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Results for “reciprocity theorem”

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

A reciprocal theorem for a mixture theory

A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

Martin, C. J.↗
NASA NTRS1985

Generalized reciprocity theorem for semiconductor devices

A reciprocity theorem is presented that relates the short-circuit current of a device, induced by a carrier generation source, to the minority-carrier Fermi level in the dark. The basic relation is general under low injection. It holds for three-dimensional devices with position dependent parameters (energy gap, electron affinity, mobility, etc.), and for transient or steady-state conditions. This theorem allows calculation of the internal quantum efficiency of a solar cell by using the analysis of the device in the dark. Other applications could involve measurements of various device parameters, interfacial surface recombination velocity at a polcrystalline silicon emitter contact, for rexample, by using steady-state or transient photon or mass-particle radiation.

Misiakos, K.↗
NASA NTRS1975

A reciprocal theorem for a mixture of interacting continuous media

Using a linearized theory of interacting continuous media composed of linear elastic solid and linear viscous fluid, a reciprocal theorem is derived which relates the solution of one initial-boundary value problem to another. As an illustration of the reciprocal theorem, we obtain the early time displacement and velocity field of a mixture occupying an infinite region and subjected to an impulsively applied moving point load acting on the solid constituent.

Lee, Y. M.↗
NASA NTRS1987

A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation

Two sets of coupled-mode equations for multiwaveguide systems are derived using a generalized reciprocity relation; one set for a lossless system, and the other for a general lossy or lossless system. The second set of equations also reduces to those of the first set in the lossless case under the condition that the transverse field components are chosen to be real. Analytical relations between the coupling coefficients are shown and applied to the coupling of mode equations. It is shown analytically that these results satisfy exactly both the reciprocity theorem and power conservation. New orthogonal relations between the supermodes are derived in matrix form, with the overlap integrals taken into account.

Chuang, Shun-Lien↗
NASA NTRS1987

A coupled mode formulation by reciprocity and a variational principle

A coupled mode formulation for parallel dielectric waveguides is presented via two methods: a reciprocity theorem and a variational principle. In the first method, a generalized reciprocity relation for two sets of field solutions satisfying Maxwell's equations and the boundary conditions in two different media, respectively, is derived. Based on the generalized reciprocity theorem, the coupled mode equations can then be formulated. The second method using a variational principle is also presented for a general waveguide system which can be lossy. The results of the variational principle can also be shown to be identical to those from the reciprocity theorem. The exact relations governing the 'conventional' and the new coupling coefficients are derived. It is shown analytically that the present formulation satisfies the reciprocity theorem and power conservation exactly, while the conventional theory violates the power conservation and reciprocity theorem by as much as 55 percent and the Hardy-Streifer (1985, 1986) theory by 0.033 percent, for example.

Chuang, Shun-Lien↗
DOE OSTI2014

Electromagnetic Reciprocity.

A reciprocity theorem is an explicit mathematical relationship between two different wavefields that can exist within the same space - time configuration. Reciprocity theorems provi de the theoretical underpinning for mod ern full waveform inversion solutions, and also suggest practical strategies for speed ing up large - scale numerical modeling of geophysical datasets . In the present work, several previously - developed electromagnetic r eciprocity theorems are generalized to accommodate a broader range of medi um, source , and receiver types. Reciprocity relations enabling the interchange of various types of point sources and point receivers within a three - dimensional electromagnetic model are derived. Two numerical modeling algorithms in current use are successfully tested for adherence to reciprocity. Finally, the reciprocity theorem forms the point of departure for a lengthy derivation of electromagnetic Frechet derivatives. These mathe matical objects quantify the sensitivity of geophysical electromagnetic data to variatio ns in medium parameters, and thus constitute indispensable tools for solution of the full waveform inverse problem. ACKNOWLEDGEMENTS Sandia National Labor atories is a multi - program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under contract DE - AC04 - 94AL85000. Signif icant portions of the work reported herein were conducted under a Cooperative Research and Development Agreement (CRADA) between Sandia National Laboratories (SNL) and CARBO Ceramics Incorporated. The author acknowledges Mr. Chad Cannan and Mr. Terry Pa lisch of CARBO Ceramics, and Ms. Amy Halloran, manager of SNL's Geophysics and Atmospheric Sciences Department, for their interest in and encouragement of this work. Special thanks are due to Dr . Lewis C. Bartel ( recently retired from Sandia National Labo ratories and now a geophysical consultant ) and Dr. Chester J. Weiss (recently rejoined with Sandia National Laboratories) for many stimulating (and reciprocal!) discussions regar ding the topic at hand.

Aldridge, David F.↗
DOE OSTI2023

Measuring the cross section of the N 15 ( α , γ ) 19 F reaction using a single-fluid bubble chamber

15 N(α, γ) 19 F is believed to be the primary means of stellar nucleosynthesis of fluorine. Here we present the use of a single-fluid bubble chamber to measure the cross section of the time-inverse photo-dissociation reaction. The method benefits from a luminosity increase of several orders of magnitude due to the use of a thicker liquid target - compared to thin films or gas targets - and from the reciprocity theorem. We discuss the results of experiments at the Thomas Jefferson National Accelerator Facility, where the cross section of the photodisintegration process 19 F(γ, α) 15 N was measured by bombarding a superheated fluid of C 3 F 8 with bremsstrahlung γ rays produced by impinging a 4 - 5.5 MeV electron beam on a Cu radiator. From the photodissociation yield the cross section was extracted by performing a convolution with a Monte Carlo–generated γ-ray beam spectrum. The measurement produced a cross section that was then time inverted using the reciprocity theorem. The cross section for the 15 N(α, γ) 19 F reaction was determined down to a value in the range of hundreds of picobarns. We report that with further improvements of the experimental setup the technique could potentially push cross section measurements down to the single picobarn range.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1998

Determination of Stress Coefficient Terms in Cracked Solids for Monoclinic Materials with Plane Symmetry at x3 = 0

Determination of all the coefficients in the crack tip field expansion for monoclinic materials under two-dimensional deformation is presented in this report. For monoclinic materials with a plane of material symmetry at x(sub 3) = 0, the in-plane deformation is decoupled from the anti-plane deformation. In the case of in-plane deformation, utilizing conservation laws of elasticity and Betti's reciprocal theorem, together with selected auxiliary fields, T-stress and third-order stress coefficients near the crack tip are evaluated first from path-independent line integrals. To determine the T-stress terms using the J-integral and Betti's reciprocal work theorem, auxiliary fields under a concentrated force and moment acting at the crack tip are used respectively. Through the use of Stroh formalism in anisotropic elasticity, analytical expressions for all the coefficients including the stress intensity factors are derived in a compact form that has surprisingly simple structure in terms of the Barnett-Lothe tensors, L. The solution forms for degenerated materials, orthotropic, and isotropic materials are presented.

Yuan, F. G.↗
DOE OSTI2025

Sedimentation and shear-induced dynamics of spheroids in fluids with spatial viscosity variations

A generalized reciprocal theorem is used to relate the force and torque induced on a particle in an inertia-less fluid with small variation in viscosity to integrals involving Stokes flow fields and the spatial dependence of viscosity. These resistivity expressions are analytically evaluated using spheroidal harmonics and then used to obtain the mobility of the spheroid during sedimentation, and in linear flows, of a fluid with linear viscosity stratification. The coupling between the rotational and translational motion induced by stratification rotates the spheroid’s centerline, creating a variety of rotational and translational dynamics dependent upon the particle’s aspect ratio, κ, and the component of the stratification unit vector in the gravity direction, d g . Spheroids with 0.55 ⪅ κ ⪅ 2.0 exhibit the largest variety of settling behaviors. Interestingly, this range covers most microplastics and typical microorganisms. One of the modes include a stable orientation dependent only on κ and d g , but independent of initial orientation, thus allowing for the potential control of settling angles and sedimentation rates. In a simple shear flow, cross-streamline migration occurs due to the stratification-induced force generated on the particle. Similarly, a particle no longer stays at the stagnation point of a uniaxial extensional flow. While fully analytical results are obtained for spheroids, numerical simulations provide a source of validation. These simulations also provide additional insights into the stratification-induced force- and torque-producing mechanisms through the stratification-induced stress, which is not accessed in the reciprocal theorem-based analytical calculations.

Geophysical and Geological Flows: Stratified flows↗
DOE OSTI2022

Validating and optimizing mismatch tolerance of Doppler backscattering measurements with the beam model (invited)

In this work, we use the beam model of Doppler backscattering (DBS), which was previously derived from beam tracing and the reciprocity theorem, to shed light on mismatch attenuation. This attenuation of the backscattered signal occurs when the wavevector of the probe beam’s electric field is not in the plane perpendicular to the magnetic field. Correcting for this effect is important for determining the amplitude of the actual density fluctuations. Previous preliminary comparisons between the model and Mega-Ampere Spherical Tokamak (MAST) plasmas were promising. In this work, we quantitatively account for this effect on DIII-D, a conventional tokamak. We compare the predicted and measured mismatch attenuation in various DIII-D, MAST, and MAST-U plasmas, showing that the beam model is applicable in a wide variety of situations. Finally, we performed a preliminary parameter sweep and found that the mismatch tolerance can be improved by optimizing the probe beam’s width and curvature at launch. This is potentially a design consideration for new DBS systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1989

Reciprocal relations for transmission coefficients - Theory and application

The authors present a rigorous proof of certain intuitively plausible reciprocal relations for time harmonic plane-wave transmission and reflection at the interface between a fluid and an anisotropic elastic solid. Precise forms of the reciprocity relations for the transmission coefficients and for the transmitted energy fluxes are derived, based on the reciprocity theorem of elastodynamics. It is shown that the reciprocity relations can be used in conjunction with measured values of peak amplitudes for transmission through a slab of the solid (water-solid-water) to obtain the water-solid coefficients. Experiments were performed for a slab of a unidirectional fiber-reinforced composite. Good agreement of the experimentally measured transmission coefficients with theoretical values was obtained.

Qu, Jianmin↗
NASA NTRS1993

A reciprocity formulation for the EM scattering by an obstacle within a large open cavity

A formulation based on a generalized reciprocity theorem is developed for analyzing the external high frequency EM scattering by a complex obstacle inside a relatively arbitrary open-ended waveguide cavity when it is illuminated by an external source. This formulation is also extended to include EM fields whose time dependence may be nonperiodic. A significant advantage of this formulation is that it allows one to break up the analysis into two independent parts; one deals with the waveguide cavity shape alone and the other with the obstacle alone. The external scattered field produced by the obstacle (in the presence of the waveguide cavity structure) is given in terms of a generalized reciprocity integral over a surface S(T) corresponding to the interior waveguide cavity cross section located conveniently but sufficiently close to the obstacle. Furthermore, the fields coupled into the cavity from the source in the exterior region generally need to propagate only one-way via the open front end (which is directly illuminated) to the interior surface S(T) in this approach, and not back, in order to find the external field scattered by the obstacle.

Pathak, Prabhakar H.↗
DOE OSTI2017

Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic half-space

Here, we consider the problem of an arbitrary shaped rigid punch pressed against the boundary of a transversely isotropic half-space and interacting with an arbitrary flat crack or inclusion, located in the plane parallel to the boundary. The set of governing integral equations is derived for the most general conditions, namely the presence of both normal and tangential stresses under the punch, as well as general loading of the crack faces. In order to verify correctness of the derivations, two different methods were used to obtain governing integral equations: generalized method of images and utilization of the reciprocal theorem. Both methods gave the same results. Axisymmetric coaxial case of interaction between a rigid inclusion and a flat circular punch both centered along the z-axis is considered as an illustrative example. Most of the final results are presented in terms of elementary functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Ideal solar cell equation in the presence of photon recycling

Previous derivations of the ideal solar cell equation based on Shockley's p-n junction diode theory implicitly assume negligible effects of photon recycling. This paper derives the equation in the presence of photon recycling that modifies the values of dark saturation and light-generated currents, using an approach applicable to arbitrary three-dimensional geometries with arbitrary doping profile and variable band gap. The work also corrects an error in previous work and proves the validity of the reciprocity theorem for charge collection in such a more general case with the previously neglected junction depletion region included.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Mueller matrix ellipsometric detection of profile asymmetry in nanoimprinted grating structures

Mueller matrix ellipsometry (MME) is applied to detect foot-like asymmetry encountered in nanoimprint lithography (NIL) processes. We present both theoretical and experimental results which show that MME has good sensitivity to both the magnitude and direction of asymmetric profiles. The physics behind the use of MME for asymmetry detection is the breaking of electromagnetic reciprocity theorem for the zeroth-order diffraction of asymmetric gratings. We demonstrate that accurate characterization of asymmetric nanoimprinted gratings can be achieved by performing MME measurements in a conical mounting with the plane of incidence parallel to grating lines and meanwhile incorporating depolarization effects into the optical model. The comparison of MME-extracted asymmetric profile with the measurement by cross-sectional scanning electron microscopy also reveals the strong potential of this technique for in-line monitoring NIL processes, where symmetric structures are desired.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗