the correctness of the analytical results. Furthermore, the performance loss due to partial relay selection is investigated.

Statistics of spatial derivatives of velocity and pressure in turbulent channel flow

NASA Astrophysics Data System (ADS)

Vreman, A. W.; Kuerten, J. G. M.

2014-08-01

Statistical profiles of the first- and second-order spatial derivatives of velocity and pressure are reported for turbulent channel flow at Reτ = 590. The statistics were extracted from a high-resolution direct numerical simulation. To quantify the anisotropic behavior of fine-scale structures, the variances of the derivatives are compared with the theoretical values for isotropic turbulence. It is shown that appropriate combinations of first- and second-order velocity derivatives lead to (directional) viscous length scales without explicit occurrence of the viscosity in the definitions. To quantify the non-Gaussian and intermittent behavior of fine-scale structures, higher-order moments and probability density functions of spatial derivatives are reported. Absolute skewnesses and flatnesses of several spatial derivatives display high peaks in the near wall region. In the logarithmic and central regions of the channel flow, all first-order derivatives appear to be significantly more intermittent than in isotropic turbulence at the same Taylor Reynolds number. Since the nine variances of first-order velocity derivatives are the distinct elements of the turbulence dissipation, the budgets of these nine variances are shown, together with the budget of the turbulence dissipation. The comparison of the budgets in the near-wall region indicates that the normal derivative of the fluctuating streamwise velocity (∂u'/∂y) plays a more important role than other components of the fluctuating velocity gradient. The small-scale generation term formed by triple correlations of fluctuations of first-order velocity derivatives is analyzed. A typical mechanism of small-scale generation near the wall (around y+ = 1), the intensification of positive ∂u'/∂y by local strain fluctuation (compression in normal and stretching in spanwise direction), is illustrated and discussed.

A QSAR study of integrase strand transfer inhibitors based on a large set of pyrimidine, pyrimidone, and pyridopyrazine carboxamide derivatives

NASA Astrophysics Data System (ADS)

de Campos, Luana Janaína; de Melo, Eduardo Borges

2017-08-01

In the present study, 199 compounds derived from pyrimidine, pyrimidone and pyridopyrazine carboxamides with inhibitory activity against HIV-1 integrase were modeled. Subsequently, a multivariate QSAR study was conducted with 54 molecules employed by Ordered Predictors Selection (OPS) and Partial Least Squares (PLS) for the selection of variables and model construction, respectively. Topological, electrotopological, geometric, and molecular descriptors were used. The selected real model was robust and free from chance correlation; in addition, it demonstrated favorable internal and external statistical quality. Once statistically validated, the training model was used to predict the activity of a second data set (n = 145). The root mean square deviation (RMSD) between observed and predicted values was 0.698. Although it is a value outside of the standards, only 15 (10.34%) of the samples exhibited higher residual values than 1 log unit, a result considered acceptable. Results of Williams and Euclidean applicability domains relative to the prediction showed that the predictions did not occur by extrapolation and that the model is representative of the chemical space of test compounds.

Constructing general partial differential equations using polynomial and neural networks.

PubMed

Zjavka, Ladislav; Pedrycz, Witold

2016-01-01

Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.

Mass Communication Research in Canada: Television and Adults.

ERIC Educational Resources Information Center

Tate, Eugene D.

This paper contains partial data from an investigation of adults and television conducted for the Canadian Royal Commission on Violence in the Communications Industry. The first section of the paper offers a discussion of the viewing behaviors of adult Canadians derived from interview data, while the second section examines the "mean world…

A second-order theory for transverse ion heating and momentum coupling due to electrostatic ion cyclotron waves

NASA Technical Reports Server (NTRS)

Miller, Ronald H.; Winske, Dan; Gary, S. P.

1992-01-01

A second-order theory for electrostatic instabilities driven by counterstreaming ion beams is developed which describes momentum coupling and heating of the plasma via wave-particle interactions. Exchange rates between the waves and particles are derived, which are suitable for the fluid equations simulating microscopic effects on macroscopic scales. Using a fully kinetic simulation, the electrostatic ion cyclotron instability due to counterstreaming H(+) beams has been simulated. A power spectrum from the kinetic simulation is used to evaluate second-order exchange rates. The calculated heating and momentum loss from second-order theory is compared to the numerical simulation.

Bender Gestalt Test Performance and the Word Recognition Skills of Disadvantaged Children

ERIC Educational Resources Information Center

Baker, E. H.; Thurber, Steven

1976-01-01

The Bender Gestalt Test and the WRAT reading section were administered to 147 disadvantaged children. The zero-order correlation of -.62 was found to be moderated by the variable of age. For younger subjects, highly significant first- and second-order partial correlations were obtained with age and/or WISC information scores held constant. (Author)

A fully Sinc-Galerkin method for Euler-Bernoulli beam models

NASA Technical Reports Server (NTRS)

Smith, R. C.; Bowers, K. L.; Lund, J.

1990-01-01

A fully Sinc-Galerkin method in both space and time is presented for fourth-order time-dependent partial differential equations with fixed and cantilever boundary conditions. The Sinc discretizations for the second-order temporal problem and the fourth-order spatial problems are presented. Alternate formulations for variable parameter fourth-order problems are given which prove to be especially useful when applying the forward techniques to parameter recovery problems. The discrete system which corresponds to the time-dependent partial differential equations of interest are then formulated. Computational issues are discussed and a robust and efficient algorithm for solving the resulting matrix system is outlined. Numerical results which highlight the method are given for problems with both analytic and singular solutions as well as fixed and cantilever boundary conditions.

A lattice Boltzmann model for the Burgers-Fisher equation.

PubMed

Zhang, Jianying; Yan, Guangwu

2010-06-01

A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption. (c) 2010 American Institute of Physics.

Nonlinear estimation theory applied to the interplanetary orbit determination problem.

NASA Technical Reports Server (NTRS)

Tapley, B. D.; Choe, C. Y.

1972-01-01

Martingale theory and appropriate smoothing properties of Loeve (1953) have been used to develop a modified Gaussian second-order filter. The performance of the filter is evaluated through numerical simulation of a Jupiter flyby mission. The observations used in the simulation are on-board measurements of the angle between Jupiter and a fixed star taken at discrete time intervals. In the numerical study, the influence of each of the second-order terms is evaluated. Five filter algorithms are used in the simulations. Four of the filters are the modified Gaussian second-order filter and three approximations derived by neglecting one or more of the second-order terms in the equations. The fifth filter is the extended Kalman-Bucy filter which is obtained by neglecting all of the second-order terms.

Quenching oscillating behaviors in fractional coupled Stuart-Landau oscillators

NASA Astrophysics Data System (ADS)

Sun, Zhongkui; Xiao, Rui; Yang, Xiaoli; Xu, Wei

2018-03-01

Oscillation quenching has been widely studied during the past several decades in fields ranging from natural sciences to engineering, but investigations have so far been restricted to oscillators with an integer-order derivative. Here, we report the first study of amplitude death (AD) in fractional coupled Stuart-Landau oscillators with partial and/or complete conjugate couplings to explore oscillation quenching patterns and dynamics. It has been found that the fractional-order derivative impacts the AD state crucially. The area of the AD state increases along with the decrease of the fractional-order derivative. Furthermore, by introducing and adjusting a limiting feedback factor in coupling links, the AD state can be well tamed in fractional coupled oscillators. Hence, it provides one an effective approach to analyze and control the oscillating behaviors in fractional coupled oscillators.

Increasing Accuracy in Computed Inviscid Boundary Conditions

NASA Technical Reports Server (NTRS)

Dyson, Roger

2004-01-01

A technique has been devised to increase the accuracy of computational simulations of flows of inviscid fluids by increasing the accuracy with which surface boundary conditions are represented. This technique is expected to be especially beneficial for computational aeroacoustics, wherein it enables proper accounting, not only for acoustic waves, but also for vorticity and entropy waves, at surfaces. Heretofore, inviscid nonlinear surface boundary conditions have been limited to third-order accuracy in time for stationary surfaces and to first-order accuracy in time for moving surfaces. For steady-state calculations, it may be possible to achieve higher accuracy in space, but high accuracy in time is needed for efficient simulation of multiscale unsteady flow phenomena. The present technique is the first surface treatment that provides the needed high accuracy through proper accounting of higher-order time derivatives. The present technique is founded on a method known in art as the Hermitian modified solution approximation (MESA) scheme. This is because high time accuracy at a surface depends upon, among other things, correction of the spatial cross-derivatives of flow variables, and many of these cross-derivatives are included explicitly on the computational grid in the MESA scheme. (Alternatively, a related method other than the MESA scheme could be used, as long as the method involves consistent application of the effects of the cross-derivatives.) While the mathematical derivation of the present technique is too lengthy and complex to fit within the space available for this article, the technique itself can be characterized in relatively simple terms: The technique involves correction of surface-normal spatial pressure derivatives at a boundary surface to satisfy the governing equations and the boundary conditions and thereby achieve arbitrarily high orders of time accuracy in special cases. The boundary conditions can now include a potentially infinite number of time derivatives of surface-normal velocity (consistent with no flow through the boundary) up to arbitrarily high order. The corrections for the first-order spatial derivatives of pressure are calculated by use of the first-order time derivative velocity. The corrected first-order spatial derivatives are used to calculate the second- order time derivatives of velocity, which, in turn, are used to calculate the corrections for the second-order pressure derivatives. The process as described is repeated, progressing through increasing orders of derivatives, until the desired accuracy is attained.

High-order asynchrony-tolerant finite difference schemes for partial differential equations

NASA Astrophysics Data System (ADS)

Aditya, Konduri; Donzis, Diego A.

2017-12-01

Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion - synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza R.; Nishikawa, Hiroaki

2014-01-01

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

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.

Rapid adsorptive removal of toxic Pb(2+) ion from aqueous solution using recyclable, biodegradable nanocomposite derived from templated partially hydrolyzed xanthan gum and nanosilica.

PubMed

Ghorai, Soumitra; Sarkar, Amit Kumar; Pal, Sagar

2014-10-01

This work studied the application of a novel biodegradable nanocomposite based on partially hydrolyzed polyacrylamide grafted xanthan gum and nanosilica (h-XG/SiO2) towards efficient and rapid removal of toxic Pb(2+) ions from aqueous environment. The uptake ability of Pb(2+) using h-XG/SiO2 has been studied in batch adsorption experiments with variation of adsorption parameters. The excellent removal rate (99.54% adsorption within 25min) and superior adsorption capacity (Qmax=1012.15mgg(-1)) of the composite material have been explained on the basis of synergistic and chelating effects of h-XG/SiO2 with Pb(2+) ion through electrostatic interactions. The kinetics, isotherm and thermodynamics studies reveal that Pb(2+) adsorb rapidly on nanocomposite surface, which is in agreement with pseudo-second-order kinetics and Langmuir adsorption isotherm models. In consequence of excellent adsorption as well as regeneration characteristics of nanocomposite, it has been found to be a promising adsorbent towards removal of Pb(2+) ions from battery industry wastewater. Copyright © 2014 Elsevier Ltd. All rights reserved.

Healthy degenerate theories with higher derivatives

NASA Astrophysics Data System (ADS)

Motohashi, Hayato; Noui, Karim; Suyama, Teruaki; Yamaguchi, Masahide; Langlois, David

2016-07-01

In the context of classical mechanics, we study the conditions under which higher-order derivative theories can evade the so-called Ostrogradsky instability. More precisely, we consider general Lagrangians with second order time derivatives, of the form L(̈phia, dot phia, phia; qi, qi) with a = 1,⋯,n and i = 1,⋯,m. For n = 1, assuming that the qi's form a nondegenerate subsystem, we confirm that the degeneracy of the kinetic matrix eliminates the Ostrogradsky instability. The degeneracy implies, in the Hamiltonian formulation of the theory, the existence of a primary constraint, which generates a secondary constraint, thus eliminating the Ostrogradsky ghost. For n > 1, we show that, in addition to the degeneracy of the kinetic matrix, one needs to impose extra conditions to ensure the presence of a sufficient number of secondary constraints that can eliminate all the Ostrogradsky ghosts. When these conditions that ensure the disappearance of the Ostrogradsky instability are satisfied, we show that the Euler-Lagrange equations, which involve a priori higher order derivatives, can be reduced to a second order system.

Second Language Acquisition.

ERIC Educational Resources Information Center

McLaughlin, Barry; Harrington, Michael

1989-01-01

A distinction is drawn between representational and processing models of second-language acquisition. The first approach is derived primarily from linguistics, the second from psychology. Both fields, it is argued, need to collaborate more fully, overcoming disciplinary narrowness in order to achieve more fruitful research. (GLR)

Anomalous transport from holography: part II

NASA Astrophysics Data System (ADS)

Bu, Yanyan; Lublinsky, Michael; Sharon, Amir

2017-03-01

This is a second study of chiral anomaly-induced transport within a holographic model consisting of anomalous U(1)_V× U(1)_A Maxwell theory in Schwarzschild-AdS_5 spacetime. In the first part, chiral magnetic/separation effects (CME/CSE) are considered in the presence of a static spatially inhomogeneous external magnetic field. Gradient corrections to CME/CSE are analytically evaluated up to third order in the derivative expansion. Some of the third order gradient corrections lead to an anomaly-induced negative B^2-correction to the diffusion constant. We also find modifications to the chiral magnetic wave nonlinear in B. In the second part, we focus on the experimentally interesting case of the axial chemical potential being induced dynamically by a constant magnetic and time-dependent electric fields. Constitutive relations for the vector/axial currents are computed employing two different approximations: (a) derivative expansion (up to third order) but fully nonlinear in the external fields, and (b) weak electric field limit but resuming all orders in the derivative expansion. A non-vanishing nonlinear axial current (CSE) is found in the first case. The dependence on magnetic field and frequency of linear transport coefficient functions is explored in the second.

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.

Linear force and moment equations for an annular smooth shaft seal perturbed both angularly and laterally

NASA Technical Reports Server (NTRS)

Fenwick, J.; Dijulio, R.; Ek, M. C.; Ehrgott, R.

1982-01-01

Coefficients are derived for equations expressing the lateral force and pitching moments associated with both planar translation and angular perturbations from a nominally centered rotating shaft with respect to a stationary seal. The coefficients for the lowest order and first derivative terms emerge as being significant and are of approximately the same order of magnitude as the fundamental coefficients derived by means of Black's equations. Second derivative, shear perturbation, and entrance coefficient variation effects are adjudged to be small.

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.

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 second-order Budkyo-type parameterization of landsurface hydrology

NASA Technical Reports Server (NTRS)

Andreou, S. A.; Eagleson, P. S.

1982-01-01

A simple, second order parameterization of the water fluxes at a land surface for use as the appropriate boundary condition in general circulation models of the global atmosphere was developed. The derived parameterization incorporates the high nonlinearities in the relationship between the near surface soil moisture and the evaporation, runoff and percolation fluxes. Based on the one dimensional statistical dynamic derivation of the annual water balance, it makes the transition to short term prediction of the moisture fluxes, through a Taylor expansion around the average annual soil moisture. A comparison of the suggested parameterization is made with other existing techniques and available measurements. A thermodynamic coupling is applied in order to obtain estimations of the surface ground temperature.

Second-order processing of four-stroke apparent motion.

PubMed

Mather, G; Murdoch, L

1999-05-01

In four-stroke apparent motion displays, pattern elements oscillate between two adjacent positions and synchronously reverse in contrast, but appear to move unidirectionally. For example, if rightward shifts preserve contrast but leftward shifts reverse contrast, consistent rightward motion is seen. In conventional first-order displays, elements reverse in luminance contrast (e.g. light elements become dark, and vice-versa). The resulting perception can be explained by responses in elementary motion detectors turned to spatio-temporal orientation. Second-order motion displays contain texture-defined elements, and there is some evidence that they excite second-order motion detectors that extract spatio-temporal orientation following the application of a non-linear 'texture-grabbing' transform by the visual system. We generated a variety of second-order four-stroke displays, containing texture-contrast reversals instead of luminance contrast reversals, and used their effectiveness as a diagnostic test for the presence of various forms of non-linear transform in the second-order motion system. Displays containing only forward or only reversed phi motion sequences were also tested. Displays defined by variation in luminance, contrast, orientation, and size were effective. Displays defined by variation in motion, dynamism, and stereo were partially or wholly ineffective. Results obtained with contrast-reversing and four-stroke displays indicate that only relatively simple non-linear transforms (involving spatial filtering and rectification) are available during second-order energy-based motion analysis.

Suboptimal and optimal order policies for fixed and varying replenishment interval with declining market

NASA Astrophysics Data System (ADS)

Yu, Jonas C. P.; Wee, H. M.; Yang, P. C.; Wu, Simon

2016-06-01

One of the supply chain risks for hi-tech products is the result of rapid technological innovation; it results in a significant decline in the selling price and demand after the initial launch period. Hi-tech products include computers and communication consumer's products. From a practical standpoint, a more realistic replenishment policy is needed to consider the impact of risks; especially when some portions of shortages are lost. In this paper, suboptimal and optimal order policies with partial backordering are developed for a buyer when the component cost, the selling price, and the demand rate decline at a continuous rate. Two mathematical models are derived and discussed: one model has the suboptimal solution with the fixed replenishment interval and a simpler computational process; the other one has the optimal solution with the varying replenishment interval and a more complicated computational process. The second model results in more profit. Numerical examples are provided to illustrate the two replenishment models. Sensitivity analysis is carried out to investigate the relationship between the parameters and the net profit.

Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid

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

Starodumov, Ilya; Kropotin, Nikolai

2016-08-10

We investigate the three-dimensional mathematical model of crystal growth called PFC (Phase Field Crystal) in a hyperbolic modification. This model is also called the modified model PFC (originally PFC model is formulated in parabolic form) and allows to describe both slow and rapid crystallization processes on atomic length scales and on diffusive time scales. Modified PFC model is described by the differential equation in partial derivatives of the sixth order in space and second order in time. The solution of this equation is possible only by numerical methods. Previously, authors created the software package for the solution of the Phasemore » Field Crystal problem, based on the method of isogeometric analysis (IGA) and PetIGA program library. During further investigation it was found that the quality of the solution can strongly depends on the discretization parameters of a numerical method. In this report, we show the features that should be taken into account during constructing the computational grid for the numerical simulation.« less

A spectral-finite difference solution of the Navier-Stokes equations in three dimensions

NASA Astrophysics Data System (ADS)

Alfonsi, Giancarlo; Passoni, Giuseppe; Pancaldo, Lea; Zampaglione, Domenico

1998-07-01

A new computational code for the numerical integration of the three-dimensional Navier-Stokes equations in their non-dimensional velocity-pressure formulation is presented. The system of non-linear partial differential equations governing the time-dependent flow of a viscous incompressible fluid in a channel is managed by means of a mixed spectral-finite difference method, in which different numerical techniques are applied: Fourier decomposition is used along the homogeneous directions, second-order Crank-Nicolson algorithms are employed for the spatial derivatives in the direction orthogonal to the solid walls and a fourth-order Runge-Kutta procedure is implemented for both the calculation of the convective term and the time advancement. The pressure problem, cast in the Helmholtz form, is solved with the use of a cyclic reduction procedure. No-slip boundary conditions are used at the walls of the channel and cyclic conditions are imposed at the other boundaries of the computing domain.Results are provided for different values of the Reynolds number at several time steps of integration and are compared with results obtained by other authors.

Second-harmonic generation in shear wave beams with different polarizations

NASA Astrophysics Data System (ADS)

Spratt, Kyle S.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2015-10-01

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

Reliable two-dimensional phase unwrapping method using region growing and local linear estimation.

PubMed

Zhou, Kun; Zaitsev, Maxim; Bao, Shanglian

2009-10-01

In MRI, phase maps can provide useful information about parameters such as field inhomogeneity, velocity of blood flow, and the chemical shift between water and fat. As phase is defined in the (-pi,pi] range, however, phase wraps often occur, which complicates image analysis and interpretation. This work presents a two-dimensional phase unwrapping algorithm that uses quality-guided region growing and local linear estimation. The quality map employs the variance of the second-order partial derivatives of the phase as the quality criterion. Phase information from unwrapped neighboring pixels is used to predict the correct phase of the current pixel using a linear regression method. The algorithm was tested on both simulated and real data, and is shown to successfully unwrap phase images that are corrupted by noise and have rapidly changing phase. (c) 2009 Wiley-Liss, Inc.

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

NASA Astrophysics Data System (ADS)

Nemoto, Ryo; Iguchi, Tatsuo

2017-09-01

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

Entangled trajectories Hamiltonian dynamics for treating quantum nuclear effects

NASA Astrophysics Data System (ADS)

Smith, Brendan; Akimov, Alexey V.

2018-04-01

A simple and robust methodology, dubbed Entangled Trajectories Hamiltonian Dynamics (ETHD), is developed to capture quantum nuclear effects such as tunneling and zero-point energy through the coupling of multiple classical trajectories. The approach reformulates the classically mapped second-order Quantized Hamiltonian Dynamics (QHD-2) in terms of coupled classical trajectories. The method partially enforces the uncertainty principle and facilitates tunneling. The applicability of the method is demonstrated by studying the dynamics in symmetric double well and cubic metastable state potentials. The methodology is validated using exact quantum simulations and is compared to QHD-2. We illustrate its relationship to the rigorous Bohmian quantum potential approach, from which ETHD can be derived. Our simulations show a remarkable agreement of the ETHD calculation with the quantum results, suggesting that ETHD may be a simple and inexpensive way of including quantum nuclear effects in molecular dynamics simulations.

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

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

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

2016-05-01

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

A study of the applicability of nucleation theory to quasi-thermodynamic transitions of second and higher Ehrenfest-order

NASA Technical Reports Server (NTRS)

Barker, R. E., Jr.; Campbell, K. W.

1985-01-01

The applicability of classical nucleation theory to second (and higher) order thermodynamic transitions in the Ehrenfest sense has been investigated and expressions have been derived upon which the qualitative and quantitative success of the basic approach must ultimately depend. The expressions describe the effect of temperature undercooling, hydrostatic pressure, and tensile stress upon the critical parameters, the critical nucleus size, and critical free energy barrier, for nucleation in a thermodynamic transition of any general order. These expressions are then specialized for the case of first and second order transitions. The expressions for the case of undercooling are then used in conjunction with literature data to estimate values for the critical quantities in a system undergoing a pseudo-second order transition (the glass transition in polystyrene). Methods of estimating the interfacial energy gamma in systems undergoing a first and second order transition are also discussed.

Modeling of Inverted Annular Film Boiling using an integral method

NASA Astrophysics Data System (ADS)

Sridharan, Arunkumar

In modeling Inverted Annular Film Boiling (IAFB), several important phenomena such as interaction between the liquid and the vapor phases and irregular nature of the interface, which greatly influence the momentum and heat transfer at the interface, need to be accounted for. However, due to the complexity of these phenomena, they were not modeled in previous studies. Since two-phase heat transfer equations and relationships rely heavily on experimental data, many closure relationships that were used in previous studies to solve the problem are empirical in nature. Also, in deriving the relationships, the experimental data were often extrapolated beyond the intended range of conditions, causing errors in predictions. In some cases, empirical correlations that were derived from situations other than IAFB, and whose applicability to IAFB was questionable, were used. Moreover, arbitrary constants were introduced in the model developed in previous studies to provide good fit to the experimental data. These constants have no physical basis, thereby leading to questionable accuracy in the model predictions. In the present work, modeling of Inverted Annular Film Boiling (IAFB) is done using Integral Method. Two-dimensional formulation of IAFB is presented. Separate equations for the conservation of mass, momentum and energy are derived from first principles, for the vapor film and the liquid core. Turbulence is incorporated in the formulation. The system of second-order partial differential equations is integrated over the radial direction to obtain a system of integral differential equations. In order to solve the system of equations, second order polynomial profiles are used to describe the nondimensional velocity and temperatures. The unknown coefficients in the profiles are functions of the axial direction alone. Using the boundary conditions that govern the physical problem, equations for the unknown coefficients are derived in terms of the primary dependent variables: wall shear stress, interfacial shear stress, film thickness, pressure, wall temperature and the mass transfer rate due to evaporation. A system of non-linear first order coupled ordinary differential equations is obtained. Due to the inherent mathematical complexity of the system of equations, simplifying assumptions are made to obtain a numerical solution. The system of equations is solved numerically to obtain values of the unknown quantities at each subsequent axial location. Derived quantities like void fraction and heat transfer coefficient are calculated at each axial location. The calculation is terminated when the void fraction reaches a value of 0.6, the upper limit of IAFB. The results obtained agree with the experimental trends observed. Void fraction increases along the heated length, while the heat transfer coefficient drops due to the increased resistance of the vapor film as expected.

A green method for the quantification of plastics-derived endocrine disruptors in beverages by chemometrics-assisted liquid chromatography with simultaneous diode array and fluorescent detection.

PubMed

Vidal, Rocío B Pellegrino; Ibañez, Gabriela A; Escandar, Graciela M

2016-10-01

The aim of this study was to develop a novel analytical method for the determination of bisphenol A, nonylphenol, octylphenol, diethyl phthalate, dibutyl phthalate and diethylhexyl phthalate, compounds known for their endocrine-disruptor properties, based on liquid chromatography with simultaneous diode array and fluorescent detection. Following the principles of green analytical chemistry, solvent consumption and chromatographic run time were minimized. To deal with the resulting incomplete resolution in the chromatograms, a second-order calibration was proposed. Second-order data (elution time-absorbance wavelength and elution time-fluorescence emission wavelength matrices) were obtained and processed by multivariate curve resolution-alternating least-squares (MCR-ALS). Applying MCR-ALS allowed quantification of the analytes even in the presence of partially overlapped chromatographic and spectral bands among these compounds and the potential interferents. The obtained results from the analysis of beer, wine, soda, juice, water and distilled beverage samples were compared with gas chromatography-mass spectrometry (GC-MS). Limits of detection (LODs) in the range 0.04-0.38ngmL(-1) were estimated in real samples after a very simple solid-phase extraction. All the samples were found to contain at least three EDs, in concentrations as high as 334ngmL(-1). Copyright © 2016 Elsevier B.V. All rights reserved.

Estimating Turbulent Surface Fluxes from Small Unmanned Aircraft: Evaluation of Current Abilities

NASA Astrophysics Data System (ADS)

de Boer, G.; Lawrence, D.; Elston, J.; Cassano, J. J.; Mack, J.; Wildmann, N.; Nigro, M. A.; Ivey, M.; Wolfe, D. E.; Muschinski, A.

2014-12-01

Heat transfer between the atmosphere and Earth's surface represents a key component to understanding Earth energy balance, making it important in understanding and simulating climate. Arguably, the oceanic air-sea interface and Polar sea-ice-air interface are amongst the most challenging in which to measure these fluxes. This difficulty results partially from challenges associated with infrastructure deployment on these surfaces and partially from an inability to obtain spatially representative values over a potentially inhomogeneous surface. Traditionally sensible (temperature) and latent (moisture) fluxes are estimated using one of several techniques. A preferred method involves eddy-correlation where cross-correlation between anomalies in vertical motion (w) and temperature (T) or moisture (q) is used to estimate heat transfer. High-frequency measurements of these quantities can be derived using tower-mounted instrumentation. Such systems have historically been deployed over land surfaces or on ships and buoys to calculate fluxes at the air-land or air-sea interface, but such deployments are expensive and challenging to execute, resulting in a lack of spatially diverse measurements. A second ("bulk") technique involves the observation of horizontal windspeed, temperature and moisture at a given altitude over an extended time period in order to estimate the surface fluxes. Small Unmanned Aircraft Systems (sUAS) represent a unique platform from which to derive these fluxes. These sUAS can be small ( 1 m), lightweight ( 700 g), low cost ( $2000) and relatively easy to deploy to remote locations and over inhomogeneous surfaces. We will give an overview of the ability of sUAS to provide measurements necessary for estimating surface turbulent fluxes. This discussion is based on flights in the vicinity of the 1000 ft. Boulder Atmospheric Observatory (BAO) tower, and over the US Department of Energy facility at Oliktok Point, Alaska. We will present initial comparisons between UAS-derived turbulent fluxes and those derived from tower-based instrumentation and discuss differences in the context of sensor technology and flight patterns employed to collect data.

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…

The Glimm scheme for perfect fluids on plane-symmetric Gowdy spacetimes

NASA Astrophysics Data System (ADS)

Barnes, A. P.; Lefloch, P. G.; Schmidt, B. G.; Stewart, J. M.

2004-11-01

We propose a new, augmented formulation of the coupled Euler Einstein equations for perfect fluids on plane-symmetric Gowdy spacetimes. The unknowns of the augmented system are the density and velocity of the fluid and the first- and second-order spacetime derivatives of the metric. We solve the Riemann problem for the augmented system, allowing propagating discontinuities in both the fluid variables and the first- and second-order derivatives of the geometry coefficients. Our main result, based on Glimm's random choice scheme, is the existence of solutions with bounded total variation of the Euler Einstein equations, up to the first time where a blow-up singularity (unbounded first-order derivatives of the geometry coefficients) occurs. We demonstrate the relevance of the augmented system for numerical relativity. We also consider general vacuum spacetimes and solve a Riemann problem, by relying on a theorem by Rendall on the characteristic value problem for the Einstein equations.

Quasi-phases and pseudo-transitions in one-dimensional models with nearest neighbor interactions

NASA Astrophysics Data System (ADS)

de Souza, S. M.; Rojas, Onofre

2018-01-01

There are some particular one-dimensional models, such as the Ising-Heisenberg spin models with a variety of chain structures, which exhibit unexpected behaviors quite similar to the first and second order phase transition, which could be confused naively with an authentic phase transition. Through the analysis of the first derivative of free energy, such as entropy, magnetization, and internal energy, a "sudden" jump that closely resembles a first-order phase transition at finite temperature occurs. However, by analyzing the second derivative of free energy, such as specific heat and magnetic susceptibility at finite temperature, it behaves quite similarly to a second-order phase transition exhibiting an astonishingly sharp and fine peak. The correlation length also confirms the evidence of this pseudo-transition temperature, where a sharp peak occurs at the pseudo-critical temperature. We also present the necessary conditions for the emergence of these quasi-phases and pseudo-transitions.

First- and Second-Order Sensitivity Analysis of a P-Version Finite Element Equation Via Automatic Differentiation

NASA Technical Reports Server (NTRS)

Hou, Gene

1998-01-01

Sensitivity analysis is a technique for determining derivatives of system responses with respect to design parameters. Among many methods available for sensitivity analysis, automatic differentiation has been proven through many applications in fluid dynamics and structural mechanics to be an accurate and easy method for obtaining derivatives. Nevertheless, the method can be computational expensive and can require a high memory space. This project will apply an automatic differentiation tool, ADIFOR, to a p-version finite element code to obtain first- and second- order then-nal derivatives, respectively. The focus of the study is on the implementation process and the performance of the ADIFOR-enhanced codes for sensitivity analysis in terms of memory requirement, computational efficiency, and accuracy.

Association between pathology and texture features of multi parametric MRI of the prostate

NASA Astrophysics Data System (ADS)

Kuess, Peter; Andrzejewski, Piotr; Nilsson, David; Georg, Petra; Knoth, Johannes; Susani, Martin; Trygg, Johan; Helbich, Thomas H.; Polanec, Stephan H.; Georg, Dietmar; Nyholm, Tufve

2017-10-01

The role of multi-parametric (mp)MRI in the diagnosis and treatment of prostate cancer has increased considerably. An alternative to visual inspection of mpMRI is the evaluation using histogram-based (first order statistics) parameters and textural features (second order statistics). The aims of the present work were to investigate the relationship between benign and malignant sub-volumes of the prostate and textures obtained from mpMR images. The performance of tumor prediction was investigated based on the combination of histogram-based and textural parameters. Subsequently, the relative importance of mpMR images was assessed and the benefit of additional imaging analyzed. Finally, sub-structures based on the PI-RADS classification were investigated as potential regions to automatically detect maligned lesions. Twenty-five patients who received mpMRI prior to radical prostatectomy were included in the study. The imaging protocol included T2, DWI, and DCE. Delineation of tumor regions was performed based on pathological information. First and second order statistics were derived from each structure and for all image modalities. The resulting data were processed with multivariate analysis, using PCA (principal component analysis) and OPLS-DA (orthogonal partial least squares discriminant analysis) for separation of malignant and healthy tissue. PCA showed a clear difference between tumor and healthy regions in the peripheral zone for all investigated images. The predictive ability of the OPLS-DA models increased for all image modalities when first and second order statistics were combined. The predictive value reached a plateau after adding ADC and T2, and did not increase further with the addition of other image information. The present study indicates a distinct difference in the signatures between malign and benign prostate tissue. This is an absolute prerequisite for automatic tumor segmentation, but only the first step in that direction. For the specific identified signature, DCE did not add complementary information to T2 and ADC maps.

Experts' Understanding of Partial Derivatives Using the Partial Derivative Machine

ERIC Educational Resources Information Center

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

2015-01-01

Partial derivatives are used in a variety of different ways within physics. Thermodynamics, in particular, uses partial derivatives in ways that students often find especially confusing. We are at the beginning of a study of the teaching of partial derivatives, with a goal of better aligning the teaching of multivariable calculus with the needs of…

Stationary axisymmetric exteriors for perturbations of isolated bodies in general relativity, to second order

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

MacCallum, Malcolm A. H.; Mars, Marc; Vera, Rauel

Perturbed stationary axisymmetric isolated bodies, e.g. stars, represented by a matter-filled interior and an asymptotically flat vacuum exterior joined at a surface where the Darmois matching conditions are satisfied, are considered. The initial state is assumed to be static. The perturbations of the matching conditions are derived and used as boundary conditions for the perturbed Ernst equations in the exterior region. The perturbations are calculated to second order. The boundary conditions are overdetermined: necessary and sufficient conditions for their compatibility are derived. The special case of perturbations of spherical bodies is given in detail.

A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

NASA Astrophysics Data System (ADS)

Bilyeu, David

This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For code development, a one-dimensional solver for the Euler equations was developed. This work is an extension of Chang's work on the fourth-order CESE method for solving a one-dimensional scalar convection equation. A generic formulation for the nth-order CESE method, where n ≥ 4, was derived. Indeed, numerical implementation of the scheme confirmed that the order of convergence was consistent with the order of the scheme. For the two- and three-dimensional solvers, SOLVCON was used as the basic framework for code implementation. A new solver kernel for the fourth-order CESE method has been developed and integrated into the framework provided by SOLVCON. The main part of SOLVCON, which deals with unstructured meshes and parallel computing, remains intact. The SOLVCON code for data transmission between computer nodes for High Performance Computing (HPC). To validate and verify the newly developed high-order CESE algorithms, several one-, two- and three-dimensional simulations where conducted. For the arbitrary order, one-dimensional, CESE solver, three sets of governing equations were selected for simulation: (i) the linear convection equation, (ii) the linear acoustic equations, (iii) the nonlinear Euler equations. All three systems of equations were used to verify the order of convergence through mesh refinement. In addition the Euler equations were used to solve the Shu-Osher and Blastwave problems. These two simulations demonstrated that the new high-order CESE methods can accurately resolve discontinuities in the flow field.For the two-dimensional, fourth-order CESE solver, the Euler equation was employed in four different test cases. The first case was used to verify the order of convergence through mesh refinement. The next three cases demonstrated the ability of the new solver to accurately resolve discontinuities in the flows. This was demonstrated through: (i) the interaction between acoustic waves and an entropy pulse, (ii) supersonic flow over a circular blunt body, (iii) supersonic flow over a guttered wedge. To validate and verify the three-dimensional, fourth-order CESE solver, two different simulations where selected. The first used the linear convection equations to demonstrate fourth-order convergence. The second used the Euler equations to simulate supersonic flow over a spherical body to demonstrate the scheme's ability to accurately resolve shocks. All test cases used are well known benchmark problems and as such, there are multiple sources available to validate the numerical results. Furthermore, the simulations showed that the high-order CESE solver was stable at a CFL number near unity.

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 1: Technical discussion

NASA Technical Reports Server (NTRS)

Lancaster, J. E.

1973-01-01

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical solution to the problem on N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The derivation of the second-order solution is summarized by showing the essential steps, some in functional form. The general asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-earth, and interplanetary solutions. The results show that the accuracies of the asymptotic solutions range from an order of magnitude better than conic approximations to that of numerical integration itself. Also, since no iterations are required, the asymptotic boundary value solutions are obtained in a fraction of the time required for comparable numerically integrated solutions. The subject of minimizing the second-order error is discussed, and recommendations made for further work directed toward achieving a uniform accuracy in all applications.

Coulomb Scattering in the Massless Nelson Model III: Ground State Wave Functions and Non-commutative Recurrence Relations

NASA Astrophysics Data System (ADS)

Dybalski, Wojciech; Pizzo, Alessandro

2018-02-01

Let $H_{P,\\sigma}$ be the single-electron fiber Hamiltonians of the massless Nelson model at total momentum $P$ and infrared cut-off $\\sigma>0$. We establish detailed regularity properties of the corresponding $n$-particle ground state wave functions $f^n_{P,\\sigma}$ as functions of $P$ and $\\sigma$. In particular, we show that \\[ |\\partial_{P^j}f^{n}_{P,\\sigma}(k_1,\\ldots, k_n)|, \\ \\ |\\partial_{P^j} \\partial_{P^{j'}} f^{n}_{P,\\sigma}(k_1,\\ldots, k_n)| \\leq \\frac{1}{\\sqrt{n!}} \\frac{(c\\lambda_0)^n}{\\sigma^{\\delta_{\\lambda_0}}} \\prod_{i=1}^n\\frac{ \\chi_{[\\sigma,\\kappa)}(k_i)}{|k_i|^{3/2}}, \\] where $c$ is a numerical constant, $\\lambda_0\\mapsto \\delta_{\\lambda_0}$ is a positive function of the maximal admissible coupling constant which satisfies $\\lim_{\\lambda_0\\to 0}\\delta_{\\lambda_0}=0$ and $\\chi_{[\\sigma,\\kappa)}$ is the (approximate) characteristic function of the energy region between the infrared cut-off $\\sigma$ and the ultraviolet cut-off $\\kappa$. While the analysis of the first derivative is relatively straightforward, the second derivative requires a new strategy. By solving a non-commutative recurrence relation we derive a novel formula for $f^n_{P,\\sigma}$ with improved infrared properties. In this representation $\\partial_{P^{j'}}\\partial_{P^{j}}f^n_{P,\\sigma}$ is amenable to sharp estimates obtained by iterative analytic perturbation theory in part II of this series of papers. The bounds stated above are instrumental for scattering theory of two electrons in the Nelson model, as explained in part I of this series.

Experts' understanding of partial derivatives using the partial derivative machine

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

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

Kang, Hyun-Ju; Chung, Chin-Wook, E-mail: joykang@hanyang.ac.kr; Choi, Hyeok

A modified central difference method (MCDM) is proposed to obtain the electron energy distribution functions (EEDFs) in single Langmuir probes. Numerical calculation of the EEDF with MCDM is simple and has less noise. This method provides the second derivatives at a given point as the weighted average of second order central difference derivatives calculated at different voltage intervals, weighting each by the square of the interval. In this paper, the EEDFs obtained from MCDM are compared to those calculated via the averaged central difference method. It is found that MCDM effectively suppresses the noises in the EEDF, while the samemore » number of points are used to calculate of the second derivative.« less

Second-order closure PBL model with new third-order moments: Comparison with LES data

NASA Technical Reports Server (NTRS)

Canuto, V. M.; Minotti, F.; Ronchi, C.; Ypma, R. M.; Zeman, O.

1994-01-01

This paper contains two parts. In the first part, a new set of diagnostic equations is derived for the third-order moments for a buoyancy-driven flow, by exact inversion of the prognostic equations for the third-order moment equations in the stationary case. The third-order moments exhibit a universal structure: they all are a linear combination of the derivatives of all the second-order moments, bar-w(exp 2), bar-w theta, bar-theta(exp 2), and bar-q(exp 2). Each term of the sum contains a turbulent diffusivity D(sub t), which also exhibits a universal structure of the form D(sub t) = a nu(sub t) + b bar-w theta. Since the sign of the convective flux changes depending on stable or unstable stratification, D(sub t) varies according to the type of stratification. Here nu(sub t) approximately equal to wl (l is a mixing length and w is an rms velocity) represents the 'mechanical' part, while the 'buoyancy' part is represented by the convective flux bar-w theta. The quantities a and b are functions of the variable N(sub tau)(exp 2), where N(exp 2) = g alpha derivative of Theta with respect to z and tau is the turbulence time scale. The new expressions for the third-order moments generalize those of Zeman and Lumley, which were subsequently adopted by Sun and Ogura, Chen and Cotton, and Finger and Schmidt in their treatments of the convective boundary layer. In the second part, the new expressions for the third-order moments are used to solve the ensemble average equations describing a purely convective boundary laye r heated from below at a constant rate. The computed second- and third-order moments are then compared with the corresponding Large Eddy Simulation (LES) results, most of which are obtained by running a new LES code, and part of which are taken from published results. The ensemble average results compare favorably with the LES data.

Stability and Hamiltonian formulation of higher derivative theories

NASA Astrophysics Data System (ADS)

Schmidt, Hans-Jürgen

1994-06-01

We analyze the presuppositions leading to instabilities in theories of order higher than second. The type of fourth-order gravity which leads to an inflationary (quasi-de Sitter) period of cosmic evolution by inclusion of one curvature-squared term (i.e., the Starobinsky model) is used as an example. The corresponding Hamiltonian formulation (which is necessary for deducing the Wheeler-DeWitt equation) is found both in the Ostrogradski approach and in another form. As an example, a closed form solution of the Wheeler-DeWitt equation for a spatially flat Friedmann model and L=R2 is found. The method proposed by Simon to bring fourth order gravity to second order can be (if suitably generalized) applied to bring sixth-order gravity to second order.

On isochronous derivatives of the first and second order in space dynamics tasks

NASA Technical Reports Server (NTRS)

Bakshiyan, B. T.; Sukhanov, A. A.

1979-01-01

The first and second isochronous derivatives are calculated from the vector of state of dynamic system using its initial value. Use is made of the method of finding a fundamental solution of conjugate variational equations. This solution and the corresponding universal relationship for isochronous derivatives are found for the two-body problem in a form which is simple and suitable for computer programming. The form of these relationships was obtained for motion which differs from parabolic motion. Formulas are given for isochronous derivatives using the gravitational parameter in the two-body problem.

Partial least-squares with residual bilinearization for the spectrofluorimetric determination of pesticides. A solution of the problems of inner-filter effects and matrix interferents.

PubMed

Piccirilli, Gisela N; Escandar, Graciela M

2006-09-01

This paper demonstrates for the first time the power of a chemometric second-order algorithm for predicting, in a simple way and using spectrofluorimetric data, the concentration of analytes in the presence of both the inner-filter effect and unsuspected species. The simultaneous determination of the systemic fungicides carbendazim and thiabendazole was achieved and employed for the discussion of the scopes of the applied second-order chemometric tools: parallel factor analysis (PARAFAC) and partial least-squares with residual bilinearization (PLS/RBL). The chemometric study was performed using fluorescence excitation-emission matrices obtained after the extraction of the analytes over a C18-membrane surface. The ability of PLS/RBL to recognize and overcome the significant changes produced by thiabendazole in both the excitation and emission spectra of carbendazim is demonstrated. The high performance of the selected PLS/RBL method was established with the determination of both pesticides in artificial and real samples.

Partitioning of organophosphorus pesticides into phosphatidylcholine small unilamellar vesicles studied by second-derivative spectrophotometry

NASA Astrophysics Data System (ADS)

Takegami, Shigehiko; Kitamura, Keisuke; Ohsugi, Mayuko; Ito, Aya; Kitade, Tatsuya

2015-06-01

In order to quantitatively examine the lipophilicity of the widely used organophosphorus pesticides (OPs) chlorfenvinphos (CFVP), chlorpyrifos-methyl (CPFM), diazinon (DZN), fenitrothion (FNT), fenthion (FT), isofenphos (IFP), profenofos (PFF) and pyraclofos (PCF), their partition coefficient (Kp) values between phosphatidylcholine (PC) small unilamellar vesicles (SUVs) and water (liposome-water system) were determined by second-derivative spectrophotometry. The second-derivative spectra of these OPs in the presence of PC SUV showed a bathochromic shift according to the increase in PC concentration and distinct derivative isosbestic points, demonstrating the complete elimination of the residual background signal effects that were observed in the absorption spectra. The Kp values were calculated from the second-derivative intensity change induced by addition of PC SUV and obtained with a good precision of R.S.D. below 10%. The Kp values were in the order of CPFM > FT > PFF > PCF > IFP > CFVP > FNT ⩾ DZN and did not show a linear correlation relationship with the reported partition coefficients obtained using an n-octanol-water system (R2 = 0.530). Also, the results quantitatively clarified the effect of chemical-group substitution in OPs on their lipophilicity. Since the partition coefficient for the liposome-water system is more effective for modeling the quantitative structure-activity relationship than that for the n-octanol-water system, the obtained results are toxicologically important for estimating the accumulation of these OPs in human cell membranes.

Generalized contractive mappings and weakly α-admissible pairs in G-metric spaces.

PubMed

Hussain, N; Parvaneh, V; Hoseini Ghoncheh, S J

2014-01-01

The aim of this paper is to present some coincidence and common fixed point results for generalized (ψ, φ)-contractive mappings using partially weakly G-α-admissibility in the setup of G-metric space. As an application of our results, periodic points of weakly contractive mappings are obtained. We also derive certain new coincidence point and common fixed point theorems in partially ordered G-metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results.

Generalized Contractive Mappings and Weakly α-Admissible Pairs in G-Metric Spaces

PubMed Central

Hussain, N.; Parvaneh, V.; Hoseini Ghoncheh, S. J.

2014-01-01

The aim of this paper is to present some coincidence and common fixed point results for generalized (ψ, φ)-contractive mappings using partially weakly G-α-admissibility in the setup of G-metric space. As an application of our results, periodic points of weakly contractive mappings are obtained. We also derive certain new coincidence point and common fixed point theorems in partially ordered G-metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results. PMID:25202742

The company they keep: Background similarity influences transfer of aftereffects from second- to first-order stimuli

PubMed Central

Qian, Ning; Dayan, Peter

2013-01-01

A wealth of studies has found that adapting to second-order visual stimuli has little effect on the perception of first-order stimuli. This is physiologically and psychologically troubling, since many cells show similar tuning to both classes of stimuli, and since adapting to first-order stimuli leads to aftereffects that do generalize to second-order stimuli. Focusing on high-level visual stimuli, we recently proposed the novel explanation that the lack of transfer arises partially from the characteristically different backgrounds of the two stimulus classes. Here, we consider the effect of stimulus backgrounds in the far more prevalent, lower-level, case of the orientation tilt aftereffect. Using a variety of first- and second-order oriented stimuli, we show that we could increase or decrease both within- and cross-class adaptation aftereffects by increasing or decreasing the similarity of the otherwise apparently uninteresting or irrelevant backgrounds of adapting and test patterns. Our results suggest that similarity between background statistics of the adapting and test stimuli contributes to low-level visual adaptation, and that these backgrounds are thus not discarded by visual processing but provide contextual modulation of adaptation. Null cross-adaptation aftereffects must also be interpreted cautiously. These findings reduce the apparent inconsistency between psychophysical and neurophysiological data about first- and second-order stimuli. PMID:23732217

A new non-iterative reconstruction method for the electrical impedance tomography problem

NASA Astrophysics Data System (ADS)

Ferreira, A. D.; Novotny, A. A.

2017-03-01

The electrical impedance tomography (EIT) problem consists in determining the distribution of the electrical conductivity of a medium subject to a set of current fluxes, from measurements of the corresponding electrical potentials on its boundary. EIT is probably the most studied inverse problem since the fundamental works by Calderón from the 1980s. It has many relevant applications in medicine (detection of tumors), geophysics (localization of mineral deposits) and engineering (detection of corrosion in structures). In this work, we are interested in reconstructing a number of anomalies with different electrical conductivity from the background. Since the EIT problem is written in the form of an overdetermined boundary value problem, the idea is to rewrite it as a topology optimization problem. In particular, a shape functional measuring the misfit between the boundary measurements and the electrical potentials obtained from the model is minimized with respect to a set of ball-shaped anomalies by using the concept of topological derivatives. It means that the objective functional is expanded and then truncated up to the second order term, leading to a quadratic and strictly convex form with respect to the parameters under consideration. Thus, a trivial optimization step leads to a non-iterative second order reconstruction algorithm. As a result, the reconstruction process becomes very robust with respect to noisy data and independent of any initial guess. Finally, in order to show the effectiveness of the devised reconstruction algorithm, some numerical experiments into two spatial dimensions are presented, taking into account total and partial boundary measurements.

Equivalent Relaxations of Optimal Power Flow

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

Bose, S; Low, SH; Teeraratkul, T

2015-03-01

Several convex relaxations of the optimal power flow (OPF) problem have recently been developed using both bus injection models and branch flow models. In this paper, we prove relations among three convex relaxations: a semidefinite relaxation that computes a full matrix, a chordal relaxation based on a chordal extension of the network graph, and a second-order cone relaxation that computes the smallest partial matrix. We prove a bijection between the feasible sets of the OPF in the bus injection model and the branch flow model, establishing the equivalence of these two models and their second-order cone relaxations. Our results implymore » that, for radial networks, all these relaxations are equivalent and one should always solve the second-order cone relaxation. For mesh networks, the semidefinite relaxation and the chordal relaxation are equally tight and both are strictly tighter than the second-order cone relaxation. Therefore, for mesh networks, one should either solve the chordal relaxation or the SOCP relaxation, trading off tightness and the required computational effort. Simulations are used to illustrate these results.« less

Wavelet Analysis Used for Spectral Background Removal in the Determination of Glucose from Near-Infrared Single-Beam Spectra

PubMed Central

Wan, Boyong; Small, Gary W.

2010-01-01

Wavelet analysis is developed as a preprocessing tool for use in removing background information from near-infrared (near-IR) single-beam spectra before the construction of multivariate calibration models. Three data sets collected with three different near-IR spectrometers are investigated that involve the determination of physiological levels of glucose (1-30 mM) in a simulated biological matrix containing alanine, ascorbate, lactate, triacetin, and urea in phosphate buffer. A factorial design is employed to optimize the specific wavelet function used and the level of decomposition applied, in addition to the spectral range and number of latent variables associated with a partial least-squares calibration model. The prediction performance of the computed models is studied with separate data acquired after the collection of the calibration spectra. This evaluation includes one data set collected over a period of more than six months. Preprocessing with wavelet analysis is also compared to the calculation of second-derivative spectra. Over the three data sets evaluated, wavelet analysis is observed to produce better-performing calibration models, with improvements in concentration predictions on the order of 30% being realized relative to models based on either second-derivative spectra or spectra preprocessed with simple additive and multiplicative scaling correction. This methodology allows the construction of stable calibrations directly with single-beam spectra, thereby eliminating the need for the collection of a separate background or reference spectrum. PMID:21035604

Wavelet analysis used for spectral background removal in the determination of glucose from near-infrared single-beam spectra.

PubMed

Wan, Boyong; Small, Gary W

2010-11-29

Wavelet analysis is developed as a preprocessing tool for use in removing background information from near-infrared (near-IR) single-beam spectra before the construction of multivariate calibration models. Three data sets collected with three different near-IR spectrometers are investigated that involve the determination of physiological levels of glucose (1-30 mM) in a simulated biological matrix containing alanine, ascorbate, lactate, triacetin, and urea in phosphate buffer. A factorial design is employed to optimize the specific wavelet function used and the level of decomposition applied, in addition to the spectral range and number of latent variables associated with a partial least-squares calibration model. The prediction performance of the computed models is studied with separate data acquired after the collection of the calibration spectra. This evaluation includes one data set collected over a period of more than 6 months. Preprocessing with wavelet analysis is also compared to the calculation of second-derivative spectra. Over the three data sets evaluated, wavelet analysis is observed to produce better-performing calibration models, with improvements in concentration predictions on the order of 30% being realized relative to models based on either second-derivative spectra or spectra preprocessed with simple additive and multiplicative scaling correction. This methodology allows the construction of stable calibrations directly with single-beam spectra, thereby eliminating the need for the collection of a separate background or reference spectrum. Copyright © 2010 Elsevier B.V. All rights reserved.

Creating Weather System Ensembles Through Synergistic Process Modeling and Machine Learning

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Studying the Global Bifurcation Involving Wada Boundary Metamorphosis by a Method of Generalized Cell Mapping with Sampling-Adaptive Interpolation

NASA Astrophysics Data System (ADS)

Liu, Xiao-Ming; Jiang, Jun; Hong, Ling; Tang, Dafeng

In this paper, a new method of Generalized Cell Mapping with Sampling-Adaptive Interpolation (GCMSAI) is presented in order to enhance the efficiency of the computation of one-step probability transition matrix of the Generalized Cell Mapping method (GCM). Integrations with one mapping step are replaced by sampling-adaptive interpolations of third order. An explicit formula of interpolation error is derived for a sampling-adaptive control to switch on integrations for the accuracy of computations with GCMSAI. By applying the proposed method to a two-dimensional forced damped pendulum system, global bifurcations are investigated with observations of boundary metamorphoses including full to partial and partial to partial as well as the birth of fully Wada boundary. Moreover GCMSAI requires a computational time of one thirtieth up to one fiftieth compared to that of the previous GCM.

Time-dependent Second Order Scattering Theory for Weather Radar with a Finite Beam Width

NASA Technical Reports Server (NTRS)

Kobayashi, Satoru; Tanelli, Simone; Im, Eastwood; Ito, Shigeo; Oguchi, Tomohiro

2006-01-01

Multiple scattering effects from spherical water particles of uniform diameter are studied for a W-band pulsed radar. The Gaussian transverse beam-profile and the rectangular pulse-duration are used for calculation. An second-order analytical solution is derived for a single layer structure, based on a time-dependent radiative transfer theory as described in the authors' companion paper. When the range resolution is fixed, increase in footprint radius leads to increase in the second order reflectivity that is defined as the ratio of the second order return to the first order one. This feature becomes more serious as the range increases. Since the spaceborne millimeter-wavelength radar has a large footprint radius that is competitive to the mean free path, the multiple scattering effect must be taken into account for analysis.

Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections.

PubMed

Sergiievskyi, Volodymyr P; Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel

2014-06-05

Molecular density functional theory (MDFT) offers an efficient implicit-solvent method to estimate molecule solvation free-energies, whereas conserving a fully molecular representation of the solvent. Even within a second-order approximation for the free-energy functional, the so-called homogeneous reference fluid approximation, we show that the hydration free-energies computed for a data set of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by 2-3 orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canonical to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justification to empirical partial molar volume corrections that have been proposed recently.

An investigation of promotional mix considerations for mail-order prescriptions: facilitating the market's acceptance of a partial health care-cost remedy.

PubMed

Strutton, D; Pelton, L E; True, S L

1993-01-01

While the U.S. health care system is confronted by a daunting assortment of problems, the foremost crisis almost certainly involves the excessive costs of health care. Mail-order prescriptions offer a modest, albeit worthwhile, measure of relief from high health care costs. This study investigates the information search behaviors and product perceptions that characterize current users and nonusers of mail-order prescriptions. Implications and recommendations concerned with the development of promotional strategies for mail-order prescriptions are derived from the findings.

Novel spectrophotometric determination of chloramphenicol and dexamethasone in the presence of non labeled interfering substances using univariate methods and multivariate regression model updating

NASA Astrophysics Data System (ADS)

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

2015-04-01

Smart and novel spectrophotometric and chemometric methods have been developed and validated for the simultaneous determination of a binary mixture of chloramphenicol (CPL) and dexamethasone sodium phosphate (DSP) in presence of interfering substances without prior separation. The first method depends upon derivative subtraction coupled with constant multiplication. The second one is ratio difference method at optimum wavelengths which were selected after applying derivative transformation method via multiplying by a decoding spectrum in order to cancel the contribution of non labeled interfering substances. The third method relies on partial least squares with regression model updating. They are so simple that they do not require any preliminary separation steps. Accuracy, precision and linearity ranges of these methods were determined. Moreover, specificity was assessed by analyzing synthetic mixtures of both drugs. The proposed methods were successfully applied for analysis of both drugs in their pharmaceutical formulation. The obtained results have been statistically compared to that of an official spectrophotometric method to give a conclusion that there is no significant difference between the proposed methods and the official ones with respect to accuracy and precision.

A suite of global, cross-scale topographic variables for environmental and biodiversity modeling

NASA Astrophysics Data System (ADS)

Amatulli, Giuseppe; Domisch, Sami; Tuanmu, Mao-Ning; Parmentier, Benoit; Ranipeta, Ajay; Malczyk, Jeremy; Jetz, Walter

2018-03-01

Topographic variation underpins a myriad of patterns and processes in hydrology, climatology, geography and ecology and is key to understanding the variation of life on the planet. A fully standardized and global multivariate product of different terrain features has the potential to support many large-scale research applications, however to date, such datasets are unavailable. Here we used the digital elevation model products of global 250 m GMTED2010 and near-global 90 m SRTM4.1dev to derive a suite of topographic variables: elevation, slope, aspect, eastness, northness, roughness, terrain roughness index, topographic position index, vector ruggedness measure, profile/tangential curvature, first/second order partial derivative, and 10 geomorphological landform classes. We aggregated each variable to 1, 5, 10, 50 and 100 km spatial grains using several aggregation approaches. While a cross-correlation underlines the high similarity of many variables, a more detailed view in four mountain regions reveals local differences, as well as scale variations in the aggregated variables at different spatial grains. All newly-developed variables are available for download at Data Citation 1 and for download and visualization at http://www.earthenv.org/topography.

Expanded solutions of force-free electrodynamics on general Kerr black holes

NASA Astrophysics Data System (ADS)

Li, Huiquan; Wang, Jiancheng

2017-07-01

In this work, expanded solutions of force-free magnetospheres on general Kerr black holes are derived through a radial distance expansion method. From the regular conditions both at the horizon and at spatial infinity, two previously known asymptotical solutions (one of them is actually an exact solution) are identified as the only solutions that satisfy the same conditions at the two boundaries. Taking them as initial conditions at the boundaries, expanded solutions up to the first few orders are derived by solving the stream equation order by order. It is shown that our extension of the exact solution can (partially) cure the problems of the solution: it leads to magnetic domination and a mostly timelike current for restricted parameters.

Method development for the determination of coumarin compounds by capillary electrophoresis with indirect laser-induced fluorescence detection.

PubMed

Wang, Weiping; Tang, Jianghong; Wang, Shumin; Zhou, Lei; Hu, Zhide

2007-04-27

A capillary zone electrophoresis (CZE) with indirect laser-induced fluorescence detection (ILIFD) method is described for the simultaneous determination of esculin, esculetin, isofraxidin, genistein, naringin and sophoricoside. The baseline separation was achieved within 5 min with running buffer (pH 9.4) composed of 5mM borate, 20% methanol (v/v) as organic modifier, 10(-7)M fluorescein sodium as background fluorophore and 20 kV of applied voltage at 30 degrees C of cartridge temperature. Good linearity relationships (correlation coefficients >0.9900) between the second-order derivative peak-heights (RFU) and concentrations of the analytes (mol L(-1)) were obtained. The detection limits for all analytes in second-order derivative electrophoregrams were in the range of 3.8-15 microM. The RSD data of intra-day for migration times and second-order derivative peak-height were less than 0.95 and 5.02%, respectively. This developed method was applied to the analysis of the courmin compounds in herb plants with recoveries in the range of 94.7-102.1%. In this work, although the detection sensitivity was lower than that of direct LIF, yet the method would extend the application range of LIF detection.

Variable horizon in a peridynamic medium

DOE PAGES

Silling, Stewart A.; Littlewood, David J.; Seleson, Pablo

2015-12-10

Here, a notion of material homogeneity is proposed for peridynamic bodies with variable horizon but constant bulk properties. A relation is derived that scales the force state according to the position-dependent horizon while keeping the bulk properties unchanged. Using this scaling relation, if the horizon depends on position, artifacts called ghost forces may arise in a body under a homogeneous deformation. These artifacts depend on the second derivative of the horizon and can be reduced by employing a modified equilibrium equation using a new quantity called the partial stress. Bodies with piecewise constant horizon can be modeled without ghost forcesmore » by using a simpler technique called a splice. As a limiting case of zero horizon, both the partial stress and splice techniques can be used to achieve local-nonlocal coupling. Computational examples, including dynamic fracture in a one-dimensional model with local-nonlocal coupling, illustrate the methods.« less

Identification of biomarkers associated with partial epithelial to mesenchymal transition in the secretome of slug over-expressing hepatocellular carcinoma cells.

PubMed

Karaosmanoğlu, Oğuzhan; Banerjee, Sreeparna; Sivas, Hülya

2018-06-01

Hepatocellular carcinoma (HCC) is the second leading cause of cancer-related deaths worldwide. Complete epithelial to mesenchymal transition (EMT) has long been considered as a crucial step for metastasis initiation. It has, however, become apparent that many carcinoma cells can metastasize without complete loss of epithelial traits or with incomplete gain of mesenchymal traits, i.e., partial EMT. Here, we aimed to determine the similarities and differences between complete and partial EMT through over-expression of the EMT-associated transcription factor Slug in different HCC-derived cell lines. Slug over-expressing HCC-derived HepG2 and Huh7 cells were assessed for their EMT, chemo-resistance and stemness features using Western blotting, qRT-PCR, neutral red uptake, doxorubicin accumulation and scratch wound healing assays. We also collected conditioned media from Slug over-expressing HCC cells and analyzed its exosomal protein content for the presence of chemo-resistance and partial EMT markers using MALDI-TOF/TOF and ELISA assays, respectively. We found that Slug over-expression resulted in the induction of both complete and partial EMT in the different HCC-derived cell lines tested. Complete EMT was characterized by downregulation of E-cadherin and upregulation of ZEB2. Partial EMT was characterized by upregulation of E-cadherin and downregulation of vimentin and ZEB2. Interestingly, we found that Slug induced chemo-resistance through downregulation of the ATP binding cassette (ABC) transporter ABCB1 and upregulation of the ABC transporter ABCG2, as well as through expression of CD133, a stemness marker that exhibited a similar expression pattern in cells with either a complete or a partial EMT phenotype. In addition, we found that Slug-mediated partial EMT was associated with enhanced exosomal secretion of post-translationally modified fibronectin 1 (FN1), collagen type II alpha 1 (COL2A1) and native fibrinogen gamma chain (FGG). From our data we conclude that the exosomal proteins identified may be considered as potential non-invasive biomarkers for chemo-resistance and partial EMT in HCC.

Conductance scaling of junctions of Luttinger-liquid wires out of equilibrium

NASA Astrophysics Data System (ADS)

Aristov, D. N.; Wölfle, P.

2018-05-01

We develop the renormalization group theory of the conductances of N -lead junctions of spinless Luttinger-liquid wires as functions of bias voltages applied to N independent Fermi-liquid reservoirs. Based on the perturbative results up to second order in the interaction we demonstrate that the conductances obey scaling. The corresponding renormalization group β functions are derived up to second order.

Hydrodynamic Drag Reduction

DTIC Science & Technology

2015-04-01

Computational Engineering unstructured RANS/LES/DES solver , Tenasi, was used to predict drag and simulate the free surface flow around the ACV over a...using a second-order accurate Roe approximate Riemann scheme, while viscous fluxes are evaluated using a second-order directional derivative approach...Predictions of rigid body ship motions for the SI75 container ship in incident waves and methodology for a one-way coupling of the Tenasi flow solver

Hypergeometric Series Solution to a Class of Second-Order Boundary Value Problems via Laplace Transform with Applications to Nanofluids

NASA Astrophysics Data System (ADS)

Ebaid, Abdelhalim; Wazwaz, Abdul-Majid; Alali, Elham; Masaedeh, Basem S.

2017-03-01

Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.

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

Motohashi, Hayato; Noui, Karim; Laboratoire APC - Astroparticule et Cosmologie,Université Paris Diderot Paris 7,75013 Paris

In the context of classical mechanics, we study the conditions under which higher-order derivative theories can evade the so-called Ostrogradsky instability. More precisely, we consider general Lagrangians with second order time derivatives, of the form L(ϕ{sup ¨a}, ϕ-dot {sup a},ϕ{sup a}; q-dot {sup i},q{sup i}) with a=1,⋯,n and i=1,⋯,m. For n=1, assuming that the q{sup i}’s form a nondegenerate subsystem, we confirm that the degeneracy of the kinetic matrix eliminates the Ostrogradsky instability. The degeneracy implies, in the Hamiltonian formulation of the theory, the existence of a primary constraint, which generates a secondary constraint, thus eliminating the Ostrogradsky ghost. Formore » n>1, we show that, in addition to the degeneracy of the kinetic matrix, one needs to impose extra conditions to ensure the presence of a sufficient number of secondary constraints that can eliminate all the Ostrogradsky ghosts. When these conditions that ensure the disappearance of the Ostrogradsky instability are satisfied, we show that the Euler-Lagrange equations, which involve a priori higher order derivatives, can be reduced to a second order system.« less

On the 4D generalized Proca action for an Abelian vector field

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

Allys, Erwan; Almeida, Juan P. Beltrán; Peter, Patrick

We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated Stückelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the Stückelberg field describing the longitudinal mode, which is in agreement with the results of http://dx.doi.org/10.1088/1475-7516/2014/05/015 and http://dx.doi.org/10.1016/j.physletb.2016.04.017 and complements those of http://dx.doi.org/10.1088/1475-7516/2016/02/004.more » We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field A{sub μ}, the Faraday tensor F{sub μν} and its Hodge dual F-tilde{sub μν}.« less

Mass transport in morphogenetic processes: A second gradient theory for volumetric growth and material remodeling

NASA Astrophysics Data System (ADS)

Ciarletta, P.; Ambrosi, D.; Maugin, G. A.

2012-03-01

In this work, we derive a novel thermo-mechanical theory for growth and remodeling of biological materials in morphogenetic processes. This second gradient hyperelastic theory is the first attempt to describe both volumetric growth and mass transport phenomena in a single-phase continuum model, where both stress- and shape-dependent growth regulations can be investigated. The diffusion of biochemical species (e.g. morphogens, growth factors, migration signals) inside the material is driven by configurational forces, enforced in the balance equations and in the set of constitutive relations. Mass transport is found to depend both on first- and on second-order material connections, possibly withstanding a chemotactic behavior with respect to diffusing molecules. We find that the driving forces of mass diffusion can be written in terms of covariant material derivatives reflecting, in a purely geometrical manner, the presence of a (first-order) torsion and a (second-order) curvature. Thermodynamical arguments show that the Eshelby stress and hyperstress tensors drive the rearrangement of the first- and second-order material inhomogeneities, respectively. In particular, an evolution law is proposed for the first-order transplant, extending a well-known result for inelastic materials. Moreover, we define the first stress-driven evolution law of the second-order transplant in function of the completely material Eshelby hyperstress. The theory is applied to two biomechanical examples, showing how an Eshelbian coupling can coordinate volumetric growth, mass transport and internal stress state, both in physiological and pathological conditions. Finally, possible applications of the proposed model are discussed for studying the unknown regulation mechanisms in morphogenetic processes, as well as for optimizing scaffold architecture in regenerative medicine and tissue engineering.

Equations of condition for high order Runge-Kutta-Nystrom formulae

NASA Technical Reports Server (NTRS)

Bettis, D. G.

1974-01-01

Derivation of the equations of condition of order eight for a general system of second-order differential equations approximated by the basic Runge-Kutta-Nystrom algorithm. For this general case, the number of equations of condition is considerably larger than for the special case where the first derivative is not present. Specifically, it is shown that, for orders two through eight, the number of equations for each order is 1, 1, 1, 2, 3, 5, and 9 for the special case and is 1, 1, 2, 5, 13, 34, and 95 for the general case.

Reduced Order Podolsky Model

NASA Astrophysics Data System (ADS)

Thibes, Ronaldo

2017-02-01

We perform the canonical and path integral quantizations of a lower-order derivatives model describing Podolsky's generalized electrodynamics. The physical content of the model shows an auxiliary massive vector field coupled to the usual electromagnetic field. The equivalence with Podolsky's original model is studied at classical and quantum levels. Concerning the dynamical time evolution, we obtain a theory with two first-class and two second-class constraints in phase space. We calculate explicitly the corresponding Dirac brackets involving both vector fields. We use the Senjanovic procedure to implement the second-class constraints and the Batalin-Fradkin-Vilkovisky path integral quantization scheme to deal with the symmetries generated by the first-class constraints. The physical interpretation of the results turns out to be simpler due to the reduced derivatives order permeating the equations of motion, Dirac brackets and effective action.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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.

The fifth-order partial differential equation for the description of the α + β Fermi-Pasta-Ulam model

NASA Astrophysics Data System (ADS)

Kudryashov, Nikolay A.; Volkov, Alexandr K.

2017-01-01

We study a new nonlinear partial differential equation of the fifth order for the description of perturbations in the Fermi-Pasta-Ulam mass chain. This fifth-order equation is an expansion of the Gardner equation for the description of the Fermi-Pasta-Ulam model. We use the potential of interaction between neighbouring masses with both quadratic and cubic terms. The equation is derived using the continuous limit. Unlike the previous works, we take into account higher order terms in the Taylor series expansions. We investigate the equation using the Painlevé approach. We show that the equation does not pass the Painlevé test and can not be integrated by the inverse scattering transform. We use the logistic function method and the Laurent expansion method to find travelling wave solutions of the fifth-order equation. We use the pseudospectral method for the numerical simulation of wave processes, described by the equation.

Gas evolution from spheres

NASA Astrophysics Data System (ADS)

Longhurst, G. R.

1991-04-01

Gas evolution from spherical solids or liquids where no convective processes are active is analyzed. Three problem classes are considered: (1) constant concentration boundary, (2) Henry's law (first order) boundary, and (3) Sieverts' law (second order) boundary. General expressions are derived for dimensionless times and transport parameters appropriate to each of the classes considered. However, in the second order case, the non-linearities of the problem require the presence of explicit dimensional variables in the solution. Sample problems are solved to illustrate the method.

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.

Identification of Medicinal Mugua Origin by Near Infrared Spectroscopy Combined with Partial Least-squares Discriminant Analysis.

PubMed

Han, Bangxing; Peng, Huasheng; Yan, Hui

2016-01-01

Mugua is a common Chinese herbal medicine. There are three main medicinal origin places in China, Xuancheng City Anhui Province, Qijiang District Chongqing City, Yichang City, Hubei Province, and suitable for food origin places Linyi City Shandong Province. To construct a qualitative analytical method to identify the origin of medicinal Mugua by near infrared spectroscopy (NIRS). Partial least squares discriminant analysis (PLSDA) model was established after the Mugua derived from five different origins were preprocessed by the original spectrum. Moreover, the hierarchical cluster analysis was performed. The result showed that PLSDA model was established. According to the relationship of the origins-related important score and wavenumber, and K-mean cluster analysis, the Muguas derived from different origins were effectively identified. NIRS technology can quickly and accurately identify the origin of Mugua, provide a new method and technology for the identification of Chinese medicinal materials. After preprocessed by D1+autoscale, more peaks were increased in the preprocessed Mugua in the near infrared spectrumFive latent variable scores could reflect the information related to the origin place of MuguaOrigins of Mugua were well-distinguished according to K. mean value clustering analysis. Abbreviations used: TCM: Traditional Chinese Medicine, NIRS: Near infrared spectroscopy, SG: Savitzky-Golay smoothness, D1: First derivative, D2: Second derivative, SNV: Standard normal variable transformation, MSC: Multiplicative scatter correction, PLSDA: Partial least squares discriminant analysis, LV: Latent variable, VIP scores: Important score.

Multistability of second-order competitive neural networks with nondecreasing saturated activation functions.

PubMed

Nie, Xiaobing; Cao, Jinde

2011-11-01

In this paper, second-order interactions are introduced into competitive neural networks (NNs) and the multistability is discussed for second-order competitive NNs (SOCNNs) with nondecreasing saturated activation functions. Firstly, based on decomposition of state space, Cauchy convergence principle, and inequality technique, some sufficient conditions ensuring the local exponential stability of 2N equilibrium points are derived. Secondly, some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region. Thirdly, the theory is extended to more general saturated activation functions with 2r corner points and a sufficient criterion is given under which the SOCNNs can have (r+1)N locally exponentially stable equilibrium points. Even if there is no second-order interactions, the obtained results are less restrictive than those in some recent works. Finally, three examples with their simulations are presented to verify the theoretical analysis.

Absorbing boundary conditions for second-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Jiang, Hong; Wong, Yau Shu

1989-01-01

A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.

On the Asymmetric Zero-Range in the Rarefaction Fan

NASA Astrophysics Data System (ADS)

Gonçalves, Patrícia

2014-02-01

We consider one-dimensional asymmetric zero-range processes starting from a step decreasing profile leading, in the hydrodynamic limit, to the rarefaction fan of the associated hydrodynamic equation. Under that initial condition, and for totally asymmetric jumps, we show that the weighted sum of joint probabilities for second class particles sharing the same site is convergent and we compute its limit. For partially asymmetric jumps, we derive the Law of Large Numbers for a second class particle, under the initial configuration in which all positive sites are empty, all negative sites are occupied with infinitely many first class particles and there is a single second class particle at the origin. Moreover, we prove that among the infinite characteristics emanating from the position of the second class particle it picks randomly one of them. The randomness is given in terms of the weak solution of the hydrodynamic equation, through some sort of renormalization function. By coupling the constant-rate totally asymmetric zero-range with the totally asymmetric simple exclusion, we derive limiting laws for more general initial conditions.

Design of a compensation for an ARMA model of a discrete time system. M.S. Thesis

NASA Technical Reports Server (NTRS)

Mainemer, C. I.

1978-01-01

The design of an optimal dynamic compensator for a multivariable discrete time system is studied. Also the design of compensators to achieve minimum variance control strategies for single input single output systems is analyzed. In the first problem the initial conditions of the plant are random variables with known first and second order moments, and the cost is the expected value of the standard cost, quadratic in the states and controls. The compensator is based on the minimum order Luenberger observer and it is found optimally by minimizing a performance index. Necessary and sufficient conditions for optimality of the compensator are derived. The second problem is solved in three different ways; two of them working directly in the frequency domain and one working in the time domain. The first and second order moments of the initial conditions are irrelevant to the solution. Necessary and sufficient conditions are derived for the compensator to minimize the variance of the output.

Application of an Extended Parabolic Equation to the Calculation of the Mean Field and the Transverse and Longitudinal Mutual Coherence Functions Within Atmospheric Turbulence

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2005-01-01

Solutions are derived for the generalized mutual coherence function (MCF), i.e., the second order moment, of a random wave field propagating through a random medium within the context of the extended parabolic equation. Here, "generalized" connotes the consideration of both the transverse as well as the longitudinal second order moments (with respect to the direction of propagation). Such solutions will afford a comparison between the results of the parabolic equation within the pararaxial approximation and those of the wide-angle extended theory. To this end, a statistical operator method is developed which gives a general equation for an arbitrary spatial statistical moment of the wave field. The generality of the operator method allows one to obtain an expression for the second order field moment in the direction longitudinal to the direction of propagation. Analytical solutions to these equations are derived for the Kolmogorov and Tatarskii spectra of atmospheric permittivity fluctuations within the Markov approximation.

Deriving preference order of post-mining land-uses through MLSA framework: application of an outranking technique

NASA Astrophysics Data System (ADS)

Soltanmohammadi, Hossein; Osanloo, Morteza; Aghajani Bazzazi, Abbas

2009-08-01

This study intends to take advantage of a previously developed framework for mined land suitability analysis (MLSA) consisted of economical, social, technical and mine site factors to achieve a partial and also a complete pre-order of feasible post-mining land-uses. Analysis by an outranking multi-attribute decision-making (MADM) technique, called PROMETHEE (preference ranking organization method for enrichment evaluation), was taken into consideration because of its clear advantages on the field of MLSA as compared with MADM ranking techniques. Application of the proposed approach on a mined land can be completed through some successive steps. First, performance of the MLSA attributes is scored locally by each individual decision maker (DM). Then the assigned performance scores are normalized and the deviation amplitudes of non-dominated alternatives are calculated. Weights of the attributes are calculated by another MADM technique namely, analytical hierarchy process (AHP) in a separate procedure. Using the Gaussian preference function beside the weights, the preference indexes of the land-use alternatives are obtained. Calculation of the outgoing and entering flows of the alternatives and one by one comparison of these values will lead to partial pre-order of them and calculation of the net flows, will lead to a ranked preference for each land-use. At the final step, utilizing the PROMETHEE group decision support system which incorporates judgments of all the DMs, a consensual ranking can be derived. In this paper, preference order of post-mining land-uses for a hypothetical mined land has been derived according to judgments of one DM to reveal applicability of the proposed approach.

On the sensitivity of complex, internally coupled systems

NASA Technical Reports Server (NTRS)

Sobieszczanskisobieski, Jaroslaw

1988-01-01

A method is presented for computing sensitivity derivatives with respect to independent (input) variables for complex, internally coupled systems, while avoiding the cost and inaccuracy of finite differencing performed on the entire system analysis. The method entails two alternative algorithms: the first is based on the classical implicit function theorem formulated on residuals of governing equations, and the second develops the system sensitivity equations in a new form using the partial (local) sensitivity derivatives of the output with respect to the input of each part of the system. A few application examples are presented to illustrate the discussion.

Partitioning of organophosphorus pesticides into phosphatidylcholine small unilamellar vesicles studied by second-derivative spectrophotometry.

PubMed

Takegami, Shigehiko; Kitamura, Keisuke; Ohsugi, Mayuko; Ito, Aya; Kitade, Tatsuya

2015-06-15

In order to quantitatively examine the lipophilicity of the widely used organophosphorus pesticides (OPs) chlorfenvinphos (CFVP), chlorpyrifos-methyl (CPFM), diazinon (DZN), fenitrothion (FNT), fenthion (FT), isofenphos (IFP), profenofos (PFF) and pyraclofos (PCF), their partition coefficient (Kp) values between phosphatidylcholine (PC) small unilamellar vesicles (SUVs) and water (liposome-water system) were determined by second-derivative spectrophotometry. The second-derivative spectra of these OPs in the presence of PC SUV showed a bathochromic shift according to the increase in PC concentration and distinct derivative isosbestic points, demonstrating the complete elimination of the residual background signal effects that were observed in the absorption spectra. The Kp values were calculated from the second-derivative intensity change induced by addition of PC SUV and obtained with a good precision of R.S.D. below 10%. The Kp values were in the order of CPFM>FT>PFF>PCF>IFP>CFVP>FNT⩾DZN and did not show a linear correlation relationship with the reported partition coefficients obtained using an n-octanol-water system (R(2)=0.530). Also, the results quantitatively clarified the effect of chemical-group substitution in OPs on their lipophilicity. Since the partition coefficient for the liposome-water system is more effective for modeling the quantitative structure-activity relationship than that for the n-octanol-water system, the obtained results are toxicologically important for estimating the accumulation of these OPs in human cell membranes. Copyright © 2015 Elsevier B.V. All rights reserved.

Comprehensive Reactive Receiver Modeling for Diffusive Molecular Communication Systems: Reversible Binding, Molecule Degradation, and Finite Number of Receptors.

PubMed

Ahmadzadeh, Arman; Arjmandi, Hamidreza; Burkovski, Andreas; Schober, Robert

2016-10-01

This paper studies the problem of receiver modeling in molecular communication systems. We consider the diffusive molecular communication channel between a transmitter nano-machine and a receiver nano-machine in a fluid environment. The information molecules released by the transmitter nano-machine into the environment can degrade in the channel via a first-order degradation reaction and those that reach the receiver nano-machine can participate in a reversible bimolecular reaction with receiver receptor proteins. Thereby, we distinguish between two scenarios. In the first scenario, we assume that the entire surface of the receiver is covered by receptor molecules. We derive a closed-form analytical expression for the expected received signal at the receiver, i.e., the expected number of activated receptors on the surface of the receiver. Then, in the second scenario, we consider the case where the number of receptor molecules is finite and the uniformly distributed receptor molecules cover the receiver surface only partially. We show that the expected received signal for this scenario can be accurately approximated by the expected received signal for the first scenario after appropriately modifying the forward reaction rate constant. The accuracy of the derived analytical results is verified by Brownian motion particle-based simulations of the considered environment, where we also show the impact of the effect of receptor occupancy on the derived analytical results.

Nonsingular expansions of the gravity potential and its derivatives at satellite altitudes in the ellipsoidal coordinate system

NASA Astrophysics Data System (ADS)

Vershkov, A. N.; Petrovskaya, M. S.

2016-11-01

The series in ellipsoidal harmonics for derivatives of the Earth's gravity potential are used only on the reference ellipsoid enveloping the Earth due to their very complex mathematical structure. In the current study, the series in ellipsoidal harmonics are constructed for first- and second-order derivatives of the potential at satellite altitudes; their structure is similar to the series on the reference ellipsoid. The point P is chosen at a random satellite altitude; then, the ellipsoid of revolution is described, which passes through this point and is confocal to the reference ellipsoid. An object-centered coordinate system with the origin at the point P is considered. Using a sequence of transformations, the nonsingular series in ellipsoidal harmonics is constructed for first and second derivatives of the potential in the object-centered coordinate system. These series can be applied to develop a model of the Earth's potential, based on combined use of surface gravitational force measurements, data on the satellite orbital position, its acceleration, or measurements of the gravitational force gradients of the first and second order. The technique is applicable to any other planet of the Solar System.

Irreversible thermodynamics of Poisson processes with reaction.

PubMed

Méndez, V; Fort, J

1999-11-01

A kinetic model is derived to study the successive movements of particles, described by a Poisson process, as well as their generation. The irreversible thermodynamics of this system is also studied from the kinetic model. This makes it possible to evaluate the differences between thermodynamical quantities computed exactly and up to second-order. Such differences determine the range of validity of the second-order approximation to extended irreversible thermodynamics.

Comparison of day snorkeling, night snorkeling, and electrofishing to estimate bull trout abundance and size structure in a second-order Idaho stream

Treesearch

Russell F. Thurow; Daniel J. Schill

1996-01-01

Biologists lack sufficient information to develop protocols for sampling the abundance and size structure of bull trout Salvelinus confluentus. We compared summer estimates of the abundance and size structure of bull trout in a second-order central Idaho stream, derived by day snorkeling, night snorkeling, and electrofishing. We also examined the influence of water...

Toward a better understanding of helicopter stability derivatives

NASA Technical Reports Server (NTRS)

Hansen, R. S.

1982-01-01

An amended six degree of freedom helicopter stability and control derivative model was developed in which body acceleration and control rate derivatives were included in the Taylor series expansion. These additional derivatives were derived from consideration of the effects of the higher order rotor flapping dynamics, which are known to be inadequately represented in the conventional six degree of freedom, quasistatic stability derivative model. The amended model was a substantial improvement over the conventional model, effectively doubling the unsable bandwidth and providing a more accurate representation of the short period and cross axis characteristics. Further investigations assessed the applicability of the two stability derivative model structures for flight test parameter identification. Parameters were identified using simulation data generated from a higher order base line model having sixth order rotor tip path plane dynamics. Three lower order models were identified: one using the conventional stability derivative model structure, a second using the amended six degree of freedom model structure, and a third model having eight degrees of freedom that included a simplified rotor tip path plane tilt representation.

Spacecraft attitude determination using a second-order nonlinear filter

NASA Technical Reports Server (NTRS)

Vathsal, S.

1987-01-01

The stringent attitude determination accuracy and faster slew maneuver requirements demanded by present-day spacecraft control systems motivate the development of recursive nonlinear filters for attitude estimation. This paper presents the second-order filter development for the estimation of attitude quaternion using three-axis gyro and star tracker measurement data. Performance comparisons have been made by computer simulation of system models and filter mechanization. It is shown that the second-order filter consistently performs better than the extended Kalman filter when the performance index of the root sum square estimation error of the quaternion vector is compared. The second-order filter identifies the gyro drift rates faster than the extended Kalman filter. The uniqueness of this algorithm is the online generation of the time-varying process and measurement noise covariance matrices, derived as a function or the process and measurement nonlinearity, respectively.

Second-order small disturbance theory for hypersonic flow over power-law bodies. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Townsend, J. C.

1974-01-01

A mathematical method for determining the flow field about power-law bodies in hypersonic flow conditions is developed. The second-order solutions, which reflect the effects of the second-order terms in the equations, are obtained by applying the method of small perturbations in terms of body slenderness parameter to the zeroth-order solutions. The method is applied by writing each flow variable as the sum of a zeroth-order and a perturbation function, each multiplied by the axial variable raised to a power. The similarity solutions are developed for infinite Mach number. All results obtained are for no flow through the body surface (as a boundary condition), but the derivation indicates that small amounts of blowing or suction through the wall can be accommodated.

Adjoint-based constant-mass partial derivatives

DOE PAGES

Favorite, Jeffrey A.

2017-09-01

In transport theory, adjoint-based partial derivatives with respect to mass density are constant-volume derivatives. Likewise, adjoint-based partial derivatives with respect to surface locations (i.e., internal interface locations and the outer system boundary) are constant-density derivatives. This study derives the constant-mass partial derivative of a response with respect to an internal interface location or the outer system boundary and the constant-mass partial derivative of a response with respect to the mass density of a region. Numerical results are given for a multiregion two-dimensional (r-z) cylinder for three very different responses: the uncollided gamma-ray flux at an external detector point, k effmore » of the system, and the total neutron leakage. Finally, results from the derived formulas compare extremely well with direct perturbation calculations.« less

Reionization and its imprint of the cosmic microwave background

NASA Technical Reports Server (NTRS)

Dodelson, Scott; Jubas, Jay M.

1995-01-01

Early reionization changes the pattern of anisotropies expected in the cosmic microwave backgrond. To explore these changes, we derive from first principles the equations governing anisotropies, focusing on the interactions of photons with electrons. Vishniac (1987) claimed that second-order terms can be large in a reionized universe, so we derive equations correct to second order in the perturbations. There are many more second-order terms than were considered by Vishniac. To understand the basic physics involved, we present a simple analytic approximation to the first-order equation. Then, turning to the second order equation, we show that the Vishniac term is indeed the only important one. We also present numerical results for a variety of ionization histories (in a standard cold dark matter universe) and show quantitatively how the signal in several experiments depends on the ionization history. The most pronounced indication of a reionized universe would be seen in very small scale experiments; the expected signal in the Owens Valley experiment is smaller by a factor of order 10 if the last scattering surface is at a redshift z approximately = 100 as it would be if the universe were reionized very early. On slightly larger scales, the expected signal in a reionized universe is smaller than it would be with standard recombination, but only a factor of 2 or so. The signal is even smaller in these experiments in the intermediate case where some photons last scattered at the standard recombination epoch.

Finite-difference time-domain synthesis of infrasound propagation through an absorbing atmosphere.

PubMed

de Groot-Hedlin, C

2008-09-01

Equations applicable to finite-difference time-domain (FDTD) computation of infrasound propagation through an absorbing atmosphere are derived and examined in this paper. It is shown that over altitudes up to 160 km, and at frequencies relevant to global infrasound propagation, i.e., 0.02-5 Hz, the acoustic absorption in dB/m varies approximately as the square of the propagation frequency plus a small constant term. A second-order differential equation is presented for an atmosphere modeled as a compressible Newtonian fluid with low shear viscosity, acted on by a small external damping force. It is shown that the solution to this equation represents pressure fluctuations with the attenuation indicated above. Increased dispersion is predicted at altitudes over 100 km at infrasound frequencies. The governing propagation equation is separated into two partial differential equations that are first order in time for FDTD implementation. A numerical analysis of errors inherent to this FDTD method shows that the attenuation term imposes additional stability constraints on the FDTD algorithm. Comparison of FDTD results for models with and without attenuation shows that the predicted transmission losses for the attenuating media agree with those computed from synthesized waveforms.

A second-order closure analysis of turbulent diffusion flames. [combustion physics

NASA Technical Reports Server (NTRS)

Varma, A. K.; Fishburne, E. S.; Beddini, R. A.

1977-01-01

A complete second-order closure computer program for the investigation of compressible, turbulent, reacting shear layers was developed. The equations for the means and the second order correlations were derived from the time-averaged Navier-Stokes equations and contain third order and higher order correlations, which have to be modeled in terms of the lower-order correlations to close the system of equations. In addition to fluid mechanical turbulence models and parameters used in previous studies of a variety of incompressible and compressible shear flows, a number of additional scalar correlations were modeled for chemically reacting flows, and a typical eddy model developed for the joint probability density function for all the scalars. The program which is capable of handling multi-species, multistep chemical reactions, was used to calculate nonreacting and reacting flows in a hydrogen-air diffusion flame.

A novel method for calculating and measuring the second-order buoyancy experienced by a magnet immersed in magnetic fluid

NASA Astrophysics Data System (ADS)

Yu, Jun; Hao, Du; Li, Decai

2018-01-01

The phenomenon whereby an object whose density is greater than magnetic fluid can be suspended stably in magnetic fluid under the magnetic field is one of the peculiar properties of magnetic fluids. Examples of applications based on the peculiar properties of magnetic fluid are sensors and actuators, dampers, positioning systems and so on. Therefore, the calculation and measurement of magnetic levitation force of magnetic fluid is of vital importance. This paper concerns the peculiar second-order buoyancy experienced by a magnet immersed in magnetic fluid. The expression for calculating the second-order buoyancy was derived, and a novel method for calculating and measuring the second-order buoyancy was proposed based on the expression. The second-order buoyancy was calculated by ANSYS and measured experimentally using the novel method. To verify the novel method, the second-order buoyancy was measured experimentally with a nonmagnetic rod stuck on the top surface of the magnet. The results of calculations and experiments show that the novel method for calculating the second-order buoyancy is correct with high accuracy. In addition, the main causes of error were studied in this paper, including magnetic shielding of magnetic fluid and the movement of magnetic fluid in a nonuniform magnetic field.

Modeling self-consistent multi-class dynamic traffic flow

NASA Astrophysics Data System (ADS)

Cho, Hsun-Jung; Lo, Shih-Ching

2002-09-01

In this study, we present a systematic self-consistent multiclass multilane traffic model derived from the vehicular Boltzmann equation and the traffic dispersion model. The multilane domain is considered as a two-dimensional space and the interaction among vehicles in the domain is described by a dispersion model. The reason we consider a multilane domain as a two-dimensional space is that the driving behavior of road users may not be restricted by lanes, especially motorcyclists. The dispersion model, which is a nonlinear Poisson equation, is derived from the car-following theory and the equilibrium assumption. Under the concept that all kinds of users share the finite section, the density is distributed on a road by the dispersion model. In addition, the dynamic evolution of the traffic flow is determined by the systematic gas-kinetic model derived from the Boltzmann equation. Multiplying Boltzmann equation by the zeroth, first- and second-order moment functions, integrating both side of the equation and using chain rules, we can derive continuity, motion and variance equation, respectively. However, the second-order moment function, which is the square of the individual velocity, is employed by previous researches does not have physical meaning in traffic flow. Although the second-order expansion results in the velocity variance equation, additional terms may be generated. The velocity variance equation we propose is derived from multiplying Boltzmann equation by the individual velocity variance. It modifies the previous model and presents a new gas-kinetic traffic flow model. By coupling the gas-kinetic model and the dispersion model, a self-consistent system is presented.

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.

Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

NASA Astrophysics Data System (ADS)

Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

2018-06-01

The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

The CoRoT target HD 49933: a possible seismic signature of heavy elements ionization in the deep convective zone

NASA Astrophysics Data System (ADS)

Brito, Ana; Lopes, Ilídio

2017-04-01

We use a seismic diagnostic, based on the derivative of the phase shift of the acoustic waves reflected by the surface, to probe the outer layers of the star HD 49933. This diagnostic is particularly sensitive to partial ionization processes occurring above the base of the convective zone. The regions of partial ionization of light elements, hydrogen and helium, have well-known seismological signatures. In this work, we detect a different seismic signature in the acoustic frequencies, which we showed to correspond to the location where the partial ionization of heavy elements occurs. The location of the corresponding acoustic glitch lies between the region of the second ionization of helium and the base of the convective zone, approximately 5 per cent below the surface of the stars.

Pressure Dependences of Elastic Constants of AMg6 Aluminum-Magnesium Alloy and n-AMg6/C60 Nanocomposite Alloy

NASA Astrophysics Data System (ADS)

Prokhorov, V. M.; Gromnitskaya, E. L.

2018-04-01

The ultrasonic study results for dependence of the elastic wave velocities and second-order elasticity coefficients of the polycrystalline aluminum alloy AMg6 and its nanocomposite n-AMg6/C60 on hydrostatic pressure up to 1.6 GPa have been described. The ultrasonic research has been carried out using a highpressure ultrasonic piezometer based on the piston-cylinder device. The pressure derivatives of the secondorder elastic constants of these materials established in the present study have been compared with the results of the third-order elastic constants measurements of the test alloys using the Thurston-Brugger method. Involving available literature data, we determined the relationships between the pressure derivatives of the second-order elastic constants of the AMg6 alloy and the Mg-content and nanostructuring.

Automated symbolic calculations in nonequilibrium thermodynamics

NASA Astrophysics Data System (ADS)

Kröger, Martin; Hütter, Markus

2010-12-01

We cast the Jacobi identity for continuous fields into a local form which eliminates the need to perform any partial integration to the expense of performing variational derivatives. This allows us to test the Jacobi identity definitely and efficiently and to provide equations between different components defining a potential Poisson bracket. We provide a simple Mathematica TM notebook which allows to perform this task conveniently, and which offers some additional functionalities of use within the framework of nonequilibrium thermodynamics: reversible equations of change for fields, and the conservation of entropy during the reversible dynamics. Program summaryProgram title: Poissonbracket.nb Catalogue identifier: AEGW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGW_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.: 227 952 No. of bytes in distributed program, including test data, etc.: 268 918 Distribution format: tar.gz Programming language: Mathematica TM 7.0 Computer: Any computer running Mathematica TM 6.0 and later versions Operating system: Linux, MacOS, Windows RAM: 100 Mb Classification: 4.2, 5, 23 Nature of problem: Testing the Jacobi identity can be a very complex task depending on the structure of the Poisson bracket. The Mathematica TM notebook provided here solves this problem using a novel symbolic approach based on inherent properties of the variational derivative, highly suitable for the present tasks. As a by product, calculations performed with the Poisson bracket assume a compact form. Solution method: The problem is first cast into a form which eliminates the need to perform partial integration for arbitrary functionals at the expense of performing variational derivatives. The corresponding equations are conveniently obtained using the symbolic programming environment Mathematica TM. Running time: For the test cases and most typical cases in the literature, the running time is of the order of seconds or minutes, respectively.

Students' Understanding of Mathematical Expressions in Physical Chemistry Contexts: An Analysis Using Sherin's Symbolic Forms

ERIC Educational Resources Information Center

Becker, Nicole; Towns, Marcy

2012-01-01

Undergraduate physical chemistry courses require students to be proficient in calculus in order to develop an understanding of thermodynamics concepts. Here we present the findings of a study that examines student understanding of mathematical expressions, including partial derivative expressions, in two undergraduate physical chemistry courses.…

Estimating of higher order velocity moments and their derivatives in boundary layer by Smoke Image Velocimetry

NASA Astrophysics Data System (ADS)

Mikheev, N. I.; Goltsman, A. E.; Salekhova, I. G.; Saushin, I. I.

2017-11-01

The results of an experimental evaluation of the third-order moments profiles of velocity fluctuations and their partial derivatives in a zero pressure-gradient turbulent boundary layer are presented. Profiles of characteristics are estimated on the basis of the dynamics of two-component instantaneous velocity vector fields measured by the optical method Smoke Image Velocimetry (SIV). Comparison SIV-measurements with the results of measurements by a thermoanemometer and DNS data with similar Reθ and Reτ showed good agreement between the profiles of +, +, ∂+/∂y+ и ∂+/∂y+ obtained by SIV and DNS.

Recursive least-squares learning algorithms for neural networks

NASA Astrophysics Data System (ADS)

Lewis, Paul S.; Hwang, Jenq N.

1990-11-01

This paper presents the development of a pair of recursive least squares (ItLS) algorithms for online training of multilayer perceptrons which are a class of feedforward artificial neural networks. These algorithms incorporate second order information about the training error surface in order to achieve faster learning rates than are possible using first order gradient descent algorithms such as the generalized delta rule. A least squares formulation is derived from a linearization of the training error function. Individual training pattern errors are linearized about the network parameters that were in effect when the pattern was presented. This permits the recursive solution of the least squares approximation either via conventional RLS recursions or by recursive QR decomposition-based techniques. The computational complexity of the update is 0(N2) where N is the number of network parameters. This is due to the estimation of the N x N inverse Hessian matrix. Less computationally intensive approximations of the ilLS algorithms can be easily derived by using only block diagonal elements of this matrix thereby partitioning the learning into independent sets. A simulation example is presented in which a neural network is trained to approximate a two dimensional Gaussian bump. In this example RLS training required an order of magnitude fewer iterations on average (527) than did training with the generalized delta rule (6 1 BACKGROUND Artificial neural networks (ANNs) offer an interesting and potentially useful paradigm for signal processing and pattern recognition. The majority of ANN applications employ the feed-forward multilayer perceptron (MLP) network architecture in which network parameters are " trained" by a supervised learning algorithm employing the generalized delta rule (GDIt) [1 2]. The GDR algorithm approximates a fixed step steepest descent algorithm using derivatives computed by error backpropagatiori. The GDII algorithm is sometimes referred to as the backpropagation algorithm. However in this paper we will use the term backpropagation to refer only to the process of computing error derivatives. While multilayer perceptrons provide a very powerful nonlinear modeling capability GDR training can be very slow and inefficient. In linear adaptive filtering the analog of the GDR algorithm is the leastmean- squares (LMS) algorithm. Steepest descent-based algorithms such as GDR or LMS are first order because they use only first derivative or gradient information about the training error to be minimized. To speed up the training process second order algorithms may be employed that take advantage of second derivative or Hessian matrix information. Second order information can be incorporated into MLP training in different ways. In many applications especially in the area of pattern recognition the training set is finite. In these cases block learning can be applied using standard nonlinear optimization techniques [3 4 5].

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

Wintermeyer, Niklas; Winters, Andrew R., E-mail: awinters@math.uni-koeln.de; Gassner, Gregor J.

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving schememore » we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.« less

Activities, self-referent memory beliefs, and cognitive performance: evidence for direct and mediated relations.

PubMed

Jopp, Daniela; Hertzog, Christopher

2007-12-01

In this study, the authors investigated the role of activities and self-referent memory beliefs for cognitive performance in a life-span sample. A factor analysis identified 8 activity factors, including Developmental Activities, Experiential Activities, Social Activities, Physical Activities, Technology Use, Watching Television, Games, and Crafts. A second-order general activity factor was significantly related to a general factor of cognitive function as defined by ability tests. Structural regression models suggested that prediction of cognition by activity level was partially mediated by memory beliefs, controlling for age, education, health, and depressive affect. Models adding paths from general and specific activities to aspects of crystallized intelligence suggested additional unique predictive effects for some activities. In alternative models, nonsignificant effects of beliefs on activities were detected when cognition predicted both variables, consistent with the hypothesis that beliefs derive from monitoring cognition and have no influence on activity patterns. PsycINFO Database Record (c) 2008 APA, all rights reserved.

On multiple solutions of non-Newtonian Carreau fluid flow over an inclined shrinking sheet

NASA Astrophysics Data System (ADS)

Khan, Masood; Sardar, Humara; Gulzar, M. Mudassar; Alshomrani, Ali Saleh

2018-03-01

This paper presents the multiple solutions of a non-Newtonian Carreau fluid flow over a nonlinear inclined shrinking surface in presence of infinite shear rate viscosity. The governing boundary layer equations are derived for the Carreau fluid with infinite shear rate viscosity. The suitable transformations are employed to alter the leading partial differential equations to a set of ordinary differential equations. The consequential non-linear ODEs are solved numerically by an active numerical approach namely Runge-Kutta Fehlberg fourth-fifth order method accompanied by shooting technique. Multiple solutions are presented graphically and results are shown for various physical parameters. It is important to state that the velocity and momentum boundary layer thickness reduce with increasing viscosity ratio parameter in shear thickening fluid while opposite trend is observed for shear thinning fluid. Another important observation is that the wall shear stress is significantly decreased by the viscosity ratio parameter β∗ for the first solution and opposite trend is observed for the second solution.

Development of MCAERO wing design panel method with interactive graphics module

NASA Technical Reports Server (NTRS)

Hawk, J. D.; Bristow, D. R.

1984-01-01

A reliable and efficient iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical pressure distribution. The design process is initialized by using MCAERO (MCAIR 3-D Subsonic Potential Flow Analysis Code) to analyze a baseline configuration. A second program DMCAERO is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter by applying a first-order expansion to the baseline equations in MCAERO. This matrix is calculated only once but is used in each iteration cycle to calculate the geometry perturbation and to analyze the perturbed geometry. The potential on the new geometry is calculated by linear extrapolation from the baseline solution. This extrapolated potential is converted to velocity by numerical differentiation, and velocity is converted to pressure by using Bernoulli's equation. There is an interactive graphics option which allows the user to graphically display the results of the design process and to interactively change either the geometry or the prescribed pressure distribution.

Simultaneous determination of α-asarone and β-asarone in Acorus tatarinowii using excitation-emission matrix fluorescence coupled with chemometrics methods

NASA Astrophysics Data System (ADS)

Bai, Xue-Mei; Liu, Tie; Liu, De-Long; Wei, Yong-Ju

2018-02-01

A chemometrics-assisted excitation-emission matrix (EEM) fluorescence method was proposed for simultaneous determination of α-asarone and β-asarone in Acorus tatarinowii. Using the strategy of combining EEM data with chemometrics methods, the simultaneous determination of α-asarone and β-asarone in the complex Traditional Chinese medicine system was achieved successfully, even in the presence of unexpected interferents. The physical or chemical separation step was avoided due to the use of ;mathematical separation;. Six second-order calibration methods were used including parallel factor analysis (PARAFAC), alternating trilinear decomposition (ATLD), alternating penalty trilinear decomposition (APTLD), self-weighted alternating trilinear decomposition (SWATLD), the unfolded partial least-squares (U-PLS) and multidimensional partial least-squares (N-PLS) with residual bilinearization (RBL). In addition, HPLC method was developed to further validate the presented strategy. Consequently, for the validation samples, the analytical results obtained by six second-order calibration methods were almost accurate. But for the Acorus tatarinowii samples, the results indicated a slightly better predictive ability of N-PLS/RBL procedure over other methods.

A second-order all-digital phase-locked loop

NASA Technical Reports Server (NTRS)

Holmes, J. K.; Tegnelia, C. R.

1974-01-01

A simple second-order digital phase-locked loop has been designed to synchronize itself to a square-wave subcarrier. Analysis and experimental performance are given for both acquisition behavior and steady-state phase error performance. In addition, the damping factor and the noise bandwidth are derived analytically. Although all the data are given for the square-wave subcarrier case, the results are applicable to arbitrary subcarriers that are odd symmetric about their transition region.

Optimized formulas for the gravitational field of a tesseroid

NASA Astrophysics Data System (ADS)

Grombein, Thomas; Seitz, Kurt; Heck, Bernhard

2013-07-01

Various tasks in geodesy, geophysics, and related geosciences require precise information on the impact of mass distributions on gravity field-related quantities, such as the gravitational potential and its partial derivatives. Using forward modeling based on Newton's integral, mass distributions are generally decomposed into regular elementary bodies. In classical approaches, prisms or point mass approximations are mostly utilized. Considering the effect of the sphericity of the Earth, alternative mass modeling methods based on tesseroid bodies (spherical prisms) should be taken into account, particularly in regional and global applications. Expressions for the gravitational field of a point mass are relatively simple when formulated in Cartesian coordinates. In the case of integrating over a tesseroid volume bounded by geocentric spherical coordinates, it will be shown that it is also beneficial to represent the integral kernel in terms of Cartesian coordinates. This considerably simplifies the determination of the tesseroid's potential derivatives in comparison with previously published methodologies that make use of integral kernels expressed in spherical coordinates. Based on this idea, optimized formulas for the gravitational potential of a homogeneous tesseroid and its derivatives up to second-order are elaborated in this paper. These new formulas do not suffer from the polar singularity of the spherical coordinate system and can, therefore, be evaluated for any position on the globe. Since integrals over tesseroid volumes cannot be solved analytically, the numerical evaluation is achieved by means of expanding the integral kernel in a Taylor series with fourth-order error in the spatial coordinates of the integration point. As the structure of the Cartesian integral kernel is substantially simplified, Taylor coefficients can be represented in a compact and computationally attractive form. Thus, the use of the optimized tesseroid formulas particularly benefits from a significant decrease in computation time by about 45 % compared to previously used algorithms. In order to show the computational efficiency and to validate the mathematical derivations, the new tesseroid formulas are applied to two realistic numerical experiments and are compared to previously published tesseroid methods and the conventional prism approach.

A nonlocal species concentration theory for diffusion and phase changes in electrode particles of lithium ion batteries

NASA Astrophysics Data System (ADS)

Zhang, Tao; Kamlah, Marc

2018-01-01

A nonlocal species concentration theory for diffusion and phase changes is introduced from a nonlocal free energy density. It can be applied, say, to electrode materials of lithium ion batteries. This theory incorporates two second-order partial differential equations involving second-order spatial derivatives of species concentration and an additional variable called nonlocal species concentration. Nonlocal species concentration theory can be interpreted as an extension of the Cahn-Hilliard theory. In principle, nonlocal effects beyond an infinitesimal neighborhood are taken into account. In this theory, the nonlocal free energy density is split into the penalty energy density and the variance energy density. The thickness of the interface between two phases in phase segregated states of a material is controlled by a normalized penalty energy coefficient and a characteristic interface length scale. We implemented the theory in COMSOL Multiphysics^{circledR } for a spherically symmetric boundary value problem of lithium insertion into a Li_xMn_2O_4 cathode material particle of a lithium ion battery. The two above-mentioned material parameters controlling the interface are determined for Li_xMn_2O_4 , and the interface evolution is studied. Comparison to the Cahn-Hilliard theory shows that nonlocal species concentration theory is superior when simulating problems where the dimensions of the microstructure such as phase boundaries are of the same order of magnitude as the problem size. This is typically the case in nanosized particles of phase-separating electrode materials. For example, the nonlocality of nonlocal species concentration theory turns out to make the interface of the local concentration field thinner than in Cahn-Hilliard theory.

Third-order elastic constants of diamond determined from experimental data

DOE PAGES

Winey, J. M.; Hmiel, A.; Gupta, Y. M.

2016-06-01

The pressure derivatives of the second-order elastic constants (SOECs) of diamond were determined by analyzing previous sound velocity measurements under hydrostatic stress [McSkimin and Andreatch, J. Appl. Phys. 43, 294 (1972)]. Furthermore, our analysis corrects an error in the previously reported results.We present a complete and corrected set of third-order elastic constants (TOECs) using the corrected pressure derivatives, together with published data for the nonlinear elastic response of shock compressed diamond [Lang and Gupta, Phys. Rev. Lett. 106, 125502 (2011)] and it differs significantly from TOECs published previously.

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules

1999-01-01

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

Modified current follower-based immittance function simulators

NASA Astrophysics Data System (ADS)

Alpaslan, Halil; Yuce, Erkan

2017-12-01

In this paper, four immittance function simulators consisting of a single modified current follower with single Z- terminal and a minimum number of passive components are proposed. The first proposed circuit can provide +L parallel with +R and the second proposed one can realise -L parallel with -R. The third proposed structure can provide +L series with +R and the fourth proposed one can realise -L series with -R. However, all the proposed immittance function simulators need a single resistive matching constraint. Parasitic impedance effects on all the proposed immittance function simulators are investigated. A second-order current-mode (CM) high-pass filter derived from the first proposed immittance function simulator is given as an application example. Also, a second-order CM low-pass filter derived from the third proposed immittance function simulator is given as an application example. A number of simulation results based on SPICE programme and an experimental test result are given to verify the theory.

Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion

NASA Astrophysics Data System (ADS)

Zhang, Wei-Guo; Li, Zhe; Liu, Yong-Jun

2018-01-01

In this paper, we study the pricing problem of the continuously monitored fixed and floating strike geometric Asian power options in a mixed fractional Brownian motion environment. First, we derive both closed-form solutions and mixed fractional partial differential equations for fixed and floating strike geometric Asian power options based on delta-hedging strategy and partial differential equation method. Second, we present the lower and upper bounds of the prices of fixed and floating strike geometric Asian power options under the assumption that both risk-free interest rate and volatility are interval numbers. Finally, numerical studies are performed to illustrate the performance of our proposed pricing model.

Desert soil clay content estimation using reflectance spectroscopy preprocessed by fractional derivative

PubMed Central

Tiyip, Tashpolat; Ding, Jianli; Zhang, Dong; Liu, Wei; Wang, Fei; Tashpolat, Nigara

2017-01-01

Effective pretreatment of spectral reflectance is vital to model accuracy in soil parameter estimation. However, the classic integer derivative has some disadvantages, including spectral information loss and the introduction of high-frequency noise. In this paper, the fractional order derivative algorithm was applied to the pretreatment and partial least squares regression (PLSR) was used to assess the clay content of desert soils. Overall, 103 soil samples were collected from the Ebinur Lake basin in the Xinjiang Uighur Autonomous Region of China, and used as data sets for calibration and validation. Following laboratory measurements of spectral reflectance and clay content, the raw spectral reflectance and absorbance data were treated using the fractional derivative order from the 0.0 to the 2.0 order (order interval: 0.2). The ratio of performance to deviation (RPD), determinant coefficients of calibration (Rc2), root mean square errors of calibration (RMSEC), determinant coefficients of prediction (Rp2), and root mean square errors of prediction (RMSEP) were applied to assess the performance of predicting models. The results showed that models built on the fractional derivative order performed better than when using the classic integer derivative. Comparison of the predictive effects of 22 models for estimating clay content, calibrated by PLSR, showed that those models based on the fractional derivative 1.8 order of spectral reflectance (Rc2 = 0.907, RMSEC = 0.425%, Rp2 = 0.916, RMSEP = 0.364%, and RPD = 2.484 ≥ 2.000) and absorbance (Rc2 = 0.888, RMSEC = 0.446%, Rp2 = 0.918, RMSEP = 0.383% and RPD = 2.511 ≥ 2.000) were most effective. Furthermore, they performed well in quantitative estimations of the clay content of soils in the study area. PMID:28934274

Basic research for the geodynamics program

NASA Technical Reports Server (NTRS)

1991-01-01

The mathematical models of space very long base interferometry (VLBI) observables suitable for least squares covariance analysis were derived and estimatability problems inherent in the space VLBI system were explored, including a detailed rank defect analysis and sensitivity analysis. An important aim is to carry out a comparative analysis of the mathematical models of the ground-based VLBI and space VLBI observables in order to describe the background in detail. Computer programs were developed in order to check the relations, assess errors, and analyze sensitivity. In order to investigate the estimatability of different geodetic and geodynamic parameters from the space VLBI observables, the mathematical models for time delay and time delay rate observables of space VLBI were analytically derived along with the partial derivatives with respect to the parameters. Rank defect analysis was carried out both by analytical and numerical testing of linear dependencies between the columns of the normal matrix thus formed. Definite conclusions were formed about the rank defects in the system.

Stable static structures in models with higher-order derivatives

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

Bazeia, D., E-mail: bazeia@fisica.ufpb.br; Departamento de Física, Universidade Federal de Campina Grande, 58109-970 Campina Grande, PB; Lobão, A.S.

2015-09-15

We investigate the presence of static solutions in generalized models described by a real scalar field in four-dimensional space–time. We study models in which the scalar field engenders higher-order derivatives and spontaneous symmetry breaking, inducing the presence of domain walls. Despite the presence of higher-order derivatives, the models keep to equations of motion second-order differential equations, so we focus on the presence of first-order equations that help us to obtain analytical solutions and investigate linear stability on general grounds. We then illustrate the general results with some specific examples, showing that the domain wall may become compact and that themore » zero mode may split. Moreover, if the model is further generalized to include k-field behavior, it may contribute to split the static structure itself.« less

Effects of Second-Order Hydrodynamics on a Semisubmersible Floating Offshore Wind Turbine: Preprint

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

Bayati, I.; Jonkman, J.; Robertson, A.

2014-07-01

The objective of this paper is to assess the second-order hydrodynamic effects on a semisubmersible floating offshore wind turbine. Second-order hydrodynamics induce loads and motions at the sum- and difference-frequencies of the incident waves. These effects have often been ignored in offshore wind analysis, under the assumption that they are significantly smaller than first-order effects. The sum- and difference-frequency loads can, however, excite eigenfrequencies of the system, leading to large oscillations that strain the mooring system or vibrations that cause fatigue damage to the structure. Observations of supposed second-order responses in wave-tank tests performed by the DeepCwind consortium at themore » MARIN offshore basin suggest that these effects might be more important than originally expected. These observations inspired interest in investigating how second-order excitation affects floating offshore wind turbines and whether second-order hydrodynamics should be included in offshore wind simulation tools like FAST in the future. In this work, the effects of second-order hydrodynamics on a floating semisubmersible offshore wind turbine are investigated. Because FAST is currently unable to account for second-order effects, a method to assess these effects was applied in which linearized properties of the floating wind system derived from FAST (including the 6x6 mass and stiffness matrices) are used by WAMIT to solve the first- and second-order hydrodynamics problems in the frequency domain. The method has been applied to the OC4-DeepCwind semisubmersible platform, supporting the NREL 5-MW baseline wind turbine. The loads and response of the system due to the second-order hydrodynamics are analysed and compared to first-order hydrodynamic loads and induced motions in the frequency domain. Further, the second-order loads and induced response data are compared to the loads and motions induced by aerodynamic loading as solved by FAST.« less

FDTD simulation of EM wave propagation in 3-D media

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

Wang, T.; Tripp, A.C.

1996-01-01

A finite-difference, time-domain solution to Maxwell`s equations has been developed for simulating electromagnetic wave propagation in 3-D media. The algorithm allows arbitrary electrical conductivity and permittivity variations within a model. The staggered grid technique of Yee is used to sample the fields. A new optimized second-order difference scheme is designed to approximate the spatial derivatives. Like the conventional fourth-order difference scheme, the optimized second-order scheme needs four discrete values to calculate a single derivative. However, the optimized scheme is accurate over a wider wavenumber range. Compared to the fourth-order scheme, the optimized scheme imposes stricter limitations on the time stepmore » sizes but allows coarser grids. The net effect is that the optimized scheme is more efficient in terms of computation time and memory requirement than the fourth-order scheme. The temporal derivatives are approximated by second-order central differences throughout. The Liao transmitting boundary conditions are used to truncate an open problem. A reflection coefficient analysis shows that this transmitting boundary condition works very well. However, it is subject to instability. A method that can be easily implemented is proposed to stabilize the boundary condition. The finite-difference solution is compared to closed-form solutions for conducting and nonconducting whole spaces and to an integral-equation solution for a 3-D body in a homogeneous half-space. In all cases, the finite-difference solutions are in good agreement with the other solutions. Finally, the use of the algorithm is demonstrated with a 3-D model. Numerical results show that both the magnetic field response and electric field response can be useful for shallow-depth and small-scale investigations.« less

Finite Moment Tensors of Southern California Earthquakes

NASA Astrophysics Data System (ADS)

Jordan, T. H.; Chen, P.; Zhao, L.

2003-12-01

We have developed procedures for inverting broadband waveforms for the finite moment tensors (FMTs) of regional earthquakes. The FMT is defined in terms of second-order polynomial moments of the source space-time function and provides the lowest order representation of a finite fault rupture; it removes the fault-plane ambiguity of the centroid moment tensor (CMT) and yields several additional parameters of seismological interest: the characteristic length L{c}, width W{c}, and duration T{c} of the faulting, as well as the directivity vector {v}{d} of the fault slip. To formulate the inverse problem, we follow and extend the methods of McGuire et al. [2001, 2002], who have successfully recovered the second-order moments of large earthquakes using low-frequency teleseismic data. We express the Fourier spectra of a synthetic point-source waveform in its exponential (Rytov) form and represent the observed waveform relative to the synthetic in terms two frequency-dependent differential times, a phase delay δ τ {p}(ω ) and an amplitude-reduction time δ τ {q}(ω ), which we measure using Gee and Jordan's [1992] isolation-filter technique. We numerically calculate the FMT partial derivatives in terms of second-order spatiotemporal gradients, which allows us to use 3D finite-difference seismograms as our isolation filters. We have applied our methodology to a set of small to medium-sized earthquakes in Southern California. The errors in anelastic structure introduced perturbations larger than the signal level caused by finite source effect. We have therefore employed a joint inversion technique that recovers the CMT parameters of the aftershocks, as well as the CMT and FMT parameters of the mainshock, under the assumption that the source finiteness of the aftershocks can be ignored. The joint system of equations relating the δ τ {p} and δ τ {q} data to the source parameters of the mainshock-aftershock cluster is denuisanced for path anomalies in both observables; this projection operation effectively corrects the mainshock data for path-related amplitude anomalies in a way similar to, but more flexible than, empirical Green function (EGF) techniques.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

NASA Astrophysics Data System (ADS)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall Laws

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

El Jarroudi, M.; Brillard, A.

2008-06-15

We consider a new way of establishing Navier wall laws. Considering a bounded domain {omega} of R{sup N}, N=2,3, surrounded by a thin layer {sigma}{sub {epsilon}}, along a part {gamma}{sub 2} of its boundary {partial_derivative}{omega}, we consider a Navier-Stokes flow in {omega} union {partial_derivative}{omega} union {sigma}{sub {epsilon}} with Reynolds' number of order 1/{epsilon} in {sigma}{sub {epsilon}}. Using {gamma}-convergence arguments, we describe the asymptotic behaviour of the solution of this problem and get a general Navier law involving a matrix of Borel measures having the same support contained in the interface {gamma}{sub 2}. We then consider two special cases where wemore » characterize this matrix of measures. As a further application, we consider an optimal control problem within this context.« less

Partial oxidation power plant with reheating and method thereof

DOEpatents

Newby, Richard A.; Yang, Wen-Ching; Bannister, Ronald L.

1999-01-01

A system and method for generating power having an air compression/partial oxidation system, a turbine, and a primary combustion system. The air compression/partial oxidation system receives a first air stream and a fuel stream and produces a first partially oxidized fuel stream and a first compressed air stream therefrom. The turbine expands the first partially oxidized fuel stream while being cooled by the first compressed air stream to produce a heated air stream. The heated air stream is injected into the expanding first partially oxidized fuel stream, thereby reheating it in the turbine. A second partially oxidized fuel stream is emitted from the turbine. The primary combustion system receives said second partially oxidized fuel stream and a second air stream, combusts said second partially oxidized fuel stream, and produces rotating shaft power and an emission stream therefrom.

Matter bispectrum beyond Horndeski theories

NASA Astrophysics Data System (ADS)

Hirano, Shin'ichi; Kobayashi, Tsutomu; Tashiro, Hiroyuki; Yokoyama, Shuichiro

2018-05-01

The Horndeski scalar-tensor theory and its recent extensions allow nonlinear derivative interactions of the scalar degree of freedom. We study the matter bispectrum of large scale structure as a probe of these modified gravity theories, focusing in particular on the effect of the terms that newly appear in the so-called "beyond Horndeski" theories. We derive the second-order solution for the matter density perturbations and find that the interactions beyond Horndeski lead to a new time-dependent coefficient in the second-order kernel which differs in general from the standard value of general relativity and the Horndeski theory. This can deform the matter bispectrum at the folded triangle configurations (k1+k2=k3 ), while it is never possible within the Horndeski theory.

Generalized heat-transport equations: parabolic and hyperbolic models

NASA Astrophysics Data System (ADS)

Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio

2018-03-01

We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.

The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun

1993-01-01

The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.

Capacity of MIMO free space optical communications using multiple partially coherent beams propagation through non-Kolmogorov strong turbulence.

PubMed

Deng, Peng; Kavehrad, Mohsen; Liu, Zhiwen; Zhou, Zhou; Yuan, Xiuhua

2013-07-01

We study the average capacity performance for multiple-input multiple-output (MIMO) free-space optical (FSO) communication systems using multiple partially coherent beams propagating through non-Kolmogorov strong turbulence, assuming equal gain combining diversity configuration and the sum of multiple gamma-gamma random variables for multiple independent partially coherent beams. The closed-form expressions of scintillation and average capacity are derived and then used to analyze the dependence on the number of independent diversity branches, power law α, refractive-index structure parameter, propagation distance and spatial coherence length of source beams. Obtained results show that, the average capacity increases more significantly with the increase in the rank of MIMO channel matrix compared with the diversity order. The effect of the diversity order on the average capacity is independent of the power law, turbulence strength parameter and spatial coherence length, whereas these effects on average capacity are gradually mitigated as the diversity order increases. The average capacity increases and saturates with the decreasing spatial coherence length, at rates depending on the diversity order, power law and turbulence strength. There exist optimal values of the spatial coherence length and diversity configuration for maximizing the average capacity of MIMO FSO links over a variety of atmospheric turbulence conditions.

Accuracy-preserving source term quadrature for third-order edge-based discretization

NASA Astrophysics Data System (ADS)

Nishikawa, Hiroaki; Liu, Yi

2017-09-01

In this paper, we derive a family of source term quadrature formulas for preserving third-order accuracy of the node-centered edge-based discretization for conservation laws with source terms on arbitrary simplex grids. A three-parameter family of source term quadrature formulas is derived, and as a subset, a one-parameter family of economical formulas is identified that does not require second derivatives of the source term. Among the economical formulas, a unique formula is then derived that does not require gradients of the source term at neighbor nodes, thus leading to a significantly smaller discretization stencil for source terms. All the formulas derived in this paper do not require a boundary closure, and therefore can be directly applied at boundary nodes. Numerical results are presented to demonstrate third-order accuracy at interior and boundary nodes for one-dimensional grids and linear triangular/tetrahedral grids over straight and curved geometries.

Three-point functions in duality-invariant higher-derivative gravity

DOE PAGES

Naseer, Usman; Zwiebach, Barton

2016-03-21

Here, doubled α'-geometry is the simplest higher-derivative gravitational theory with exact global duality symmetry. We use the double metric formulation of this theory to compute on-shell three-point functions to all orders in α'. A simple pattern emerges when comparing with the analogous bosonic and heterotic three-point functions. As in these theories, the amplitudes factorize. The theory has no Gauss-Bonnet term, but contains a Riemann-cubed interaction to second order in α'.

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect.

PubMed

Ma, Jinpeng; Sun, Yong; Yuan, Xiaoming; Kurths, Jürgen; Zhan, Meng

2016-01-01

Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

{open_quotes}Quadrupoled{close_quotes} materials for second-order nonlinear optics

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

Hubbard, S.F.; Petschek, R.G.; Singer, K.D.

1997-10-01

We describe a new approach to second-order nonlinear optical materials, namely quadrupoling. This approach is valid in the regime of Kleinman (full permutation) symmetry breaking, and thus requires a two- or three dimensional microscopic nonlinearity at wavelengths away from material resonances. This {open_quotes}quadrupolar{close_quotes} nonlinearity arises from the second rank pseudotensor of the rotationally invariant representation of the second-order nonlinear optical tensor. We have experimentally investigated candidate molecules comprised of chiral camphorquinone derivatives by measuring the scalar invariant associated with the rank two pseudotensor using hyper-Rayleigh scattering. We have found sizable scalar figures of merit for several compounds using light formore » which the second harmonic wavelengths are greater than 100 nm longer than the absorption peak location. At these wavelengths, the quadrupolar scalar is as large as the polar (EFISH) scalar of p-nitroaniline. Prospects for applications are discussed.« less

Adsorption of 2,4-dichlorophenoxyacetic acid and 4-chloro-2-metylphenoxyacetic acid onto activated carbons derived from various lignocellulosic materials.

PubMed

Doczekalska, Beata; Kuśmierek, Krzysztof; Świątkowski, Andrzej; Bartkowiak, Monika

2018-05-04

Adsorption of 2,4-dichlorophenoxyacetic acid (2,4-D) and 4-chloro-2-metylphenoxyacetic acid (MCPA) from aqueous solution onto activated carbons derived from various lignocellulosic materials including willow, miscanthus, flax, and hemp shives was investigated. The adsorption kinetic data were analyzed using two kinetic models: the pseudo-first order and pseudo-second order equations. The adsorption kinetics of both herbicides was better represented by the pseudo-second order model. The adsorption isotherms of 2,4-D and MCPA on the activated carbons were analyzed using the Freundlich and Langmuir isotherm models. The equilibrium data followed the Langmuir isotherm. The effect of pH on the adsorption was also studied. The results showed that the activated carbons prepared from the lignocellulosic materials are efficient adsorbents for the removal of 2,4-D and MCPA from aqueous solutions.

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.

Determination of nongeometric effects: equivalence between Artmann's and Tamir's generalized methods.

PubMed

Perez, Liliana I; Echarri, Rodolfo M; Garea, María T; Santiago, Guillermo D

2011-03-01

This work shows that all first- and second-order nongeometric effects on propagation, total or partial reflection, and transmission can be understood and evaluated considering the superposition of two plane waves. It also shows that this description yields results that are qualitatively and quantitatively compatible with those obtained by Fourier analysis of beams with Gaussian intensity distribution in any type of interface. In order to show this equivalence, we start by describing the first- and second-order nongeometric effects, and we calculate them analytically by superposing two plane waves. Finally, these results are compared with those obtained for the nongeometric effects of Gaussian beams in isotropic interfaces and are applied to different types of interfaces. A simple analytical expression for the angular shift is obtained considering the transmission of an extraordinary beam in a uniaxial-isotropic interface.

Predictions of nucleation theory applied to Ehrenfest thermodynamic transitions

NASA Technical Reports Server (NTRS)

Barker, R. E., Jr.; Campbell, K. W.

1984-01-01

A modified nucleation theory is used to determine a critical nucleus size and a critical activation-energy barrier for second-order Ehrenfest thermodynamic transitions as functions of the degree of undercooling, the interfacial energy, the heat-capacity difference, the specific volume of the transformed phase, and the equilibrium transition temperature. The customary approximations of nucleation theory are avoided by expanding the Gibbs free energy in a Maclaurin series and applying analytical thermodynamic expressions to evaluate the expansion coefficients. Nonlinear correction terms for first-order-transition calculations are derived, and numerical results are presented graphically for water and polystyrene as examples of first-order and quasi-second-order transitions, respectively.

Computational Algorithms or Identification of Distributed Parameter Systems

DTIC Science & Technology

1993-04-24

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

Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

NASA Astrophysics Data System (ADS)

Chen, Shanzhen; Jiang, Xiaoyun

2012-08-01

In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.

Partial oxidation power plant with reheating and method thereof

DOEpatents

Newby, R.A.; Yang, W.C.; Bannister, R.L.

1999-08-10

A system and method are disclosed for generating power having an air compression/partial oxidation system, a turbine, and a primary combustion system. The air compression/partial oxidation system receives a first air stream and a fuel stream and produces a first partially oxidized fuel stream and a first compressed air stream therefrom. The turbine expands the first partially oxidized fuel stream while being cooled by the first compressed air stream to produce a heated air stream. The heated air stream is injected into the expanding first partially oxidized fuel stream, thereby reheating it in the turbine. A second partially oxidized fuel stream is emitted from the turbine. The primary combustion system receives said second partially oxidized fuel stream and a second air stream, combusts said second partially oxidized fuel stream, and produces rotating shaft power and an emission stream therefrom. 2 figs.

An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2018-06-01

In this work, we investigate numerically a model governed by a multidimensional nonlinear wave equation with damping and fractional diffusion. The governing partial differential equation considers the presence of Riesz space-fractional derivatives of orders in (1, 2], and homogeneous Dirichlet boundary data are imposed on a closed and bounded spatial domain. The model under investigation possesses an energy function which is preserved in the undamped regime. In the damped case, we establish the property of energy dissipation of the model using arguments from functional analysis. Motivated by these results, we propose an explicit finite-difference discretization of our fractional model based on the use of fractional centered differences. Associated to our discrete model, we also propose discretizations of the energy quantities. We establish that the discrete energy is conserved in the undamped regime, and that it dissipates in the damped scenario. Among the most important numerical features of our scheme, we show that the method has a consistency of second order, that it is stable and that it has a quadratic order of convergence. Some one- and two-dimensional simulations are shown in this work to illustrate the fact that the technique is capable of preserving the discrete energy in the undamped regime. For the sake of convenience, we provide a Matlab implementation of our method for the one-dimensional scenario.

Higher-derivative operators and effective field theory for general scalar-tensor theories

NASA Astrophysics Data System (ADS)

Solomon, Adam R.; Trodden, Mark

2018-02-01

We discuss the extent to which it is necessary to include higher-derivative operators in the effective field theory of general scalar-tensor theories. We explore the circumstances under which it is correct to restrict to second-order operators only, and demonstrate this using several different techniques, such as reduction of order and explicit field redefinitions. These methods are applied, in particular, to the much-studied Horndeski theories. The goal is to clarify the application of effective field theory techniques in the context of popular cosmological models, and to explicitly demonstrate how and when higher-derivative operators can be cast into lower-derivative forms suitable for numerical solution techniques.

A fourth order accurate finite difference scheme for the computation of elastic waves

NASA Technical Reports Server (NTRS)

Bayliss, A.; Jordan, K. E.; Lemesurier, B. J.; Turkel, E.

1986-01-01

A finite difference for elastic waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-elastic interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.

Third-order 2N-storage Runge-Kutta schemes with error control

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Kennedy, Christopher A.

1994-01-01

A family of four-stage third-order explicit Runge-Kutta schemes is derived that requires only two storage locations and has desirable stability characteristics. Error control is achieved by embedding a second-order scheme within the four-stage procedure. Certain schemes are identified that are as efficient and accurate as conventional embedded schemes of comparable order and require fewer storage locations.

Topological Constraints on Transvection between White Genes within the Transposing Element Te35b in Drosophila Melanogaster

PubMed Central

Gubb, D.; Roote, J.; Trenear, J.; Coulson, D.; Ashburner, M.

1997-01-01

The transposable element TE35B carries two copies of the white (w) gene at 35B1.2 on the second chromosome. These w genes are suppressed in a zeste-1 (z(1)) mutant background in a synapsis-dependent manner. Single-copy derivatives of the original TE35B stock give red eyes when heterozygous, but zeste eyes when homozygous. TE35B derivatives carrying single, double or triple copies of w were crossed to generate flies carrying from two to five ectopic w genes. Within this range, z(1)-mediated suppression is insensitive to copynumber and does not distinguish between w genes that are in cis or in trans. Suppression does not require the juxtaposition of even numbers of w genes, but is extremely sensitive to chromosomal topology. When arranged in a tight cluster, in triple-copy TE derivatives, w genes are nonsuppressible. Breakpoints falling within TE35B and separating two functional w genes act as partial suppressors of z(1). Similarly, breakpoints immediately proximal or distal to both w genes give partial suppression. This transvection-dependent downregulation of w genes may result from mis-activation of the X-chromosome dosage compensation mechanism. PMID:9215897

Methods for preparation of cyclopentadienyliron (II) arenes

DOEpatents

Keipert, Steven J.

1991-01-01

Two improved methods for preparation of compounds with the structure shown in equation X [(Cp)--Fe--(Ar)].sup.+.sub.b X.sup.b- (X) where Cp is an eta.sup.5 complexed, substituted or unsubstituted, cyclopentadienyl or indenyl anion, Ar is an eta.sup.6 complexed substituted or unsubstituted, pi-arene ligand anad X is a b-valent anion where b is an integer between 1 and 3. The two methods, which differ in the source of the cyclopentadienyl anion - Lewis acid complex, utilize a Lewis acid assisted ligand transfer reaction. The cyclopentadienyl anion ligand, assisted by a Lewis acid is transferred to ferrous ion in the presence of an arene. In the first method, the cyclopentadienyl anion is derived from ferrocene and ferrous chloride. In this reaction, the cyclopentadienyliron (II) arene product is derived partially from ferrocene and partially from the ferrous salt. In the second method, the cyclopentadienyl anion - Lewis acid complex is formed by direct reaction of the Lewis acid with an inorganic cyclopentadienide salt. The cyclopentadienyliron (II) arene product of this reaction is derived entirely from the ferrous salt. Cyclopentadienyliron (II) arene cations are of great interest due to their utility as photoactivatable catalysts for a variety of polymerization reactions.

The Riemann-Lanczos equations in general relativity and their integrability

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2008-06-01

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

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

NASA Technical Reports Server (NTRS)

Ball, R. E.

1972-01-01

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

Nematic order on the surface of a three-dimensional topological insulator

NASA Astrophysics Data System (ADS)

Lundgren, Rex; Yerzhakov, Hennadii; Maciejko, Joseph

2017-12-01

We study the spontaneous breaking of rotational symmetry in the helical surface state of three-dimensional topological insulators due to strong electron-electron interactions, focusing on time-reversal invariant nematic order. Owing to the strongly spin-orbit coupled nature of the surface state, the nematic order parameter is linear in the electron momentum and necessarily involves the electron spin, in contrast with spin-degenerate nematic Fermi liquids. For a chemical potential at the Dirac point (zero doping), we find a first-order phase transition at zero temperature between isotropic and nematic Dirac semimetals. This extends to a thermal phase transition that changes from first to second order at a finite-temperature tricritical point. At finite doping, we find a transition between isotropic and nematic helical Fermi liquids that is second order even at zero temperature. Focusing on finite doping, we discuss various observable consequences of nematic order, such as anisotropies in transport and the spin susceptibility, the partial breakdown of spin-momentum locking, collective modes and induced spin fluctuations, and non-Fermi-liquid behavior at the quantum critical point and in the nematic phase.

Sample size adjustments for varying cluster sizes in cluster randomized trials with binary outcomes analyzed with second-order PQL mixed logistic regression.

PubMed

Candel, Math J J M; Van Breukelen, Gerard J P

2010-06-30

Adjustments of sample size formulas are given for varying cluster sizes in cluster randomized trials with a binary outcome when testing the treatment effect with mixed effects logistic regression using second-order penalized quasi-likelihood estimation (PQL). Starting from first-order marginal quasi-likelihood (MQL) estimation of the treatment effect, the asymptotic relative efficiency of unequal versus equal cluster sizes is derived. A Monte Carlo simulation study shows this asymptotic relative efficiency to be rather accurate for realistic sample sizes, when employing second-order PQL. An approximate, simpler formula is presented to estimate the efficiency loss due to varying cluster sizes when planning a trial. In many cases sampling 14 per cent more clusters is sufficient to repair the efficiency loss due to varying cluster sizes. Since current closed-form formulas for sample size calculation are based on first-order MQL, planning a trial also requires a conversion factor to obtain the variance of the second-order PQL estimator. In a second Monte Carlo study, this conversion factor turned out to be 1.25 at most. (c) 2010 John Wiley & Sons, Ltd.

Exact statistical results for binary mixing and reaction in variable density turbulence

NASA Astrophysics Data System (ADS)

Ristorcelli, J. R.

2017-02-01

We report a number of rigorous statistical results on binary active scalar mixing in variable density turbulence. The study is motivated by mixing between pure fluids with very different densities and whose density intensity is of order unity. Our primary focus is the derivation of exact mathematical results for mixing in variable density turbulence and we do point out the potential fields of application of the results. A binary one step reaction is invoked to derive a metric to asses the state of mixing. The mean reaction rate in variable density turbulent mixing can be expressed, in closed form, using the first order Favre mean variables and the Reynolds averaged density variance, ⟨ρ2⟩ . We show that the normalized density variance, ⟨ρ2⟩ , reflects the reduction of the reaction due to mixing and is a mix metric. The result is mathematically rigorous. The result is the variable density analog, the normalized mass fraction variance ⟨c2⟩ used in constant density turbulent mixing. As a consequence, we demonstrate that use of the analogous normalized Favre variance of the mass fraction, c″ ⁣2˜ , as a mix metric is not theoretically justified in variable density turbulence. We additionally derive expressions relating various second order moments of the mass fraction, specific volume, and density fields. The central role of the density specific volume covariance ⟨ρ v ⟩ is highlighted; it is a key quantity with considerable dynamical significance linking various second order statistics. For laboratory experiments, we have developed exact relations between the Reynolds scalar variance ⟨c2⟩ its Favre analog c″ ⁣2˜ , and various second moments including ⟨ρ v ⟩ . For moment closure models that evolve ⟨ρ v ⟩ and not ⟨ρ2⟩ , we provide a novel expression for ⟨ρ2⟩ in terms of a rational function of ⟨ρ v ⟩ that avoids recourse to Taylor series methods (which do not converge for large density differences). We have derived analytic results relating several other second and third order moments and see coupling between odd and even order moments demonstrating a natural and inherent skewness in the mixing in variable density turbulence. The analytic results have applications in the areas of isothermal material mixing, isobaric thermal mixing, and simple chemical reaction (in progress variable formulation).

Oscillator strengths, first-order properties, and nuclear gradients for local ADC(2).

PubMed

Schütz, Martin

2015-06-07

We describe theory and implementation of oscillator strengths, orbital-relaxed first-order properties, and nuclear gradients for the local algebraic diagrammatic construction scheme through second order. The formalism is derived via time-dependent linear response theory based on a second-order unitary coupled cluster model. The implementation presented here is a modification of our previously developed algorithms for Laplace transform based local time-dependent coupled cluster linear response (CC2LR); the local approximations thus are state specific and adaptive. The symmetry of the Jacobian leads to considerable simplifications relative to the local CC2LR method; as a result, a gradient evaluation is about four times less expensive. Test calculations show that in geometry optimizations, usually very similar geometries are obtained as with the local CC2LR method (provided that a second-order method is applicable). As an exemplary application, we performed geometry optimizations on the low-lying singlet states of chlorophyllide a.

An Upwind Solver for the National Combustion Code

NASA Technical Reports Server (NTRS)

Sockol, Peter M.

2011-01-01

An upwind solver is presented for the unstructured grid National Combustion Code (NCC). The compressible Navier-Stokes equations with time-derivative preconditioning and preconditioned flux-difference splitting of the inviscid terms are used. First order derivatives are computed on cell faces and used to evaluate the shear stresses and heat fluxes. A new flux limiter uses these same first order derivatives in the evaluation of left and right states used in the flux-difference splitting. The k-epsilon turbulence equations are solved with the same second-order method. The new solver has been installed in a recent version of NCC and the resulting code has been tested successfully in 2D on two laminar cases with known solutions and one turbulent case with experimental data.

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.

Computer program for Bessel and Hankel functions

NASA Technical Reports Server (NTRS)

Kreider, Kevin L.; Saule, Arthur V.; Rice, Edward J.; Clark, Bruce J.

1991-01-01

A set of FORTRAN subroutines for calculating Bessel and Hankel functions is presented. The routines calculate Bessel and Hankel functions of the first and second kinds, as well as their derivatives, for wide ranges of integer order and real or complex argument in single or double precision. Depending on the order and argument, one of three evaluation methods is used: the power series definition, an Airy function expansion, or an asymptotic expansion. Routines to calculate Airy functions and their derivatives are also included.

Errors from approximation of ODE systems with reduced order models

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

Vassilevska, Tanya

2016-12-30

This is a code to calculate the error from approximation of systems of ordinary differential equations (ODEs) by using Proper Orthogonal Decomposition (POD) Reduced Order Models (ROM) methods and to compare and analyze the errors for two POD ROM variants. The first variant is the standard POD ROM, the second variant is a modification of the method using the values of the time derivatives (a.k.a. time-derivative snapshots). The code compares the errors from the two variants under different conditions.

On the boundedness and integration of non-oscillatory solutions of certain linear differential equations of second order.

PubMed

Tunç, Cemil; Tunç, Osman

2016-01-01

In this paper, certain system of linear homogeneous differential equations of second-order is considered. By using integral inequalities, some new criteria for bounded and [Formula: see text]-solutions, upper bounds for values of improper integrals of the solutions and their derivatives are established to the considered system. The obtained results in this paper are considered as extension to the results obtained by Kroopnick (2014) [1]. An example is given to illustrate the obtained results.

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.

Relative importance of first and second derivatives of nuclear magnetic resonance chemical shifts and spin-spin coupling constants for vibrational averaging.

PubMed

Dracínský, Martin; Kaminský, Jakub; Bour, Petr

2009-03-07

Relative importance of anharmonic corrections to molecular vibrational energies, nuclear magnetic resonance (NMR) chemical shifts, and J-coupling constants was assessed for a model set of methane derivatives, differently charged alanine forms, and sugar models. Molecular quartic force fields and NMR parameter derivatives were obtained quantum mechanically by a numerical differentiation. In most cases the harmonic vibrational function combined with the property second derivatives provided the largest correction of the equilibrium values, while anharmonic corrections (third and fourth energy derivatives) were found less important. The most computationally expensive off-diagonal quartic energy derivatives involving four different coordinates provided a negligible contribution. The vibrational corrections of NMR shifts were small and yielded a convincing improvement only for very accurate wave function calculations. For the indirect spin-spin coupling constants the averaging significantly improved already the equilibrium values obtained at the density functional theory level. Both first and complete second shielding derivatives were found important for the shift corrections, while for the J-coupling constants the vibrational parts were dominated by the diagonal second derivatives. The vibrational corrections were also applied to some isotopic effects, where the corrected values reasonably well reproduced the experiment, but only if a full second-order expansion of the NMR parameters was included. Contributions of individual vibrational modes for the averaging are discussed. Similar behavior was found for the methane derivatives, and for the larger and polar molecules. The vibrational averaging thus facilitates interpretation of previous experimental results and suggests that it can make future molecular structural studies more reliable. Because of the lengthy numerical differentiation required to compute the NMR parameter derivatives their analytical implementation in future quantum chemistry packages is desirable.

Propagation of partially coherent controllable dark hollow beams with various symmetries in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Wang, Haiyan; Li, Xiangyin

2010-01-01

Normalized intensity distribution, the complex degree of coherence and power in the bucket for partially coherent controllable dark hollow beams (DHBs) with various symmetries propagating in atmospheric turbulence are derived using tensor method and investigated in detail. Analytical results show that, after sufficient propagation distance, partially coherent DHBs with various symmetries eventually become circular Gaussian beam (without dark hollow) in turbulent atmosphere, which is different from its propagation properties in free space. The partially coherent DHBs return to a circular Gaussian beam rapidly for stronger turbulence, higher coherence, lower beam order, smaller p or smaller beam waist width. Another interesting observation is that the profile of the complex degree of coherence attains a similar profile to that of the average intensity of the related beam propagating in a turbulent atmosphere. Besides the laser power focusablity of DHBs are better than that of Gaussian beam propagating in turbulent atmosphere.

Aminosugar derivatives as potential anti-human immunodeficiency virus agents.

PubMed Central

Karpas, A; Fleet, G W; Dwek, R A; Petursson, S; Namgoong, S K; Ramsden, N G; Jacob, G S; Rademacher, T W

1988-01-01

Recent data suggest that aminosugar derivatives which inhibit glycoprotein processing have potential anti-human immunodeficiency virus (HIV) activity. These inhibitory effects may be due to disruption of cell fusion and subsequent cell-cell transmission of the acquired immunodeficiency syndrome (AIDS) virus. Free virus particles able to bind CD4-positive cells are still produced in the presence of these compounds with only partial reduction of infectivity. We now report a method to score in parallel both the degree of antiviral activity and the effect on cell division of aminosugar derivatives. We find that (i) the compounds 1,4-dideoxy-1,4-imino-L-arabinitol and N-(5-carboxymethyl-1-pentyl)-1,5-imino-L-fucitol partially inhibit the cytopathic effect (giant cell formation, etc.) of HIV and yield of infectious virus; (ii) the compounds N-methyldeoxynojirimycin and N-ethyldeoxynojirimycin reduce the yield of infectious HIV by an order of four and three logarithms, respectively; and (iii) one compound, N-butyldeoxynojirimycin, of the 47 compounds previously screened reduces infectious viral particles by a logarithmic order greater than five at noncytotoxic concentrations. In addition, long-term growth of infected cells in the presence of N-butyldeoxynojirimycin gradually decreases the proportion of infected cells, leading to eventual elimination of HIV from culture. This result suggests that replication is associated with cytolysis. The ability to break the cycle of replication and reinfection has important implications in the chemotherapy of AIDS. PMID:3264071

The elimination of influence of disturbing bodies' coordinates and derivatives discontinuity on the accuracy of asteroid motion simulation

NASA Astrophysics Data System (ADS)

Baturin, A. P.; Votchel, I. A.

2013-12-01

The problem of asteroid motion sumulation has been considered. At present this simulation is being performed by means of numerical integration taking into account the pertubations from planets and the Moon with some their ephemerides (DE405, DE422, etc.). All these ephemerides contain coefficients for Chebyshev polinomials for the great amount of equal interpolation intervals. However, all ephemerides has been constructed to keep at the junctions of adjacent intervals a continuity of just coordinates and their first derivatives (just in 16-digit decimal format corre-sponding to 64-bit floating-point numbers). But as for the second and higher order derivatives, they have breaks at these junctions. These breaks, if they are within an integration step, decrease the accuracy of numerical integration. If to consider 34-digit format (128-bit floating point numbers) the coordinates and their first derivatives will also have breaks (at 15-16 decimal digit) at interpolation intervals' junctions. Two ways of elimination of influence of such breaks have been considered. The first one is a "smoothing" of ephemerides so that planets' coordinates and their de-rivatives up to some order will be continuous at the junctions. The smoothing algorithm is based on conditional least-square fitting of coefficients for Chebyshev polynomials, the conditions are equalities of coordinates and derivatives up to some order "from the left" and "from the right" at the each junction. The algorithm has been applied for the smoothing of ephemerides DE430 just up to the first-order derivatives. The second way is a correction of integration step so that junctions does not lie within the step and always coincide with its end. But this way may be applied just at 16-digit decimal precision because it assumes a continuity of planets' coordinates and their first derivatives. Both ways was applied in forward and backward numerical integration for asteroids Apophis and 2012 DA14 by means of 15- and 31-order Everhart method at 16- and 34-digit decimal precision correspondently. The ephemerides DE430 (in its original and smoothed form) has been used for the calculation of perturbations. The results of the research indicate that the integration step correction increases a numercal integration accuracy by 3-4 orders. If, in addition, to replace the original ephemerides by the smoothed ones the accuracy increases approximately by 10 orders.

An improved finite-difference analysis of uncoupled vibrations of tapered cantilever beams

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1983-01-01

An improved finite difference procedure for determining the natural frequencies and mode shapes of tapered cantilever beams undergoing uncoupled vibrations is presented. Boundary conditions are derived in the form of simple recursive relations involving the second order central differences. Results obtained by using the conventional first order central differences and the present second order central differences are compared, and it is observed that the present second order scheme is more efficient than the conventional approach. An important advantage offered by the present approach is that the results converge to exact values rapidly, and thus the extrapolation of the results is not necessary. Consequently, the basic handicap with the classical finite difference method of solution that requires the Richardson's extrapolation procedure is eliminated. Furthermore, for the cases considered herein, the present approach produces consistent lower bound solutions.

Research on the sonic boom problem. Part 1: Second-order solutions for the flow field around slender bodies in supersonic flow for sonic boom analysis

NASA Technical Reports Server (NTRS)

Landahl, M.; Loefgren, P.

1973-01-01

A second-order theory for supersonic flow past slender bodies is presented. Through the introduction of characteristic coordinates as independent variables and the expansion procedure proposed by Lin and Oswatitsch, a uniformly valid solution is obtained for the whole flow field in the axisymmetric case and for far field in the general three-dimensional case. For distances far from the body the theory is an extension of Whitham's first-order solution and for the domain close to the body it is a modification of Van Dyke's second-order solution in the axisymmetric case. From the theory useful formulas relating flow deflections to the Whitham F-function are derived, which permits one to determine the sonic boom strength from wind tunnel measurements fairly close to the body.

Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization

NASA Astrophysics Data System (ADS)

Takemiya, Tetsushi

In modern aerospace engineering, the physics-based computational design method is becoming more important, as it is more efficient than experiments and because it is more suitable in designing new types of aircraft (e.g., unmanned aerial vehicles or supersonic business jets) than the conventional design method, which heavily relies on historical data. To enhance the reliability of the physics-based computational design method, researchers have made tremendous efforts to improve the fidelity of models. However, high-fidelity models require longer computational time, so the advantage of efficiency is partially lost. This problem has been overcome with the development of variable fidelity optimization (VFO). In VFO, different fidelity models are simultaneously employed in order to improve the speed and the accuracy of convergence in an optimization process. Among the various types of VFO methods, one of the most promising methods is the approximation management framework (AMF). In the AMF, objective and constraint functions of a low-fidelity model are scaled at a design point so that the scaled functions, which are referred to as "surrogate functions," match those of a high-fidelity model. Since scaling functions and the low-fidelity model constitutes surrogate functions, evaluating the surrogate functions is faster than evaluating the high-fidelity model. Therefore, in the optimization process, in which gradient-based optimization is implemented and thus many function calls are required, the surrogate functions are used instead of the high-fidelity model to obtain a new design point. The best feature of the AMF is that it may converge to a local optimum of the high-fidelity model in much less computational time than the high-fidelity model. However, through literature surveys and implementations of the AMF, the author xx found that (1) the AMF is very vulnerable when the computational analysis models have numerical noise, which is very common in high-fidelity models, and that (2) the AMF terminates optimization erroneously when the optimization problems have constraints. The first problem is due to inaccuracy in computing derivatives in the AMF, and the second problem is due to erroneous treatment of the trust region ratio, which sets the size of the domain for an optimization in the AMF. In order to solve the first problem of the AMF, automatic differentiation (AD) technique, which reads the codes of analysis models and automatically generates new derivative codes based on some mathematical rules, is applied. If derivatives are computed with the generated derivative code, they are analytical, and the required computational time is independent of the number of design variables, which is very advantageous for realistic aerospace engineering problems. However, if analysis models implement iterative computations such as computational fluid dynamics (CFD), which solves system partial differential equations iteratively, computing derivatives through the AD requires a massive memory size. The author solved this deficiency by modifying the AD approach and developing a more efficient implementation with CFD, and successfully applied the AD to general CFD software. In order to solve the second problem of the AMF, the governing equation of the trust region ratio, which is very strict against the violation of constraints, is modified so that it can accept the violation of constraints within some tolerance. By accepting violations of constraints during the optimization process, the AMF can continue optimization without terminating immaturely and eventually find the true optimum design point. With these modifications, the AMF is referred to as "Robust AMF," and it is applied to airfoil and wing aerodynamic design problems using Euler CFD software. The former problem has 21 design variables, and the latter 64. In both problems, derivatives computed with the proposed AD method are first compared with those computed with the finite differentiation (FD) method, and then, the Robust AMF is implemented along with the sequential quadratic programming (SQP) optimization method with only high-fidelity models. The proposed AD method computes derivatives more accurately and faster than the FD method, and the Robust AMF successfully optimizes shapes of the airfoil and the wing in a much shorter time than SQP with only high-fidelity models. These results clearly show the effectiveness of the Robust AMF. Finally, the feasibility of reducing computational time for calculating derivatives and the necessity of AMF with an optimum design point always in the feasible region are discussed as future work.

Gravitational radiation from compact binary systems: Gravitational waveforms and energy loss to second post-Newtonian order

NASA Astrophysics Data System (ADS)

Will, Clifford M.; Wiseman, Alan G.

1996-10-01

We derive the gravitational waveform and gravitational-wave energy flux generated by a binary star system of compact objects (neutron stars or black holes), accurate through second post-Newtonian order (O[(v/c)4]=O[(Gm/rc2)2]) beyond the lowest-order quadrupole approximation. We cast the Einstein equations into the form of a flat-spacetime wave equation together with a harmonic gauge condition, and solve it formally as a retarded integral over the past null cone of the chosen field point. The part of this integral that involves the matter sources and the near-zone gravitational field is evaluated in terms of multipole moments using standard techniques; the remainder of the retarded integral, extending over the radiation zone, is evaluated in a novel way. The result is a manifestly convergent and finite procedure for calculating gravitational radiation to arbitrary orders in a post-Newtonian expansion. Through second post-Newtonian order, the radiation is also shown to propagate toward the observer along true null rays of the asymptotically Schwarzschild spacetime, despite having been derived using flat-spacetime wave equations. The method cures defects that plagued previous ``brute-force'' slow-motion approaches to the generation of gravitational radiation, and yields results that agree perfectly with those recently obtained by a mixed post-Minkowskian post-Newtonian method. We display explicit formulas for the gravitational waveform and the energy flux for two-body systems, both in arbitrary orbits and in circular orbits. In an appendix, we extend the formalism to bodies with finite spatial extent, and derive the spin corrections to the waveform and energy loss.

Observation model and parameter partials for the JPL geodetic (GPS) modeling software 'GPSOMC'

NASA Technical Reports Server (NTRS)

Sovers, O. J.

1990-01-01

The physical models employed in GPSOMC, the modeling module of the GIPSY software system developed at JPL for analysis of geodetic Global Positioning Satellite (GPS) measurements are described. Details of the various contributions to range and phase observables are given, as well as the partial derivatives of the observed quantities with respect to model parameters. A glossary of parameters is provided to enable persons doing data analysis to identify quantities with their counterparts in the computer programs. The present version is the second revision of the original document which it supersedes. The modeling is expanded to provide the option of using Cartesian station coordinates; parameters for the time rates of change of universal time and polar motion are also introduced.

Revisit of the relationship between the elastic properties and sound velocities at high pressures

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

Wang, Chenju; Yan, Xiaozhen; Institute of Atomic and Molecular Sciences, Sichuan University, Chengdu 610065

2014-09-14

The second-order elastic constants and stress-strain coefficients are defined, respectively, as the second derivatives of the total energy and the first derivative of the stress with respect to strain. Since the Lagrangian and infinitesimal strain are commonly used in the two definitions above, the second-order elastic constants and stress-strain coefficients are separated into two categories, respectively. In general, any of the four physical quantities is employed to characterize the elastic properties of materials without differentiation. Nevertheless, differences may exist among them at non-zero pressures, especially high pressures. Having explored the confusing issue systemically in the present work, we find thatmore » the four quantities are indeed different from each other at high pressures and these differences depend on the initial stress applied on materials. Moreover, the various relations between the four quantities depicting elastic properties of materials and high-pressure sound velocities are also derived from the elastic wave equations. As examples, we calculated the high-pressure sound velocities of cubic tantalum and hexagonal rhenium using these nexus. The excellent agreement of our results with available experimental data suggests the general applicability of the relations.« less

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

Favorite, Jeffrey A.

In transport theory, adjoint-based partial derivatives with respect to mass density are constant-volume derivatives. Likewise, adjoint-based partial derivatives with respect to surface locations (i.e., internal interface locations and the outer system boundary) are constant-density derivatives. This study derives the constant-mass partial derivative of a response with respect to an internal interface location or the outer system boundary and the constant-mass partial derivative of a response with respect to the mass density of a region. Numerical results are given for a multiregion two-dimensional (r-z) cylinder for three very different responses: the uncollided gamma-ray flux at an external detector point, k effmore » of the system, and the total neutron leakage. Finally, results from the derived formulas compare extremely well with direct perturbation calculations.« less

Second-order optical effects in several pyrazolo-quinoline derivatives

NASA Astrophysics Data System (ADS)

Makowska-Janusik, M.; Gondek, E.; Kityk, I. V.; Wisła, J.; Sanetra, J.; Danel, A.

2004-11-01

Using optical poling of several pyazolo-quinoline (PAQ) derivatives we have found an existence of sufficiently high second order optical susceptibility at wavelength 1.76 μm varying in the range 0.9-2.8 pm/V. The performed quantum chemical simulations of the UV-absorption for isolated, solvated and incorporated into the polymethacrylate (PMMA) polymer films have shown that the PM3 method is the best among the semi-empirical ones to simulate the optical properties. The calculations of the hyperpolarizabilites have shown a good correlation with experimentally measured susceptibilities obtained from the optical poling. We have found that experimental susceptibility depends on linear molecular polarizability and photoinducing changes of the molecular dipole moment. It is clearly seen for the PAQ4-PAQ6 molecules possessing halogen atoms with relatively large polarizabilities.

Spatial statistical analysis of basal stem root disease under natural field epidemic of oil palm

NASA Astrophysics Data System (ADS)

Kamu, Assis; Phin, Chong Khim; Seman, Idris Abu; Wan, Hoong Hak; Mun, Ho Chong

2015-02-01

Oil palm or scientifically known as Elaeis guineensis Jacq. is the most important commodity crop in Malaysia and has greatly contributed to the economy growth of the country. As far as disease is concerned in the industry, Basal Stem Rot (BSR) caused by Ganoderma boninence remains the most important disease. BSR disease is the most widely studied with information available for oil palm disease in Malaysia. However, there is still limited study on the spatial as well as temporal pattern or distribution of the disease especially under natural field epidemic condition in oil palm plantation. The objective of this study is to spatially identify the pattern of BSR disease under natural field epidemic using two geospatial analytical techniques, which are quadrat analysis for the first order properties of partial pattern analysis and nearest-neighbor analysis (NNA) for the second order properties of partial pattern analysis. Two study sites were selected with different age of tree. Both sites are located in Tawau, Sabah and managed by the same company. The results showed that at least one of the point pattern analysis used which is NNA (i.e. the second order properties of partial pattern analysis) has confirmed the disease is complete spatial randomness. This suggests the spread of the disease is not from tree to tree and the age of palm does not play a significance role in determining the spatial pattern of the disease. From the spatial pattern of the disease, it would help in the disease management program and for the industry in the future. The statistical modelling is expected to help in identifying the right model to estimate the yield loss of oil palm due to BSR disease in the future.

Second-order numerical solution of time-dependent, first-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Shah, Patricia L.; Hardin, Jay

1995-01-01

A finite difference scheme is developed to find an approximate solution of two similar hyperbolic equations, namely a first-order plane wave and spherical wave problem. Finite difference approximations are made for both the space and time derivatives. The result is a conditionally stable equation yielding an exact solution when the Courant number is set to one.

Ecological scenarios analyzed and evaluated by a shallow lake model.

PubMed

Kardaetz, Sascha; Strube, Torsten; Brüggemann, Rainer; Nützmann, Gunnar

2008-07-01

We applied the complex ecosystem model EMMO, which was adopted to the shallow lake Müggelsee (Germany), in order to evaluate a large set of ecological scenarios. By means of EMMO, 33 scenarios and 17 indicators were defined to characterize their effects on the lake ecosystem. The indicators were based on model outputs of EMMO and can be separated into biological indicators, such as chlorophyll-a and cyanobacteria, and hydro-chemical indicators, such as phosphorus. The question to be solved was, what is the ranking of the scenarios based on their characterization by these 17 indicators? And how can we handle high quantities of complex data within evaluation procedures? The scenario evaluation was performed by partial order theory which, however, did not provide a clear result. By subsequently applying the hierarchical cluster analysis (complete linkage) it was possible to reduce the data matrix to indicator and scenario representatives. Even though this step implies losses of information, it simplifies the application of partial order theory and the post processing by METEOR. METEOR is derived from partial order theory and allows the stepwise aggregation of indicators, which subsequently leads to a distinct and clear decision. In the final evaluation result the best scenario was the one which defines a minimum nutrient input and no phosphorus release from the sediment while the worst scenario is characterized by a maximum nutrient input and extensive phosphorus release from the sediment. The reasonable and comprehensive results show that the combination of partial order, cluster analysis and METEOR can handle big amounts of data in a very clear and transparent way, and therefore is ideal in the context of complex ecosystem models, like that we applied.

Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate.

PubMed

Kotlyar, Victor V; Almazov, Anton A; Khonina, Svetlana N; Soifer, Victor A; Elfstrom, Henna; Turunen, Jari

2005-05-01

We deduce and study an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) that imparts an arbitrary-order phase singularity on the light field. Estimates for the optical vortex radius that depends on the singularity's integer order n (also termed topological charge, or order of the dislocation) have been derived. The near-zero vortex intensity is shown to be proportional to rho2n, where p is the radial coordinate. Also, an analytical expression for Fresnel diffraction of the Gaussian beam by a SPP with nth-order singularity is analyzed. The far-field intensity distribution is derived. The radius of maximal intensity is shown to depend on the singularity number. The behavior of the Gaussian beam intensity after a SPP with second-order singularity (n = 2) is studied in more detail. The parameters of the light beams generated numerically with the Fresnel transform and via analytical formulas are in good agreement. In addition, the light fields with first- and second-order singularities were generated by a 32-level SPP fabricated on the resist by use of the electron-beam lithography technique.

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.

On the identification of continuous vibrating systems modelled by hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Udwadia, F. E.; Garba, J. A.

1983-01-01

This paper deals with the identification of spatially varying parameters in systems of finite spatial extent which can be described by second order hyperbolic differential equations. Two questions have been addressed. The first deals with 'partial identification' and inquires into the possibility of retrieving all the eigenvalues of the system from response data obtained at one location x-asterisk epsilon (0, 1). The second deals with the identification of the distributed coefficients rho(x), a(x) and b(x). Sufficient conditions for unique identification of all the eigenvalues of the system are obtained, and conditions under which the coefficients can be uniquely identified using suitable response data obtained at one point in the spatial domain are determined. Application of the results and their usefulness is demonstrated in the identification of the properties of tall building structural systems subjected to dynamic load environments.

Deep tissue near infrared second derivative spectrophotometry for the assessment of claudication in peripheral arterial disease.

PubMed

Koutsiaris, Aristotle G

2017-01-01

The purpose of this study was the application of a second derivative near infrared spectrophotometric (NIRS) technique to the human calf muscle in order to see if peripheral arterial disease (PAD) patients can be discriminated from control subjects, before, during and after a standard treadmill exercise test. Three groups of human subjects were studied: group A consisted of 10 control subjects and groups B and C were formed by PAD patients classified as Fontaine's stage 2a (5 patients) and 2b (10 patients), respectively. The measurement protocol for all groups was 9.75 minutes of standing up (phase 1), 1 minute of exercise (phase 2) and 1 minute of rest (phase 3). Seven variables were defined at different times from the onset of the measurement protocol. All variables were significantly higher (p < 0.05) in group A in comparison to groups B and C. The level of significance was ten times higher (p < 0.005) at the onset (15 seconds) of the experiment and during phases 2 and 3. However, none of the variables in group B was significantly different from those in group C. It is shown for the first time that a second derivative NIRS technique can discriminate (p = 0.003) healthy subjects from PAD patients, in just 15 seconds of standing, with no exercise requirement. More experiments are required in order to uncover the full potential of the technique in the diagnosis of the PAD.

Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions

NASA Astrophysics Data System (ADS)

Kamiński, Wojciech; Steinhaus, Sebastian

2013-12-01

We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters. This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron. To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor. Furthermore, we expand the discussion of the asymptotic formula to next to leading order terms, prove some of their properties and derive a recursion relation for the full 6j symbol.

On the Well-Definedness of the Order of an Ordinary Differential Equation

ERIC Educational Resources Information Center

Dobbs, David E.

2006-01-01

It is proved that if the differential equations "y[(n)] = f(x,y,y[prime],...,y[(n-1)])" and "y[(m)] = g(x,y,y[prime],...,y[(m-1)])" have the same particular solutions in a suitable region where "f" and "g" are continuous real-valued functions with continuous partial derivatives (alternatively, continuous functions satisfying the classical…

Thermal equation of state of TiC: A synchrotron x-ray diffraction study

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

Yu Xiaohui; National Lab for Condensed Matter Physics, Institute of Physics, CAS, Beijing 100080; Department of Physics, University of Science and Technology of China, Hefei 230026

2010-06-15

The pressure-volume-temperature measurements were carried out for titanium carbide (TiC) at pressures and temperatures up to 8.1 GPa and 1273 K using energy-dispersive synchrotron x-ray diffraction. Thermoelastic parameters were derived for TiC based on a modified high-temperature Birch-Murnaghan equation of state and a thermal pressure approach. With the pressure derivative of the bulk modulus, K{sub 0}{sup '}, fixed at 4.0, we obtain: the ambient bulk modulus K{sub 0}=268(6) GPa, which is comparable to previously reported value; temperature derivative of bulk modulus at constant pressure ({partial_derivative}K{sub T}/{partial_derivative}T){sub P}=-0.026(9) GPa K{sup -1}, volumetric thermal expansivity {alpha}{sub T}(K{sup -1})=a+bT with a=1.62(12)x10{sup -5} K{supmore » -1} and b=1.07(17)x10{sup -8} K{sup -2}, pressure derivative of thermal expansion ({partial_derivative}{alpha}/{partial_derivative}P){sub T}=(-3.62{+-}1.14)x10{sup -7} GPa{sup -1} K{sup -1}, and temperature derivative of bulk modulus at constant volume ({partial_derivative}K{sub T}/{partial_derivative}T){sub V}=-0.015(8) GPa K{sup -1}. These results provide fundamental thermophysical properties for TiC for the first time and are important to theoretical and computational modeling of transition metal carbides.« less

Thermal equation-of-state of TiC: a synchrotron x-ray diffraction study

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

Yu, Xiaohui; Lin, Zhijun; Zhang, Jianzhong

2009-01-01

The pressure (P)-volume (V)-temperature (T) measurements were carried out for titanium carbide at pressures and temperatures up to 8.1 GPa and 1273 K using energy-dispersive synchrotron x-ray diffraction. Thermoelastic parameters were derived for TiC based on a modified high-temperature Birch-Murnaghan equation of state and a thermal-pressure approach. With the pressure derivative of the bulk modulus, K'{sub 0}, fixed at 4.0, we obtain: the ambient bulk modulus K{sub 0} = 268(6) GPa, temperature derivative of bulk modulus at constant pressure ({partial_derivative}K{sub T}/{partial_derivative}T){sub p} = -0.026(9) GPa K{sup -1}, volumetric thermal expansivity a{sub T}(K{sup -1}) = a + bT with a =more » 1.62(12) x 10{sup -5} K{sup -1} and b = 1.07(17) x 10{sup -8} K{sup -2}, pressure derivative of thermal expansion ({partial_derivative}a/{partial_derivative}P){sub T} = (-3.62 {+-} 1.14) x 10{sup -7} GPa{sup -1} K{sup -1}, and temperature derivative of bulk modulus at constant volume ({partial_derivative}K{sub T}/{partial_derivative}T){sub v} = -0.015 (8) GPa K{sup -1}. These results provide fundamental thermo physical properties for TiC and are important to theoretical and computational modeling of transition metal carbides.« less

Consensus Algorithms for Networks of Systems with Second- and Higher-Order Dynamics

NASA Astrophysics Data System (ADS)

Fruhnert, Michael

This thesis considers homogeneous networks of linear systems. We consider linear feedback controllers and require that the directed graph associated with the network contains a spanning tree and systems are stabilizable. We show that, in continuous-time, consensus with a guaranteed rate of convergence can always be achieved using linear state feedback. For networks of continuous-time second-order systems, we provide a new and simple derivation of the conditions for a second-order polynomials with complex coefficients to be Hurwitz. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. Based on the conditions found, methods to compute feedback gains are proposed. We show that gains can be chosen such that consensus is achieved robustly over a variety of communication structures and system dynamics. We also consider the use of static output feedback. For networks of discrete-time second-order systems, we provide a new and simple derivation of the conditions for a second-order polynomials with complex coefficients to be Schur. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. We show that consensus can always be achieved for marginally stable systems and discretized systems. Simple conditions for consensus achieving controllers are obtained when the Laplacian eigenvalues are all real. For networks of continuous-time time-variant higher-order systems, we show that uniform consensus can always be achieved if systems are quadratically stabilizable. In this case, we provide a simple condition to obtain a linear feedback control. For networks of discrete-time higher-order systems, we show that constant gains can be chosen such that consensus is achieved for a variety of network topologies. First, we develop simple results for networks of time-invariant systems and networks of time-variant systems that are given in controllable canonical form. Second, we formulate the problem in terms of Linear Matrix Inequalities (LMIs). The condition found simplifies the design process and avoids the parallel solution of multiple LMIs. The result yields a modified Algebraic Riccati Equation (ARE) for which we present an equivalent LMI condition.

Simplified combustion noise theory yielding a prediction of fluctuating pressure level

NASA Technical Reports Server (NTRS)

Huff, R. G.

1984-01-01

The first order equations for the conservation of mass and momentum in differential form are combined for an ideal gas to yield a single second order partial differential equation in one dimension and time. Small perturbation analysis is applied. A Fourier transformation is performed that results in a second order, constant coefficient, nonhomogeneous equation. The driving function is taken to be the source of combustion noise. A simplified model describing the energy addition via the combustion process gives the required source information for substitution in the driving function. This enables the particular integral solution of the nonhomogeneous equation to be found. This solution multiplied by the acoustic pressure efficiency predicts the acoustic pressure spectrum measured in turbine engine combustors. The prediction was compared with the overall sound pressure levels measured in a CF6-50 turbofan engine combustor and found to be in excellent agreement.

An improved 2D MoF method by using high order derivatives

NASA Astrophysics Data System (ADS)

Chen, Xiang; Zhang, Xiong

2017-11-01

The MoF (Moment of Fluid) method is one of the most accurate approaches among various interface reconstruction algorithms. Alike other second order methods, the MoF method needs to solve an implicit optimization problem to obtain the optimal approximate interface, so an iteration process is inevitable under most circumstances. In order to solve the optimization efficiently, the properties of the objective function are worthy of studying. In 2D problems, the first order derivative has been deduced and applied in the previous researches. In this paper, the high order derivatives of the objective function are deduced on the convex polygon. We show that the nth (n ≥ 2) order derivatives are discontinuous, and the number of the discontinuous points is two times the number of the polygon edge. A rotation algorithm is proposed to successively calculate these discontinuous points, thus the target interval where the optimal solution is located can be determined. Since the high order derivatives of the objective function are continuous in the target interval, the iteration schemes based on high order derivatives can be used to improve the convergence rate. Moreover, when iterating in the target interval, the value of objective function and its derivatives can be directly updated without explicitly solving the volume conservation equation. The direct update makes a further improvement of the efficiency especially when the number of edges of the polygon is increasing. The Halley's method, which is based on the first three order derivatives, is applied as the iteration scheme in this paper and the numerical results indicate that the CPU time is about half of the previous method on the quadrilateral cell and is about one sixth on the decagon cell.

On the Tracy-Widomβ Distribution for β=6

NASA Astrophysics Data System (ADS)

Grava, Tamara; Its, Alexander; Kapaev, Andrei; Mezzadri, Francesco

2016-11-01

We study the Tracy-Widom distribution function for Dyson's β-ensemble with β = 6. The starting point of our analysis is the recent work of I. Rumanov where he produces a Lax-pair representation for the Bloemendal-Virág equation. The latter is a linear PDE which describes the Tracy-Widom functions corresponding to general values of β. Using his Lax pair, Rumanov derives an explicit formula for the Tracy-Widom β=6 function in terms of the second Painlevé transcendent and the solution of an auxiliary ODE. Rumanov also shows that this formula allows him to derive formally the asymptotic expansion of the Tracy-Widom function. Our goal is to make Rumanov's approach and hence the asymptotic analysis it provides rigorous. In this paper, the first one in a sequel, we show that Rumanov's Lax-pair can be interpreted as a certain gauge transformation of the standard Lax pair for the second Painlevé equation. This gauge transformation though contains functional parameters which are defined via some auxiliary nonlinear ODE which is equivalent to the auxiliary ODE of Rumanov's formula. The gauge-interpretation of Rumanov's Lax-pair allows us to highlight the steps of the original Rumanov's method which needs rigorous justifications in order to make the method complete. We provide a rigorous justification of one of these steps. Namely, we prove that the Painlevé function involved in Rumanov's formula is indeed, as it has been suggested by Rumanov, the Hastings-McLeod solution of the second Painlevé equation. The key issue which we also discuss and which is still open is the question of integrability of the auxiliary ODE in Rumanov's formula. We note that this question is crucial for the rigorous asymptotic analysis of the Tracy-Widom function. We also notice that our work is a partial answer to one of the problems related to the β-ensembles formulated by Percy Deift during the June 2015 Montreal Conference on integrable systems.

On a modified streamline curvature method for the Euler equations

NASA Technical Reports Server (NTRS)

Cordova, Jeffrey Q.; Pearson, Carl E.

1988-01-01

A modification of the streamline curvature method leads to a quasilinear second-order partial differential equation for the streamline coordinate function. The existence of a stream function is not required. The method is applied to subsonic and supersonic nozzle flow, and to axially symmetric flow with swirl. For many situations, the associated numerical method is both fast and accurate.

Reformulating the Schrödinger equation as a Shabat-Zakharov system

NASA Astrophysics Data System (ADS)

Boonserm, Petarpa; Visser, Matt

2010-02-01

We reformulate the second-order Schrödinger equation as a set of two coupled first-order differential equations, a so-called "Shabat-Zakharov system" (sometimes called a "Zakharov-Shabat" system). There is considerable flexibility in this approach, and we emphasize the utility of introducing an "auxiliary condition" or "gauge condition" that is used to cut down the degrees of freedom. Using this formalism, we derive the explicit (but formal) general solution to the Schrödinger equation. The general solution depends on three arbitrarily chosen functions, and a path-ordered exponential matrix. If one considers path ordering to be an "elementary" process, then this represents complete quadrature, albeit formal, of the second-order linear ordinary differential equation.

Symbolic Algebra Development for Higher-Order Electron Propagator Formulation and Implementation.

PubMed

Tamayo-Mendoza, Teresa; Flores-Moreno, Roberto

2014-06-10

Through the use of symbolic algebra, implemented in a program, the algebraic expression of the elements of the self-energy matrix for the electron propagator to different orders were obtained. In addition, a module for the software package Lowdin was automatically generated. Second- and third-order electron propagator results have been calculated to test the correct operation of the program. It was found that the Fortran 90 modules obtained automatically with our algorithm succeeded in calculating ionization energies with the second- and third-order electron propagator in the diagonal approximation. The strategy for the development of this symbolic algebra program is described in detail. This represents a solid starting point for the automatic derivation and implementation of higher-order electron propagator methods.

Modeling and simulation of continuous wave velocity radar based on third-order DPLL

NASA Astrophysics Data System (ADS)

Di, Yan; Zhu, Chen; Hong, Ma

2015-02-01

Second-order digital phase-locked-loop (DPLL) is widely used in traditional Continuous wave (CW) velocity radar with poor performance in high dynamic conditions. Using the third-order DPLL can improve the performance. Firstly, the echo signal model of CW radar is given. Secondly, theoretical derivations of the tracking performance in different velocity conditions are given. Finally, simulation model of CW radar is established based on Simulink tool. Tracking performance of the two kinds of DPLL in different acceleration and jerk conditions is studied by this model. The results show that third-order PLL has better performance in high dynamic conditions. This model provides a platform for further research of CW radar.

Second-order Boltzmann equation: gauge dependence and gauge invariance

NASA Astrophysics Data System (ADS)

Naruko, Atsushi; Pitrou, Cyril; Koyama, Kazuya; Sasaki, Misao

2013-08-01

In the context of cosmological perturbation theory, we derive the second-order Boltzmann equation describing the evolution of the distribution function of radiation without a specific gauge choice. The essential steps in deriving the Boltzmann equation are revisited and extended given this more general framework: (i) the polarization of light is incorporated in this formalism by using a tensor-valued distribution function; (ii) the importance of a choice of the tetrad field to define the local inertial frame in the description of the distribution function is emphasized; (iii) we perform a separation between temperature and spectral distortion, both for the intensity and polarization for the first time; (iv) the gauge dependence of all perturbed quantities that enter the Boltzmann equation is derived, and this enables us to check the correctness of the perturbed Boltzmann equation by explicitly showing its gauge-invariance for both intensity and polarization. We finally discuss several implications of the gauge dependence for the observed temperature.

A comparison of Redlich-Kister polynomial and cubic spline representations of the chemical potential in phase field computations

DOE PAGES

Teichert, Gregory H.; Gunda, N. S. Harsha; Rudraraju, Shiva; ...

2016-12-18

Free energies play a central role in many descriptions of equilibrium and non-equilibrium properties of solids. Continuum partial differential equations (PDEs) of atomic transport, phase transformations and mechanics often rely on first and second derivatives of a free energy function. The stability, accuracy and robustness of numerical methods to solve these PDEs are sensitive to the particular functional representations of the free energy. In this communication we investigate the influence of different representations of thermodynamic data on phase field computations of diffusion and two-phase reactions in the solid state. First-principles statistical mechanics methods were used to generate realistic free energymore » data for HCP titanium with interstitially dissolved oxygen. While Redlich-Kister polynomials have formed the mainstay of thermodynamic descriptions of multi-component solids, they require high order terms to fit oscillations in chemical potentials around phase transitions. Here, we demonstrate that high fidelity fits to rapidly fluctuating free energy functions are obtained with spline functions. As a result, spline functions that are many degrees lower than Redlich-Kister polynomials provide equal or superior fits to chemical potential data and, when used in phase field computations, result in solution times approaching an order of magnitude speed up relative to the use of Redlich-Kister polynomials.« less

Analysis of nonlinear axial vibration of single-walled carbon nanotubes using Homotopy perturbation method

NASA Astrophysics Data System (ADS)

Fatahi-Vajari, A.; Azimzadeh, Z.

2018-05-01

This paper investigates the nonlinear axial vibration of single-walled carbon nanotubes (SWCNTs) based on Homotopy perturbation method (HPM). A second order partial differential equation that governs the nonlinear axial vibration for such nanotubes is derived using doublet mechanics (DM) theory. To obtain the nonlinear natural frequency in axial vibration mode, this nonlinear equation is solved using HPM. The influences of some commonly used boundary conditions, amplitude of vibration, changes in vibration modes and variations of the nanotubes geometrical parameters on the nonlinear axial vibration characteristics of SWCNTs are discussed. It was shown that unlike the linear one, the nonlinear natural frequency is dependent to maximum vibration amplitude. Increasing the maximum vibration amplitude decreases the natural frequency of vibration compared to the predictions of the linear models. However, with increase in tube length, the effect of the amplitude on the natural frequency decreases. It was also shown that the amount and variation of nonlinear natural frequency is more apparent in higher mode vibration and two clamped boundary conditions. To show the accuracy and capability of this method, the results obtained herein were compared with the fourth order Runge-Kuta numerical results and good agreement was observed. It is notable that the results generated herein are new and can be served as a benchmark for future works.

Second derivatives for approximate spin projection methods

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

Thompson, Lee M.; Hratchian, Hrant P., E-mail: hhratchian@ucmerced.edu

2015-02-07

The use of broken-symmetry electronic structure methods is required in order to obtain correct behavior of electronically strained open-shell systems, such as transition states, biradicals, and transition metals. This approach often has issues with spin contamination, which can lead to significant errors in predicted energies, geometries, and properties. Approximate projection schemes are able to correct for spin contamination and can often yield improved results. To fully make use of these methods and to carry out exploration of the potential energy surface, it is desirable to develop an efficient second energy derivative theory. In this paper, we formulate the analytical secondmore » derivatives for the Yamaguchi approximate projection scheme, building on recent work that has yielded an efficient implementation of the analytical first derivatives.« less

Concerted Mitigation of O···H and C(π)···H Interactions Prospects Sixfold Gain in Optical Nonlinearity of Ionic Stilbazolium Derivatives

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

Cole, Jacqueline M.; Lin, Tze-Chia; Edwards, Alison J.

2015-03-04

DAST (4-dimethylamino-N-methyl-4-stilbazolium tosylate) is the most commercially successful organic nonlinear optical (NLO) material for frequency-doubling, integrated optics, and THz wave applications. Its success is predicated on its high optical nonlinearity with concurrent sufficient thermal stability. Many chemical derivatives of DAST have therefore been developed to optimize their properties; yet, to date, none have surpassed the overall superiority of DAST for NLO photonic applications. This is perhaps because DAST is an ionic salt wherein its NLO-active cation is influenced by multiple types of subtle intermolecular forces that are hard to quantify, thus, making difficult the molecular engineering of better functioning DASTmore » derivatives. Here, we establish a model parameter, ηinter, that isolates the influence of intermolecular interactions on second-order optical nonlinearity in DAST and its derivatives, using second-harmonic generation (SHG) as a qualifier; by systematically mapping intercorrelations of all possible pairs of intermolecular interactions to ηinter, we uncover a relationship between concerted intermolecular interactions and SHG output. This correlation reveals that a sixfold gain in the intrinsic second-order NLO performance of DAST is possible, by eliminating the identified interactions. This prediction offers the first opportunity to systematically design next-generation DAST-based photonic device nanotechnology to realize such a prospect.« less

Fluid-dynamically coupled solid propellant combustion instability - cold flow simulation

NASA Astrophysics Data System (ADS)

Ben-Reuven, M.

1983-10-01

The near-wall processes in an injected, axisymmetric, viscous flow is examined. Solid propellant rocket instability, in which cold flow simulation is evaluated as a tool to elucidate possible instability driving mechanisms is studied. One such prominent mechanism seems to be visco-acoustic coupling. The formulation is presented in terms of a singular boundary layer problem, with detail (up to second order) given only to the near wall region. The injection Reynolds number is assumed large, and its inverse square root serves as an appropriate small perturbation quantity. The injected Mach number is also small, and taken of the same order as the aforesaid small quantity. The radial-dependence of the inner solutions up to second order is solved, in polynominal form. This leaves the (x,t) dependence to much simpler partial differential equations. Particular results demonstrate the existence of a first order pressure perturbation, which arises due to the dissipative near wall processes. This pressure and the associated viscous friction coefficient are shown to agree very well with experimental injected flow data.

A chemometric-assisted method for the simultaneous determination of malachite green and crystal violet in water based on absorbance-pH data generated by a homemade pH gradient apparatus.

PubMed

Yu, Shuling; Yuan, Xuejie; Yang, Jing; Yuan, Jintao; Shi, Jiahua; Wang, Yali; Chen, Yuewen; Gao, Shufang

2015-01-01

An attractive method of generating second-order data was developed by a dropping technique to generate pH gradient simultaneously coupled with diode-array spectrophotometer scanning. A homemade apparatus designed for the pH gradient. The method and the homemade apparatus were used to simultaneously determine malachite green (MG) and crystal violet (CV) in water samples. The absorbance-pH second-order data of MG or CV were obtained from the spectra of MG or CV in a series of pH values of HCl-KCl solution. The second-order data of mixtures containing MG and CV that coexisted with interferents were analyzed using multidimensional partial least-squares with residual bilinearization. The method and homemade apparatus were used to simultaneously determine MG and CV in fish farming water samples and in river ones with satisfactory results. The presented method and the homemade apparatus could serve as an alternative tool to handle some analysis problems. Copyright © 2015 Elsevier B.V. All rights reserved.

Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator

NASA Astrophysics Data System (ADS)

Wu, Baisheng; Liu, Weijia; Lim, C. W.

2017-07-01

A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate.

Growth responses of Neurospora crassa to increased partial pressures of the noble gases and nitrogen.

PubMed

Buchheit, R G; Schreiner, H R; Doebbler, G F

1966-02-01

Buchheit, R. G. (Union Carbide Corp., Tonawanda, N.Y.), H. R. Schreiner, and G. F. Doebbler. Growth responses of Neurospora crassa to increased partial pressures of the noble gases and nitrogen. J. Bacteriol. 91:622-627. 1966.-Growth rate of the fungus Neurospora crassa depends in part on the nature of metabolically "inert gas" present in its environment. At high partial pressures, the noble gas elements (helium, neon, argon, krypton, and xenon) inhibit growth in the order: Xe > Kr> Ar > Ne > He. Nitrogen (N(2)) closely resembles He in inhibitory effectiveness. Partial pressures required for 50% inhibition of growth were: Xe (0.8 atm), Kr (1.6 atm), Ar (3.8 atm), Ne (35 atm), and He ( approximately 300 atm). With respect to inhibition of growth, the noble gases and N(2) differ qualitatively and quantitatively from the order of effectiveness found with other biological effects, i.e., narcosis, inhibition of insect development, depression of O(2)-dependent radiation sensitivity, and effects on tissue-slice glycolysis and respiration. Partial pressures giving 50% inhibition of N. crassa growth parallel various physical properties (i.e., solubilities, solubility ratios, etc.) of the noble gases. Linear correlation of 50% inhibition pressures to the polarizability and of the logarithm of pressure to the first and second ionization potentials suggests the involvement of weak intermolecular interactions or charge-transfer in the biological activity of the noble gases.

The application of the mesh-free method in the numerical simulations of the higher-order continuum structures

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

Sun, Yuzhou, E-mail: yuzhousun@126.com; Chen, Gensheng; Li, Dongxia

2016-06-08

This paper attempts to study the application of mesh-free method in the numerical simulations of the higher-order continuum structures. A high-order bending beam considers the effect of the third-order derivative of deflections, and can be viewed as a one-dimensional higher-order continuum structure. The moving least-squares method is used to construct the shape function with the high-order continuum property, the curvature and the third-order derivative of deflections are directly interpolated with nodal variables and the second- and third-order derivative of the shape function, and the mesh-free computational scheme is establish for beams. The coupled stress theory is introduced to describe themore » special constitutive response of the layered rock mass in which the bending effect of thin layer is considered. The strain and the curvature are directly interpolated with the nodal variables, and the mesh-free method is established for the layered rock mass. The good computational efficiency is achieved based on the developed mesh-free method, and some key issues are discussed.« less

Observation model and parameter partials for the JPL VLBI parameter estimation software MODEST/1991

NASA Technical Reports Server (NTRS)

Sovers, O. J.

1991-01-01

A revision is presented of MASTERFIT-1987, which it supersedes. Changes during 1988 to 1991 included introduction of the octupole component of solid Earth tides, the NUVEL tectonic motion model, partial derivatives for the precession constant and source position rates, the option to correct for source structure, a refined model for antenna offsets, modeling the unique antenna at Richmond, FL, improved nutation series due to Zhu, Groten, and Reigber, and reintroduction of the old (Woolard) nutation series for simulation purposes. Text describing the relativistic transformations and gravitational contributions to the delay model was also revised in order to reflect the computer code more faithfully.

Partial trisomy 16p (16p12.2→pter) and partial monosomy 22q (22q13.31 →qter) presenting with fetal ascites and ventriculomegaly: prenatal diagnosis and array comparative genomic hybridization characterization.

PubMed

Chen, Chih-Ping; Su, Yi-Ning; Young, Richard Shih-Hung; Tsai, Fuu-Jen; Wu, Pei-Chen; Chern, Schu-Rern; Town, Dai-Dyi; Pan, Chen-Wen; Wang, Wayseen

2010-12-01

To present prenatal diagnosis and array comparative genomic hybridization (aCGH) characterization of partial trisomy 16p (16p12.2→pter) and partial monosomy 22q (22q13.31→qter) presenting with fetal ascites and ventriculomegaly in the second trimester. A 31-year-old woman, gravida 2, para 1, was referred to the hospital at 20 weeks of gestation because of fetal ascites. Amniocentesis revealed a derivative chromosome 22. Subsequent parental karyotyping revealed that the father carried a balanced reciprocal translocation between 16p12 and 22q13. Bacterial artificial chromosome-based aCGH using amniocyte DNA demonstrated partial trisomy 16p and partial monosomy 22q [arr cgh 16p13.3p12.2 (CTD-3077J14→RP11-650D5)x3, 22q13.31q13.33 (RP1-111J24→CTD-3035C16)x1]. Oligonucleotide-based aCGH showed a 20.9-Mb duplication of distal 16p and an approximate 3.7-Mb deletion of distal 22q. Level II ultrasound revealed fetal ascites and ventriculomegaly. The pregnancy was terminated and a malformed male fetus was delivered with craniofacial dysmorphism and abnormalities of the digits. The fetal karyotype was 46,XY,der(22)t(16;22)(p12.2;q13.31)pat. The paternal karyotype was 46,XY,t(16;22)(p12.2;q13.31). Partial trisomy 16p can be associated with fetal ascites and ventriculomegaly in the second trimester. Prenatal sonographic detection of fetal ascites in association with ventriculomegaly should alert chromosomal abnormalities and prompt cytogenetic investigation, which may lead to the identification of an unexpected parental translocation involving chromosomal segments associated with cerebral and vascular abnormalities. Copyright © 2010 Taiwan Association of Obstetric & Gynecology. Published by Elsevier B.V. All rights reserved.

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.

New results on the realizability of Reynolds stress turbulence closures

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Abid, Ridha; Durbin, Paul A.

1993-01-01

The realizability of Reynolds stress models in homogeneous turbulence is critically assessed from a theoretical standpoint. It is proven that a well known second-order closure formulated by Shih and Lumley using the strong realizability constraints of Schumann is, in fact, not a realizable model. The problem arises from the failure to properly satisfy the necessary positive second time derivative constraint when a principal Reynolds stress vanishes - a fatal flaw that becomes apparent when the non-analytic terms in their model are made single-valued as required on physical grounds. It is furthermore shown that the centrifugal acceleration generated by rotations of the principal axes of the Reynolds stress tensor can make the second derivative singular at the most extreme limits of realizable turbulence. This previously overlooked effect appears to make it impossible to identically satisfy the strong form of realizability in any version of the present generation of second-order closures. On the other hand, models properly formulated to satisfy the weak form of realizability - wherein states of one or two component turbulence are not accessible in finite time are found to be realizable. However, unlike the simpler and more commonly used second order closures, these models can be ill-behaved near the extreme limits of realizable turbulence due to the way that higher-degree nonlinearities are often unnecessarily introduced to satisfy realizability. Illustrative computations of homogeneous shear flows are presented to demonstrate these points which can have important implications for turbulence modeling.

COMMENT Comment on 'Conservation laws of higher order nonlinear PDEs and the variational conservation laws in the class with mixed derivatives'

NASA Astrophysics Data System (ADS)

Sarlet, W.

2010-11-01

In a recent paper (R Narain and A H Kara 2010 J. Phys. A: Math. Theor. 43 085205), the authors claim to be applying Noether's theorem to higher-order partial differential equations and state that in a large class of examples 'the resultant conserved flows display some previously unknown interesting 'divergence properties' owing to the presence of the mixed derivatives' (citation from their abstract). It turns out that what this obscure sentence is meant to say is that the vector whose divergence must be zero (according to Noether's theorem), turns out to have non-zero divergence and subsequently must be modified to obtain a true conservation law. Clearly this cannot be right: we explain in detail the main source of the error.

Higher-Order Hamiltonian Model for Unidirectional Water Waves

NASA Astrophysics Data System (ADS)

Bona, J. L.; Carvajal, X.; Panthee, M.; Scialom, M.

2018-04-01

Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of these more complex equations is that their solutions corresponding to physically relevant initial perturbations of the rest state may be accurate on a much longer timescale. The initial value problem for the class of equations that emerges from our derivation is then considered. A local well-posedness theory is straightforwardly established by a contraction mapping argument. A subclass of these equations possess a special Hamiltonian structure that implies the local theory can be continued indefinitely.

Monte Carlo modeling of spatial coherence: free-space diffraction

PubMed Central

Fischer, David G.; Prahl, Scott A.; Duncan, Donald D.

2008-01-01

We present a Monte Carlo method for propagating partially coherent fields through complex deterministic optical systems. A Gaussian copula is used to synthesize a random source with an arbitrary spatial coherence function. Physical optics and Monte Carlo predictions of the first- and second-order statistics of the field are shown for coherent and partially coherent sources for free-space propagation, imaging using a binary Fresnel zone plate, and propagation through a limiting aperture. Excellent agreement between the physical optics and Monte Carlo predictions is demonstrated in all cases. Convergence criteria are presented for judging the quality of the Monte Carlo predictions. PMID:18830335

Structure and reactivity of boron-ate complexes derived from primary and secondary boronic esters.

PubMed

Feeney, Kathryn; Berionni, Guillaume; Mayr, Herbert; Aggarwal, Varinder K

2015-06-05

Boron-ate complexes derived from primary and secondary boronic esters and aryllithiums have been isolated, and the kinetics of their reactions with carbenium ions studied. The second-order rate constants have been used to derive nucleophilicity parameters for the boron-ate complexes, revealing that nucleophilicity increased with (i) electron-donating aromatics on boron, (ii) neopentyl glycol over pinacol boronic esters, and (iii) 12-crown-4 ether.

Chemical composition of matrix-embedded ternary II-VI nanocrystals derived from first- and second-order Raman spectra

NASA Astrophysics Data System (ADS)

Azhniuk, Yu. M.; Hutych, Yu. I.; Lopushansky, V. V.; Prymak, M. V.; Gomonnai, A. V.; Zahn, D. R. T.

2016-12-01

A one- and multiphonon Raman scattering study is performed for an extensive set of CdS1-xSex, Cd1-yZnyS, Cd1-yZnySe, and CdSe1-xTex nanocrystals to investigate the applicability of first- and second-order Raman spectra for the determination of the matrix-embedded ternary nanocrystal composition. For one-mode ternary systems both the LO and 2LO phonon frequencies in the Raman spectra are shown to be a good measure of the nanocrystal composition. For two-mode systems, the approaches based on the difference of the LO phonon frequencies (first-order Raman spectra) or double LO overtone and combination tone frequencies (second-order Raman spectra) as well as on the LO phonon band intensity ratios are analysed. The weak electron-phonon coupling in the II-VI nanocrystals and the polaron constant values for the nanocrystal sublattices are discussed.

Work Engagement among Rescue Workers: Psychometric Properties of the Portuguese UWES

PubMed Central

Sinval, Jorge; Marques-Pinto, Alexandra; Queirós, Cristina; Marôco, João

2018-01-01

Rescue workers have a stressful and risky occupation where being engaged is crucial to face physical and emotional risks in order to help other persons. This study aims to estimate work engagement levels of rescue workers (namely comparing nurses, firefighters, and police officers) and to assess the validity evidence related to the internal structure of the Portuguese versions of the UWES-17 and UWES-9, namely, dimensionality, measurement invariance between occupational groups, and reliability of the scores. To evaluate the dimensionality, we compared the fit of the three-factor model with the fit of a second-order model. A Portuguese version of the instrument was applied to a convenience sample of 3,887 rescue workers (50% nurses, 39% firefighters, and 11% police officers). Work engagement levels were moderate to high, with firefighters being the highest and nurses being the lowest engaged. Psychometric properties were evaluated in the three-factor original structure revealing acceptable fit to the data in the UWES-17, although the UWES-9 had better psychometric properties. Given the observed statistically significant correlations between the three original factors, we proposed a 2nd hierarchal structure that we named work engagement. The UWES-9 first-order model obtained full uniqueness measurement invariance, and the second-order model obtained partial (metric) second-order invariance. PMID:29403403

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.

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

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

An efficient and robust algorithm for two dimensional time dependent incompressible Navier-Stokes equations: High Reynolds number flows

NASA Technical Reports Server (NTRS)

Goodrich, John W.

1991-01-01

An algorithm is presented for unsteady two-dimensional incompressible Navier-Stokes calculations. This algorithm is based on the fourth order partial differential equation for incompressible fluid flow which uses the streamfunction as the only dependent variable. The algorithm is second order accurate in both time and space. It uses a multigrid solver at each time step. It is extremely efficient with respect to the use of both CPU time and physical memory. It is extremely robust with respect to Reynolds number.

Evaluation of the kinetic oxidation of aqueous volatile organic compounds by permanganate.

PubMed

Mahmoodlu, Mojtaba G; Hassanizadeh, S Majid; Hartog, Niels

2014-07-01

The use of permanganate solutions for in-situ chemical oxidation (ISCO) is a well-established groundwater remediation technology, particularly for targeting chlorinated ethenes. The kinetics of oxidation reactions is an important ISCO remediation design aspect that affects the efficiency and oxidant persistence. The overall rate of the ISCO reaction between oxidant and contaminant is typically described using a second-order kinetic model while the second-order rate constant is determined experimentally by means of a pseudo first order approach. However, earlier studies of chlorinated hydrocarbons have yielded a wide range of values for the second-order rate constants. Also, there is limited insight in the kinetics of permanganate reactions with fuel-derived groundwater contaminants such as toluene and ethanol. In this study, batch experiments were carried out to investigate and compare the oxidation kinetics of aqueous trichloroethylene (TCE), ethanol, and toluene in an aqueous potassium permanganate solution. The overall second-order rate constants were determined directly by fitting a second-order model to the data, instead of typically using the pseudo-first-order approach. The second-order reaction rate constants (M(-1) s(-1)) for TCE, toluene, and ethanol were 8.0×10(-1), 2.5×10(-4), and 6.5×10(-4), respectively. Results showed that the inappropriate use of the pseudo-first-order approach in several previous studies produced biased estimates of the second-order rate constants. In our study, this error was expressed as a function of the extent (P/N) in which the reactant concentrations deviated from the stoichiometric ratio of each oxidation reaction. The error associated with the inappropriate use of the pseudo-first-order approach is negatively correlated with the P/N ratio and reached up to 25% of the estimated second-order rate constant in some previous studies of TCE oxidation. Based on our results, a similar relation is valid for the other volatile organic compounds studied. Copyright © 2013 Elsevier B.V. All rights reserved.

Effect of boron on the structural and magnetic properties of Co{sub 2}FeSi{sub 1-x}B{sub x} Heusler alloys

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

Ramudu, M., E-mail: macrams2@gmail.com; Raja, M. Manivel; Kamat, S. V.

2016-05-23

The partial substitution of Si with B on the structural and magnetic properties of Co{sub 2}FeSi{sub 1-x}Bx (x = 0-0.5) alloys was systematically investigated. X-ray and microstructural investigations show the presence of second phase at the grain boundaries which increases with increasing boron content. From thermal analysis studies, it was observed that L2{sub 1}-B2 ordering temperature remain constant whereas the melting point decreases with increase in boron addition and merges with ordering temperature at x = 0.5. The increase in T{sub C} for the alloys x ≥ 0.25 was attributed to the increase in second phase due to boron.

Some new methods in geomagnetic field modeling applied to the 1960 - 1980 epoch

NASA Technical Reports Server (NTRS)

Langel, R. A.; Estes, R. H.; Mead, G. H.

1981-01-01

The utilization of satellite and surface data together permitted the incorporation of a solution for the anomaly field at each observatory. The residuals of the observatory measurements to such models is commensurate with the actual measurment accuracy. Incorporation of the anomaly estimation enabled the inclusion of stable time derivatives of the spherical harmonic coefficients up to the third derivative. A spherical harmonic model is derived with degree and order 13 in its constant and first time derivative terms, six in its second derivative terms and four in its third derivative terms.

Thermal Equation of State of TiC: A Synchrotron X-ray Diffraction

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

Yu, X.; Lin, Z; Zhang, J

2010-01-01

The pressure-volume-temperature measurements were carried out for titanium carbide (TiC) at pressures and temperatures up to 8.1 GPa and 1273 K using energy-dispersive synchrotron x-ray diffraction. Thermoelastic parameters were derived for TiC based on a modified high-temperature Birch-Murnaghan equation of state and a thermal pressure approach. With the pressure derivative of the bulk modulus, K{prime}{sub 0}, fixed at 4.0, we obtain: the ambient bulk modulus K{sub 0} = 268(6) GPa, which is comparable to previously reported value; temperature derivative of bulk modulus at constant pressure ({partial_derivative}K{sub T}/{partial_derivative}T){sub P} = -0.026(9) GPa K{sup -1}, volumetric thermal expansivity {alpha}{sub T}(K{sup -1}) =more » a+b T with a = 1.62(12) x 10{sup -5} K{sup -1} and b = 1.07(17) x 10{sup -8}K{sup -2}, pressure derivative of thermal expansion ({partial_derivative}{sub {alpha}}/{partial_derivative}{sub P}){sub T} = (-3.62 {+-} 1.14) x 10{sup -7} GPa{sup -1} K{sup -1}, and temperature derivative of bulk modulus at constant volume ({partial_derivative}K{sub T}/{partial_derivative}T){sub V} = -0.015(8) GPa K{sup -1}. These results provide fundamental thermophysical properties for TiC for the first time and are important to theoretical and computational modeling of transition metal carbides.« less

Superconvergent second order Cartesian method for solving free boundary problem for invadopodia formation

NASA Astrophysics Data System (ADS)

Gallinato, Olivier; Poignard, Clair

2017-06-01

In this paper, we present a superconvergent second order Cartesian method to solve a free boundary problem with two harmonic phases coupled through the moving interface. The model recently proposed by the authors and colleagues describes the formation of cell protrusions. The moving interface is described by a level set function and is advected at the velocity given by the gradient of the inner phase. The finite differences method proposed in this paper consists of a new stabilized ghost fluid method and second order discretizations for the Laplace operator with the boundary conditions (Dirichlet, Neumann or Robin conditions). Interestingly, the method to solve the harmonic subproblems is superconvergent on two levels, in the sense that the first and second order derivatives of the numerical solutions are obtained with the second order of accuracy, similarly to the solution itself. We exhibit numerical criteria on the data accuracy to get such properties and numerical simulations corroborate these criteria. In addition to these properties, we propose an appropriate extension of the velocity of the level-set to avoid any loss of consistency, and to obtain the second order of accuracy of the complete free boundary problem. Interestingly, we highlight the transmission of the superconvergent properties for the static subproblems and their preservation by the dynamical scheme. Our method is also well suited for quasistatic Hele-Shaw-like or Muskat-like problems.

Molecular hyperpolarizabilities of new bimetallic ferrocenyl derivatives

NASA Astrophysics Data System (ADS)

Loucif-Saïbi, R.; Delaire, J. A.; Bonazzola, L.; Doisneau, G.; Balavoine, G.; Fillebeen-Khan, T.; Ledoux, I.; Puccetti, G.

1992-11-01

We have investigated the influence of complexation of ferrocenyl derivatives on the second-order hyperpolarizabilities β. This was performed using dc electric field induced second harmonic generation (EFISHG) technique at 1.34 and 1.9 μm. For these new bimetallic ferrocenyl derivatives, significantly increased β values were observed. Our best β value (123.5 × 10 -30 esu at 1.34 μm) is comparable to the highest reported values for organometallic complexes. The nature of the second metal ion has a weak influence on the β values, in consequence to the change of geometry of the associated complex. The validity of the two-level model has been examined in detail: we found that it applies fairly well for the monometallic complexes if one takes into account only the low energy MLCT transition but the contribution of upper levels cannot be ruled out for bimetallic complexes.

Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing

NASA Astrophysics Data System (ADS)

Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.

2017-08-01

The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.

A second-order frequency-aided digital phase-locked loop for Doppler rate tracking

NASA Astrophysics Data System (ADS)

Chie, C. M.

1980-08-01

A second-order digital phase-locked loop (DPLL) has a finite lock range which is a function of the frequency of the incoming signal to be tracked. For this reason, it is not capable of tracking an input with Doppler rate for an indefinite period of time. In this correspondence, an analytical expression for the hold-in time is derived. In addition, an all-digital scheme to alleviate this problem is proposed based on the information obtained from estimating the input signal frequency.

Transoptr — A second order beam transport design code with optimization and constraints

NASA Astrophysics Data System (ADS)

Heighway, E. A.; Hutcheon, R. M.

1981-08-01

This code was written initially to design an achromatic and isochronous reflecting magnet and has been extended to compete in capability (for constrained problems) with TRANSPORT. Its advantage is its flexibility in that the user writes a routine to describe his transport system. The routine allows the definition of general variables from which the system parameters can be derived. Further, the user can write any constraints he requires as algebraic equations relating the parameters. All variables may be used in either a first or second order optimization.

On the thermodynamics of the Swift-Hohenberg theory

NASA Astrophysics Data System (ADS)

Espath, L. F. R.; Sarmiento, A. F.; Dalcin, L.; Calo, V. M.

2017-11-01

We present the microbalance including the microforces, the first- and second-order microstresses for the Swift-Hohenberg equation concomitantly with their constitutive equations, which are consistent with the free-energy imbalance. We provide an explicit form for the microstress structure for a free-energy functional endowed with second-order spatial derivatives. Additionally, we generalize the Swift-Hohenberg theory via a proper constitutive process. Finally, we present one highly resolved three-dimensional numerical simulation to demonstrate the particular form of the resulting microstresses and their interactions in the evolution of the Swift-Hohenberg equation.

On explicit algebraic stress models for complex turbulent flows

NASA Technical Reports Server (NTRS)

Gatski, T. B.; Speziale, C. G.

1992-01-01

Explicit algebraic stress models that are valid for three-dimensional turbulent flows in noninertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope who based his analysis on the Launder, Reece, and Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -- as well as anistropic eddy visosity models -- is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.

Transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto model

NASA Astrophysics Data System (ADS)

Kundu, Prosenjit; Khanra, Pitambar; Hens, Chittaranjan; Pal, Pinaki

2017-11-01

We investigate transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto (SK) model on complex networks both analytically and numerically. We analytically derive self-consistent equations for group angular velocity and order parameter for the model in the thermodynamic limit. Using the self-consistent equations we investigate transition to synchronization in SK model on uncorrelated scale-free (SF) and Erdős-Rényi (ER) networks in detail. Depending on the degree distribution exponent (γ ) of SF networks and phase-frustration parameter, the population undergoes from first-order transition [explosive synchronization (ES)] to second-order transition and vice versa. In ER networks transition is always second order irrespective of the values of the phase-lag parameter. We observe that the critical coupling strength for the onset of synchronization is decreased by phase-frustration parameter in case of SF network where as in ER network, the phase-frustration delays the onset of synchronization. Extensive numerical simulations using SF and ER networks are performed to validate the analytical results. An analytical expression of critical coupling strength for the onset of synchronization is also derived from the self-consistent equations considering the vanishing order parameter limit.

The Law of Self-Acting Machines and Irreversible Processes with Reversible Replicas

NASA Astrophysics Data System (ADS)

Valev, Pentcho

2002-11-01

Clausius and Kelvin saved Carnot theorem and developed the second law by assuming that Carnot machines can work in the absence of an operator and that all the irreversible processes have reversible replicas. The former assumption restored Carnot theorem as an experience of mankind whereas the latter generated "the law of ever increasing entropy". Both assumptions are wrong so it makes sense to return to Carnot theorem (or some equivalent) and test it experimentally. Two testable paradigms - the system performing two types of reversible work and the system in dynamical equilibrium - suggest that perpetuum mobile of the second kind in the presence of an operator is possible. The deviation from the second law prediction, expressed as difference between partial derivatives in a Maxwell relation, measures the degree of structural-functional evolution for the respective system.

MHD Flow and Heat Transfer of a Generalized Burgers’ Fluid due to a Periodic Oscillating and Periodic Heating Plate

NASA Astrophysics Data System (ADS)

Bai, Yu; Jiang, Yue-Hua; Zhang, Yan; Zhao, Hao-Jie

2017-10-01

This paper investigates the MHD flow and heat transfer of the incompressible generalized Burgers’ fluid due to a periodic oscillating plate with the effects of the second order slip and periodic heating plate. The momentum equation is formulated with multi-term fractional derivatives, and by means of viscous dissipation, the fractional derivative is considered in the energy equation. A finite difference scheme is established based on the G1-algorithm, whose convergence is confirmed by the comparison with the analytical solution in an example. Meanwhile the numerical solutions of velocity, temperature and shear stress are obtained. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Increasing the fractional derivative parameter α, the velocity and temperature have a decreasing trend, while the influences of fractional derivative parameter β on the velocity and temperature behave conversely. Increasing the absolute value of the first order slip parameter and the second order slip parameter both cause a decrease of velocity. Furthermore, with the decreasing of the magnetic parameter, the shear stress decreases. Supported by the National Natural Science Foundations of China under Grant Nos. 21576023, 51406008, the National Key Research Program of China under Grant Nos. 2016YFC0700601, 2016YFC0700603 and the BUCEA Post Graduate Innovation Project (PG2017032)

Consistent second-order boundary implementations for convection-diffusion lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Chew, Jia Wei

2018-02-01

In this study, an alternative second-order boundary scheme is proposed under the framework of the convection-diffusion lattice Boltzmann (LB) method for both straight and curved geometries. With the proposed scheme, boundary implementations are developed for the Dirichlet, Neumann and linear Robin conditions in a consistent way. The Chapman-Enskog analysis and the Hermite polynomial expansion technique are first applied to derive the explicit expression for the general distribution function with second-order accuracy. Then, the macroscopic variables involved in the expression for the distribution function is determined by the prescribed macroscopic constraints and the known distribution functions after streaming [see the paragraph after Eq. (29) for the discussions of the "streaming step" in LB method]. After that, the unknown distribution functions are obtained from the derived macroscopic information at the boundary nodes. For straight boundaries, boundary nodes are directly placed at the physical boundary surface, and the present scheme is applied directly. When extending the present scheme to curved geometries, a local curvilinear coordinate system and first-order Taylor expansion are introduced to relate the macroscopic variables at the boundary nodes to the physical constraints at the curved boundary surface. In essence, the unknown distribution functions at the boundary node are derived from the known distribution functions at the same node in accordance with the macroscopic boundary conditions at the surface. Therefore, the advantages of the present boundary implementations are (i) the locality, i.e., no information from neighboring fluid nodes is required; (ii) the consistency, i.e., the physical boundary constraints are directly applied when determining the macroscopic variables at the boundary nodes, thus the three kinds of conditions are realized in a consistent way. It should be noted that the present focus is on two-dimensional cases, and theoretical derivations as well as the numerical validations are performed in the framework of the two-dimensional five-velocity lattice model.

Deriving Laws from Ordering Relations

NASA Technical Reports Server (NTRS)

Knuth, Kevin H.

2003-01-01

It took much effort in the early days of non-Euclidean geometry to break away from the mindset that all spaces are flat and that two distinct parallel lines do not cross. Up to that point, all that was known was Euclidean geometry, and it was difficult to imagine anything else. We have suffered a similar handicap brought on by the enormous relevance of Boolean algebra to the problems of our age-logic and set theory. Previously, I demonstrated that the algebra of questions is not Boolean, but rather is described by the free distributive algebra. To get to this stage took much effort, as many obstacles-most self-placed-had to be overcome. As Boolean algebras were all I had ever known, it was almost impossible for me to imagine working with an algebra where elements do not have complements. With this realization, it became very clear that the sum and product rules of probability theory at the most basic level had absolutely nothing to do with the Boolean algebra of logical statements. Instead, a measure of degree of inclusion can be invented for many different partially ordered sets, and the sum and product rules fall out of the associativity and distributivity of the algebra. To reinforce this very important idea, this paper will go over how these constructions are made, while focusing on the underlying assumptions. I will derive the sum and product rules for a distributive lattice in general and demonstrate how this leads to probability theory on the Boolean lattice and is related to the calculus of quantum mechanical amplitudes on the partially ordered set of experimental setups. I will also discuss the rules that can be derived from modular lattices and their relevance to the cross-ratio of projective geometry.

A combined QSAR and partial order ranking approach to risk assessment.

PubMed

Carlsen, L

2006-04-01

QSAR generated data appear as an attractive alternative to experimental data as foreseen in the proposed new chemicals legislation REACH. A preliminary risk assessment for the aquatic environment can be based on few factors, i.e. the octanol-water partition coefficient (Kow), the vapour pressure (VP) and the potential biodegradability of the compound in combination with the predicted no-effect concentration (PNEC) and the actual tonnage in which the substance is produced. Application of partial order ranking, allowing simultaneous inclusion of several parameters leads to a mutual prioritisation of the investigated substances, the prioritisation possibly being further analysed through the concept of linear extensions and average ranks. The ranking uses endpoint values (log Kow and log VP) derived from strictly linear 'noise-deficient' QSAR models as input parameters. Biodegradation estimates were adopted from the BioWin module of the EPI Suite. The population growth impairment of Tetrahymena pyriformis was used as a surrogate for fish lethality.

Unbalanced field RF electron gun

DOEpatents

Hofler, Alicia

2013-11-12

A design for an RF electron gun having a gun cavity utilizing an unbalanced electric field arrangement. Essentially, the electric field in the first (partial) cell has higher field strength than the electric field in the second (full) cell of the electron gun. The accompanying method discloses the use of the unbalanced field arrangement in the operation of an RF electron gun in order to accelerate an electron beam.

Generation of linear dynamic models from a digital nonlinear simulation

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Krosel, S. M.

1979-01-01

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Hollow Gaussian Schell-model beam and its propagation

NASA Astrophysics Data System (ADS)

Wang, Li-Gang; Wang, Li-Qin

2008-03-01

In this paper, we present a new model, hollow Gaussian Schell-model beams (HGSMBs), to describe the practical dark hollow beams. An analytical propagation formula for HGSMBs passing through a paraxial first-order optical system is derived based on the theory of coherence. Based on the derived formula, an application example showing the influence of spatial coherence on the propagation of beams is illustrated. It is found that the beam propagating properties of HGSMBs will be greatly affected by their spatial coherence. Our model provides a very convenient way for analyzing the propagation properties of partially coherent dark hollow beams.

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

NASA Astrophysics Data System (ADS)

Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Kopriva, David A.

2017-07-01

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

A Second Order Semi-Discrete Cosserat Rod Model Suitable for Dynamic Simulations in Real Time

NASA Astrophysics Data System (ADS)

Lang, Holger; Linn, Joachim

2009-09-01

We present an alternative approach for a semi-discrete viscoelastic Cosserat rod model that allows both fast dynamic computations within milliseconds and accurate results compared to detailed finite element solutions. The model is able to represent extension, shearing, bending and torsion. For inner dissipation, a consistent damping potential from Antman is chosen. The continuous equations of motion, which consist a system of nonlinear hyperbolic partial differential algebraic equations, are derived from a two dimensional variational principle. The semi-discrete balance equations are obtained by spatial finite difference schemes on a staggered grid and standard index reduction techniques. The right-hand side of the model and its Jacobian can be chosen free of higher algebraic (e.g. root) or transcendent (e.g. trigonometric or exponential) functions and is therefore extremely cheap to evaluate numerically. For the time integration of the system, we use well established stiff solvers. As our model yields computational times within milliseconds, it is suitable for interactive manipulation. It reflects structural mechanics solutions sufficiently correct, as comparison with detailed finite element results shows.

A new computational method for reacting hypersonic flows

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

A unified convergence theory of a numerical method, and applications to the replenishment policies.

PubMed

Mi, Xiang-jiang; Wang, Xing-hua

2004-01-01

In determining the replenishment policy for an inventory system, some researchers advocated that the iterative method of Newton could be applied to the derivative of the total cost function in order to get the optimal solution. But this approach requires calculation of the second derivative of the function. Avoiding this complex computation we use another iterative method presented by the second author. One of the goals of this paper is to present a unified convergence theory of this method. Then we give a numerical example to show the application of our theory.

Periodic and rational solutions of the reduced Maxwell-Bloch equations

NASA Astrophysics Data System (ADS)

Wei, Jiao; Wang, Xin; Geng, Xianguo

2018-06-01

We investigate the reduced Maxwell-Bloch (RMB) equations which describe the propagation of short optical pulses in dielectric materials with resonant non-degenerate transitions. The general Nth-order periodic solutions are provided by means of the Darboux transformation. The Nth-order degenerate periodic and Nth-order rational solutions containing several free parameters with compact determinant representations are derived from two different limiting cases of the obtained general periodic solutions, respectively. Explicit expressions of these solutions from first to second order are presented. Typical nonlinear wave patterns for the four components of the RMB equations such as single-peak, double-peak-double-dip, double-peak and single-dip structures in the second-order rational solutions are shown. This kind of the rational solutions correspond to rogue waves in the reduced Maxwell-Bloch equations.

Optical nonlinearities of excitons in monolayer MoS2

NASA Astrophysics Data System (ADS)

Soh, Daniel B. S.; Rogers, Christopher; Gray, Dodd J.; Chatterjee, Eric; Mabuchi, Hideo

2018-04-01

We calculate linear and nonlinear optical susceptibilities arising from the excitonic states of monolayer MoS2 for in-plane light polarizations, using second-quantized bound and unbound exciton operators. Optical selection rules are critical for obtaining the susceptibilities. We derive the valley-chirality rule for the second-order harmonic generation in monolayer MoS2 and find that the third-order harmonic process is efficient only for linearly polarized input light while the third-order two-photon process (optical Kerr effect) is efficient for circularly polarized light using a higher order exciton state. The absence of linear absorption due to the band gap and the unusually strong two-photon third-order nonlinearity make the monolayer MoS2 excitonic structure a promising resource for coherent nonlinear photonics.

Rapid determination of crocins in saffron by near-infrared spectroscopy combined with chemometric techniques

NASA Astrophysics Data System (ADS)

Li, Shuailing; Shao, Qingsong; Lu, Zhonghua; Duan, Chengli; Yi, Haojun; Su, Liyang

2018-02-01

Saffron is an expensive spice. Its primary effective constituents are crocin I and II, and the contents of these compounds directly affect the quality and commercial value of saffron. In this study, near-infrared spectroscopy was combined with chemometric techniques for the determination of crocin I and II in saffron. Partial least squares regression models were built for the quantification of crocin I and II. By comparing different spectral ranges and spectral pretreatment methods (no pretreatment, vector normalization, subtract a straight line, multiplicative scatter correction, minimum-maximum normalization, eliminate the constant offset, first derivative, and second derivative), optimum models were developed. The root mean square error of cross-validation values of the best partial least squares models for crocin I and II were 1.40 and 0.30, respectively. The coefficients of determination for crocin I and II were 93.40 and 96.30, respectively. These results show that near-infrared spectroscopy can be combined with chemometric techniques to determine the contents of crocin I and II in saffron quickly and efficiently.

Loudness enhancement: Monaural, binaural and dichotic

NASA Technical Reports Server (NTRS)

Elmasian, R. O.; Galambos, R.

1975-01-01

It is shown that when one tone burst precedes another by 100 msec variations in the intensity of the first systematically influences the loudness of second. When the first burst is more intense than the second, the second is increased and when the first burst is less intense, the loudness of the second is decreased. This occurs in monaural, binaural and dichotic paradigms of signal presentation. Where both bursts are presented to the same ear there is more enhancement with less intersubject variability than when they are presented to different ears. Monaural enhancements as large as 30 db can readily be demonstrated, but decrements rarely exceed 5 db. Possible physiological mechanisms are discussed for this loudness enhancement, which apparently shares certain characteristics with time-order-error, assimilation, and temporal partial masking experiments.

Rogue wave solutions for the infinite integrable nonlinear Schrödinger equation hierarchy.

PubMed

Ankiewicz, A; Akhmediev, N

2017-07-01

We present rogue wave solutions of the integrable nonlinear Schrödinger equation hierarchy with an infinite number of higher-order terms. The latter include higher-order dispersion and higher-order nonlinear terms. In particular, we derive the fundamental rogue wave solutions for all orders of the hierarchy, with exact expressions for velocities, phase, and "stretching factors" in the solutions. We also present several examples of exact solutions of second-order rogue waves, including rogue wave triplets.

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Amphiphilic copolymers based on polyoxazoline and grape seed vegetable oil derivatives: self-assemblies and dynamic light scattering

NASA Astrophysics Data System (ADS)

Travelet, Christophe; Stemmelen, Mylène; Lapinte, Vincent; Dubreuil, Frédéric; Robin, Jean-Jacques; Borsali, Redouane

2013-06-01

The self-assembly in solution of original structures of amphiphilic partially natural copolymers based on polyoxazoline [more precisely poly(2-methyl-2-oxazoline) (POx)] and grape seed vegetable oil derivatives (linear, T-, and trident-structure) is investigated. The results show that such systems are found, using dynamic light scattering (DLS), to spontaneously self-organize into monomodal, narrow-size, and stable nanoparticles in aqueous medium. The obtained hydrodynamic diameters ( D h) range from 8.6 to 32.5 nm. Specifically, such size increases strongly with increasing natural block (i.e., lipophilic species) length due to higher hydrophobic interactions (from 10.1 nm for C19 to 19.2 nm for C57). Furthermore, increasing the polyoxazoline (i.e., hydrophilic block) length leads to a moderate linear increase of the D h-values. Therefore, the first-order size effect comes from the natural lipophilic block, whereas the characteristic size can be tuned more finely (i.e., in a second-order) by choosing appropriately the polyoxazoline length. The DLS results in terms of characteristic size are corroborated using nanoparticle tracking analysis (NTA), and also by atomic force microscopy (AFM) and transmission electron microscopy (TEM) imaging where well-defined spherical and individual nanoparticles exhibit a very good mechanical resistance upon drying. Moreover, changing the lipophilic block architecture from linear to T-shape, while keeping the same molar mass, generates a branching and thus a shrinking by a factor of 2 of the nanoparticle volume, as observed by DLS. In this paper, it is clearly shown that the self-assemblies of amphiphilic block copolymer obtained from grape seed vegetable oil derivatives (sustainable renewable resources) as well as their tunability are of great interest for biomass valorization at the nanoscale level [continuation of the article by Stemmelen et al. (Polym Chem 4:1445-1458, 2013)].

SteamTables: An approach of multiple variable sets

NASA Astrophysics Data System (ADS)

Verma, Mahendra P.

2009-10-01

Using the IAPWS-95 formulation, an ActiveX component SteamTablesIIE in Visual Basic 6.0 is developed to calculate thermodynamic properties of pure water as a function of two independent intensive variables: (1) temperature ( T) or pressure ( P) and (2) T, P, volume ( V), internal energy ( U), enthalpy ( H), entropy ( S) or Gibbs free energy ( G). The second variable cannot be the same as variable 1. Additionally, it calculates the properties along the separation boundaries (i.e., sublimation, saturation, critical isochor, ice I melting, ice III to ice IIV melting and minimum volume curves) considering the input parameter as T or P for the variable 1. SteamTablesIIE is an extension of the ActiveX component SteamTables implemented earlier considering T (190 to 2000 K) and P (3.23×10 -8 to 10000 MPa) as independent variables. It takes into account the following 27 intensive properties: temperature ( T), pressure ( P), fraction, state, volume ( V), density ( Den), compressibility factor ( Z0), internal energy ( U), enthalpy ( H), Gibbs free energy ( G), Helmholtz free energy ( A), entropy ( S), heat capacity at constant pressure ( C p), heat capacity at constant volume ( C v), coefficient of thermal expansion ( CTE), isothermal compressibility ( Z iso), speed of sound ( VelS), partial derivative of P with T at constant V ( dPdT), partial derivative of T with V at constant P ( dTdV), partial derivative of V with P at constant T ( dVdP), Joule-Thomson coefficient ( JTC), isothermal throttling coefficient ( IJTC), viscosity ( Vis), thermal conductivity ( ThrmCond), surface tension ( SurfTen), Prandtl number ( PrdNum) and dielectric constant ( DielCons).

Derivative spectrophotometric method for simultaneous determination of clindamycin phosphate and tretinoin in pharmaceutical dosage forms.

PubMed

Barazandeh Tehrani, Maliheh; Namadchian, Melika; Fadaye Vatan, Sedigheh; Souri, Effat

2013-04-10

A derivative spectrophotometric method was proposed for the simultaneous determination of clindamycin and tretinoin in pharmaceutical dosage forms. The measurement was achieved using the first and second derivative signals of clindamycin at (1D) 251 nm and (2D) 239 nm and tretinoin at (1D) 364 nm and (2D) 387 nm.The proposed method showed excellent linearity at both first and second derivative order in the range of 60-1200 and 1.25-25 μg/ml for clindamycin phosphate and tretinoin respectively. The within-day and between-day precision and accuracy was in acceptable range (CV<3.81%, error<3.20%). Good agreement between the found andadded concentrations indicates successful application of the proposed method for simultaneous determination of clindamycin and tretinoin in synthetic mixtures and pharmaceutical dosage form.

Onomatopeya, Derivacion y el Sufijo -azo. (Onomatopeia, Derivation, and the Suffix -azo).

ERIC Educational Resources Information Center

Corro, Raymond L.

1985-01-01

The nature and source of onomatopeic words in Spanish are discussed in order of decreasing resemblance to the sound imitated. The first group of onomatopeic words are the interjections, in which sound effects and animal sounds are expressed. Repetition is often used to enhance the effect. The second group includes verbs and nouns derived from the…

Multistep integration formulas for the numerical integration of the satellite problem

NASA Technical Reports Server (NTRS)

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

1981-01-01

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

Second order gradiometer and dc SQUID integrated on a planar substrate

NASA Astrophysics Data System (ADS)

van Nieuwenhuyzen, G. J.; de Waal, V. J.

1985-02-01

An integrated system of a thin-film niobium dc superconducting quantum interference device (SQUID) and a second order gradiometer on a planar substrate is described. The system consists of a dc SQUID with eight loops in parallel, each sensitive to the second derivative ∂2Bz/∂x2 of the magnetic field. The calculated SQUID inductance is 1.3 nH. With an overall size of 16×16.5 mm2 a sensitivity of 1.5×10-9 Tm-2 Hz-1/2 is obtained. The measured transfer function for uniform fields perpendicular to the plane of the gradiometer is 2.1×10-7 T Φ-10.

Coupled tensorial forms of the second-order effective Hamiltonian for open-subshell atoms in jj-coupling

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

Jursenas, Rytis, E-mail: Rytis.Jursenas@tfai.vu.l; Merkelis, Gintaras

2011-01-15

General expressions for the second-order effective atomic Hamiltonian are derived for open-subshell atoms in jj-coupling. The expansion terms are presented as N-body (N=0,1,2,3) effective operators given in the second quantization representation in coupled tensorial form. Two alternative coupled tensorial forms for each expansion term have been developed. To reduce the number of expressions of the effective Hamiltonian, the reduced matrix elements of antisymmetric two-particle wavefunctions are involved in the consideration. The general expressions presented allow the determination of the spin-angular part of expansion terms when studying correlation effects dealing with a number of problems in atomic structure calculations.

Some aspects of the thermodynamic behaviour of the lead-doped Bi-2223 system

NASA Astrophysics Data System (ADS)

Tetenbaum, M.; Maroni, V. A.

1996-02-01

A thermodynamic assessment of lead-doped Bi-2223 with emphasis on compositions and oxygen partial pressures within the homogeneity region prior to solid-state decomposition is presented. Equations for the variation of oxygen partial pressure with composition and temperature have been derived from our EMF measurements. Long-term metastability was indicated during cycling over a temperature range of ∼ 700-815°C of a lead-doped Bi-2223 sample having an oxygen-deficient stoichiometry of 9.64 prior to solid-state decomposition corresponding to the diphasic CuOCu 2O system. A trend of increasing negative values of the partial molar enthalpy Δ overlineH( O 2) and entropy Δ overlineS( O2 with increasing oxygen deficiency of the condensed phase indicated an increase in ordering of the cuprate structure prior to solid-state decomposition.

Some User's Insights Into ADIFOR 2.0D

NASA Technical Reports Server (NTRS)

Giesy, Daniel P.

2002-01-01

Some insights are given which were gained by one user through experience with the use of the ADIFOR 2.0D software for automatic differentiation of Fortran code. These insights are generally in the area of the user interface with the generated derivative code - particularly the actual form of the interface and the use of derivative objects, including "seed" matrices. Some remarks are given as to how to iterate application of ADIFOR in order to generate second derivative code.

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.

Sixth- and eighth-order Hermite integrator for N-body simulations

NASA Astrophysics Data System (ADS)

Nitadori, Keigo; Makino, Junichiro

2008-10-01

We present sixth- and eighth-order Hermite integrators for astrophysical N-body simulations, which use the derivatives of accelerations up to second-order ( snap) and third-order ( crackle). These schemes do not require previous values for the corrector, and require only one previous value to construct the predictor. Thus, they are fairly easy to implement. The additional cost of the calculation of the higher-order derivatives is not very high. Even for the eighth-order scheme, the number of floating-point operations for force calculation is only about two times larger than that for traditional fourth-order Hermite scheme. The sixth-order scheme is better than the traditional fourth-order scheme for most cases. When the required accuracy is very high, the eighth-order one is the best. These high-order schemes have several practical advantages. For example, they allow a larger number of particles to be integrated in parallel than the fourth-order scheme does, resulting in higher execution efficiency in both general-purpose parallel computers and GRAPE systems.

A family of four stages embedded explicit six-step methods with eliminated phase-lag and its derivatives for the numerical solution of the second order problems

NASA Astrophysics Data System (ADS)

Simos, T. E.

2017-11-01

A family of four stages high algebraic order embedded explicit six-step methods, for the numerical solution of second order initial or boundary-value problems with periodical and/or oscillating solutions, are studied in this paper. The free parameters of the new proposed methods are calculated solving the linear system of equations which is produced by requesting the vanishing of the phase-lag of the methods and the vanishing of the phase-lag's derivatives of the schemes. For the new obtained methods we investigate: • Its local truncation error (LTE) of the methods.• The asymptotic form of the LTE obtained using as model problem the radial Schrödinger equation.• The comparison of the asymptotic forms of LTEs for several methods of the same family. This comparison leads to conclusions on the efficiency of each method of the family.• The stability and the interval of periodicity of the obtained methods of the new family of embedded finite difference pairs.• The applications of the new obtained family of embedded finite difference pairs to the numerical solution of several second order problems like the radial Schrödinger equation, astronomical problems etc. The above applications lead to conclusion on the efficiency of the methods of the new family of embedded finite difference pairs.

Medical image registration by combining global and local information: a chain-type diffeomorphic demons algorithm.

PubMed

Liu, Xiaozheng; Yuan, Zhenming; Zhu, Junming; Xu, Dongrong

2013-12-07

The demons algorithm is a popular algorithm for non-rigid image registration because of its computational efficiency and simple implementation. The deformation forces of the classic demons algorithm were derived from image gradients by considering the deformation to decrease the intensity dissimilarity between images. However, the methods using the difference of image intensity for medical image registration are easily affected by image artifacts, such as image noise, non-uniform imaging and partial volume effects. The gradient magnitude image is constructed from the local information of an image, so the difference in a gradient magnitude image can be regarded as more reliable and robust for these artifacts. Then, registering medical images by considering the differences in both image intensity and gradient magnitude is a straightforward selection. In this paper, based on a diffeomorphic demons algorithm, we propose a chain-type diffeomorphic demons algorithm by combining the differences in both image intensity and gradient magnitude for medical image registration. Previous work had shown that the classic demons algorithm can be considered as an approximation of a second order gradient descent on the sum of the squared intensity differences. By optimizing the new dissimilarity criteria, we also present a set of new demons forces which were derived from the gradients of the image and gradient magnitude image. We show that, in controlled experiments, this advantage is confirmed, and yields a fast convergence.

Augmented Ehrenfest dynamics yields a rate for surface hopping

NASA Astrophysics Data System (ADS)

Subotnik, Joseph E.

2010-04-01

We present a new algorithm for mixed quantum-classical dynamics that helps bridge the gap between mean-field (Ehrenfest) and surface-hopping dynamics by defining a natural rate of decoherence. In order to derive this decoherence result, we have expanded the number of independent variables in the usual Ehrenfest routine so that mixed quantum-classical derivatives are now propagated in time alongside the usual Ehrenfest variables. Having done so, we compute a unique rate of decoherence using two independent approaches: (i) by comparing the equations of motion for the joint nuclear-electronic probability density in phase space according to Ehrenfest dynamics versus partial Wigner transform dynamics and (ii) by introducing a frozen Gaussian interpretation of Ehrenfest dynamics which allows nuclear wave packets to separate. The first consequence of this work is a means to rigorously check the accuracy of standard Ehrenfest dynamics. Second, this paper suggests a nonadiabatic dynamics algorithm, whereby the nuclei are propagated on the mean-field (Ehrenfest) potential energy surface and undergo stochastic decoherence events. Our work resembles the surface-hopping algorithm of Schwartz and co-workers [J. Chem. Phys. 123, 234106 (2005)]—only now without any adjustable parameters. For the case of two electronic states, we present numerical results on the so-called "Tully problems" and emphasize that future numerical benchmarking is still needed. Future work will also treat the problem of three or more electronic states.

The E-Step of the MGROUP EM Algorithm. Program Statistics Research Technical Report No. 93-37.

ERIC Educational Resources Information Center

Thomas, Neal

Mislevy (1984, 1985) introduced an EM algorithm for estimating the parameters of a latent distribution model that is used extensively by the National Assessment of Educational Progress. Second order asymptotic corrections are derived and applied along with more common first order asymptotic corrections to approximate the expectations required by…

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.

Flexible system model reduction and control system design based upon actuator and sensor influence functions

NASA Technical Reports Server (NTRS)

Yam, Yeung; Johnson, Timothy L.; Lang, Jeffrey H.

1987-01-01

A model reduction technique based on aggregation with respect to sensor and actuator influence functions rather than modes is presented for large systems of coupled second-order differential equations. Perturbation expressions which can predict the effects of spillover on both the reduced-order plant model and the neglected plant model are derived. For the special case of collocated actuators and sensors, these expressions lead to the derivation of constraints on the controller gains that are, given the validity of the perturbation technique, sufficient to guarantee the stability of the closed-loop system. A case study demonstrates the derivation of stabilizing controllers based on the present technique. The use of control and observation synthesis in modifying the dimension of the reduced-order plant model is also discussed. A numerical example is provided for illustration.

Statistical mechanics of self-driven Carnot cycles.

PubMed

Smith, E

1999-10-01

The spontaneous generation and finite-amplitude saturation of sound, in a traveling-wave thermoacoustic engine, are derived as properties of a second-order phase transition. It has previously been argued that this dynamical phase transition, called "onset," has an equivalent equilibrium representation, but the saturation mechanism and scaling were not computed. In this work, the sound modes implementing the engine cycle are coarse-grained and statistically averaged, in a partition function derived from microscopic dynamics on criteria of scale invariance. Self-amplification performed by the engine cycle is introduced through higher-order modal interactions. Stationary points and fluctuations of the resulting phenomenological Lagrangian are analyzed and related to background dynamical currents. The scaling of the stable sound amplitude near the critical point is derived and shown to arise universally from the interaction of finite-temperature disorder, with the order induced by self-amplification.

Multi-off-grid methods in multi-step integration of ordinary differential equations

NASA Technical Reports Server (NTRS)

Beaudet, P. R.

1974-01-01

Description of methods of solving first- and second-order systems of differential equations in which all derivatives are evaluated at off-grid locations in order to circumvent the Dahlquist stability limitation on the order of on-grid methods. The proposed multi-off-grid methods require off-grid state predictors for the evaluation of the n derivatives at each step. Progressing forward in time, the off-grid states are predicted using a linear combination of back on-grid state values and off-grid derivative evaluations. A comparison is made between the proposed multi-off-grid methods and the corresponding Adams and Cowell on-grid integration techniques in integrating systems of ordinary differential equations, showing a significant reduction in the error at larger step sizes in the case of the multi-off-grid integrator.

Random-order fractional bistable system and its stochastic resonance

NASA Astrophysics Data System (ADS)

Gao, Shilong; Zhang, Li; Liu, Hui; Kan, Bixia

2017-01-01

In this paper, the diffusion motion of Brownian particles in a viscous liquid suffering from stochastic fluctuations of the external environment is modeled as a random-order fractional bistable equation, and as a typical nonlinear dynamic behavior, the stochastic resonance phenomena in this system are investigated. At first, the derivation process of the random-order fractional bistable system is given. In particular, the random-power-law memory is deeply discussed to obtain the physical interpretation of the random-order fractional derivative. Secondly, the stochastic resonance evoked by random-order and external periodic force is mainly studied by numerical simulation. In particular, the frequency shifting phenomena of the periodical output are observed in SR induced by the excitation of the random order. Finally, the stochastic resonance of the system under the double stochastic excitations of the random order and the internal color noise is also investigated.

Covariate-adjusted Spearman's rank correlation with probability-scale residuals.

PubMed

Liu, Qi; Li, Chun; Wanga, Valentine; Shepherd, Bryan E

2018-06-01

It is desirable to adjust Spearman's rank correlation for covariates, yet existing approaches have limitations. For example, the traditionally defined partial Spearman's correlation does not have a sensible population parameter, and the conditional Spearman's correlation defined with copulas cannot be easily generalized to discrete variables. We define population parameters for both partial and conditional Spearman's correlation through concordance-discordance probabilities. The definitions are natural extensions of Spearman's rank correlation in the presence of covariates and are general for any orderable random variables. We show that they can be neatly expressed using probability-scale residuals (PSRs). This connection allows us to derive simple estimators. Our partial estimator for Spearman's correlation between X and Y adjusted for Z is the correlation of PSRs from models of X on Z and of Y on Z, which is analogous to the partial Pearson's correlation derived as the correlation of observed-minus-expected residuals. Our conditional estimator is the conditional correlation of PSRs. We describe estimation and inference, and highlight the use of semiparametric cumulative probability models, which allow preservation of the rank-based nature of Spearman's correlation. We conduct simulations to evaluate the performance of our estimators and compare them with other popular measures of association, demonstrating their robustness and efficiency. We illustrate our method in two applications, a biomarker study and a large survey. © 2017, The International Biometric Society.

Spacetime encodings. III. Second order Killing tensors

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

Brink, Jeandrew

2010-01-15

This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher-order Killing tensors. The relationship between the components of the Killing equations and metric functions are given explicitly. The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations. A geometric picture ofmore » what the orbital invariants may represent is built. Requiring that a SAV spacetime admits a second-order Killing tensor is very restrictive, selecting very few candidates from the group of all possible SAV spacetimes. This restriction arises due to the fact that the consistency conditions associated with the Killing equations require that the field variables obey a second-order differential equation, as opposed to a fourth-order differential equation that imposes the weaker condition that the spacetime be SAV. This paper introduces ideas that could lead to the explicit computation of more general orbital invariants in the form of higher-order Killing tensors.« less

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk

NASA Astrophysics Data System (ADS)

Gorenflo, R.; Mainardi, F.

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in (0,2] and skewness theta (\\verttheta\\vertlemin \\{alpha ,2-alpha \\}), and the first-order time derivative with a Caputo derivative of order beta in (0,1] . The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process. We view it as a generalized diffusion process that we call fractional diffusion process, and present an integral representation of the fundamental solution. A more general approach to anomalous diffusion is however known to be provided by the master equation for a continuous time random walk (CTRW). We show how this equation reduces to our fractional diffusion equation by a properly scaled passage to the limit of compressed waiting times and jump widths. Finally, we describe a method of simulation and display (via graphics) results of a few numerical case studies.

A continued fraction resummation form of bath relaxation effect in the spin-boson model

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

Gong, Zhihao; Tang, Zhoufei; Wu, Jianlan, E-mail: jianlanwu@zju.edu.cn

2015-02-28

In the spin-boson model, a continued fraction form is proposed to systematically resum high-order quantum kinetic expansion (QKE) rate kernels, accounting for the bath relaxation effect beyond the second-order perturbation. In particular, the analytical expression of the sixth-order QKE rate kernel is derived for resummation. With higher-order correction terms systematically extracted from higher-order rate kernels, the resummed quantum kinetic expansion approach in the continued fraction form extends the Pade approximation and can fully recover the exact quantum dynamics as the expansion order increases.

On the Coriolis effect in acoustic waveguides.

PubMed

Wegert, Henry; Reindl, Leonard M; Ruile, Werner; Mayer, Andreas P

2012-05-01

Rotation of an elastic medium gives rise to a shift of frequency of its acoustic modes, i.e., the time-period vibrations that exist in it. This frequency shift is investigated by applying perturbation theory in the regime of small ratios of the rotation velocity and the frequency of the acoustic mode. In an expansion of the relative frequency shift in powers of this ratio, upper bounds are derived for the first-order and the second-order terms. The derivation of the theoretical upper bounds of the first-order term is presented for linear vibration modes as well as for stable nonlinear vibrations with periodic time dependence that can be represented by a Fourier series.

Navier-Stokes computation of compressible turbulent flows with a second order closure, part 1

NASA Technical Reports Server (NTRS)

Haminh, Hieu; Kollmann, Wolfgang; Vandromme, Dany

1990-01-01

A second order closure turbulence model for compressible flows is developed and implemented in a 2D Reynolds-averaged Navier-Stokes solver. From the beginning where a kappa-epsilon turbulence model was implemented in the bidiagonal implicit method of MACCORMACK (referred to as the MAC3 code) to the final stage of implementing a full second order closure in the efficient line Gauss-Seidel algorithm, numerous work was done, individually and collectively. Besides the collaboration itself, the final product of this work is a second order closure derived from the Launder, Reece, and Rodi model to account for near wall effects, which has been called FRAME model, which stands for FRench-AMerican-Effort. During the reporting period, two different problems were worked out. The first was to provide Ames researchers with a reliable compressible boundary layer code including a wide collection of turbulence models for quick testing of new terms, both in two equations and in second order closure (LRR and FRAME). The second topic was to complete the implementation of the FRAME model in the MAC5 code. The work related to these two different contributions is reported. dilatation in presence of stron shocks. This work, which has been conducted during a work at the Center for Turbulence Research with Zeman aimed also to cros-check earlier assumptions by Rubesin and Vandromme.

Autologous Bone Marrow-Derived Mesenchymal Stem Cells Modulate Molecular Markers of Inflammation in Dogs with Cruciate Ligament Rupture.

PubMed

Muir, Peter; Hans, Eric C; Racette, Molly; Volstad, Nicola; Sample, Susannah J; Heaton, Caitlin; Holzman, Gerianne; Schaefer, Susan L; Bloom, Debra D; Bleedorn, Jason A; Hao, Zhengling; Amene, Ermias; Suresh, M; Hematti, Peiman

2016-01-01

Mid-substance rupture of the canine cranial cruciate ligament rupture (CR) and associated stifle osteoarthritis (OA) is an important veterinary health problem. CR causes stifle joint instability and contralateral CR often develops. The dog is an important model for human anterior cruciate ligament (ACL) rupture, where rupture of graft repair or the contralateral ACL is also common. This suggests that both genetic and environmental factors may increase ligament rupture risk. We investigated use of bone marrow-derived mesenchymal stem cells (BM-MSCs) to reduce systemic and stifle joint inflammatory responses in dogs with CR. Twelve dogs with unilateral CR and contralateral stable partial CR were enrolled prospectively. BM-MSCs were collected during surgical treatment of the unstable CR stifle and culture-expanded. BM-MSCs were subsequently injected at a dose of 2x106 BM-MSCs/kg intravenously and 5x106 BM-MSCs by intra-articular injection of the partial CR stifle. Blood (entry, 4 and 8 weeks) and stifle synovial fluid (entry and 8 weeks) were obtained after BM-MSC injection. No adverse events after BM-MSC treatment were detected. Circulating CD8+ T lymphocytes were lower after BM-MSC injection. Serum C-reactive protein (CRP) was decreased at 4 weeks and serum CXCL8 was increased at 8 weeks. Synovial CRP in the complete CR stifle was decreased at 8 weeks. Synovial IFNγ was also lower in both stifles after BM-MSC injection. Synovial/serum CRP ratio at diagnosis in the partial CR stifle was significantly correlated with development of a second CR. Systemic and intra-articular injection of autologous BM-MSCs in dogs with partial CR suppresses systemic and stifle joint inflammation, including CRP concentrations. Intra-articular injection of autologous BM-MSCs had profound effects on the correlation and conditional dependencies of cytokines using causal networks. Such treatment effects could ameliorate risk of a second CR by modifying the stifle joint inflammatory response associated with cranial cruciate ligament matrix degeneration or damage.

Autologous Bone Marrow-Derived Mesenchymal Stem Cells Modulate Molecular Markers of Inflammation in Dogs with Cruciate Ligament Rupture

PubMed Central

Muir, Peter; Hans, Eric C.; Racette, Molly; Volstad, Nicola; Sample, Susannah J.; Heaton, Caitlin; Holzman, Gerianne; Schaefer, Susan L.; Bloom, Debra D.; Bleedorn, Jason A.; Hao, Zhengling; Amene, Ermias; Suresh, M.; Hematti, Peiman

2016-01-01

Mid-substance rupture of the canine cranial cruciate ligament rupture (CR) and associated stifle osteoarthritis (OA) is an important veterinary health problem. CR causes stifle joint instability and contralateral CR often develops. The dog is an important model for human anterior cruciate ligament (ACL) rupture, where rupture of graft repair or the contralateral ACL is also common. This suggests that both genetic and environmental factors may increase ligament rupture risk. We investigated use of bone marrow-derived mesenchymal stem cells (BM-MSCs) to reduce systemic and stifle joint inflammatory responses in dogs with CR. Twelve dogs with unilateral CR and contralateral stable partial CR were enrolled prospectively. BM-MSCs were collected during surgical treatment of the unstable CR stifle and culture-expanded. BM-MSCs were subsequently injected at a dose of 2x106 BM-MSCs/kg intravenously and 5x106 BM-MSCs by intra-articular injection of the partial CR stifle. Blood (entry, 4 and 8 weeks) and stifle synovial fluid (entry and 8 weeks) were obtained after BM-MSC injection. No adverse events after BM-MSC treatment were detected. Circulating CD8+ T lymphocytes were lower after BM-MSC injection. Serum C-reactive protein (CRP) was decreased at 4 weeks and serum CXCL8 was increased at 8 weeks. Synovial CRP in the complete CR stifle was decreased at 8 weeks. Synovial IFNγ was also lower in both stifles after BM-MSC injection. Synovial/serum CRP ratio at diagnosis in the partial CR stifle was significantly correlated with development of a second CR. Systemic and intra-articular injection of autologous BM-MSCs in dogs with partial CR suppresses systemic and stifle joint inflammation, including CRP concentrations. Intra-articular injection of autologous BM-MSCs had profound effects on the correlation and conditional dependencies of cytokines using causal networks. Such treatment effects could ameliorate risk of a second CR by modifying the stifle joint inflammatory response associated with cranial cruciate ligament matrix degeneration or damage. PMID:27575050

Effects of Radiation Damping in Extreme Ultra-intense Laser-Plasma Interaction

NASA Astrophysics Data System (ADS)

Pandit, Rishi R.

Recent advances in the development of intense short pulse lasers are significant. Now it is available to access a laser with intensity 1021W/cm2 by focusing a petawatt class laser. In a few years, the intensity will exceed 1022W/cm2 , at which intensity electrons accelerated by the laser get energy more than 100 MeV and start to emit radiation strongly. Resultingly, the damping of electron motion can become large. In order to study this problem, we developed a code to solve a set of equations describing the evolution of a strong electromagnetic wave interacting with a single electron. Usually the equation of motion of an electron including radiation damping under the influence of electromagnetic fields is derived from the Lorentz-Dirac equation treating the damping as a perturbation. So far people had used the first order damping equation. This is because the second order term seems to be small and actually it is negligible under 1022W/cm2 intensity. The derivation of 2nd order equation is also complicated and challenging. We derived the second order damping equations for the first time and implemented in the code. The code was then tested via single particle motion in the extreme intensity laser. It was found that the 1st order damping term is reasonable up to the intensity 1022W/cm2, but the 2nd oder term becomes not negligible and comparable in magnitude to the first order term beyond 1023W/cm2. The radiation damping model was introduced using a one-dimensional particle-in-cell code (PIC), and tested in the laser-plasma interaction at extreme intensity. The strong damping of hot electrons in high energy tail was demonstrated in PIC simulations.

Structures and Optical Properties of Hydrazones Derived from Biological Polyenes

NASA Astrophysics Data System (ADS)

Nakashima, Takayasu; Yamada, Takashi; Hashimoto, Hideki; Kobayashi, Takayoshi

2001-08-01

A set of hydrazone molecules was derived from a series of biological polyenes that have different polyene chain-lengths with common substituent group of 2,4-dinitrophenylhydrazine. Their structures were determined by high-resolution NMR spectroscopy as well as X-ray crystallography, and their optical properties were investigated by room and low temperature optical absorption spectroscopy. Among the derivatives so far synthesized, the one that has the shortest polyene chain (C13-DNPH) afforded single crystals without inversion symmetry, hence applicable for the second-order nonlinear optical devices. Molecular structures in the crystals were closely inspected in order to explain the cause to violate the inversion symmetry. Hydrazones derived in this study gave rise to two transition moments along the molecular axis. Comparison of the optical absorption spectra among the derivatives showed a unique phenomenon that could be attributed to the crossover of the excited state potential energy surfaces along the elongation of the polyene chain-lengths.

Structures and Optical Properties of Hydrazones Derived from Biological Polyenes

NASA Astrophysics Data System (ADS)

Nakashima, Takayasu; Yamada, Takashi; Hashimoto, Hideki; Kobayashi, Takayoshi

A set of hydrazone molecules was derived from a series of biological polyenes that have different polyene chain-lengths with common substituent group of 2,4-dinitrophenylhydrazine. Their structures were determined by high-resolution NMR spectroscopy as well as X-ray crystallography, and their optical properties were investigated by room and low temperature optical absorption spectroscopy. Among the derivatives so far synthesized, the one that has the shortest polyene chain (C13-DNPH) afforded single crystals without inversion symmetry, hence applicable for the second-order nonlinear optical devices. Molecular structures in the crystals were closely inspected in order to explain the cause to violate the inversion symmetry. Hydrazones derived in this study gave rise to two transition moments along the molecular axis. Comparison of the optical absorption spectra among the derivatives showed a unique phenomenon that could be attributed to the crossover of the excited state potential energy surfaces along the elongation of the polyene chain-lengths.

On simplified application of multidimensional Savitzky-Golay filters and differentiators

NASA Astrophysics Data System (ADS)

Shekhar, Chandra

2016-02-01

I propose a simplified approach for multidimensional Savitzky-Golay filtering, to enable its fast and easy implementation in scientific and engineering applications. The proposed method, which is derived from a generalized framework laid out by Thornley (D. J. Thornley, "Novel anisotropic multidimensional convolution filters for derivative estimation and reconstruction" in Proceedings of International Conference on Signal Processing and Communications, November 2007), first transforms any given multidimensional problem into a unique one, by transforming coordinates of the sampled data nodes to unity-spaced, uniform data nodes, and then performs filtering and calculates partial derivatives on the unity-spaced nodes. It is followed by transporting the calculated derivatives back onto the original data nodes by using the chain rule of differentiation. The burden to performing the most cumbersome task, which is to carry out the filtering and to obtain derivatives on the unity-spaced nodes, is almost eliminated by providing convolution coefficients for a number of convolution kernel sizes and polynomial orders, up to four spatial dimensions. With the availability of the convolution coefficients, the task of filtering at a data node reduces merely to multiplication of two known matrices. Simplified strategies to adequately address near-boundary data nodes and to calculate partial derivatives there are also proposed. Finally, the proposed methodologies are applied to a three-dimensional experimentally obtained data set, which shows that multidimensional Savitzky-Golay filters and differentiators perform well in both the internal and the near-boundary regions of the domain.

Ionization of pyridine: Interplay of orbital relaxation and electron correlation.

PubMed

Trofimov, A B; Holland, D M P; Powis, I; Menzies, R C; Potts, A W; Karlsson, L; Gromov, E V; Badsyuk, I L; Schirmer, J

2017-06-28

The valence shell ionization spectrum of pyridine was studied using the third-order algebraic-diagrammatic construction approximation scheme for the one-particle Green's function and the outer-valence Green's function method. The results were used to interpret angle resolved photoelectron spectra recorded with synchrotron radiation in the photon energy range of 17-120 eV. The lowest four states of the pyridine radical cation, namely, 2 A 2 (1a 2 -1 ), 2 A 1 (7a 1 -1 ), 2 B 1 (2b 1 -1 ), and 2 B 2 (5b 2 -1 ), were studied in detail using various high-level electronic structure calculation methods. The vertical ionization energies were established using the equation-of-motion coupled-cluster approach with single, double, and triple excitations (EOM-IP-CCSDT) and the complete basis set extrapolation technique. Further interpretation of the electronic structure results was accomplished using Dyson orbitals, electron density difference plots, and a second-order perturbation theory treatment for the relaxation energy. Strong orbital relaxation and electron correlation effects were shown to accompany ionization of the 7a 1 orbital, which formally represents the nonbonding σ-type nitrogen lone-pair (nσ) orbital. The theoretical work establishes the important roles of the π-system (π-π* excitations) in the screening of the nσ-hole and of the relaxation of the molecular orbitals in the formation of the 7a 1 (nσ) -1 state. Equilibrium geometric parameters were computed using the MP2 (second-order Møller-Plesset perturbation theory) and CCSD methods, and the harmonic vibrational frequencies were obtained at the MP2 level of theory for the lowest three cation states. The results were used to estimate the adiabatic 0-0 ionization energies, which were then compared to the available experimental and theoretical data. Photoelectron anisotropy parameters and photoionization partial cross sections, derived from the experimental spectra, were compared to predictions obtained with the continuum multiple scattering approach.

Equations of motion for train derailment dynamics

DOT National Transportation Integrated Search

2007-09-11

This paper describes a planar or two-dimensional model to : examine the gross motions of rail cars in a generalized train : derailment. Three coupled, second-order differential equations : are derived from Newton's Laws to calculate rigid-body car : ...

Nonlinear chiral plasma transport in rotating coordinates

NASA Astrophysics Data System (ADS)

Dayi, Ömer F.; Kilinçarslan, Eda

2017-08-01

The nonlinear transport features of inhomogeneous chiral plasma in the presence of electromagnetic fields, in rotating coordinates are studied within the relaxation time approach. The chiral distribution functions up to second order in the electric field in rotating coordinates and the derivatives of chemical potentials are established by solving the Boltzmann transport equation. First, the vector and axial current densities in the weakly ionized chiral plasma for vanishing magnetic field are calculated. They involve the rotational analogues of the Hall effect as well as several new terms arising from the Coriolis and fictitious centrifugal forces. Then in the short relaxation time regime the angular velocity and electromagnetic fields are treated as perturbations. The current densities are obtained by retaining the terms up to second order in perturbations. The time evolution equations of the inhomogeneous chemical potentials are derived by demanding that collisions conserve the particle number densities.

Hidden Markov model tracking of continuous gravitational waves from young supernova remnants

NASA Astrophysics Data System (ADS)

Sun, L.; Melatos, A.; Suvorova, S.; Moran, W.; Evans, R. J.

2018-02-01

Searches for persistent gravitational radiation from nonpulsating neutron stars in young supernova remnants are computationally challenging because of rapid stellar braking. We describe a practical, efficient, semicoherent search based on a hidden Markov model tracking scheme, solved by the Viterbi algorithm, combined with a maximum likelihood matched filter, the F statistic. The scheme is well suited to analyzing data from advanced detectors like the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO). It can track rapid phase evolution from secular stellar braking and stochastic timing noise torques simultaneously without searching second- and higher-order derivatives of the signal frequency, providing an economical alternative to stack-slide-based semicoherent algorithms. One implementation tracks the signal frequency alone. A second implementation tracks the signal frequency and its first time derivative. It improves the sensitivity by a factor of a few upon the first implementation, but the cost increases by 2 to 3 orders of magnitude.

Reexamining competitive priorities: Empirical study in service sector

NASA Astrophysics Data System (ADS)

Idris, Fazli; Mohammad, Jihad

2015-02-01

The general objective of this study is to validate the multi-level concept of competitive priorities using reflective-formative model at a higher order for service industries. An empirical study of 228 firms from 9 different service industries is conducted to answer the objective of this study. Partial least square analysis with SmartPLS 2.0 was used to perform the analysis. Finding revealed six priorities: cost, flexibility, delivery, quality talent management, quality tangibility, and innovativeness. It emerges that quality are expanded into two types; one is related to managing talent for process improvement and the second one is the physical appearance and tangibility of the service quality. This study has confirmed competitive priorities as formative second-order hierarchical latent construct by using rigorous empirical evidence. Implications, limitation and suggestion for future research are accordingly discussed in this paper.

Derivative Sign Patterns in Two Dimensions

ERIC Educational Resources Information Center

Schilling, Kenneth

2013-01-01

Given a function defined on a subset of the plane whose partial derivatives never change sign, the signs of the partial derivatives form a two-dimensional pattern. We explore what patterns are possible for various planar domains.

Development of a Kalman Filter in the Gauss-Helmert Model for Reliability Analysis in Orientation Determination with Smartphone Sensors

PubMed Central

Ettlinger, Andreas; Neuner, Hans; Burgess, Thomas

2018-01-01

The topic of indoor positioning and indoor navigation by using observations from smartphone sensors is very challenging as the determined trajectories can be subject to significant deviations compared to the route travelled in reality. Especially the calculation of the direction of movement is the critical part of pedestrian positioning approaches such as Pedestrian Dead Reckoning (“PDR”). Due to distinct systematic effects in filtered trajectories, it can be assumed that there are systematic deviations present in the observations from smartphone sensors. This article has two aims: one is to enable the estimation of partial redundancies for each observation as well as for observation groups. Partial redundancies are a measure for the reliability indicating how well systematic deviations can be detected in single observations used in PDR. The second aim is to analyze the behavior of partial redundancy by modifying the stochastic and functional model of the Kalman filter. The equations relating the observations to the orientation are condition equations, which do not exhibit the typical structure of the Gauss-Markov model (“GMM”), wherein the observations are linear and can be formulated as functions of the states. To calculate and analyze the partial redundancy of the observations from smartphone-sensors used in PDR, the system equation and the measurement equation of a Kalman filter as well as the redundancy matrix need to be derived in the Gauss-Helmert model (“GHM”). These derivations are introduced in this article and lead to a novel Kalman filter structure based on condition equations, enabling reliability assessment of each observation. PMID:29385076

Development of a Kalman Filter in the Gauss-Helmert Model for Reliability Analysis in Orientation Determination with Smartphone Sensors.

PubMed

Ettlinger, Andreas; Neuner, Hans; Burgess, Thomas

2018-01-31

The topic of indoor positioning and indoor navigation by using observations from smartphone sensors is very challenging as the determined trajectories can be subject to significant deviations compared to the route travelled in reality. Especially the calculation of the direction of movement is the critical part of pedestrian positioning approaches such as Pedestrian Dead Reckoning ("PDR"). Due to distinct systematic effects in filtered trajectories, it can be assumed that there are systematic deviations present in the observations from smartphone sensors. This article has two aims: one is to enable the estimation of partial redundancies for each observation as well as for observation groups. Partial redundancies are a measure for the reliability indicating how well systematic deviations can be detected in single observations used in PDR. The second aim is to analyze the behavior of partial redundancy by modifying the stochastic and functional model of the Kalman filter. The equations relating the observations to the orientation are condition equations, which do not exhibit the typical structure of the Gauss-Markov model ("GMM"), wherein the observations are linear and can be formulated as functions of the states. To calculate and analyze the partial redundancy of the observations from smartphone-sensors used in PDR, the system equation and the measurement equation of a Kalman filter as well as the redundancy matrix need to be derived in the Gauss-Helmert model ("GHM"). These derivations are introduced in this article and lead to a novel Kalman filter structure based on condition equations, enabling reliability assessment of each observation.

Solving matrix effects exploiting the second-order advantage in the resolution and determination of eight tetracycline antibiotics in effluent wastewater by modelling liquid chromatography data with multivariate curve resolution-alternating least squares and unfolded-partial least squares followed by residual bilinearization algorithms II. Prediction and figures of merit.

PubMed

García, M D Gil; Culzoni, M J; De Zan, M M; Valverde, R Santiago; Galera, M Martínez; Goicoechea, H C

2008-02-01

A new powerful algorithm (unfolded-partial least squares followed by residual bilinearization (U-PLS/RBL)) was applied for first time on second-order liquid chromatography with diode array detection (LC-DAD) data and compared with a well-known established method (multivariate curve resolution-alternating least squares (MCR-ALS)) for the simultaneous determination of eight tetracyclines (tetracycline, oxytetracycline, meclocycline, minocycline, metacycline, chlortetracycline, demeclocycline and doxycycline) in wastewaters. Tetracyclines were pre-concentrated using Oasis Max C18 cartridges and then separated on a Thermo Aquasil C18 (150 mm x 4.6mm, 5 microm) column. The whole method was validated using Milli-Q water samples and both univariate and multivariate analytical figures of merit were obtained. Additionally, two data pre-treatment were applied (baseline correction and piecewise direct standardization), which allowed to correct the effect of breakthrough and to reduce the total interferences retained after pre-concentration of wastewaters. The results showed that the eight tetracycline antibiotics can be successfully determined in wastewaters, the drawbacks due to matrix interferences being adequately handled and overcome by using U-PSL/RBL.

Two-Point Turbulence Closure Applied to Variable Resolution Modeling

NASA Technical Reports Server (NTRS)

Girimaji, Sharath S.; Rubinstein, Robert

2011-01-01

Variable resolution methods have become frontline CFD tools, but in order to take full advantage of this promising new technology, more formal theoretical development is desirable. Two general classes of variable resolution methods can be identified: hybrid or zonal methods in which RANS and LES models are solved in different flow regions, and bridging or seamless models which interpolate smoothly between RANS and LES. This paper considers the formulation of bridging methods using methods of two-point closure theory. The fundamental problem is to derive a subgrid two-equation model. We compare and reconcile two different approaches to this goal: the Partially Integrated Transport Model, and the Partially Averaged Navier-Stokes method.

Wigner distribution function and kurtosis parameter of vortex beams propagating through turbulent atmosphere

NASA Astrophysics Data System (ADS)

Suo, Qiangbo; Han, Yiping; Cui, Zhiwei

2017-09-01

Based on the extended Huygens-Fresnel integral, the analytical expressions for the Wigner distribution function (WDF) and kurtosis parameter of partially coherent flat-topped vortex (PCFTV) beams propagating through atmospheric turbulence and free space are derived. The WDF and kurtosis parameter of PCFTV beams through turbulent atmosphere are discussed with numerical examples. The numerical results show that the beam quality depends on the structure constants, the inner scale turbulence, the outer scale turbulence, the spatial correlation length, the wave length and the beam order. PCFTV beams are less affected by turbulence than partially flat-topped coherent (PCFT) beams under the same conditions, and will be useful in free-space optical communications.

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

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

NASA Astrophysics Data System (ADS)

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

2007-02-01

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

Alternating direction implicit methods for parabolic equations with a mixed derivative

NASA Technical Reports Server (NTRS)

Beam, R. M.; Warming, R. F.

1980-01-01

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A(0)-stable linear two-step methods in conjunction with the method of approximate factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A(0)-stable method. The parameter space for which the resulting ADI schemes are second-order accurate and unconditionally stable is determined. Some numerical examples are given.

Alternating direction implicit methods for parabolic equations with a mixed derivative

NASA Technical Reports Server (NTRS)

Beam, R. M.; Warming, R. F.

1979-01-01

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A sub 0-stable linear two-step methods in conjunction with the method of approximation factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A sub 0-stable method. The parameter space for which the resulting ADI schemes are second order accurate and unconditionally stable is determined. Some numerical examples are given.

Efficiency of unconstrained minimization techniques in nonlinear analysis

NASA Technical Reports Server (NTRS)

Kamat, M. P.; Knight, N. F., Jr.

1978-01-01

Unconstrained minimization algorithms have been critically evaluated for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth, first, or second order depending upon the highest derivative of the function required by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives clearly suggests using analytically derived gradients instead of finite difference approximations. The use of analytic gradients results in better control of the number of minimizations required for convergence to the exact solution.

Growth Responses of Neurospora crassa to Increased Partial Pressures of the Noble Gases and Nitrogen

PubMed Central

Buchheit, R. G.; Schreiner, H. R.; Doebbler, G. F.

1966-01-01

Buchheit, R. G. (Union Carbide Corp., Tonawanda, N.Y.), H. R. Schreiner, and G. F. Doebbler. Growth responses of Neurospora crassa to increased partial pressures of the noble gases and nitrogen. J. Bacteriol. 91:622–627. 1966.—Growth rate of the fungus Neurospora crassa depends in part on the nature of metabolically “inert gas” present in its environment. At high partial pressures, the noble gas elements (helium, neon, argon, krypton, and xenon) inhibit growth in the order: Xe > Kr> Ar ≫ Ne ≫ He. Nitrogen (N2) closely resembles He in inhibitory effectiveness. Partial pressures required for 50% inhibition of growth were: Xe (0.8 atm), Kr (1.6 atm), Ar (3.8 atm), Ne (35 atm), and He (∼ 300 atm). With respect to inhibition of growth, the noble gases and N2 differ qualitatively and quantitatively from the order of effectiveness found with other biological effects, i.e., narcosis, inhibition of insect development, depression of O2-dependent radiation sensitivity, and effects on tissue-slice glycolysis and respiration. Partial pressures giving 50% inhibition of N. crassa growth parallel various physical properties (i.e., solubilities, solubility ratios, etc.) of the noble gases. Linear correlation of 50% inhibition pressures to the polarizability and of the logarithm of pressure to the first and second ionization potentials suggests the involvement of weak intermolecular interactions or charge-transfer in the biological activity of the noble gases. PMID:5883104

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.

Derivation of WECC Distributed PV System Model Parameters from Quasi-Static Time-Series Distribution System Simulations

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

Mather, Barry A; Boemer, Jens C.; Vittal, Eknath

The response of low voltage networks with high penetration of PV systems to transmission network faults will, in the future, determine the overall power system performance during certain hours of the year. The WECC distributed PV system model (PVD1) is designed to represent small-scale distribution-connected systems. Although default values are provided by WECC for the model parameters, tuning of those parameters seems to become important in order to accurately estimate the partial loss of distributed PV systems for bulk system studies. The objective of this paper is to describe a new methodology to determine the WECC distributed PV system (PVD1)more » model parameters and to derive parameter sets obtained for six distribution circuits of a Californian investor-owned utility with large amounts of distributed PV systems. The results indicate that the parameters for the partial loss of distributed PV systems may differ significantly from the default values provided by WECC.« less

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

NASA Astrophysics Data System (ADS)

Wu, Zedong; Liu, Hongwei; Alkhalifah, Tariq

2018-07-01

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

Critical behavior study around the ferromagnetic phase transition in Pr2Pt2In

NASA Astrophysics Data System (ADS)

Tchokonté, M. B. Tchoula; Mboukam, J. J.; Sondezi, B. M.; Bashir, A. K. H.; Britz, D.; Strydom, A. M.; Kaczorowski, D.

2018-05-01

The magnetic ordering in Pr2Pt2In was investigated by means of magnetization and magnetic susceptibility measurements. The compound was found to order ferromagnetically at TC = 8.8(2) K with a second-order phase transition. The derived critical exponents β = 0.325(2), γ = 1.058(2) and δ = 4.26(4) are close to those expected for a 3D Ising ferromagnet.

Fixed Point Results for G-α-Contractive Maps with Application to Boundary Value Problems

PubMed Central

Roshan, Jamal Rezaei

2014-01-01

We unify the concepts of G-metric, metric-like, and b-metric to define new notion of generalized b-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes of G-α-admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, some examples and an application to the existence of a solution for the first-order periodic boundary value problem are provided here to illustrate the usability of the obtained results. PMID:24895655

Optimal control of first order distributed systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Johnson, T. L.

1972-01-01

The problem of characterizing optimal controls for a class of distributed-parameter systems is considered. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables, which are constrained at the boundary by a finite number of algebraic relations. Multiple control inputs, extending over the entire spatial region occupied by the system ("distributed controls') are to be designed so that the response of the system is optimal. A major example involving boundary control of an unstable low-density plasma is developed from physical laws.

Measuring and assessing maintainability at the end of high level design

NASA Technical Reports Server (NTRS)

Briand, Lionel C.; Morasca, Sandro; Basili, Victor R.

1993-01-01

Software architecture appears to be one of the main factors affecting software maintainability. Therefore, in order to be able to predict and assess maintainability early in the development process we need to be able to measure the high-level design characteristics that affect the change process. To this end, we propose a measurement approach, which is based on precise assumptions derived from the change process, which is based on Object-Oriented Design principles and is partially language independent. We define metrics for cohesion, coupling, and visibility in order to capture the difficulty of isolating, understanding, designing and validating changes.

Boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Panaras, Argyris G.

1987-01-01

A set of higher-order boundary-layer equations is derived valid for three-dimensional compressible flows. The equations are written in a generalized curvilinear coordinate system, in which the surface coordinates are nonorthogonal; the third axis is restricted to be normal to the surface. Also, higher-order viscous terms which are retained depend on the surface curvature of the body. Thus, the equations are suitable for the calculation of the boundary layer about arbitrary vehicles. As a starting point, the Navier-Stokes equations are derived in a tensorian notation. Then by means of an order-of-magnitude analysis, the boundary-layer equations are developed. To provide an interface between the analytical partial differentiation notation and the compact tensor notation, a brief review of the most essential theorems of the tensor analysis related to the equations of the fluid dynamics is given. Many useful quantities, such as the contravariant and the covariant metrics and the physical velocity components, are written in both notations.

Derivative spectrophotometric method for simultaneous determination of clindamycin phosphate and tretinoin in pharmaceutical dosage forms

PubMed Central

2013-01-01

A derivative spectrophotometric method was proposed for the simultaneous determination of clindamycin and tretinoin in pharmaceutical dosage forms. The measurement was achieved using the first and second derivative signals of clindamycin at (1D) 251 nm and (2D) 239 nm and tretinoin at (1D) 364 nm and (2D) 387 nm. The proposed method showed excellent linearity at both first and second derivative order in the range of 60–1200 and 1.25–25 μg/ml for clindamycin phosphate and tretinoin respectively. The within-day and between-day precision and accuracy was in acceptable range (CV<3.81%, error<3.20%). Good agreement between the found and added concentrations indicates successful application of the proposed method for simultaneous determination of clindamycin and tretinoin in synthetic mixtures and pharmaceutical dosage form. PMID:23575006

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

The complete mitogenome of the whale shark parasitic copepod Pandarus rhincodonicus norman, Newbound & Knott (Crustacea; Siphonostomatoida; Pandaridae)--a new gene order for the copepoda.

PubMed

Austin, Christopher M; Tan, Mun Hua; Lee, Yin Peng; Croft, Laurence J; Meekan, Mark G; Pierce, Simon J; Gan, Han Ming

2016-01-01

The complete mitochondrial genome of the parasitic copepod Pandarus rhincodonicus was obtained from a partial genome scan using the HiSeq sequencing system. The Pandarus rhincodonicus mitogenome has 14,480 base pairs (62% A+T content) made up of 12 protein-coding genes, 2 ribosomal subunit genes, 22 transfer RNAs, and a putative 384 bp non-coding AT-rich region. This Pandarus mitogenome sequence is the first for the family Pandaridae, the second for the order Siphonostomatoida and the sixth for the Copepoda.