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Results for “JACOBIAN FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

TU-F-CAMPUS-J-03: Elasticity Functions Based On 4DCT Images to Predict Tumor and Normal Tissue Response to Radiation for Patients with Lung Cancers

Purpose: To investigate radiotherapy outcomes by incorporating 4DCT-based physiological and tumor elasticity functions for lung cancer patients. Methods: 4DCT images were acquired from 28 lung SBRT patients before radiation treatment. Deformable image registration (DIR) was performed from the end-inhale to the end-exhale using a B-Spline-based algorithm (Elastix, an open source software package). The resultant displacement vector fields (DVFs) were used to calculate a relative Jacobian function (RV) for each patient. The computed functions in the lung and tumor regions represent lung ventilation and tumor elasticity properties, respectively. The 28 patients were divided into two groups: 16 with two-year tumor local control (LC) and 12 with local failure (LF). The ventilation and elasticity related RV functions were calculated for each of these patients. Results: The LF patients have larger RV values than the LC patients. The mean RV value in the lung region was 1.15 (±0.67) for the LF patients, higher than 1.06 (±0.59) for the LC patients. In the tumor region, the elasticity-related RV values are 1.2 (±0.97) and 0.86 (±0.64) for the LF and LC patients, respectively. Among the 16 LC patients, 3 have the mean RV values greater than 1.0 in the tumors. These tumors were located near the diaphragm, where the displacements are relatively large.. RV functions calculated in the tumor were better correlated with treatment outcomes than those calculated in the lung. Conclusion: The ventilation and elasticity-related RV functions in the lung and tumor regions were calculated from 4DCT image and the resultant values showed differences between the LC and LF patients. Further investigation of the impact of the displacements on the computed RV is warranted. Results suggest that the RV images might be useful for evaluation of treatment outcome for lung cancer patients.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2011

Compact formulas for guiding-center orbits in axisymmetric tokamak geometry

Compact formulas for trapped-particle and passing-particle guiding-center orbits in axisymmetric tokamak geometry are given in terms of the Jacobi elliptic functions and complete elliptic integrals. These formulas can find applications in bounce-center kinetic theory as well as guiding-center Fokker-Planck kinetic theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

Breatherlike electromagnetic wave propagation in an antiferromagnetic medium with Dzyaloshinsky-Moriya interaction

We investigate the nature of propagation of electromagnetic waves (EMWs) in an antiferromagnetic medium with Dzyaloshinsky-Moriya (DM) interaction environment. The interplay of bilinear and DM exchange spin coupling with the magnetic field component of the EMW has been studied by solving Maxwell's equations coupled with a nonlinear spin equation for the magnetization of the medium. We made a nonuniform expansion of the magnetization and magnetic field along the direction of propagation of EMW, in the framework of reductive perturbation method, and the dynamics of the system is found to be governed by a generalized derivative nonlinear Schroedinger (DNLS) equation. We employ the Jacobi-elliptic function method to solve the DNLS equation, and the electromagnetic wave propagation in an antiferromagnetic medium is governed by the breatherlike spatially and temporally coherent localized modes under the influence of DM interaction parameter.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Analysis of the Trusted Inertial Terrain-Aided Navigation Measurement Function

The trusted inertial terrain-aided navigation (TITAN) algorithm leverages an airborne vertical synthetic aperture radar to measure the range to the closest ground points along several prescribed iso-Doppler contours. These TITAN minimum-range, prescribed-Doppler measurements are the result of a constrained nonlinear optimization problem whose optimization function and constraints both depend on the radar position and velocity. Owing to the complexity of this measurement definition, analysis of the TITAN algorithm is lacking in prior work. This publication offers such an analysis, making the following three contributions: (1) an analytical solution to the TITAN constrained optimization measurement problem, (2) a derivation of the TITAN measurement function Jacobian, and (3) a derivation of the Cramér-Rao lower bound on the estimated position and velocity error covariance. These three contributions are verified via Monte Carlo simulations over synthetic terrain, which further reveal two remarkable properties of the TITAN algorithm: (1) the along-track positioning errors tend to be smaller than the cross-track positioning errors, and (2) the cross-track positioning errors are independent of the terrain roughness.

TITAN↗
DOE OSTI2013

Force-free Jacobian equilibria for Vlasov-Maxwell plasmas

New analytic force-free Vlasov-Maxwell equilibria for thin current sheets are presented. The magnetic flux densities are expressed in terms of Jacobian elliptic functions of one Cartesian spatial coordinate. The magnetic flux densities reduce to previously reported hyperbolic functions in one limit and sinusoidal functions in another limit of the modulus k. A much wider class of nonlinear force-free Vlasov-Maxwell equilibria open expanded possibilities for modeling of solar system, astrophysical and laboratory plasmas. Modified Maxwellian distribution functions are determined explicitly in terms of Jacobian elliptic functions. Conditions for double peaked distribution functions that could be unstable are developed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

To the Theory of C{sub 0}-Operator Orthogonal Polynomials

Operator orthogonal polynomials are considered whose arguments are generators of strongly continuous semigroups of transformations of class C{sub 0} acting in a Banach space. Earlier such polynomials were considered by the authors in the case of the Chebyshev polynomials of the first and second kind. In this paper, more general classes of operator orthogonal polynomials are considered, which include the Jacobi and Aptekarev polynomials. Integral representations of operator fractional-rational functions and also of Bessel operator-valued functions of an imaginary argument are presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Extremal trajectories in a nilpotent sub-Riemannian problem on the Engel group

On the Engel group a nilpotent sub-Riemannian problem is considered, a 4-dimensional optimal control problem with a 2-dimensional linear control and an integral cost functional. It arises as a nilpotent approximation to nonholonomic systems with 2-dimensional control in a 4-dimensional space (for example, a system describing the navigation of a mobile robot with trailer). A parametrization of extremal trajectories by Jacobi functions is obtained. A discrete symmetry group and its fixed points, which are Maxwell points, are described. An estimate for the cut time (the time of the loss of optimality) on extremal trajectories is derived on this basis. Bibliography: 25 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Dynamics of Jacobi's elliptic spatial waves in a nonlinear optical grating

This paper presents the results of our study on the dynamics of Jacobi's elliptic spatial waves in a nonlinear optical grating based on a generalized coupled-mode model. We discuss the characteristics of their amplitudes, widths, and spatial periods as well as their bifurcation in the associated phase plane. Our study on the dynamical propagation of perturbed profiles reveal that these waves can suffer breathing and broadening due to the diffraction effect. A remarkable split-off phenomenon of a spatial wave with wide stripes into several narrow and shallow oblique stripes is observed, as well as their passing and bouncing collisions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Traveling Wave Solutions of the Gardner Equation and Motion of Plane Curves Governed by the mKdV Flow

The Gardner equation is well-known in the mathematical literature since the late sixties of 20th century. Initially, it appeared in the context of the construction of local conservation laws admitted by the KdV equation. Later on, the Gardner equation was generalized and found to be applicable in various branches of physics (solid-state and plasma physics, fluid dynamics and quantum field theory). In this paper, we examine the travelling wave solutions of the Gardner equation and derive the full set of solutions to the corresponding reduced equation in terms of Weierstrass and Jacobi elliptic functions. Then, we use the travelling wave solutions of the focusing mKdV equation and obtain in explicit analytic form exact solutions of a special type of plane curve flow, known as the mKdV flow.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Jacobian consistency of a one-parametric class of smoothing Fischer–Burmeister functions for SOCCP

The Jacobian consistency of smoothing functions plays an important role for achieving the rapid convergence of Newton methods or Newton-like methods with an appropriate parameter control. In this paper, we study the properties, derive the computable formula for the Jacobian matrix and prove the Jacobian consistency of a one-parametric class of smoothing Fischer–Burmeister functions for second-order cone complementarity problems proposed by Tang et al. (Comput Appl Math 33:655–669, 2014). Then we apply its Jacobian consistency to a smoothing Newton method with the appropriate parameter control presented by Chen et al. (Math Comput 67:519–540, 1998), and show the global convergence and local quadratic convergence of the algorithm for solving the SOCCP under rather weak assumptions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Higher-Order Corrections to Optimisers based on Newton's Method

The Newton, Gauss–Newton and Levenberg–Marquardt methods all use the first derivative of a vector function (the Jacobian) to minimise its sum of squares. When the Jacobian matrix is ill-conditioned, the function varies much faster in some directions than others and the space of possible improvement in sum of squares becomes a long narrow ellipsoid in the linear model. This means that even a small amount of nonlinearity in the problem parameters can cause a proposed point far down the long axis of the ellipsoid to fall outside of the actual curved valley of improved values, even though it is quite nearby. This paper presents a differential equation that ‘follows’ these valleys, based on the technique of geodesic acceleration, which itself provides a 2 nd order improvement to the Levenberg–Marquardt iteration step. Higher derivatives of this equation are computed that allow n th order improvements to the optimisation methods to be derived. These higher-order accelerated methods up to 4 th order are tested numerically and shown to provide substantial reduction of both number of steps and computation time.

43 PARTICLE ACCELERATORS↗
DOE OSTI2010

Type A Jacobi Elliptic One-Monopole

We present new classical generalized one-monopole solution of the SU(2) Yang-Mills-Higgs theory with the Higgs field in the adjoint representation. We show that this generalized solution with {Theta}-winding number m = 1 and {phi}-winding number n = 1 is an axially symmetric Jacobi elliptic generalization of the 't Hooft-Polyakov one-monopole. We construct this axially symmetric one-monopole solution by generalizing the large distance asymptotic solution of the 't Hooft-Polyakov one-monopole to the Jacobi elliptic functions and solving the second order equations of motion numerically when the Higgs potential is vanishing. This solution is a regular non-BPS finite energy solution.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Electron-impact double ionization of He by applying the Jacobi matrix approach to the Faddeev-Merkuriev equations

We apply the Jacobi matrix method to the Faddeev-Merkuriev differential equations in order to calculate the three-body wave function that describes the double continuum of an atomic two-electron system. This function is used to evaluate within the first-order Born approximation, the fully differential cross sections for (e,3e) processes in helium. The calculations are performed in the case of a coplanar geometry in which the incident electron is fast and both ejected electrons are slow. Quite unexpectedly, the results obtained by reducing our double-continuum wave function to its asymptotic expression are in satisfactory agreement with all the experimental data of Lahmam-Bennani et al.[A. Lahaman-Bennani et al., Phys. Rev. A 59, 3548 (1999); A. Kheifets et al., J. Phys. B 32, 5047 (1999).] without any need for renormalizing the data. When the full double-continuum wave function is used, the agreement of the results with the experimental data improves significantly. However, a detailed analysis of the calculations shows that full convergence in terms of the basis size is not reached. This point is discussed in detail.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Raynal–Revai coefficients for a general kinematic rotation

In a three-body system, transitions between different sets of normalized Jacobi coordinates are described as general kinematic transformations that include an orthogonal or a pseudoorthogonal rotation. For such rotations, the Raynal–Revai coefficients execute a unitary transformation between three-body hyperspherical functions. Recurrence relations that make it possible to calculate the Raynal–Revai coefficients for arbitrary angular momenta are derived on the basis of linearized representations of products of hyperspherical functions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Interaction of elliptically polarised cross-degenerate cnoidal waves in an isotropic gyrotropic medium with spatial dispersion of cubic nonlinearity

Three unusual classes of particular analytical solutions to a system of four nonlinear equations are found for slowly varying complex amplitudes of circularly polarised components of the electric field. The system describes the self-action and interaction of two elliptically polarised plane waves collinearly propagating in an isotropic medium with second-order frequency dispersion and spatial dispersion of cubic nonlinearity. The solutions correspond to self-consistent combinations of two elliptically polarised cnoidal waves whose mutually orthogonal polarisation components vary in accordance with pairwise identical laws during propagation. At the same time, the amplitudes of the component with the same circular polarisation are proportional to two different elliptic Jacobi functions with the same periods. (nonlinear optical phenomena)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗