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Results for “BOUNDARY-VALUE PROBLEMS”

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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Boundary values of the Schwarzian derivative of a regular function

Regular functions f in the half-plane Imz>0 admitting an asymptotic expansion f(z)=c{sub 1}z+c{sub 2}z{sup 2}+c{sub 3}z{sup 3}+{gamma}(z)z{sup 3}, where c{sub 1}>0, Imc{sub 2}=0 and the angular limit <lim{sub z{yields}0{gamma}}(z)=0, are considered. For various conditions on the function f inequalities for the real part of the Schwarzian derivative S{sub f}(0)=6(c{sub 3}/c{sub 1}-c{sub 2}{sup 2}/c{sub 1}{sup 2}) are established. These inequalities complement and refine some known versions of Schwarz's lemma. The results obtained are close to the well-known Burns-Krantz rigidity theorem on regular self-maps and its generalizations due to Tauraso, Vlacci and Shoikhet. Bibliography: 16 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Solvability of the Dirichlet problem for a general second-order elliptic equation

The paper is concerned with studying the solvability of the Dirichlet problem for the second-order elliptic equation ; in a bounded domain Q subset of R{sub n}, n{>=}2, with C{sup 1}-smooth boundary and boundary condition u{sub 0} element of L{sub 2}({partial deriv}Q). Conditions for the existence of an (n-1)-dimensionally continuous solution are obtained, the resulting solvability condition is shown to be similar in form to the solvability condition in the conventional generalized setting (in W{sub 2}{sup 1}(Q)). In particular, the problem is shown to have an (n-1)-dimensionally continuous solution for all u{sub 0} element of L{sub 2}({partial deriv}Q) and all f and F from the appropriate function spaces, provided that the homogeneous problem (with zero boundary conditions and zero right-hand side) has no nonzero solutions in W{sub 2}{sup 1}(Q). Bibliography: 14 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

The Dirichlet problem for a second-order elliptic equation with an L{sub p} boundary function

We consider a Dirichlet problem in which the boundary value of a solution is understood as the L{sub p}-limit, p>1, of traces of this solution on surfaces 'parallel' to the boundary. We suggest a setting of this problem which (in contrast to the notion of solution in W{sub p,loc}{sup 1}) enables us to study the solvability of the problem without making smoothness assumptions on the coefficients inside the domain. In particular, for an equation in selfadjoint form without lower-order terms, under the same conditions as those used for p=2, we prove unique solvability and establish a bound for an analogue of the area integral. Bibliography: 37 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

An inverse theorem on 'economic' maps

We prove that the bound from the theorem on 'economic' maps is best possible. Namely, for m>n+d we construct a map from an n-dimensional simplex to an m-dimensional Euclidean space for which (and for any close map) there exists a d-dimensional plane whose preimage has cardinality not less than the upper bound [(dn+n+1)/(m-n-d)]+d from the theorem on 'economic' maps. Bibliography: 16 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Convergence of multipoint Pade approximants of piecewise analytic functions

The behaviour as n{yields}{infinity} of multipoint Pade approximants to a function which is (piecewise) holomorphic on a union of finitely many continua is investigated. The convergence of multipoint Pade approximants is proved for a function which extends holomorphically from these continua to a union of domains whose boundaries have a certain symmetry property. An analogue of Stahl's theorem is established for two-point Pade approximants to a pair of functions, either of which is a multivalued analytic function with finitely many branch points. Bibliography: 11 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Boundary uniqueness theorems for functions whose integrals over hyperbolic discs vanish

Sharp conditions are found describing the admissible rate of decrease of a nontrivial function whose integrals over all hyperbolic discs with fixed radius vanish. For the first time, the boundary behaviour of the function is investigated in a neighbourhood of a single point on the boundary of the domain of definition. Bibliography: 17 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

The inverse problem of recovering the source in a parabolic equation under a condition of nonlocal observation

We study the inverse problem for a parabolic equation of recovering the source, that is, the right-hand side F(x,t)=h(x,t)f(x), where the function f(x) is unknown. To find f(x), along with the initial and boundary conditions, we also introduce an additional condition of nonlocal observation of the form ∫{sub 0}{sup T}u(x,t) dμ(t)=χ(x). We prove the Fredholm property for the problem stated in this way, and obtain sufficient conditions for the existence and uniqueness of a solution. These conditions are of the form of readily verifiable inequalities and put no restrictions on the value of T>0 or the diameter of the domain Ω under consideration. The proof uses a priori estimates and the qualitative properties of solutions of initial-boundary value problems for parabolic equations. Bibliography: 40 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Quasinormal modes of self-dual warped AdS{sub 3} black hole in topological massive gravity

We consider the scalar, vector and spinor field perturbations in the background of self-dual warped AdS{sub 3} black hole of topological massive gravity. The corresponding exact expressions for quasinormal modes are obtained by analytically solving the perturbation equations and imposing the vanishing Dirichlet boundary condition at asymptotic infinity. It is expected that the quasinormal modes agree with the poles of retarded Green's functions of the CFT dual to self-dual warped AdS{sub 3} black hole. Our results provide a quantitative test of the warped AdS/CFT correspondence.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Harmonic analysis for the characterization and correction of geometric distortion in MRI

Purpose: Magnetic resonance imaging (MRI) is gaining widespread use in radiation therapy planning, patient setup verification, and real-time guidance of radiation delivery. Successful implementation of these technologies relies on the development of simple and efficient methods to characterize and monitor the geometric distortions arising due to system imperfections and gradient nonlinearities. To this end, the authors present the theory and validation of a novel harmonic approach to the quantification of system-related distortions in MRI. Methods: The theory of spatial encoding in MRI is applied to demonstrate that the 3D distortion vector field (DVF) is given by the solution of a second-order boundary value problem (BVP). This BVP is comprised of Laplace’s equation and a limited measurement of the distortion on the boundary of a specified region of interest (ROI). An analytical series expansion solving this BVP within a spherical ROI is obtained, and a statistical uncertainty analysis is performed to determine how random errors in the boundary measurements propagate to the ROI interior. This series expansion is then evaluated to obtain volumetric DVF mappings that are compared to reference data obtained on a 3 T full-body scanner. This validation is performed within two spheres of 20 cm diameter (one centered at the scanner origin and the other offset +3 cm along each of the transverse directions). Initially, a high-order mapping requiring measurements at 5810 boundary points is used. Then, after exploring the impact of the boundary sampling density and the effect of series truncation, a reduced-order mapping requiring measurements at 302 boundary points is evaluated. Results: The volumetric DVF mappings obtained from the harmonic analysis are in good agreement with the reference data. Following distortion correction using the high-order mapping, the authors estimate a reduction in the mean distortion magnitude from 0.86 to 0.42 mm and from 0.93 to 0.39 mm within the central and offset ROIs, respectively. In addition, the fraction of points with a distortion magnitude greater than 1 mm is reduced from 35.6% to 2.8% and from 40.4% to 1.5%, respectively. Similarly, following correction using the reduced-order mapping, the mean distortion magnitude reduces to 0.45–0.42 mm within the central and offset ROIs, and the fraction of points with a distortion magnitude greater than 1 mm is reduced to 2.8% and 1.5%, respectively. Conclusions: A novel harmonic approach to the characterization of system-related distortions in MRI is presented. This method permits a complete and accurate mapping of the DVF within a specified ROI using a limited measurement of the distortion on the ROI boundary. This technique eliminates the requirement to exhaustively sample the DVF at a dense 3D array of points, thereby permitting the design of simple, inexpensive phantoms that may incorporate additional modules for auxiliary quality assurance objectives.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS2009

Investigation of Boundary Conditions for Flexible Multibody Spacecraft Dynamics

In support of both the Space Shuttle and International Space Station programs, a set of generic multibody dynamics algorithms integrated within the Trick simulation environment have addressed the variety of on-orbit manipulator simulation requirements for engineering analysis, procedures development and crew familiarization/training at the NASA Johnson Space Center (JSC). Enhancements to these dynamics algorithms are now being driven by a new set of Constellation program requirements for flexible multibody spacecraft simulation. One particular issue that has been discussed within the NASA community is the assumption of cantilever-type flexible body boundary conditions. This assumption has been commonly utilized within manipulator multibody dynamics formulations as it simplifies the computation of relative motion for articulated flexible topologies. Moreover, its use for modeling of space-based manipulators such as the Shuttle Remote Manipulator System (SRMS) and Space Station Remote Manipulator System (SSRMS) has been extensively validated against flight data. For more general flexible spacecraft applications, however, the assumption of cantilever-type boundary conditions may not be sufficient. This paper describes the boundary condition assumptions that were used in the original formulation, demonstrates that this formulation can be augmented to accommodate systems in which the assumption of cantilever boundary conditions no longer applies, and verifies the approach through comparison with an independent model previously validated against experimental hardware test data from a spacecraft flexible dynamics emulator.

Boundary-value problems↗
NASA NTRS1990

Computing Deformations Of Rubbery Materials

Better use made of experimental data in finite-element computations. New formulation of constitutive equations of rubbery, nonlinearly elastic material enables finite-element analysis of boundary-value stress-and-strain problems involving arbitrary shapes and loads. In development of formulation, principal stretches used as arguments of strain-energy-density function.

Peng, Steven T. J.↗
NASA NTRS1990

Solving time-dependent two-dimensional eddy current problems

Transient eddy current calculations are presented for an EM wave-scattering and field-penetrating case in which a two-dimensional transverse magnetic field is incident on a good (i.e., not perfect) and infinitely long conductor. The problem thus posed is of initial boundary-value interface type, where the boundary of the conductor constitutes the interface. A potential function is used for time-domain modeling of the situation, and finite difference-time domain techniques are used to march the potential function explicitly in time. Attention is given to the case of LF radiation conditions.

Lee, Min Eig↗
NASA NTRS1989

Singular trajectories for time-optimal half-loop maneuvers of a high alpha fighter aircraft

Consideration is given to the problem of deriving a time-optimal open-loop control for the half-loop maneuver of a high-alpha aircraft, with initial conditions Mach 0.6 and 15,000 feet. Pontriagin's maximum principle is used to derive candidate optimal solutions. Using the two-point boundary-value algorithm, the flight path angle is maximized for various increasing specified final times until a final time of 13.6 sec yields a 180-deg flight-path angle. As the final time increased from 0.0 to 13.6 sec, the optimization process revealed 13 distinct switching structures of the control law, of which 11 contained singular arcs, and two had double singular arcs.

Hoffman, Eric↗
NASA NTRS1990

Spurious frequencies as a result of numerical boundary treatments

The stability theory for finite difference Initial Boundary-Value approximations to systems of hyperbolic partial differential equations states that the exclusion of eigenvalues and generalized eigenvalues is a sufficient condition for stability. The theory, however, does not discuss the nature of numerical approximations in the presence of such eigenvalues. In fact, as was shown previously, for the problem of vortex shedding by a 2-D cylinder in subsonic flow, stating boundary conditions in terms of the primitive (non-characteristic) variables may lead to such eigenvalues, causing perturbations that decay slowly in space and remain periodic time. Characteristic formulation of the boundary conditions avoided this problem. A more systematic study of the behavior of the (linearized) one-dimensional gas dynamic equations under various sets of oscillation-inducing legal boundary conditions is reported.

Abarbanel, Saul↗
DOE OSTI2011

Classical theory of cylindrical nonlinear optics: Second-harmonic generation

The second-harmonic generation of cylindrical electromagnetic waves in a nonlinear nondispersive medium is investigated two separate ways. One method uses the exact solutions of the Maxwell equations, which describe propagation of cylindrical electromagnetic waves, and the other method uses the traditional coupled-wave equations, which are derived from the interaction between cylindrical electromagnetic waves and a nonlinear nondispersive medium. The results obtained by these two methods are concordant with each other. We also show that both methods are useful in dealing with the problem of cylindrical second-harmonic generation and each of them has particular advantages in several aspects. The method of using the exact solution can solve problems of second-harmonic generation under initial-value and boundary-value conditions and the approach of using coupled-wave equations can be directly extended to describe other nonlinear phenomena such as sum-frequency and four-wave mixing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Combination of the Laguerre Transform with the Boundary-element Method for the Solution of Integral Equations with Retarded Kernel

We apply the Laguerre transform with respect to time to a time-dependent boundary-value integral equation encountered in the solution of three-dimensional Dirichlet initial-boundary-value problems for the homogeneous wave equation with homogeneous initial conditions by using the retarded potential of single layer. The obtained system of boundary integral equations is reduced to a sequence of Fredholm integral equations of the first kind that differ solely by the recursively dependent right-hand sides. To find their numerical solution, we use the boundary-element method. We establish an asymptotic estimate of the error of numerical solution and present the results of numerical simulations aimed at finding the solutions of retarded-potential integral equations for model examples.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

Altitude/path-angle transitions in fuel-optimal problems for transport aircraft

Altitude/path angle transitions to fuel-optimal, energy climb and descent paths are examined for subsonic transport aircraft. These transitions are termed boundary layers in singular perturbation theory, the framework used herein to simplify solutions to the state-Euler system. The energy climb and descent paths provide equilibrium or stationary points for the boundary layer system, and thus for moderate transitions, presumed valid for the class of aircraft considered, the boundary layer system may be linearized. This simplification allows derivation of an explicit solution to the two-point boundary-value, boundary layer problem and, as a consequence, yields a nearly optimal control law, in feedback form, for the transitions. Numerical simulation results using the feedback control law are presented for a Boeing 737 airframe (NASA-ATOPS Vehicle) employing twin JT8D-7-7A engines.

Gracey, C.↗
NASA NTRS1992

Computational aspects of helicopter trim analysis and damping levels from Floquet theory

Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.

Gaonkar, Gopal H.↗