Diffracted wavefield by an arbitrary aperture from Maggi-Rubinowicz transformation

NASA Astrophysics Data System (ADS)

Ganci, S.

2008-01-01

Fraunhofer diffraction patterns through apertures in opaque screens are the cases of most interest in optics. The major purpose of this paper is to establish a general and explicit formula for calculating diffracted wavefield from Maggi-Rubinowicz transformation. The 2-D integration (Rayleigh-Sommerfeld or Helmholtz-Kirchhoff integral formulas) is reduced to a 1-D integration over the rim of the aperture. Some examples for elliptical and polygonal apertures are given.

A comparison of finite element and analytic models of acoustic scattering from rough poroelastic interfaces.

PubMed

Bonomo, Anthony L; Isakson, Marcia J; Chotiros, Nicholas P

2015-04-01

The finite element method is used to model acoustic scattering from rough poroelastic surfaces. Both monostatic and bistatic scattering strengths are calculated and compared with three analytic models: Perturbation theory, the Kirchhoff approximation, and the small-slope approximation. It is found that the small-slope approximation is in very close agreement with the finite element results for all cases studied and that perturbation theory and the Kirchhoff approximation can be considered valid in those instances where their predictions match those given by the small-slope approximation.

Computer Simulation Of An In-Process Surface Finish Sensor.

NASA Astrophysics Data System (ADS)

Rakels, Jan H.

1987-01-01

It is generally accepted, that optical methods are the most promising for the in-process measurement of surface finish. These methods have the advantages of being non-contacting and fast data acquisition. Furthermore, these optical instruments can be easily retrofitted on existing machine-tools. In the Micro-Engineering Centre at the University of Warwick, an optical sensor has been developed which can measure the rms roughness, slope and wavelength of turned and precision ground surfaces during machining. The operation of this device is based upon the Kirchhoff-Fresnel diffraction integral. Application of this theory to ideal turned and ground surfaces is straightforward, and indeed the calculated diffraction patterns are in close agreement with patterns produced by an actual optical instrument. Since it is mathematically difficult to introduce real machine-tool behaviour into the diffraction integral, a computer program has been devised, which simulates the operation of the optical sensor. The program produces a diffraction pattern as a graphical output. Comparison between computer generated and actual diffraction patterns of the same surfaces show a high correlation. The main aim of this program is to construct an atlas, which maps known machine-tool errors versus optical diffraction patterns. This atlas can then be used for machine-tool condition diagnostics. It has been found that optical monitoring is very sensitive to minor defects. Therefore machine-tool detoriation can be detected before it is detrimental.

Comparison of microfacet BRDF model to modified Beckmann-Kirchhoff BRDF model for rough and smooth surfaces.

PubMed

Butler, Samuel D; Nauyoks, Stephen E; Marciniak, Michael A

2015-11-02

A popular class of BRDF models is the microfacet models, where geometric optics is assumed. In contrast, more complex physical optics models may more accurately predict the BRDF, but the calculation is more resource intensive. These seemingly disparate approaches are compared in detail for the rough and smooth surface approximations of the modified Beckmann-Kirchhoff BRDF model, assuming Gaussian surface statistics. An approximation relating standard Fresnel reflection with the semi-rough surface polarization term, Q, is presented for unpolarized light. For rough surfaces, the angular dependence of direction cosine space is shown to be identical to the angular dependence in the microfacet distribution function. For polished surfaces, the same comparison shows a breakdown in the microfacet models. Similarities and differences between microfacet BRDF models and the modified Beckmann-Kirchhoff model are identified. The rationale for the original Beckmann-Kirchhoff F(bk)(2) geometric term relative to both microfacet models and generalized Harvey-Shack model is presented. A modification to the geometric F(bk)(2) term in original Beckmann-Kirchhoff BRDF theory is proposed.

Multiplicity of solutions for the noncooperative Schrödinger-Kirchhoff system involving the fractional p-Laplacian in R^N

NASA Astrophysics Data System (ADS)

Liang, Sihua; Zhang, Jihui

2017-06-01

In this paper, we investigate the existence of solutions for the noncooperative Schrödinger-Kirchhoff-type system involving the fractional p-Laplacian and critical nonlinearities in RN. By applying the Limit Index Theory due to Li (Nonlinear Anal 25:1371-1389, 1995) and the fractional version of concentration-compactness principle, we obtain the existence and multiplicity of solutions for the above systems under some suitable assumptions. To our best knowledge, it seems that this is the first time to exploit the existence of solutions for the noncooperative Schrödinger-Kirchhoff-type system involving the fractional p-Laplacian and critical nonlinearity in RN.

Bound Electron States in Skew-symmetric Quantum Wire Intersections

DTIC Science & Technology

2014-01-01

18 1.2.3 Kirchhoffs Rule for Quantum Wires . . . . . . . . . . . 19 1.3 Novel numerical methods development . . . . . . . . . . . . . 19 2...regions, though this is not as obvious as it is for bulges. CHAPTER 1. LITERATURE REVIEW 19 1.2.3 Kirchhoffs Rule for Quantum Wires One particle quantum...scattering theory on an arbitrary finite graph with n open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general

A Fast Method of Deriving the Kirchhoff Formula for Moving Surfaces

NASA Technical Reports Server (NTRS)

Farassat, F.; Posey, Joe W.

2007-01-01

The Kirchhoff formula for a moving surface is very useful in many wave propagation problems, particularly in the prediction of noise from rotating machinery. Several publications in the last two decades have presented derivations of the Kirchhoff formula for moving surfaces in both time and frequency domains. Here we present a method originally developed by Farassat and Myers in time domain that is both simple and direct. It is based on generalized function theory and the useful concept of imbedding the problem in the unbounded three-dimensional space. We derive an inhomogeneous wave equation with the source terms that involve Dirac delta functions with their supports on the moving data surface. This wave equation is then solved using the simple free space Green's function of the wave equation resulting in the Kirchhoff formula. The algebraic manipulations are minimal and simple. We do not need the Green's theorem in four dimensions and there is no ambiguity in the interpretation of any terms in the final formulas. Furthermore, this method also gives the simplest derivation of the classical Kirchhoff formula which has a fairly lengthy derivation in physics and applied mathematics books. The Farassat-Myers method can be used easily in frequency domain.

Measurement of Kirchhoff's stress intensity factors in bending plates

NASA Astrophysics Data System (ADS)

Bäcker, D.; Kuna, M.; Häusler, C.

2014-03-01

A measurement method of the stress intensity factors defined by KIRCHHOFF's theory for a crack in a bending plate is shown. For this purpose, a thin piezoelectric polyvinylidene fluoride film (PVDF) is attached to the surface of the cracked plate. The measured electrical voltages are coupled with the load type and the crack tip position relative to the sensor film. Stress intensity factors and the crack tip position can be determined by solving the non-linear inverse problem based on the measured signals. To guarantee solvability of the problem, more measuring electrodes on the film have to be taken in to account. To the developed sensor concept the KIRCHHOFF's plate theory has been applied. In order to connect the electrical signals and the stress intensity factors the stresses near the crack tip have to be written in eigenfunctions (see WILLIAMS [1]). The presented method was verified by means of the example of a straight crack of the length 2a in an infinite isotropic plate under all- side bending. It was found that the positioning of the electrodes is delimited by two radii. On one hand, the measurement points should not be too close to the crack tip. In this area, the Kirchhoff's plate theory cannot be used effectively. On the other hand, the measuring electrodes should be placed at a smaller distance to each other and not too far from the crack tip regarding the convergence radius of the WILLIAMS series expansion. Test calculations on a straight crack in an infinite isotropic plate showed the general applicability of the measurement method.

Issues in Optical Diffraction Theory

PubMed Central

Mielenz, Klaus D.

2009-01-01

This paper focuses on unresolved or poorly documented issues pertaining to Fresnel’s scalar diffraction theory and its modifications. In Sec. 2 it is pointed out that all thermal sources used in practice are finite in size and errors can result from insufficient coherence of the optical field. A quarter-wave criterion is applied to show how such errors can be avoided by placing the source at a large distance from the aperture plane, and it is found that in many cases it may be necessary to use collimated light as on the source side of a Fraunhofer experiment. If these precautions are not taken the theory of partial coherence may have to be used for the computations. In Sec. 3 it is recalled that for near-zone computations the Kirchhoff or Rayleigh-Sommerfeld integrals are applicable, but fail to correctly describe the energy flux across the aperture plane because they are not continuously differentiable with respect to the assumed geometrical field on the source side. This is remedied by formulating an improved theory in which the field on either side of a semi-reflecting screen is expressed as the superposition of mutually incoherent components which propagate in the opposite directions of the incident and reflected light. These components are defined as linear combinations of the Rayleigh-Sommerfeld integrals, so that they are rigorous solutions of the wave equation as well as continuously differentiable in the aperture plane. Algorithms for using the new theory for computing the diffraction patterns of circular apertures and slits at arbitrary distances z from either side of the aperture (down to z = ± 0.0003 λ) are presented, and numerical examples of the results are given. These results show that the incident geometrical field is modulated by diffraction before it reaches the aperture plane while the reflected field is spilled into the dark space. At distances from the aperture which are large compared to the wavelength λ these field expressions are reduced to the usual ones specified by Fresnel’s theory. In the specific case of a diffracting half plane the numerical results obtained were practically the same as those given by Sommerfeld’s rigorous theory. The modified theory developed in this paper is based on the explicit assumption that the scalar theory of light cannot explain plolarization effects. This premise is justified in Sec. 4, where it is shown that previous attempts to do so have produced dubious results. PMID:27504215

Displacements and evolution of optical vortices in edge-diffracted Laguerre-Gaussian beams

NASA Astrophysics Data System (ADS)

Bekshaev, Aleksandr; Chernykh, Aleksey; Khoroshun, Anna; Mikhaylovskaya, Lidiya

2017-05-01

Based on the Kirchhoff-Fresnel approximation, we consider the behavior of optical vortices (OV) upon propagation of diffracted Laguerre-Gaussian (LG) beams with topological charge ∣m∣ = 1, 2. Under conditions of weak diffraction perturbation (i.e. the diffraction obstacle covers only the far transverse periphery of the incident LG beam), these OVs describe almost perfect 3D spirals within the diffracted beam body, which is an impressive demonstration of the helical nature of an OV beam. The far-field OV positions within the diffracted beam cross section depend on the wavefront curvature of the incident OV beam, so that the input wavefront curvature is transformed into the output azimuthal OV rotation. The results are expected to be useful in OV metrology and OV beam diagnostics.

Extension of Kirchhoff's formula to radiation from moving surfaces

NASA Technical Reports Server (NTRS)

Farassat, F.; Myers, M. K.

1988-01-01

Kirchhoff's formula for radiation from a closed surface has been used recently for prediction of the noise of high speed rotors and propellers. Because the closed surface on which the boundary data are prescribed in these cases is in motion, an extension of Kirchhoff's formula to this condition is required. In this paper such a formula, obtained originally by Morgans for the interior problem, is derived for regions exterior to surfaces moving at speeds below the wave propagation speed by making use of some results of generalized function theory. It is shown that the usual Kirchhoff formula is a special case of the main result of the paper. The general result applies to a deformable surface. However, the special form it assumes for a rigid surface in motion is also noted. In addition, Morgans' result is further extended by showing that edge line integrals appear in the formula when applied to a surface that is piecewise smooth. Some possible areas of application of the formula to problems of current interest in aeroacoustics are discussed.

Extension of Kirchhoff's formula to radiation from moving surfaces

NASA Technical Reports Server (NTRS)

Farassat, F.; Myers, M. K.

1987-01-01

Kirchhoff's formula for radiation from a closed surface has been used recently for prediction of the noise of high speed rotors and propellers. Because the closed surface on which the boundary data are prescribed in these cases is in motion, an extension of Kirchhoff's formula to this condition is required. In this paper such a formula, obtained originally by Morgans for the interior problem, is derived for regions exterior to surfaces moving at speeds below the wave propagation speed by making use of some results of generalized function theory. It is shown that the usual Kirchhoff formula is a special case of the main result of the paper. The general result applies to a deformable surface. However, the special form it assumes for a rigid surface in motion is also noted. In addition, Morgans' result is further extended by showing that edge line integrals appear in the formula when applied to a surface that is piecewise smooth. Some possible areas of application of the formula to problems of current interest in aeroacoustics are discussed.

FEL amplifier performance in the Compton regime

NASA Astrophysics Data System (ADS)

Cover, R. A.; Bhowmik, A.

1984-01-01

The Kroll-Morton-Rosenbluth equations of motion for electrons in a linearly polarized, tapered wiggler are utilized to describe gain in free-electron laser amplifiers. The three-dimensional amplifier model includes the effects of density variation in the electron beam, off-axis variations in the wiggler magnetic field, and betatron oscillations. The input electromagnetic field is injected and subsequently propagated within the wiggler by computing the Fresnel-Kirchhoff diffraction integral using the Gardner-Fresnel-Kirchhoff algorithm. The injected optical beam used in evaluating amplifier performance is initially a Gaussian which in general may be astigmatic. The importance of the above effects on extraction efficiency is computed both with rigorous three-dimensional electromagnetic wave propagation and a Gaussian treatment of the field.

Far-field characteristics of the square grooved-dielectric lens antenna for the terahertz band.

PubMed

Pan, Wu; Zeng, Wei

2016-09-10

In order to improve the gain and directionality of a terahertz antenna, a square grooved-dielectric lens antenna based on a Fresnel zone plate is proposed. First, a diagonal horn, which is adopted as the primary feed antenna, is designed. Then, the far-field characteristics of the lens antenna are studied by using Fresnel-Kirchhoff diffraction theory and the paraxial approximation. The effects of the full-wave period, the focus diameter ratio, the subregion, and the dielectric substrate thickness on radiation characteristics are studied. The experimental results show that the proposed lens antenna has axisymmetric radiation patterns. The gain is over 26.1 dB, and the 3 dB main lobe beam width is lower than 5.6° across the operation band. The proposed lens antenna is qualified for applications in terahertz wireless communication systems.

A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields. I - An extended DKT element for thick-plate bending analysis. II - An extended DKQ element for thick-plate bending analysis

NASA Astrophysics Data System (ADS)

Katili, Irwan

1993-06-01

A new three-node nine-degree-of-freedom triangular plate bending element is proposed which is valid for the analysis of both thick and thin plates. The element, called the discrete Kirchhoff-Mindlin triangle (DKMT), has a proper rank, passes the patch test for thin and thick plates in an arbitrary mesh, and is free of shear locking. As an extension of the DKMT element, a four-node element with 3 degrees of freedom per node is developed. The element, referred to as DKMQ (discrete Kirchhoff-Mindlin quadrilateral) is found to provide good results for both thin and thick plates without any compatibility problems.

Cubic Zig-Zag Enrichment of the Classical Kirchhoff Kinematics for Laminated and Sandwich Plates

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2012-01-01

A detailed anaylsis and examples are presented that show how to enrich the kinematics of classical Kirchhoff plate theory by appending them with a set of continuous piecewise-cubic functions. This analysis is used to obtain functions that contain the effects of laminate heterogeneity and asymmetry on the variations of the inplane displacements and transverse shearing stresses, for use with a {3, 0} plate theory in which these distributions are specified apriori. The functions used for the enrichment are based on the improved zig-zag plate theory presented recently by Tessler, Di Scuva, and Gherlone. With the approach presented herein, the inplane displacements are represented by a set of continuous piecewise-cubic functions, and the transverse shearing stresses and strains are represented by a set of piecewise-quadratic functions that are discontinuous at the ply interfaces.

A time-domain Kirchhoff formula for the convective acoustic wave equation

PubMed Central

Ghorbaniasl, Ghader; Siozos-Rousoulis, Leonidas; Lacor, Chris

2016-01-01

Kirchhoff’s integral method allows propagated sound to be predicted, based on the pressure and its derivatives in time and space obtained on a data surface located in the linear flow region. Kirchhoff’s formula for noise prediction from high-speed rotors and propellers suffers from the limitation of the observer located in uniform flow, thus requiring an extension to arbitrarily moving media. This paper presents a Kirchhoff formulation for moving surfaces in a uniform moving medium of arbitrary configuration. First, the convective wave equation is derived in a moving frame, based on the generalized functions theory. The Kirchhoff formula is then obtained for moving surfaces in the time domain. The formula has a similar form to the Kirchhoff formulation for moving surfaces of Farassat and Myers, with the presence of additional terms owing to the moving medium effect. The equation explicitly accounts for the influence of mean flow and angle of attack on the radiated noise. The formula is verified by analytical cases of a monopole source located in a moving medium. PMID:27118912

An experimental evaluation of the application of the Kirchhoff formulation for sound radiation from an oscillating airfoil

NASA Technical Reports Server (NTRS)

Brooks, T. F.

1977-01-01

The Kirchhoff integral formulation is evaluated for its effectiveness in quantitatively predicting the sound radiated from an oscillating airfoil whose chord length is comparable with the acoustic wavelength. A rigid airfoil section was oscillated at samll amplitude in a medium at rest to produce the sound field. Simultaneous amplitude and phase measurements were made of surface pressure and surface velocity distributions and the acoustic free field. Measured surface pressure and motion are used in applying the theory, and airfoil thickness and contour are taken into account. The result was that the theory overpredicted the sound pressure level by 2 to 5, depending on direction. Differences are also noted in the sound field phase behavior.

Approximate Evaluation of Acoustical Focal Beams by Phased Array Probes for Austenitic Weld Inspections

NASA Astrophysics Data System (ADS)

Kono, Naoyuki; Miki, Masahiro; Nakamura, Motoyuki; Ehara, Kazuya

2007-03-01

Phased array techniques are capable of the sensitive detection and precise sizing of flaws or cracks in components of nuclear power plants by using arbitrary focal beams with various depths, positions and angles. Aquantitative investigation of these focal beams is essential for the optimization of array probes, especially for austenitic weld inspection, in order to improve the detectability, sizing accuracy, and signal-to-noise ratio using these beams. In the present work, focal beams generated by phased array probes are calculated based on the Fresnel-Kirchhoff diffraction integral (FKDI) method, and an approximation formula between the actual focal depth and optical focal depth is proposed as an extension of the theory for conventional spherically focusing probes. The validity of the approximation formula for the array probes is confirmed by a comparison with simulation data using the FKDI method, and the experimental data.

Determining linear vibration frequencies of a ferromagnetic shell

NASA Astrophysics Data System (ADS)

Bagdoev, A. G.; Vardanyan, A. V.; Vardanyan, S. V.; Kukudzhanov, V. N.

2007-10-01

The problems of determining the roots of dispersion equations for free bending vibrations of thin magnetoelastic plates and shells are of both theoretical and practical interest, in particular, in studying vibrations of metallic structures used in controlled thermonuclear reactors. These problems were solved on the basis of the Kirchhoff hypothesis in [1-5]. In [6], an exact spatial approach to determining the vibration frequencies of thin plates was suggested, and it was shown that it completely agrees with the solution obtained according to the Kirchhoff hypothesis. In [7-9], this exact approach was used to solve the problem on vibrations of thin magnetoelastic plates, and it was shown by cumbersome calculations that the solutions obtained according to the exact theory and the Kirchhoff hypothesis differ substantially except in a single case. In [10], the equations of the dynamic theory of elasticity in the axisymmetric problem are given. In [11], the equations for the vibration frequencies of thin ferromagnetic plates with arbitrary conductivity were obtained in the exact statement. In [12], the Kirchhoff hypothesis was used to obtain dispersion relations for a magnetoelastic thin shell. In [5, 13-16], the relations for the Maxwell tensor and the ponderomotive force for magnetics were presented. In [17], the dispersion relations for thin ferromagnetic plates in the transverse field in the spatial statement were studied analytically and numerically. In the present paper, on the basis of the exact approach, we study free bending vibrations of a thin ferromagnetic cylindrical shell. We obtain the exact dispersion equation in the form of a sixth-order determinant, which can be solved numerically in the case of a magnetoelastic thin shell. The numerical results are presented in tables and compared with the results obtained by the Kirchhoff hypothesis. We show a large number of differences in the results, even for the least frequency.

Diffraction studies applicable to 60-foot microwave research facilities

NASA Technical Reports Server (NTRS)

Schmidt, R. F.

1973-01-01

The principal features of this document are the analysis of a large dual-reflector antenna system by vector Kirchhoff theory, the evaluation of subreflector aperture-blocking, determination of the diffraction and blockage effects of a subreflector mounting structure, and an estimate of strut-blockage effects. Most of the computations are for a frequency of 15.3 GHz, and were carried out using the IBM 360/91 and 360/95 systems at Goddard Space Flight Center. The FORTRAN 4 computer program used to perform the computations is of a general and modular type so that various system parameters such as frequency, eccentricity, diameter, focal-length, etc. can be varied at will. The parameters of the 60-foot NRL Ku-band installation at Waldorf, Maryland, were entered into the program for purposes of this report. Similar calculations could be performed for the NELC installation at La Posta, California, the NASA Wallops Station facility in Virginia, and other antenna systems, by a simple change in IBM control cards. A comparison is made between secondary radiation patterns of the NRL antenna measured by DOD Satellite and those obtained by analytical/numerical methods at a frequency of 7.3 GHz.

Kirchhoff's rule for quantum wires

NASA Astrophysics Data System (ADS)

Kostrykin, V.; Schrader, R.

1999-01-01

We formulate and discuss one-particle quantum scattering theory on an arbitrary finite graph with n open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general boundary conditions at the vertices. This results in a scattering theory with n channels. The corresponding on-shell S-matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy E>0 is given explicitly in terms of the boundary conditions and the lengths of the internal lines. It is shown to be unitary, which may be viewed as the quantum version of Kirchhoff's law. We exhibit covariance and symmetry properties. It is symmetric if the boundary conditions are real. Also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low-energy behaviour of one theory gives the high-energy behaviour of the transformed theory. Finally, we provide a composition rule by which the on-shell S-matrix of a graph is factorizable in terms of the S-matrices of its subgraphs. All proofs use only known facts from the theory of self-adjoint extensions, standard linear algebra, complex function theory and elementary arguments from the theory of Hermitian symplectic forms.

A Note on the Kirchhoff and Additive Degree-Kirchhoff Indices of Graphs

NASA Astrophysics Data System (ADS)

Yang, Yujun; Klein, Douglas J.

2015-06-01

Two resistance-distance-based graph invariants, namely, the Kirchhoff index and the additive degree-Kirchhoff index, are studied. A relation between them is established, with inequalities for the additive degree-Kirchhoff index arising via the Kirchhoff index along with minimum, maximum, and average degrees. Bounds for the Kirchhoff and additive degree-Kirchhoff indices are also determined, and extremal graphs are characterised. In addition, an upper bound for the additive degree-Kirchhoff index is established to improve a previously known result.

An integral equation formulation for the diffraction from convex plates and polyhedra.

PubMed

Asheim, Andreas; Svensson, U Peter

2013-06-01

A formulation of the problem of scattering from obstacles with edges is presented. The formulation is based on decomposing the field into geometrical acoustics, first-order, and multiple-order edge diffraction components. An existing secondary-source model for edge diffraction from finite edges is extended to handle multiple diffraction of all orders. It is shown that the multiple-order diffraction component can be found via the solution to an integral equation formulated on pairs of edge points. This gives what can be called an edge source signal. In a subsequent step, this edge source signal is propagated to yield a multiple-order diffracted field, taking all diffraction orders into account. Numerical experiments demonstrate accurate response for frequencies down to 0 for thin plates and a cube. No problems with irregular frequencies, as happen with the Kirchhoff-Helmholtz integral equation, are observed for this formulation. For the axisymmetric scattering from a circular disc, a highly effective symmetric formulation results, and results agree with reference solutions across the entire frequency range.

A new scheme for velocity analysis and imaging of diffractions

NASA Astrophysics Data System (ADS)

Lin, Peng; Peng, Suping; Zhao, Jingtao; Cui, Xiaoqin; Du, Wenfeng

2018-06-01

Seismic diffractions are the responses of small-scale inhomogeneities or discontinuous geological features, which play a vital role in the exploitation and development of oil and gas reservoirs. However, diffractions are generally ignored and considered as interference noise in conventional data processing. In this paper, a new scheme for velocity analysis and imaging of seismic diffractions is proposed. Two steps compose of this scheme in our application. First, the plane-wave destruction method is used to separate diffractions from specular reflections in the prestack domain. Second, in order to accurately estimate migration velocity of the diffractions, the time-domain dip-angle gathers are derived from a Kirchhoff-based angle prestack time migration using separated diffractions. Diffraction events appear flat in the dip-angle gathers when imaged above the diffraction point with selected accurate migration velocity for diffractions. The selected migration velocity helps to produce the desired prestack imaging of diffractions. Synthetic and field examples are applied to test the validity of the new scheme. The diffraction imaging results indicate that the proposed scheme for velocity analysis and imaging of diffractions can provide more detailed information about small-scale geologic features for seismic interpretation.

A robust approach for analysing dispersion of elastic waves in an orthotropic cylindrical shell

NASA Astrophysics Data System (ADS)

Kaplunov, J.; Nobili, A.

2017-08-01

Dispersion of elastic waves in a thin orthotropic cylindrical shell is considered, within the framework of classical 2D Kirchhoff-Love theory. In contrast to direct multi-parametric analysis of the lowest propagating modes, an alternative robust approach is proposed that simply requires evaluation of the evanescent modes (quasi-static edge effect), which, at leading order, do not depend on vibration frequency. A shortened dispersion relation for the propagating modes is then derived by polynomial division and its accuracy is numerically tested against the full Kirchhoff-Love dispersion relation. It is shown that the same shortened relation may be also obtained from a refined dynamic version of the semi-membrane theory for cylindrical shells. The presented results may be relevant for modelling various types of nanotubes which, according to the latest experimental findings, possess strong material anisotropy.

A Modified Kirchhoff plate theory for Free Vibration analysis of functionally graded material plates using meshfree method

NASA Astrophysics Data System (ADS)

Nguyen Van Do, Vuong

2018-04-01

In this paper, a modified Kirchhoff theory is presented for free vibration analyses of functionally graded material (FGM) plate based on modified radial point interpolation method (RPIM). The shear deformation effects are taken account into modified theory to ignore the locking phenomenon of thin plates. Due to the proposed refined plate theory, the number of independent unknowns reduces one variable and exists with four degrees of freedom per node. The simulated free vibration results employed by the modified RPIM are compared with the other analytical solutions to verify the effectiveness and the accuracy of the developed mesh-free method. Detail parametric studies of the proposed method are then conducted including the effectiveness of thickness ratio, boundary condition and material inhomogeneity on the sample problems of square plates. Results illustrated that the modified mesh-free RPIM can effectively predict the numerical calculation as compared to the exact solutions. The obtained numerical results are indicated that the proposed method are stable and well accurate prediction to evaluate with other published analyses.

Accuracy and performance of 3D mask models in optical projection lithography

NASA Astrophysics Data System (ADS)

Agudelo, Viviana; Evanschitzky, Peter; Erdmann, Andreas; Fühner, Tim; Shao, Feng; Limmer, Steffen; Fey, Dietmar

2011-04-01

Different mask models have been compared: rigorous electromagnetic field (EMF) modeling, rigorous EMF modeling with decomposition techniques and the thin mask approach (Kirchhoff approach) to simulate optical diffraction from different mask patterns in projection systems for lithography. In addition, each rigorous model was tested for two different formulations for partially coherent imaging: The Hopkins assumption and rigorous simulation of mask diffraction orders for multiple illumination angles. The aim of this work is to closely approximate results of the rigorous EMF method by the thin mask model enhanced with pupil filtering techniques. The validity of this approach for different feature sizes, shapes and illumination conditions is investigated.

An integral equation method for calculating sound field diffracted by a rigid barrier on an impedance ground.

PubMed

Zhao, Sipei; Qiu, Xiaojun; Cheng, Jianchun

2015-09-01

This paper proposes a different method for calculating a sound field diffracted by a rigid barrier based on the integral equation method, where a virtual boundary is assumed above the rigid barrier to divide the whole space into two subspaces. Based on the Kirchhoff-Helmholtz equation, the sound field in each subspace is determined with the source inside and the boundary conditions on the surface, and then the diffracted sound field is obtained by using the continuation conditions on the virtual boundary. Simulations are carried out to verify the feasibility of the proposed method. Compared to the MacDonald method and other existing methods, the proposed method is a rigorous solution for whole space and is also much easier to understand.

Defect modelling in an interactive 3-D CAD environment

NASA Astrophysics Data System (ADS)

Reilly, D.; Potts, A.; McNab, A.; Toft, M.; Chapman, R. K.

2000-05-01

This paper describes enhancement of the NDT Workbench, as presented at QNDE '98, to include theoretical models for the ultrasonic inspection of smooth planar defects, developed by British Energy and BNFL-Magnox Generation. The Workbench is a PC-based software package for the reconstruction, visualization and analysis of 3-D ultrasonic NDT data in an interactive CAD environment. This extension of the Workbeach now provides the user with a well established modelling approach, coupled with a graphical user interface for: a) configuring the model for flaw size, shape, orientation and location; b) flexible specification of probe parameters; c) selection of scanning surface and scan pattern on the CAD component model; d) presentation of the output as a simulated ultrasound image within the component, or as graphical or tabular displays. The defect modelling facilities of the Workbench can be used for inspection procedure assessment and confirmation of data interpretation, by comparison of overlay images generated from real and simulated data. The modelling technique currently implemented is based on the Geometrical Theory of Diffraction, for simulation of strip-like, circular or elliptical crack responses in the time harmonic or time dependent cases. Eventually, the Workbench will also allow modelling using elastodynamic Kirchhoff theory.

Method of Preparation AZP4330 PR Pattern with Edge Slope 40°

NASA Astrophysics Data System (ADS)

Wu, Jie; Zhao, Hongyuan; Yu, Yuanwei; Zhu, Jian

2018-03-01

When the edge which is under the multi-film is more steep or angular, the stress in the multilayer film near the edge is concentrated, this situation will greatly reduce the reliability of electronic components. And sometimes, we need some special structure such as a slope with a specific angle in the MEMS, so that the metal line can take the signal to the output pad through the slope instead of deep step. To cover these problems, the lithography method of preparing the structure with edge slope is studied. In this paper, based on the Kirchhoff scalar diffraction theory we try to change the contact exposure gap and the post-baking time at the specific temperature to find out the effect about the edge angle of the photoresist. After test by SEM, the results were presented by using AZP4330 photoresist, we can get the PR Pattern with edge slope 40° of the process and the specific process parameters.

Laser diode side-pumped Nd:YVO4 microchip laser with film-etched microcavity mirrors.

PubMed

Li, Jiyang; Niu, Yanxiong; Chen, Sanbin; Tan, Yidong

2017-10-01

Microchip lasers are applied as the light sources on various occasions with the end-pumping scheme. However, the vibration, the temperature drift, or the mechanical deformation of the pumping light in laser diodes in the end-pumping scheme will lead to instability in the microchip laser output, which causes errors and malfunctioning in the optic systems. In this paper, the side-pumping scheme is applied for improving the disturbance-resisting ability of the microchip laser. The transverse mode and the frequency purity of the laser output are tested. To ensure unicity in the frequency of the laser output, numerical simulations based on Fresnel-Kirchhoff diffraction theory are conducted on the parameters of the microchip laser cavity. Film-etching technique is applied to restrain the area of the film and form the microcavity mirrors. The laser output with microcavity mirrors is ensured to be in single frequency and with good beam quality, which is significant in the applications of microchip lasers as the light sources in optical systems.

Numerical correction of distorted images in full-field optical coherence tomography

NASA Astrophysics Data System (ADS)

Min, Gihyeon; Kim, Ju Wan; Choi, Woo June; Lee, Byeong Ha

2012-03-01

We propose a numerical method which can numerically correct the distorted en face images obtained with a full field optical coherence tomography (FF-OCT) system. It is shown that the FF-OCT image of the deep region of a biological sample is easily blurred or degraded because the sample has a refractive index (RI) much higher than its surrounding medium in general. It is analyzed that the focal plane of the imaging system is segregated from the imaging plane of the coherence-gated system due to the RI mismatch. This image-blurring phenomenon is experimentally confirmed by imaging the chrome pattern of a resolution test target through its glass substrate in water. Moreover, we demonstrate that the blurred image can be appreciably corrected by using the numerical correction process based on the Fresnel-Kirchhoff diffraction theory. The proposed correction method is applied to enhance the image of a human hair, which permits the distinct identification of the melanin granules inside the cortex layer of the hair shaft.

Separation and imaging diffractions by a sparsity-promoting model and subspace trust-region algorithm

NASA Astrophysics Data System (ADS)

Yu, Caixia; Zhao, Jingtao; Wang, Yanfei; Wang, Chengxiang; Geng, Weifeng

2017-03-01

The small-scale geologic inhomogeneities or discontinuities, such as tiny faults, cavities or fractures, generally have spatial scales comparable to or even smaller than the seismic wavelength. Therefore, the seismic responses of these objects are coded in diffractions and an attempt to high-resolution imaging can be made if we can appropriately image them. As the amplitudes of reflections can be several orders of magnitude larger than those of diffractions, one of the key problems of diffraction imaging is to suppress reflections and at the same time to preserve diffractions. A sparsity-promoting method for separating diffractions in the common-offset domain is proposed that uses the Kirchhoff integral formula to enforce the sparsity of diffractions and the linear Radon transform to formulate reflections. A subspace trust-region algorithm that can provide globally convergent solutions is employed for solving this large-scale computation problem. The method not only allows for separation of diffractions in the case of interfering events but also ensures a high fidelity of the separated diffractions. Numerical experiment and field application demonstrate the good performance of the proposed method in imaging the small-scale geological features related to the migration channel and storage spaces of carbonate reservoirs.

A Study on the Model of Detecting the Liquid Level of Sealed Containers Based on Kirchhoff Approximation Theory.

PubMed

Zhang, Bin; Song, Wen-Ai; Wei, Yue-Juan; Zhang, Dong-Song; Liu, Wen-Yi

2017-06-15

By simulating the sound field of a round piston transducer with the Kirchhoff integral theorem and analyzing the shape of ultrasound beams and propagation characteristics in a metal container wall, this study presents a model for calculating the echo sound pressure by using the Kirchhoff paraxial approximation theory, based on which and according to different ultrasonic impedance between gas and liquid media, a method for detecting the liquid level from outside of sealed containers is proposed. Then, the proposed method is evaluated through two groups of experiments. In the first group, three kinds of liquid media with different ultrasonic impedance are used as detected objects; the echo sound pressure is calculated by using the proposed model under conditions of four sets of different wall thicknesses. The changing characteristics of the echo sound pressure in the entire detection process are analyzed, and the effects of different ultrasonic impedance of liquids on the echo sound pressure are compared. In the second group, taking water as an example, two transducers with different radii are selected to measure the liquid level under four sets of wall thickness. Combining with sound field characteristics, the influence of different size transducers on the pressure calculation and detection resolution are discussed and analyzed. Finally, the experimental results indicate that measurement uncertainly is better than ±5 mm, which meets the industrial inspection requirements.

A Study on the Model of Detecting the Liquid Level of Sealed Containers Based on Kirchhoff Approximation Theory

PubMed Central

Zhang, Bin; Song, Wen-Ai; Wei, Yue-Juan; Zhang, Dong-Song; Liu, Wen-Yi

2017-01-01

By simulating the sound field of a round piston transducer with the Kirchhoff integral theorem and analyzing the shape of ultrasound beams and propagation characteristics in a metal container wall, this study presents a model for calculating the echo sound pressure by using the Kirchhoff paraxial approximation theory, based on which and according to different ultrasonic impedance between gas and liquid media, a method for detecting the liquid level from outside of sealed containers is proposed. Then, the proposed method is evaluated through two groups of experiments. In the first group, three kinds of liquid media with different ultrasonic impedance are used as detected objects; the echo sound pressure is calculated by using the proposed model under conditions of four sets of different wall thicknesses. The changing characteristics of the echo sound pressure in the entire detection process are analyzed, and the effects of different ultrasonic impedance of liquids on the echo sound pressure are compared. In the second group, taking water as an example, two transducers with different radii are selected to measure the liquid level under four sets of wall thickness. Combining with sound field characteristics, the influence of different size transducers on the pressure calculation and detection resolution are discussed and analyzed. Finally, the experimental results indicate that measurement uncertainly is better than ±5 mm, which meets the industrial inspection requirements. PMID:28617326

Evolution of the transfer function characterization of surface scatter phenomena

NASA Astrophysics Data System (ADS)

Harvey, James E.; Pfisterer, Richard N.

2016-09-01

Based upon the empirical observation that BRDF measurements of smooth optical surfaces exhibited shift-invariant behavior when plotted versus    o , the original Harvey-Shack (OHS) surface scatter theory was developed as a scalar linear systems formulation in which scattered light behavior was characterized by a surface transfer function (STF) reminiscent of the optical transfer function (OTF) of modern image formation theory (1976). This shift-invariant behavior combined with the inverse power law behavior when plotting log BRDF versus log   o was quickly incorporated into several optical analysis software packages. Although there was no explicit smooth-surface approximation in the OHS theory, there was a limitation on both the incident and scattering angles. In 1988 the modified Harvey-Shack (MHS) theory removed the limitation on the angle of incidence; however, a moderate-angle scattering limitation remained. Clearly for large incident angles the BRDF was no longer shift-invariant as a different STF was now required for each incident angle. In 2011 the generalized Harvey-Shack (GHS) surface scatter theory, characterized by a two-parameter family of STFs, evolved into a practical modeling tool to calculate BRDFs from optical surface metrology data for situations that violate the smooth surface approximation inherent in the Rayleigh-Rice theory and/or the moderate-angle limitation of the Beckmann-Kirchhoff theory. And finally, the STF can be multiplied by the classical OTF to provide a complete linear systems formulation of image quality as degraded by diffraction, geometrical aberrations and surface scatter effects from residual optical fabrication errors.

Some Comments on the Status of Shell Theory at the End of the 20th Century: Complaints and Correctives

NASA Technical Reports Server (NTRS)

Simmonds, James G.

1998-01-01

This review is divided into complaints and correctives. Complaints are directed at: sloppy refereeing and editing; authors who fail to read or acknowledge what others have done; the mis-naming or mis-crediting of results; the misunderstanding and misuse of the Kirchhoff hypothesis; inflated claims of accuracy based on overly-simplified benchmark problems; the failure to appreciate the inherent errors in various shell models; the failure to appreciate that the physical response and mathematical structure of shell theory are fundamentally different from 3-dimensional elasticity; and the irrelevance of Cosserat-type theories. Correctives include a simple, straight-forward derivation of a general nonlinear dynamic shell theory with the following features: (1) the equations of motion and kinematics (and those of thermodynamics, if desired) are exact consequences of their 3-dimensional counterparts; (2) there are no asymptotic or series expansions through the thickness; (3) all approximations (including the Kirchhoff Hypothesis) occur in the constitutive relations; (4) in static problems, there is a mixed form of the governing equations involving a mixed-energy density and exhibiting remnants of the well-known static-geometric duality of linear theory which is numerically robust because the limiting cases of nonlinear membrane theory and inextensional bending theory fall out naturally. (These latter two special cases are known to produce numerical nightmares unless treated with great care); and (5) all equations may be expressed in coordinate-free form (although, sometimes, a hybrid form is shown to be superior).

Revealing small-scale diffracting discontinuities by an optimization inversion algorithm

NASA Astrophysics Data System (ADS)

Yu, Caixia; Zhao, Jingtao; Wang, Yanfei

2017-02-01

Small-scale diffracting geologic discontinuities play a significant role in studying carbonate reservoirs. The seismic responses of them are coded in diffracted/scattered waves. However, compared with reflections, the energy of these valuable diffractions is generally one or even two orders of magnitude weaker. This means that the information of diffractions is strongly masked by reflections in the seismic images. Detecting the small-scale cavities and tiny faults from the deep carbonate reservoirs, mainly over 6 km, poses an even bigger challenge to seismic diffractions, as the signals of seismic surveyed data are weak and have a low signal-to-noise ratio (SNR). After analyzing the mechanism of the Kirchhoff migration method, the residual of prestack diffractions located in the neighborhood of the first Fresnel aperture is found to remain in the image space. Therefore, a strategy for extracting diffractions in the image space is proposed and a regularized L 2-norm model with a smooth constraint to the local slopes is suggested for predicting reflections. According to the focusing conditions of residual diffractions in the image space, two approaches are provided for extracting diffractions. Diffraction extraction can be directly accomplished by subtracting the predicted reflections from seismic imaging data if the residual diffractions are focused. Otherwise, a diffraction velocity analysis will be performed for refocusing residual diffractions. Two synthetic examples and one field application demonstrate the feasibility and efficiency of the two proposed methods in detecting the small-scale geologic scatterers, tiny faults and cavities.

The Hamiltonian Structure of Nonlinear Elasticity: The Convective Representation of Solids, Rods, and Plates,

DTIC Science & Technology

1986-12-01

paper, we consider geometrically exact models, such as the Kirchhoff-Love-Reissner- Antman model for rods and its counterpart for plates and shells. These...equivalent model, formulated as a constrained director theory - the so-called special theory of Cosserat rods - is due to Antman (1974] - see also...Anan and Jordan [1975], Anunan and Kenny [1981]. and Antman [1984] for some applications. The dynamic version along with the parametrization discussed

MTF evaluation of in-line phase contrast imaging system

NASA Astrophysics Data System (ADS)

Sun, Xiaoran; Gao, Feng; Zhao, Huijuan; Zhang, Limin; Li, Jiao; Zhou, Zhongxing

2017-02-01

X-ray phase contrast imaging (XPCI) is a novel method that exploits the phase shift for the incident X-ray to form an image. Various XPCI methods have been proposed, among which, in-line phase contrast imaging (IL-PCI) is regarded as one of the most promising clinical methods. The contrast of the interface is enhanced due to the introduction of the boundary fringes in XPCI, thus it is generally used to evaluate the image quality of XPCI. But the contrast is a comprehensive index and it does not reflect the information of image quality in the frequency range. The modulation transfer function (MTF), which is the Fourier transform of the system point spread function, is recognized as the metric to characterize the spatial response of conventional X-ray imaging system. In this work, MTF is introduced into the image quality evaluation of the IL-PCI system. Numerous simulations based on Fresnel - Kirchhoff diffraction theory are performed with varying system settings and the corresponding MTFs were calculated for comparison. The results show that MTF can provide more comprehensive information of image quality comparing to contrast in IL-PCI.

Progress on ultrasonic flaw sizing in turbine-engine rotor components: bore and web geometries

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

Rose, J.H.; Gray, T.A.; Thompson, R.B.

1983-01-01

The application of generic flaw-sizing techniques to specific components generally involves difficulties associated with geometrical complexity and simplifications arising from a knowledge of the expected flaw distribution. This paper is concerned with the case of ultrasonic flaw sizing in turbine-engine rotor components. The sizing of flat penny-shaped cracks in the web geometry discussed and new crack-sizing algorithms based on the Born and Kirchhoff approximations are introduced. Additionally, we propose a simple method for finding the size of a flat, penny-shaped crack given only the magnitude of the scattering amplitude. The bore geometry is discussed with primary emphasis on the cylindricalmore » focusing of the incident beam. Important questions which are addressed include the effects of diffraction and the position of the flaw with respect to the focal line. The appropriate deconvolution procedures to account for these effects are introduced. Generic features of the theory are compared with experiment. Finally, the effects of focused transducers on the Born inversion algorithm are discussed.« less

Robustness of Synchrony in Complex Networks and Generalized Kirchhoff Indices

NASA Astrophysics Data System (ADS)

Tyloo, M.; Coletta, T.; Jacquod, Ph.

2018-02-01

In network theory, a question of prime importance is how to assess network vulnerability in a fast and reliable manner. With this issue in mind, we investigate the response to external perturbations of coupled dynamical systems on complex networks. We find that for specific, nonaveraged perturbations, the response of synchronous states depends on the eigenvalues of the stability matrix of the unperturbed dynamics, as well as on its eigenmodes via their overlap with the perturbation vector. Once averaged over properly defined ensembles of perturbations, the response is given by new graph topological indices, which we introduce as generalized Kirchhoff indices. These findings allow for a fast and reliable method for assessing the specific or average vulnerability of a network against changing operational conditions, faults, or external attacks.

From Airy to Abbe: quantifying the effects of wide-angle focusing for scalar spherical waves

NASA Astrophysics Data System (ADS)

Calm, Yitzi M.; Merlo, Juan M.; Burns, Michael J.; Naughton, Michael J.

2017-10-01

Recent advances in optical microscopy have enabled imaging with spatial resolution beyond the diffraction limit. This limit is sometimes taken as one of several different criteria according to different conventions, including Rayleigh’s 0.61λ /NA, Abbe’s 0.5λ /NA, and Sparrow’s 0.47λ /NA. In this paper, we perform a parametric study, numerically integrating the scalar Kirchhoff diffraction integrals, and we propose new functional forms for the resolution limits derived from scalar focusing. The new expressions remain accurate under wide angle focusing, up to 90^\\circ . Our results could materially impact the design of high intensity focused ultrasound systems, and can be used as a qualitative guideline for the design of a particular type of planar optical element: the flat lens metasurface.

Wave optics simulation of statistically rough surface scatter

NASA Astrophysics Data System (ADS)

Lanari, Ann M.; Butler, Samuel D.; Marciniak, Michael; Spencer, Mark F.

2017-09-01

The bidirectional reflectance distribution function (BRDF) describes optical scatter from surfaces by relating the incident irradiance to the exiting radiance over the entire hemisphere. Laboratory verification of BRDF models and experimentally populated BRDF databases are hampered by sparsity of monochromatic sources and ability to statistically control the surface features. Numerical methods are able to control surface features, have wavelength agility, and via Fourier methods of wave propagation, may be used to fill the knowledge gap. Monte-Carlo techniques, adapted from turbulence simulations, generate Gaussian distributed and correlated surfaces with an area of 1 cm2 , RMS surface height of 2.5 μm, and correlation length of 100 μm. The surface is centered inside a Kirchhoff absorbing boundary with an area of 16 cm2 to prevent wrap around aliasing in the far field. These surfaces are uniformly illuminated at normal incidence with a unit amplitude plane-wave varying in wavelength from 3 μm to 5 μm. The resultant scatter is propagated to a detector in the far field utilizing multi-step Fresnel Convolution and observed at angles from -2 μrad to 2 μrad. The far field scatter is compared to both a physical wave optics BRDF model (Modified Beckmann Kirchhoff) and two microfacet BRDF Models (Priest, and Cook-Torrance). Modified Beckmann Kirchhoff, which accounts for diffraction, is consistent with simulated scatter for multiple wavelengths for RMS surface heights greater than λ/2. The microfacet models, which assume geometric optics, are less consistent across wavelengths. Both model types over predict far field scatter width for RMS surface heights less than λ/2.

Kirchhoff Index of Cyclopolyacenes

NASA Astrophysics Data System (ADS)

Wang, Yan; Zhang, Wenwen

2010-10-01

The resistance distance between two vertices of a connected graph G is computed as the effective resistance between them in the corresponding network constructed from G by replacing each edge with a unit resistor. The Kirchhoff index of G is the sum of resistance distances between all pairs of vertices. In this paper, following the method of Y. J. Yang and H. P. Zhang in the proof of the Kirchhoff index of the linear hexagonal chain, we obtain the Kirchhoff index of cyclopolyacenes, denoted by HRn, in terms of its Laplacian spectrum. We show that the Kirchhoff index of HRnis approximately one third of its Wiener index.

Simulation electromagnetic scattering on bodies through integral equation and neural networks methods

NASA Astrophysics Data System (ADS)

Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.

2018-05-01

The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.

The Kirchhoff index and the matching number

NASA Astrophysics Data System (ADS)

Zhou, Bo; Trinajstić, Nenad

The Kirchhoff index of a connected (molecular) graph is the sum of the resistance-distances between all unordered pairs of vertices and may also be expressed by its Laplacian eigenvalues. We determine the minimum Kirchhoff index of connected (molecular) graphs in terms of the number of vertices and matching number and characterize the unique extremal graph. The results on the Kirchhoff index are compared with the corresponding results on the Wiener index.

A numerical wave-optical approach for the simulation of analyzer-based x-ray imaging

NASA Astrophysics Data System (ADS)

Bravin, A.; Mocella, V.; Coan, P.; Astolfo, A.; Ferrero, C.

2007-04-01

An advanced wave-optical approach for simulating a monochromator-analyzer set-up in Bragg geometry with high accuracy is presented. The polychromaticity of the incident wave on the monochromator is accounted for by using a distribution of incoherent point sources along the surface of the crystal. The resulting diffracted amplitude is modified by the sample and can be well represented by a scalar representation of the optical field where the limitations of the usual ‘weak object’ approximation are removed. The subsequent diffraction mechanism on the analyzer is described by the convolution of the incoming wave with the Green-Riemann function of the analyzer. The free space propagation up to the detector position is well reproduced by a classical Fresnel-Kirchhoff integral. The preliminary results of this innovative approach show an excellent agreement with experimental data.

Design and characteristic analysis of shaping optics for optical trepanning

NASA Astrophysics Data System (ADS)

Zeng, D.; Latham, W. P.; Kar, A.

2005-08-01

Optical trepanning is a new laser drilling method using an annular beam. The annular beams allow numerous irradiance profiles to supply laser energy to the workpiece and thus provide more flexibility in affecting the hole quality than a traditional circular laser beam. The refractive axicon system has been designed to generating a collimated annular beam. In this article, calculations of intensity distributions produced by this refractive system are made by evaluating the Kirchhoff-Fresnel diffraction. It is shown that the refractive system is able to transform a Gaussian beam into a full Gaussian annular beam. The base angle of the axicon lens, input laser beam diameter and intensity profiles are found to be important factors for the axcion refractive system. Their effects on the annular beam profiles are analyzed based on the numerical solutions of the diffraction patterns.

Visualizing light with electrons

NASA Astrophysics Data System (ADS)

Fitzgerald, J. P. S.; Word, R. C.; Koenenkamp, R.

2014-03-01

In multiphoton photoemission electron microscopy (nP-PEEM) electrons are emitted from surfaces at a rate proportional to the surface electromagnetic field amplitude. We use 2P-PEEM to give nanometer scale visualizations of light of diffracted and waveguide fields around various microstructures. We use Fourier analysis to determine the phase and amplitude of surface fields in relation to incident light from the interference patterns. To provide quick and intuitive simulations of surface fields, we employ two dimensional Fresnel-Kirchhoff integration, a technique based on freely propagating waves and Huygens' principle. We find generally good agreement between simulations and experiment. Additionally diffracted wave simulations exhibit greater phase accuracy, indicating that these waves are well represented by a two dimensional approximation. The authors gratefully acknowledge funding of this research by the US-DOE Basic Science Office under Contract DE-FG02-10ER46406.

Large computer simulations on elastic networks: Small eigenvalues and eigenvalue spectra of the Kirchhoff matrix

NASA Astrophysics Data System (ADS)

Shy, L. Y.; Eichinger, B. E.

1989-05-01

Computer simulations of the formation of trifunctional and tetrafunctional polydimethyl-siloxane networks that are crosslinked by condensation of telechelic chains with multifunctional crosslinking agents have been carried out on systems containing up to 1.05×106 chains. Eigenvalue spectra of Kirchhoff matrices for these networks have been evaluated at two levels of approximation: (1) inclusion of all midchain modes, and (2) suppression of midchain modes. By use of the recursion method of Haydock and Nex, we have been able to effectively diagonalize matrices with 730 498 rows and columns without actually constructing matrices of this size. The small eigenvalues have been computed by use of the Lanczos algorithm. We demonstrate the following results: (1) The smallest eigenvalues (with chain modes suppressed) vary as μ-2/3 for sufficiently large μ, where μ is the number of junctions in the network; (2) the eigenvalue spectra of the Kirchhoff matrices are well described by McKay's theory for random regular graphs in the range of the larger eigenvalues, but there are significant departures in the region of small eigenvalues where computed spectra have many more small eigenvalues than random regular graphs; (3) the smallest eigenvalues vary as n-1.78 where n is the number of Rouse beads in the chains that comprise the network. Computations are done for both monodisperse and polydisperse chain length distributions. Large eigenvalues associated with localized motion of the junctions are found as predicted by theory. The relationship between the small eigenvalues and the equilibrium modulus of elasticity is discussed, as is the relationship between viscoelasticity and the band edge of the spectrum.

A new multi-layer approach for progressive damage simulation in composite laminates based on isogeometric analysis and Kirchhoff-Love shells. Part I: basic theory and modeling of delamination and transverse shear

NASA Astrophysics Data System (ADS)

Bazilevs, Y.; Pigazzini, M. S.; Ellison, A.; Kim, H.

2017-11-01

In this two-part paper we introduce a new formulation for modeling progressive damage in laminated composite structures. We adopt a multi-layer modeling approach, based on Isogeometric Analysis (IGA), where each ply or lamina is represented by a spline surface, and modeled as a Kirchhoff-Love thin shell. Continuum Damage Mechanics is used to model intralaminar damage, and a new zero-thickness cohesive-interface formulation is introduced to model delamination as well as permitting laminate-level transverse shear compliance. In Part I of this series we focus on the presentation of the modeling framework, validation of the framework using standard Mode I and Mode II delamination tests, and assessment of its suitability for modeling thick laminates. In Part II of this series we focus on the application of the proposed framework to modeling and simulation of damage in composite laminates resulting from impact. The proposed approach has significant accuracy and efficiency advantages over existing methods for modeling impact damage. These stem from the use of IGA-based Kirchhoff-Love shells to represent the individual plies of the composite laminate, while the compliant cohesive interfaces enable transverse shear deformation of the laminate. Kirchhoff-Love shells give a faithful representation of the ply deformation behavior, and, unlike solids or traditional shear-deformable shells, do not suffer from transverse-shear locking in the limit of vanishing thickness. This, in combination with higher-order accurate and smooth representation of the shell midsurface displacement field, allows us to adopt relatively coarse in-plane discretizations without sacrificing solution accuracy. Furthermore, the thin-shell formulation employed does not use rotational degrees of freedom, which gives additional efficiency benefits relative to more standard shell formulations.

The Kirchhoff Index of Quasi-Tree Graphs

NASA Astrophysics Data System (ADS)

Xu, Kexiang; Liu, Hongshuang; Das, Kinkar Ch.

2015-03-01

Resistance distance was introduced by Klein and Randić as a generalisation of the classical distance. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all unordered pairs of vertices. In this article we characterise the extremal graphs with the maximal Kirchhoff index among all non-trivial quasi-tree graphs of order n. Moreover, we obtain a lower bound on the Kirchhoff index for all non-trivial quasi-tree graphs of order n.

Focal shift and the axial optical coordinate for high-aperture systems of finite Fresnel number.

PubMed

Sheppard, Colin J R; Török, Peter

2003-11-01

Analytic expressions are given for the on-axis intensity predicted by the Rayleigh-Sommerfeld and Kirchhoff diffraction integrals for a scalar optical system of high numerical aperture and finite value of Fresnel number. A definition of the axial optical coordinate is introduced that is valid for finite values of Fresnel number, for high-aperture systems, and for observation points distant from the focus. The focal shift effect is reexamined. For the case when the focal shift is small, explicit expressions are given for the focal shift and the axial peak in intensity.

Terahertz holography for imaging amplitude and phase objects.

PubMed

Hack, Erwin; Zolliker, Peter

2014-06-30

A non-monochromatic THz Quantum Cascade Laser and an uncooled micro-bolometer array detector with VGA resolution are used in a beam-splitter free holographic set-up to measure amplitude and phase objects in transmission. Phase maps of the diffraction pattern are retrieved using the Fourier transform carrier fringe method; while a Fresnel-Kirchhoff back propagation algorithm is used to reconstruct the complex object image. A lateral resolution of 280 µm and a relative phase sensitivity of about 0.5 rad are estimated from reconstructed images of a metallic Siemens star and a polypropylene test structure, respectively. Simulations corroborate the experimental results.

Limits of Kirchhoff's Laws in Plasmonics.

PubMed

Razinskas, Gary; Biagioni, Paolo; Hecht, Bert

2018-01-30

The validity of Kirchhoff's laws in plasmonic nanocircuitry is investigated by studying a junction of plasmonic two-wire transmission lines. We find that Kirchhoff's laws are valid for sufficiently small values of a phenomenological parameter κ relating the geometrical parameters of the transmission line with the effective wavelength of the guided mode. Beyond such regime, for large values of the phenomenological parameter, increasing deviations occur and the equivalent impedance description (Kirchhoff's laws) can only provide rough, but nevertheless useful, guidelines for the design of more complex plasmonic circuitry. As an example we investigate a system composed of a two-wire transmission line and a nanoantenna as the load. By addition of a parallel stub designed according to Kirchhoff's laws we achieve maximum signal transfer to the nanoantenna.

A General Approach to Kirchhoff's Laws

ERIC Educational Resources Information Center

Quintela, F. R.; Redondo, R. C.; Melchor, N. R.; Redondo, M.

2009-01-01

Kirchhoff's laws are usually considered as electrical current and voltage properties. Nevertheless, they are sometimes applied to nonelectrical systems. One way to increase their efficacy and range of applicability would be to show Kirchhoff's laws, and the properties deriving from them, as being independent of any physical system as far as…

On the relative intensity of Poisson’s spot

NASA Astrophysics Data System (ADS)

Reisinger, T.; Leufke, P. M.; Gleiter, H.; Hahn, H.

2017-03-01

The Fresnel diffraction phenomenon referred to as Poisson’s spot or spot of Arago has, beside its historical significance, become relevant in a number of fields. Among them are for example fundamental tests of the super-position principle in the transition from quantum to classical physics and the search for extra-solar planets using star shades. Poisson’s spot refers to the positive on-axis wave interference in the shadow of any spherical or circular obstacle. While the spot’s intensity is equal to the undisturbed field in the plane wave picture, its intensity in general depends on a number of factors, namely the size and wavelength of the source, the size and surface corrugation of the diffraction obstacle, and the distances between source, obstacle and detector. The intensity can be calculated by solving the Fresnel-Kirchhoff diffraction integral numerically, which however tends to be computationally expensive. We have therefore devised an analytical model for the on-axis intensity of Poisson’s spot relative to the intensity of the undisturbed wave field and successfully validated it both using a simple light diffraction setup and numerical methods. The model will be useful for optimizing future Poisson-spot matter-wave diffraction experiments and determining under what experimental conditions the spot can be observed.

Networks 90: Polymer Networks Group Meeting (10th) and IUPAC international Symposium on Polymer Networks (10th) Held in Jerusalem on 20-25 May 1990. Programme and Abstracts

DTIC Science & Technology

1990-05-25

INCLUDING ORIENTATIONAL INTERACTIONS BETWEEN CHAIN SEGMENTS B. Deloche, E.T. Samulski (France, USA) CHAIN SEGMENT ORDERING IN STRAINED BIMODAL P-2 PDMS...theory of elastomers is difficult because it requires a detailed study of many body interactions . A theory of elasticity must address the following: (1...a Kirchhoff matrix which describes the connectivity of the network (Kc) or the linear chains (Ku). The nonbonded interactions are handled with the

Elastoplastic State of an Elliptical Cylindrical Shell with a Circular Hole

NASA Astrophysics Data System (ADS)

Storozhuk, E. A.; Chernyshenko, I. S.; Pigol', O. V.

2017-11-01

Static problems for an elastoplastic elliptical cylindrical shell with a circular hole are formulated and a numerical method for solving it is developed. The basic equations are derived using the Kirchhoff-Love theory of deep shells and the theory of small elastoplastic strains. The method employs the method of additional stresses and the finite-element method. The influence of plastic strains and geometrical parameters of the shell subject to internal pressure on the distributions of stresses, strains, and displacements in the zone of their concentration is studied.

Melonic Phase Transition in Group Field Theory

NASA Astrophysics Data System (ADS)

Baratin, Aristide; Carrozza, Sylvain; Oriti, Daniele; Ryan, James; Smerlak, Matteo

2014-08-01

Group field theories have recently been shown to admit a 1/N expansion dominated by so-called `melonic graphs', dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for the melonic amplitudes in terms of a graph polynomial related to a higher-dimensional generalization of the Kirchhoff tree-matrix theorem. Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes. We restrict our study to the Boulatov-Ooguri models, which describe topological BF theories and are the basis for the construction of 4-dimensional models of quantum gravity.

Response of moderately thick laminated cross-ply composite shells subjected to random excitation

NASA Technical Reports Server (NTRS)

Elishakoff, Isaak; Cederbaum, Gabriel; Librescu, Liviu

1989-01-01

This study deals with the dynamic response of transverse shear deformable laminated shells subjected to random excitation. The analysis encompasses the following problems: (1) the dynamic response of circular cylindrical shells of finite length excited by an axisymmetric uniform ring loading, stationary in time, and (2) the response of spherical and cylindrical panels subjected to stationary random loadings with uniform spatial distribution. The associated equations governing the structural theory of shells are derived upon discarding the classical Love-Kirchhoff (L-K) assumptions. In this sense, the theory is formulated in the framework of the first-order transverse shear deformation theory (FSDT).

Quadrupole radiation from terahertz dipole antennas.

PubMed

Rudd, J V; Johnson, J L; Mittleman, D M

2000-10-15

We report what is to our knowledge the first detailed investigation of the polarization state of radiation from lens-coupled terahertz dipole antennas. The radiation exhibits a weak but measurable component that is polarized orthogonally to the orientation of the emitter dipole. The angular radiation pattern of this cross-polarized emission reveals that it is quadrupolar, rather than dipolar, in nature. One can understand this result by taking into account the photocurrent flowing in the strip lines that feed the dipole antenna. A Fresnel-Kirchhoff scalar diffraction calculation is used for calculating the frequency-dependent angular distribution of the radiation pattern, providing satisfactory agreement with the measurements.

Non-Weyl asymptotics for quantum graphs with general coupling conditions

NASA Astrophysics Data System (ADS)

Davies, E. Brian; Exner, Pavel; Lipovský, Jiří

2010-11-01

Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in the case of Kirchhoff or anti-Kirchhoff conditions. While for graphs without permutation symmetry numerous examples of non-Weyl behaviour can be constructed. Furthermore, we present an insight into what makes the Kirchhoff/anti-Kirchhoff coupling particular from the resonance point of view. Finally, we demonstrate a generalization to quantum graphs with unequal edge weights.

Physically-Based Models for the Reflection, Transmission and Subsurface Scattering of Light by Smooth and Rough Surfaces, with Applications to Realistic Image Synthesis

NASA Astrophysics Data System (ADS)

He, Xiao Dong

This thesis studies light scattering processes off rough surfaces. Analytic models for reflection, transmission and subsurface scattering of light are developed. The results are applicable to realistic image generation in computer graphics. The investigation focuses on the basic issue of how light is scattered locally by general surfaces which are neither diffuse nor specular; Physical optics is employed to account for diffraction and interference which play a crucial role in the scattering of light for most surfaces. The thesis presents: (1) A new reflectance model; (2) A new transmittance model; (3) A new subsurface scattering model. All of these models are physically-based, depend on only physical parameters, apply to a wide range of materials and surface finishes and more importantly, provide a smooth transition from diffuse-like to specular reflection as the wavelength and incidence angle are increased or the surface roughness is decreased. The reflectance and transmittance models are based on the Kirchhoff Theory and the subsurface scattering model is based on Energy Transport Theory. They are valid only for surfaces with shallow slopes. The thesis shows that predicted reflectance distributions given by the reflectance model compare favorably with experiment. The thesis also investigates and implements fast ways of computing the reflectance and transmittance models. Furthermore, the thesis demonstrates that a high level of realistic image generation can be achieved due to the physically -correct treatment of the scattering processes by the reflectance model.

Timoshenko-Type Theory in the Stability Analysis of Corrugated Cylindrical Shells

NASA Astrophysics Data System (ADS)

Semenyuk, N. P.; Neskhodovskaya, N. A.

2002-06-01

A technique is proposed for stability analysis of longitudinally corrugated shells under axial compression. The technique employs the equations of the Timoshenko-type nonlinear theory of shells. The geometrical parameters of shells are specified on discrete set of points and are approximated by segments of Fourier series. Infinite systems of homogeneous algebraic equations are derived from a variational equation written in displacements to determine the critical loads and buckling modes. Specific types of corrugated isotropic metal and fiberglass shells are considered. The calculated results are compared with those obtained within the framework of the classical theory of shells. It is shown that the Timoshenko-type theory extends significantly the possibility of exact allowance for the geometrical parameters and material properties of corrugated shells compared with Kirchhoff-Love theory.

Resistance Distances and Kirchhoff Index in Generalised Join Graphs

NASA Astrophysics Data System (ADS)

Chen, Haiyan

2017-03-01

The resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge with a unit resistor. The Kirchhoff index of a graph is defined as the sum of all the resistance distances between any pair of vertices of the graph. Let G=H[G1, G2, …, Gk ] be the generalised join graph of G1, G2, …, Gk determined by H. In this paper, we first give formulae for resistance distances and Kirchhoff index of G in terms of parameters of {G'_i}s and H. Then, we show that computing resistance distances and Kirchhoff index of G can be decomposed into simpler ones. Finally, we obtain explicit formulae for resistance distances and Kirchhoff index of G when {G'_i}s and H take some special graphs, such as the complete graph, the path, and the cycle.

On the Kirchhoff Index of Graphs

NASA Astrophysics Data System (ADS)

Das, Kinkar C.

2013-09-01

Let G be a connected graph of order n with Laplacian eigenvalues μ1 ≥ μ2 ≥ ... ≥ μn-1 > mn = 0. The Kirchhoff index of G is defined as [xxx] In this paper. we give lower and upper bounds on Kf of graphs in terms on n, number of edges, maximum degree, and number of spanning trees. Moreover, we present lower and upper bounds on the Nordhaus-Gaddum-type result for the Kirchhoff index.

Introduction to Cavitation and Supercavitation

DTIC Science & Technology

2001-02-01

supercavities and leant on the old wake theory (Helmholtz 1868; Kirchhoff 1869; Levi - Civita 1907; Villat 1913 ; Riabouchinski 1920 - those references...cavity. Phil. Mag., 34, 94 sq. TULIN, M.P. -1953- Steady two -dimensional cavity flows about slender bodies . D.T.M.B., Rept 834. WU, T.Y.T. -1956- A...above a liquid contained in a bowl: if the oscillation amplitude is large enough, bubbles can appear inside the liquid. * A solid body with sharp

Multipath modeling for aeronautical communications.

NASA Technical Reports Server (NTRS)

Painter, J. H.; Gupta, S. C.; Wilson, L. R.

1973-01-01

One of the fundamental technical problems in aeronautical digital communications is that of multipath propagation between aircraft and ground terminal. This paper examines in detail a model of the received multipath signal that is useful for application of modern detection and estimation theories. The model treats arbitrary modulation and covers the selective and nonselective cases. The necessarily nonstationary statistics of the received signal are determined from the link geometry and the surface roughness parameters via a Kirchhoff solution.

Reducible boundary conditions in coupled channels

NASA Astrophysics Data System (ADS)

Pankrashkin, Konstantin

2005-10-01

We study Hamiltonians with point interactions in spaces of vector-valued functions. Using some information from the theory of quantum graphs, we describe a class of the operators which can be reduced to the direct sum of several one-dimensional problems. It shown that such a reduction is closely connected with the invariance under channel permutations. Examples are provided by some 'model' interactions, in particular, the so-called δ, δ' and the Kirchhoff couplings.

Space-Time Fluid-Structure Interaction Computation of Flapping-Wing Aerodynamics

DTIC Science & Technology

2013-12-01

SST-VMST." The structural mechanics computations are based on the Kirchhoff -Love shell model. We use a sequential coupling technique, which is...mechanics computations are based on the Kirchhoff -Love shell model. We use a sequential coupling technique, which is ap- plicable to some classes of FSI...we use the ST-VMS method in combination with the ST-SUPS method. The structural mechanics computations are mostly based on the Kirchhoff –Love shell

Light Emission by Nonequilibrium Bodies: Local Kirchhoff Law

NASA Astrophysics Data System (ADS)

Greffet, Jean-Jacques; Bouchon, Patrick; Brucoli, Giovanni; Marquier, François

2018-04-01

The goal of this paper is to introduce a local form of Kirchhoff law to model light emission by nonequilibrium bodies. While absorption by a finite-size body is usually described using the absorption cross section, we introduce a local absorption rate per unit volume and also a local thermal emission rate per unit volume. Their equality is a local form of Kirchhoff law. We revisit the derivation of this equality and extend it to situations with subsystems in local thermodynamic equilibrium but not in equilibrium between them, such as hot electrons in a metal or electrons with different Fermi levels in the conduction band and in the valence band of a semiconductor. This form of Kirchhoff law can be used to model (i) thermal emission by nonisothermal finite-size bodies, (ii) thermal emission by bodies with carriers at different temperatures, and (iii) spontaneous emission by semiconductors under optical (photoluminescence) or electrical pumping (electroluminescence). Finally, we show that the reciprocity relation connecting light-emitting diodes and photovoltaic cells derived by Rau is a particular case of the local Kirchhoff law.

An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.; Farassat, F.

1997-01-01

The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchhoff advantage (namely nonlinear flow effects are included in the surface integration) is also available to the FW-H method if the integration surface used in the FW-H equation is not assumed impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based upon the conservation laws of fluid mechanics rather than the wave equation. This means that the FW-H equation is valid even if the integration surface is in the nonlinear region. This is demonstrated numerically in the paper. The Kirchhoff approach can lead to substantial errors if the integration surface is not positioned in the linear region. These errors may be hard to identify. Finally, new metrics based on the Sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

Generalized viscothermoelasticity theory of dual-phase-lagging model for damping analysis in circular micro-plate resonators

NASA Astrophysics Data System (ADS)

Grover, D.; Seth, R. K.

2018-05-01

Analysis and numerical results are presented for the thermoelastic dissipation of a homogeneous isotropic, thermally conducting, Kelvin-Voigt type circular micro-plate based on Kirchhoff's Love plate theory utilizing generalized viscothermoelasticity theory of dual-phase-lagging model. The analytical expressions for thermoelastic damping of vibration and frequency shift are obtained for generalized dual-phase-lagging model and coupled viscothermoelastic plates. The scaled thermoelastic damping has been illustrated in case of circular plate and axisymmetric circular plate for fixed aspect ratio for clamped and simply supported boundary conditions. It is observed that the damping of vibrations significantly depend on time delay and mechanical relaxation times in addition to thermo-mechanical coupling in circular plate under resonance conditions and plate dimensions.

Dual algebraic formulation of differential GPS

NASA Astrophysics Data System (ADS)

Lannes, A.; Dur, S.

2003-05-01

A new approach to differential GPS is presented. The corresponding theoretical framework calls on elementary concepts of algebraic graph theory. The notion of double difference, which is related to that of closure in the sense of Kirchhoff, is revisited in this context. The Moore-Penrose pseudo-inverse of the closure operator plays a key role in the corresponding dual formulation. This approach, which is very attractive from a conceptual point of view, sheds a new light on the Teunissen formulation.

A note on Kirchhoff index

NASA Astrophysics Data System (ADS)

Zhou, Bo; Trinajstić, Nenad

2008-03-01

We report lower bounds for the Kirchhoff index of a connected (molecular) graph in terms of its structural parameters such as the number of vertices (atoms), the number of edges (bonds), maximum vertex degree (valency), connectivity and chromatic number.

The limits of hamiltonian structures in three-dimensional elasticity, shells, and rods

NASA Astrophysics Data System (ADS)

Ge, Z.; Kruse, H. P.; Marsden, J. E.

1996-01-01

This paper uses Hamiltonian structures to study the problem of the limit of three-dimensional (3D) elastic models to shell and rod models. In the case of shells, we show that the Hamiltonian structure for a three-dimensional elastic body converges, in a sense made precise, to that for a shell model described by a one-director Cosserat surface as the thickness goes to zero. We study limiting procedures that give rise to unconstrained as well as constrained Cosserat director models. The case of a rod is also considered and similar convergence results are established, with the limiting model being a geometrically exact director rod model (in the framework developed by Antman, Simo, and coworkers). The resulting model may or may not have constraints, depending on the nature of the constitutive relations and their behavior under the limiting procedure. The closeness of Hamiltonian structures is measured by the closeness of Poisson brackets on certain classes of functions, as well as the Hamiltonians. This provides one way of justifying the dynamic one-director model for shells. Another way of stating the convergence result is that there is an almost-Poisson embedding from the phase space of the shell to the phase space of the 3D elastic body, which implies that, in the sense of Hamiltonian structures, the dynamics of the elastic body is close to that of the shell. The constitutive equations of the 3D model and their behavior as the thickness tends to zero dictates whether the limiting 2D model is a constrained or an unconstrained director model. We apply our theory in the specific case of a 3D Saint Venant-Kirchhoff material and derive the corresponding limiting shell and rod theories. The limiting shell model is an interesting Kirchhoff-like shell model in which the stored energy function is explicitly derived in terms of the shell curvature. For rods, one gets (with an additional inextensibility constraint) a one-director Kirchhoff elastic rod model, which reduces to the well-known Euler elastica if one adds an additional single constraint that the director lines up with the Frenet frame.

Simulation of Jet Noise with OVERFLOW CFD Code and Kirchhoff Surface Integral

NASA Technical Reports Server (NTRS)

Kandula, M.; Caimi, R.; Voska, N. (Technical Monitor)

2002-01-01

An acoustic prediction capability for supersonic axisymmetric jets was developed on the basis of OVERFLOW Navier-Stokes CFD (Computational Fluid Dynamics) code of NASA Langley Research Center. Reynolds-averaged turbulent stresses in the flow field are modeled with the aid of Spalart-Allmaras one-equation turbulence model. Appropriate acoustic and outflow boundary conditions were implemented to compute time-dependent acoustic pressure in the nonlinear source-field. Based on the specification of acoustic pressure, its temporal and normal derivatives on the Kirchhoff surface, the near-field and the far-field sound pressure levels are computed via Kirchhoff surface integral, with the Kirchhoff surface chosen to enclose the nonlinear sound source region described by the CFD code. The methods are validated by a comparison of the predictions of sound pressure levels with the available data for an axisymmetric turbulent supersonic (Mach 2) perfectly expanded jet.

Simulation of Supersonic Jet Noise with the Adaptation of Overflow CFD Code and Kirchhoff Surface Integral

NASA Technical Reports Server (NTRS)

Kandula, Max; Caimi, Raoul; Steinrock, T. (Technical Monitor)

2001-01-01

An acoustic prediction capability for supersonic axisymmetric jets was developed on the basis of OVERFLOW Navier-Stokes CFD (Computational Fluid Dynamics) code of NASA Langley Research Center. Reynolds-averaged turbulent stresses in the flow field are modeled with the aid of Spalart-Allmaras one-equation turbulence model. Appropriate acoustic and outflow boundary conditions were implemented to compute time-dependent acoustic pressure in the nonlinear source-field. Based on the specification of acoustic pressure, its temporal and normal derivatives on the Kirchhoff surface, the near-field and the far-field sound pressure levels are computed via Kirchhoff surface integral, with the Kirchhoff surface chosen to enclose the nonlinear sound source region described by the CFD code. The methods are validated by a comparison of the predictions of sound pressure levels with the available data for an axisymmetric turbulent supersonic (Mach 2) perfectly expanded jet.

Some aspects of the stability of the plane deformation mode of filaments of finite stiffness beyond the elasticity limits

NASA Astrophysics Data System (ADS)

Shimanovskii, A. V.

A method for calculating the plane bending of elastic-plastic filaments of finite stiffness is proposed on the basis of plastic flow theory. The problem considered is shown to reduce to relations similar to Kirchhoff equations for elastic work. Expressions are obtained for determining the normalized stiffness characteristics for the cross section of a filament with plastic regions containing beam theory equations as a particular case. A study is made of the effect of the plastic region size on the position of the elastic deformation-unloading interface and on the normalized stiffness of the filament cross section. Calculation results are presented in graphic form.

Single-scatter vector-wave scattering from surfaces with infinite slopes using the Kirchhoff approximation.

PubMed

Bruce, Neil C

2008-08-01

This paper presents a new formulation of the 3D Kirchhoff approximation that allows calculation of the scattering of vector waves from 2D rough surfaces containing structures with infinite slopes. This type of surface has applications, for example, in remote sensing and in testing or imaging of printed circuits. Some preliminary calculations for rectangular-shaped grooves in a plane are presented for the 2D surface method and are compared with the equivalent 1D surface calculations for the Kirchhoff and integral equation methods. Good agreement is found between the methods.

Fracture Mechanics of Thin, Cracked Plates Under Tension, Bending and Out-of-Plane Shear Loading

NASA Technical Reports Server (NTRS)

Zehnder, Alan T.; Hui, C. Y.; Potdar, Yogesh; Zucchini, Alberto

1999-01-01

Cracks in the skin of aircraft fuselages or other shell structures can be subjected to very complex stress states, resulting in mixed-mode fracture conditions. For example, a crack running along a stringer in a pressurized fuselage will be subject to the usual in-plane tension stresses (Mode-I) along with out-of-plane tearing stresses (Mode-III like). Crack growth and initiation in this case is correlated not only with the tensile or Mode-I stress intensity factor, K(sub I), but depends on a combination of parameters and on the history of crack growth. The stresses at the tip of a crack in a plate or shell are typically described in terms of either the small deflection Kirchhoff plate theory. However, real applications involve large deflections. We show, using the von-Karman theory, that the crack tip stress field derived on the basis of the small deflection theory is still valid for large deflections. We then give examples demonstrating the exact calculation of energy release rates and stress intensity factors for cracked plates loaded to large deflections. The crack tip fields calculated using the plate theories are an approximation to the actual three dimensional fields. Using three dimensional finite element analyses we have explored the relationship between the three dimensional elasticity theory and two dimensional plate theory results. The results show that for out-of-plane shear loading the three dimensional and Kirchhoff theory results coincide at distance greater than h/2 from the crack tip, where h/2 is the plate thickness. Inside this region, the distribution of stresses through the thickness can be very different from the plate theory predictions. We have also explored how the energy release rate varies as a function of crack length to plate thickness using the different theories. This is important in the implementation of fracture prediction methods using finite element analysis. Our experiments show that under certain conditions, during fatigue crack growth, the presence of out-of-plane shear loads induces a great deal of contact and friction on the crack surfaces, dramatically reducing crack growth rate. A series of experiments and a proposed computational approach for accounting for the friction is discussed.

What is the diffraction limit? From Airy to Abbe using direct numerical integration

NASA Astrophysics Data System (ADS)

Calm, Y. M.; Merlo, J. M.; Burns, M. J.; Kempa, K.; Naughton, M. J.

The resolution of a conventional optical microscope is sometimes taken from Airy's point spread function (PSF), 0 . 61 λ / NA , and sometimes from Abbe, λ / 2 NA , where NA is the numerical aperture, however modern fluorescence and near-field optical microscopies achieve spatial resolution far better than either of these limits. There is a new category of 2D metamaterials called planar optical elements (POEs), which have a microscopic thickness (< λ), macroscopic transverse dimensions (> 100 λ), and are composed of an array of nanostructured light scatterers. POEs are found in a range of micro- and nano-photonic technologies, and will influence the future optical nanoscopy. With this pretext, we shed some light on the 'diffraction limit' by numerically evaluating Kirchhoff's scalar formulae (in their exact form) and identifying the features of highly non-paraxial, 3D PSFs. We show that the Airy and Abbe criteria are connected, and we comment on the design rules for a particular type of POE: the flat lens. This work is supported by the W. M. Keck Foundation.

Solutions for a Kirchhoff equation with critical Caffarelli–Kohn–Nirenberg growth and discontinuous nonlinearity

NASA Astrophysics Data System (ADS)

dos Santos, Gelson G.; Figueiredo, Giovany M.

2018-06-01

In this paper, we study the existence of nonegative solutions to a class of nonlinear boundary value problems of the Kirchhoff type. We prove existence results when the problem has discontinuous nonlinearity and critical Caffarelli-Kohn-Nirenberg growth.

Analogies between Kirchhoff plates and functionally graded Saint-Venant beams under torsion

NASA Astrophysics Data System (ADS)

Barretta, Raffaele; Luciano, Raimondo

2015-05-01

Exact solutions of elastic Kirchhoff plates are available only for special geometries, loadings and kinematic boundary constraints. An effective solution procedure, based on an analogy between functionally graded orthotropic Saint-Venant beams under torsion and inhomogeneous isotropic Kirchhoff plates, with no kinematic boundary constraints, is proposed. The result extends the one contributed in Barretta (Acta Mech 224(12):2955-2964, 2013) for the special case of homogeneous Saint-Venant beams under torsion. Closed-form solutions for displacement, bending-twisting moment and curvature fields of an elliptic plate, corresponding to a functionally graded orthotropic beam, are evaluated. A new benchmark for computational mechanics is thus provided.

New graph polynomials in parametric QED Feynman integrals

NASA Astrophysics Data System (ADS)

Golz, Marcel

2017-10-01

In recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals for scalar theories. The transition to gauge theories is complicated not only by the fact that their parametric integrand is much larger and more involved. It is, moreover, only implicitly given as the result of certain differential operators applied to the scalar integrand exp(-ΦΓ /ΨΓ) , where ΨΓ and ΦΓ are the Kirchhoff and Symanzik polynomials of the Feynman graph Γ. In the case of quantum electrodynamics we find that the full parametric integrand inherits a rich combinatorial structure from ΨΓ and ΦΓ. In the end, it can be expressed explicitly as a sum over products of new types of graph polynomials which have a combinatoric interpretation via simple cycle subgraphs of Γ.

Asymptotic Poincare lemma and its applications

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

Ziolkowski, R.W.; Deschamps, G.A.

1984-05-01

An asymptotic version of Poincare's lemma is defined and solutions are obtained with the calculus of exterior differential forms. They are used to construct the asymptotic approximations of multidimensional oscillatory integrals whose forms are commonly encountered, for example, in electromagnetic problems. In particular, the boundary and stationary point evaluations of these integrals are considered. The former is applied to the Kirchhoff representation of a scalar field diffracted through an aperture and simply recovers the Maggi-Rubinowicz-Miyamoto-Wolf results. Asymptotic approximations in the presence of other (standard) critical points are also discussed. Techniques developed for the asymptotic Poincare lemma are used to generatemore » a general representation of the Leray form. All of the (differential form) expressions presented are generalizations of known (vector calculus) results. 14 references, 4 figures.« less

Modeling Aerodynamically Generated Sound of Helicopter Rotors

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.; Farassat, F.

2002-01-01

A great deal of progress has been made in the modeling of aerodynamically generated sound of rotors over the past decade. Although the modeling effort has focused on helicopter main rotors, the theory is generally valid for a wide range of rotor configurations. The Ffowcs Williams Hawkings (FW-H) equation has been the foundation for much of the development. The monopole and dipole source terms of the FW-H equation account for the thickness and loading noise, respectively. Bladevortex-interaction noise and broadband noise are important types of loading noise, hence much research has been directed toward the accurate modeling of these noise mechanisms. Both subsonic and supersonic quadrupole noise formulations have been developed for the prediction of high-speed impulsive noise. In an effort to eliminate the need to compute the quadrupole contribution, the FW-H equation has also been utilized on permeable surfaces surrounding all physical noise sources. Comparisons of the Kirchhoff formulation for moving surfaces with the FW-H equation have shown that the Kirchhoff formulation for moving surfaces can give erroneous results for aeroacoustic problems. Finally, significant progress has been made incorporating the rotor noise models into full vehicle noise prediction tools.

Acoustic scattering from phononic crystals with complex geometry.

PubMed

Kulpe, Jason A; Sabra, Karim G; Leamy, Michael J

2016-05-01

This work introduces a formalism for computing external acoustic scattering from phononic crystals (PCs) with arbitrary exterior shape using a Bloch wave expansion technique coupled with the Helmholtz-Kirchhoff integral (HKI). Similar to a Kirchhoff approximation, a geometrically complex PC's surface is broken into a set of facets in which the scattering from each facet is calculated as if it was a semi-infinite plane interface in the short wavelength limit. When excited by incident radiation, these facets introduce wave modes into the interior of the PC. Incorporation of these modes in the HKI, summed over all facets, then determines the externally scattered acoustic field. In particular, for frequencies in a complete bandgap (the usual operating frequency regime of many PC-based devices and the requisite operating regime of the presented theory), no need exists to solve for internal reflections from oppositely facing edges and, thus, the total scattered field can be computed without the need to consider internal multiple scattering. Several numerical examples are provided to verify the presented approach. Both harmonic and transient results are considered for spherical and bean-shaped PCs, each containing over 100 000 inclusions. This facet formalism is validated by comparison to an existing self-consistent scattering technique.

Postbuckling analysis of shear deformable composite flat panels taking into account geometrical imperfections

NASA Technical Reports Server (NTRS)

Librescu, L.; Stein, M.

1990-01-01

The effects of initial geometrical imperfections on the postbuckling response of flat laminated composite panels to uniaxial and biaxial compressive loading are investigated analytically. The derivation of the mathematical model on the basis of first-order transverse shear deformation theory is outlined, and numerical results for perfect and imperfect, single-layer and three-layer square plates with free-free, clamped-clamped, or free-clamped edges are presented in graphs and briefly characterized. The present approach is shown to be more accurate than analyses based on the classical Kirchhoff plate model.

Nonlinear Viscoelastic Analysis of Orthotropic Beams Using a General Third-Order Theory

DTIC Science & Technology

2012-06-20

Kirchhoff stress tensor, denoted by r and reduced strain tensor E e is given by rxx rzz rxz 8><>: 9>=>;¼ Q11ð0Þ Q13ð0Þ 0 Q13ð0Þ Q33ð0Þ 0 0 0 Q55ð0Þ...0.5 1 −0.5 0 0.5 1 (a) (b) Fig. 1. Graphs of (a) equi-spaced and (b) spectral lagrange interpolation functions for polynomial order of p = 11. 3762 V

Ground state sign-changing solutions for fractional Kirchhoff equations in bounded domains

NASA Astrophysics Data System (ADS)

Luo, Huxiao; Tang, Xianhua; Gao, Zu

2018-03-01

We study the existence of ground state sign-changing solutions for the fractional Kirchhoff problem. Under mild assumptions on the nonlinearity, by using some new analytical skills and the non-Nehari manifold method, we prove that the fractional Kirchhoff problem possesses a ground state sign-changing solution ub. Moreover, we show that the energy of ub is strictly larger than twice that of the ground state solutions of Nehari-type. Finally, we establish the convergence property of ub as the parameter b ↘ 0. Our results generalize some results obtained by Shuai [J. Differ. Equations 259, 1256 (2015)] and Tang and Cheng [J. Differ. Equations 261, 2384 (2016)].

An efficient parallel algorithm: Poststack and prestack Kirchhoff 3D depth migration using flexi-depth iterations

NASA Astrophysics Data System (ADS)

Rastogi, Richa; Srivastava, Abhishek; Khonde, Kiran; Sirasala, Kirannmayi M.; Londhe, Ashutosh; Chavhan, Hitesh

2015-07-01

This paper presents an efficient parallel 3D Kirchhoff depth migration algorithm suitable for current class of multicore architecture. The fundamental Kirchhoff depth migration algorithm exhibits inherent parallelism however, when it comes to 3D data migration, as the data size increases the resource requirement of the algorithm also increases. This challenges its practical implementation even on current generation high performance computing systems. Therefore a smart parallelization approach is essential to handle 3D data for migration. The most compute intensive part of Kirchhoff depth migration algorithm is the calculation of traveltime tables due to its resource requirements such as memory/storage and I/O. In the current research work, we target this area and develop a competent parallel algorithm for post and prestack 3D Kirchhoff depth migration, using hybrid MPI+OpenMP programming techniques. We introduce a concept of flexi-depth iterations while depth migrating data in parallel imaging space, using optimized traveltime table computations. This concept provides flexibility to the algorithm by migrating data in a number of depth iterations, which depends upon the available node memory and the size of data to be migrated during runtime. Furthermore, it minimizes the requirements of storage, I/O and inter-node communication, thus making it advantageous over the conventional parallelization approaches. The developed parallel algorithm is demonstrated and analysed on Yuva II, a PARAM series of supercomputers. Optimization, performance and scalability experiment results along with the migration outcome show the effectiveness of the parallel algorithm.

Stable elastic knots with no self-contact

NASA Astrophysics Data System (ADS)

Moulton, Derek E.; Grandgeorge, Paul; Neukirch, Sébastien

2018-07-01

We study an elastic rod bent into an open trefoil knot and clamped at both ends. The question we consider is whether there are stable configurations for which there are no points of self-contact. This idea can be fairly easily replicated with a thin strip of paper, but is more difficult or even impossible with a flexible wire. We search for such configurations within the space of three tuning parameters related to the degrees of freedom in a simple experiment. Mathematically, we show, both within standard Kirchhoff theory as well within an elastic strip theory, that stable and contact-free knotted configurations can be found, and we classify the corresponding parametric regions. Numerical results are complemented with an asymptotic analysis that demonstrates the presence of knots near the doubly-covered ring. In the case of the strip model, quantitative experiments of the region of good knots are also provided to validate the theory.

Numerical modeling of zero-offset laboratory data in a strong topographic environment: results for a spectral-element method and a discretized Kirchhoff integral method

NASA Astrophysics Data System (ADS)

Favretto-Cristini, Nathalie; Tantsereva, Anastasiya; Cristini, Paul; Ursin, Bjørn; Komatitsch, Dimitri; Aizenberg, Arkady M.

2014-08-01

Accurate simulation of seismic wave propagation in complex geological structures is of particular interest nowadays. However conventional methods may fail to simulate realistic wavefields in environments with great and rapid structural changes, due for instance to the presence of shadow zones, diffractions and/or edge effects. Different methods, developed to improve seismic modeling, are typically tested on synthetic configurations against analytical solutions for simple canonical problems or reference methods, or via direct comparison with real data acquired in situ. Such approaches have limitations, especially if the propagation occurs in a complex environment with strong-contrast reflectors and surface irregularities, as it can be difficult to determine the method which gives the best approximation of the "real" solution, or to interpret the results obtained without an a priori knowledge of the geologic environment. An alternative approach for seismics consists in comparing the synthetic data with high-quality data collected in laboratory experiments under controlled conditions for a known configuration. In contrast with numerical experiments, laboratory data possess many of the characteristics of field data, as real waves propagate through models with no numerical approximations. We thus present a comparison of laboratory-scaled measurements of 3D zero-offset wave reflection of broadband pulses from a strong topographic environment immersed in a water tank with numerical data simulated by means of a spectral-element method and a discretized Kirchhoff integral method. The results indicate a good quantitative fit in terms of time arrivals and acceptable fit in amplitudes for all datasets.

A simple and efficient shear-flexible plate bending element

NASA Technical Reports Server (NTRS)

Chaudhuri, Reaz A.

1987-01-01

A shear-flexible triangular element formulation, which utilizes an assumed quadratic displacement potential energy approach and is numerically integrated using Gauss quadrature, is presented. The Reissner/Mindlin hypothesis of constant cross-sectional warping is directly applied to the three-dimensional elasticity theory to obtain a moderately thick-plate theory or constant shear-angle theory (CST), wherein the middle surface is no longer considered to be the reference surface and the two rotations are replaced by the two in-plane displacements as nodal variables. The resulting finite-element possesses 18 degrees of freedom (DOF). Numerical results are obtained for two different numerical integration schemes and a wide range of meshes and span-to-thickness ratios. These, when compared with available exact, series or finite-element solutions, demonstrate accuracy and rapid convergence characteristics of the present element. This is especially true in the case of thin to very thin plates, when the present element, used in conjunction with the reduced integration scheme, outperforms its counterpart, based on discrete Kirchhoff constraint theory (DKT).

Quasi-static axisymmetric eversion hemispherical domes made of elastomers

NASA Astrophysics Data System (ADS)

Kabrits, Sergey A.; Kolpak, Eugeny P.

2016-06-01

The paper considers numerical solution for the problem of quasi-static axisymmetric eversion of a spherical shell (hemisphere) under action of external pressure. Results based on the general nonlinear theory of shells made of elastomers, proposed by K. F. Chernykh. It is used two models of shells based on the hypotheses of the Kirchhoff and Timoshenko, modified K.F. Chernykh for the case of hyperelastic rubber-like material. The article presents diagrams of equilibrium states of eversion hemispheres for both models as well as the shape of the shell at different points in the diagram.

Variational divergence in wave scattering theory with Kirchhoffean trial functions

NASA Technical Reports Server (NTRS)

Bird, J. F.

1986-01-01

In a recent study of variational improvement of the Kirchhoff approximation for electromagnetic scattering by rough surfaces, a key ingredient in the variational principle was found to diverge for important configurations (e.g., backscatter) if the polarization had any vertical component. The cause and a cure of this divergence are discussed here. The divergence is demonstrated to occur for arbitrary perfectly conducting scatterers and its universal characterstics are determined, by means of a general divergence criterion that is derived. A variational cure for the divergence is prescribed, and it is tested successfully on a standard scattering model.

A nonlinear viscoelastic constitutive equation - Yield predictions in multiaxial deformations

NASA Technical Reports Server (NTRS)

Shay, R. M., Jr.; Caruthers, J. M.

1987-01-01

Yield stress predictions of a nonlinear viscoelastic constitutive equation for amorphous polymer solids have been obtained and are compared with the phenomenological von Mises yield criterion. Linear viscoelasticity theory has been extended to include finite strains and a material timescale that depends on the instantaneous temperature, volume, and pressure. Results are presented for yield and the correct temperature and strain-rate dependence in a variety of multiaxial deformations. The present nonlinear viscoelastic constitutive equation can be formulated in terms of either a Cauchy or second Piola-Kirchhoff stress tensor, and in terms of either atmospheric or hydrostatic pressure.

Numerical Analysis of Solids at Failure

DTIC Science & Technology

2011-08-20

failure analyses include the formulation of invariant finite elements for thin Kirchhoff rods, and preliminary initial studies of growth in...analysis of the failure of other structural/mechanical systems, including the finite element modeling of thin Kirchhoff rods and the constitutive...algorithm based on the connectivity graph of the underlying finite element mesh. In this setting, the discontinuities are defined by fronts propagating

A Kirchhoff approach to seismic modeling and prestack depth migration

NASA Astrophysics Data System (ADS)

Liu, Zhen-Yue

1993-05-01

The Kirchhoff integral provides a robust method for implementing seismic modeling and prestack depth migration, which can handle lateral velocity variation and turning waves. With a little extra computation cost, the Kirchoff-type migration can obtain multiple outputs that have the same phase but different amplitudes, compared with that of other migration methods. The ratio of these amplitudes is helpful in computing some quantities such as reflection angle. I develop a seismic modeling and prestack depth migration method based on the Kirchhoff integral, that handles both laterally variant velocity and a dip beyond 90 degrees. The method uses a finite-difference algorithm to calculate travel times and WKBJ amplitudes for the Kirchhoff integral. Compared to ray-tracing algorithms, the finite-difference algorithm gives an efficient implementation and single-valued quantities (first arrivals) on output. In my finite difference algorithm, the upwind scheme is used to calculate travel times, and the Crank-Nicolson scheme is used to calculate amplitudes. Moreover, interpolation is applied to save computation cost. The modeling and migration algorithms require a smooth velocity function. I develop a velocity-smoothing technique based on damped least-squares to aid in obtaining a successful migration.

Three-dimensional flat shell-to-shell coupling: numerical challenges

NASA Astrophysics Data System (ADS)

Guo, Kuo; Haikal, Ghadir

2017-11-01

The node-to-surface formulation is widely used in contact simulations with finite elements because it is relatively easy to implement using different types of element discretizations. This approach, however, has a number of well-known drawbacks, including locking due to over-constraint when this formulation is used as a twopass method. Most studies on the node-to-surface contact formulation, however, have been conducted using solid elements and little has been done to investigate the effectiveness of this approach for beam or shell elements. In this paper we show that locking can also be observed with the node-to-surface contact formulation when applied to plate and flat shell elements even with a singlepass implementation with distinct master/slave designations, which is the standard solution to locking with solid elements. In our study, we use the quadrilateral four node flat shell element for thin (Kirchhoff-Love) plate and thick (Reissner-Mindlin) plate theory, both in their standard forms and with improved formulations such as the linked interpolation [1] and the Discrete Kirchhoff [2] elements for thick and thin plates, respectively. The Lagrange multiplier method is used to enforce the node-to-surface constraints for all elements. The results show clear locking when compared to those obtained using a conforming mesh configuration.

The Mean Curvature of the Influence Surface of Wave Equation With Sources on a Moving Surface

NASA Technical Reports Server (NTRS)

Farassat, F.; Farris, Mark

1999-01-01

The mean curvature of the influence surface of the space-time point (x, t) appears in linear supersonic propeller noise theory and in the Kirchhoff formula for a supersonic surface. Both these problems are governed by the linear wave equation with sources on a moving surface. The influence surface is also called the Sigma - surface in the aeroacoustic literature. This surface is the locus, in a frame fixed to the quiescent medium, of all the points of a radiating surface f(x, t) = 0 whose acoustic signals arrive simultaneously to an observer at position x and at the time t. Mathematically, the Sigma- surface is produced by the intersection of the characteristic conoid of the space-time point (x, t) and the moving surface. In this paper, we derive the expression for the local mean curvature of the Sigma - space of the space-time point for a moving rigid or deformable surface f(x, t) = 0. This expression is a complicated function of the geometric and kinematic parameters of the surface f(x, t) = 0. Using the results of this paper, the solution of the governing wave equation of high speed propeller noise radiation as well as the Kirchhoff formula for a supersonic surface can be written as very compact analytic expression.

Protection Relaying Scheme Based on Fault Reactance Operation Type

NASA Astrophysics Data System (ADS)

Tsuji, Kouichi

The theories of operation of existing relays are roughly divided into two types: one is the current differential types based on Kirchhoff's first law and the other is impedance types based on second law. We can apply the Kirchhoff's laws to strictly formulate fault phenomena, so the circuit equations are represented non linear simultaneous equations with variables fault point k and fault resistance Rf. This method has next two defect. 1) heavy computational burden for the iterative calculation on N-R method, 2) relay operator can not easily understand principle of numerical matrix operation. The new protection relay principles we proposed this paper focuses on the fact that the reactance component on fault point is almost zero. Two reactance Xf(S), Xf(R) on branch both ends are calculated by operation of solving linear equations. If signs of Xf(S) and Xf(R) are not same, it can be judged that the fault point exist in the branch. This reactance Xf corresponds to difference of branch reactance between actual fault point and imaginaly fault point. And so relay engineer can to understand fault location by concept of “distance". The simulation results using this new method indicates the highly precise estimation of fault locations compared with the inspected fault locations on operating transmission lines.

Resistance distance and Kirchhoff index in circulant graphs

NASA Astrophysics Data System (ADS)

Zhang, Heping; Yang, Yujun

The resistance distance rij between vertices i and j of a connected (molecular) graph G is computed as the effective resistance between nodes i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices. In this work, closed-form formulae for Kirchhoff index and resistance distances of circulant graphs are derived in terms of Laplacian spectrum and eigenvectors. Special formulae are also given for four classes of circulant graphs (complete graphs, complete graphs minus a perfect matching, cycles, Möbius ladders Mp). In particular, the asymptotic behavior of Kf(Mp) as p ? ? is obtained, that is, Kf(Mp) grows as ⅙p3 as p ? ?.

Prediction of high-speed rotor noise with a Kirchhoff formula

NASA Technical Reports Server (NTRS)

Purcell, Timothy W.; Strawn, Roger C.; Yu, Yung H.

1987-01-01

A new methodology has been developed to predict the impulsive noise generated by a transonic rotor blade. The formulation uses a full-potential finite-difference method to obtain the pressure field close to the blade. A Kirchhoff integral formulation is then used to extend these finite-difference results into the far-field. This Kirchhoff formula is written in a blade-fixed coordinate system. It requires initial data across a plane at the sonic radius. This data is provided by the finite-difference solution. Acoustic pressure predictions show excellent agreement with hover experimental data for two hover cases of 0.88 and 0.90 tip Mach number, the latter of which has delocalized transonic flow. These results represent the first successful prediction technique for peak pressure amplitudes using a computational code.

Piezoelectrically actuated flextensional micromachined ultrasound transducers--I: theory.

PubMed

Perçin, Gökhan; Khuri-Yakub, Butrus T

2002-05-01

This series of two papers considers piezoelectrically actuated flextensional micromachined ultrasound transducers (PAFMUTs) and consists of theory, fabrication, and experimental parts. The theory presented in this paper is developed for an ultrasound transducer application presented in the second part. In the absence of analytical expressions for the equivalent circuit parameters of a flextensional transducer, it is difficult to calculate its optimal parameters and dimensions and difficult to choose suitable materials. The influence of coupling between flexural and extensional deformation and that of coupling between the structure and the acoustic volume on the dynamic response of piezoelectrically actuated flextensional transducer are analyzed using two analytical methods: classical thin (Kirchhoff) plate theory and Mindlin plate theory. Classical thin plate theory and Mindlin plate theory are applied to derive two-dimensional plate equations for the transducer and to calculate the coupled electromechanical field variables such as mechanical displacement and electrical input impedance. In these methods, the variations across the thickness direction vanish by using the bending moments per unit length or stress resultants. Thus, two-dimensional plate equations for a step-wise laminated circular plate are obtained as well as two different solutions to the corresponding systems. An equivalent circuit of the transducer is also obtained from these solutions.

A Kirchhoff Approach to Seismic Modeling and Prestack Depth Migration

DTIC Science & Technology

1993-05-01

continuation of sources and geophones by finite difference (S-G finite - difference migration ), are relatively slow and dip-limited. Compared to S-G... finite - difference migration , the Kirchhoff integral implements prestack migration relatively efficiently and has no dip limitation. Liu .Mlodeling and...for modeling and migration . In this paper, a finite - difference algorithm is used to calculate traveltimes and amplitudes. With the help of

Conductance of three-terminal molecular bridge based on tight-binding theory

NASA Astrophysics Data System (ADS)

Wang, Li-Guang; Li, Yong; Yu, Ding-Wen; Katsunori, Tagami; Masaru, Tsukada

2005-05-01

The quantum transmission characteristic of three-benzene ring nano-molecular bridge is investigated theoretically by using Green's function approach based on tight-binding theory with only a π orbital per carbon atom at the site. The transmission probabilities that electrons transport through the molecular bridge from one terminal to the other two terminals are obtained. The electronic current distributions inside the molecular bridge are calculated and shown in graphical analogy by the current density method based on Fisher-Lee formula at the energy points E = ±0.42, ±1.06 and ±1.5, respectively, where the transmission spectra appear peaks. We find that the transmission spectra are related to the incident electronic energy and the molecular levels strongly and the current distributions agree well with Kirchhoff quantum current momentum conservation law.

Tunneling effects in electromagnetic wave scattering by nonspherical particles: A comparison of the Debye series and physical-geometric optics approximations

NASA Astrophysics Data System (ADS)

Bi, Lei; Yang, Ping

2016-07-01

The accuracy of the physical-geometric optics (PG-O) approximation is examined for the simulation of electromagnetic scattering by nonspherical dielectric particles. This study seeks a better understanding of the tunneling effect on the phase matrix by employing the invariant imbedding method to rigorously compute the zeroth-order Debye series, from which the tunneling efficiency and the phase matrix corresponding to the diffraction and external reflection are obtained. The tunneling efficiency is shown to be a factor quantifying the relative importance of the tunneling effect over the Fraunhofer diffraction near the forward scattering direction. Due to the tunneling effect, different geometries with the same projected cross section might have different diffraction patterns, which are traditionally assumed to be identical according to the Babinet principle. For particles with a fixed orientation, the PG-O approximation yields the external reflection pattern with reasonable accuracy, but ordinarily fails to predict the locations of peaks and minima in the diffraction pattern. The larger the tunneling efficiency, the worse the PG-O accuracy is at scattering angles less than 90°. If the particles are assumed to be randomly oriented, the PG-O approximation yields the phase matrix close to the rigorous counterpart, primarily due to error cancellations in the orientation-average process. Furthermore, the PG-O approximation based on an electric field volume-integral equation is shown to usually be much more accurate than the Kirchhoff surface integral equation at side-scattering angles, particularly when the modulus of the complex refractive index is close to unity. Finally, tunneling efficiencies are tabulated for representative faceted particles.

New test of the dynamic theory of neutron diffraction by a moving grating

NASA Astrophysics Data System (ADS)

Zakharov, Maxim; Frank, Alexander; Kulin, German; Goryunov, Semyon

2018-04-01

Recently, multiwave dynamical theory of neutron diffraction by a moving grating was developed. The theory predicts that at a certain height of the grating profile a significant suppression of the zero-order diffraction may occur. The experiment to confirm predictions of this theory was performed. The resulting diffracted UCNs spectra were measured using time-of-flight Fourier diffractometer. The experimental data were compared with the results of numerical simulation and were found in a good agreement with theoretical predictions.

Speckle phase near random surfaces

NASA Astrophysics Data System (ADS)

Chen, Xiaoyi; Cheng, Chuanfu; An, Guoqiang; Han, Yujing; Rong, Zhenyu; Zhang, Li; Zhang, Meina

2018-03-01

Based on Kirchhoff approximation theory, the speckle phase near random surfaces with different roughness is numerically simulated. As expected, the properties of the speckle phase near the random surfaces are different from that in far field. In addition, as scattering distances and roughness increase, the average fluctuations of the speckle phase become larger. Unusually, the speckle phase is somewhat similar to the corresponding surface topography. We have performed experiments to verify the theoretical simulation results. Studies in this paper contribute to understanding the evolution of speckle phase near a random surface and provide a possible way to identify a random surface structure based on its speckle phase.

Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

NASA Astrophysics Data System (ADS)

Chiang, C. K.; Xue, David Y.; Mei, Chuh

1993-04-01

A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

NASA Technical Reports Server (NTRS)

Chiang, C. K.; Xue, David Y.; Mei, Chuh

1993-01-01

A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

Vertical spatial coherence model for a transient signal forward-scattered from the sea surface

USGS Publications Warehouse

Yoerger, E.J.; McDaniel, S.T.

1996-01-01

The treatment of acoustic energy forward scattered from the sea surface, which is modeled as a random communications scatter channel, is the basis for developing an expression for the time-dependent coherence function across a vertical receiving array. The derivation of this model uses linear filter theory applied to the Fresnel-corrected Kirchhoff approximation in obtaining an equation for the covariance function for the forward-scattered problem. The resulting formulation is used to study the dependence of the covariance on experimental and environmental factors. The modeled coherence functions are then formed for various geometrical and environmental parameters and compared to experimental data.

Quantization and fractional quantization of currents in periodically driven stochastic systems. I. Average currents

NASA Astrophysics Data System (ADS)

Chernyak, Vladimir Y.; Klein, John R.; Sinitsyn, Nikolai A.

2012-04-01

This article studies Markovian stochastic motion of a particle on a graph with finite number of nodes and periodically time-dependent transition rates that satisfy the detailed balance condition at any time. We show that under general conditions, the currents in the system on average become quantized or fractionally quantized for adiabatic driving at sufficiently low temperature. We develop the quantitative theory of this quantization and interpret it in terms of topological invariants. By implementing the celebrated Kirchhoff theorem we derive a general and explicit formula for the average generated current that plays a role of an efficient tool for treating the current quantization effects.

Linear network representation of multistate models of transport.

PubMed Central

Sandblom, J; Ring, A; Eisenman, G

1982-01-01

By introducing external driving forces in rate-theory models of transport we show how the Eyring rate equations can be transformed into Ohm's law with potentials that obey Kirchhoff's second law. From such a formalism the state diagram of a multioccupancy multicomponent system can be directly converted into linear network with resistors connecting nodal (branch) points and with capacitances connecting each nodal point with a reference point. The external forces appear as emf or current generators in the network. This theory allows the algebraic methods of linear network theory to be used in solving the flux equations for multistate models and is particularly useful for making proper simplifying approximation in models of complex membrane structure. Some general properties of linear network representation are also deduced. It is shown, for instance, that Maxwell's reciprocity relationships of linear networks lead directly to Onsager's relationships in the near equilibrium region. Finally, as an example of the procedure, the equivalent circuit method is used to solve the equations for a few transport models. PMID:7093425

New Computational Methods for the Prediction and Analysis of Helicopter Noise

NASA Technical Reports Server (NTRS)

Strawn, Roger C.; Oliker, Leonid; Biswas, Rupak

1996-01-01

This paper describes several new methods to predict and analyze rotorcraft noise. These methods are: 1) a combined computational fluid dynamics and Kirchhoff scheme for far-field noise predictions, 2) parallel computer implementation of the Kirchhoff integrations, 3) audio and visual rendering of the computed acoustic predictions over large far-field regions, and 4) acoustic tracebacks to the Kirchhoff surface to pinpoint the sources of the rotor noise. The paper describes each method and presents sample results for three test cases. The first case consists of in-plane high-speed impulsive noise and the other two cases show idealized parallel and oblique blade-vortex interactions. The computed results show good agreement with available experimental data but convey much more information about the far-field noise propagation. When taken together, these new analysis methods exploit the power of new computer technologies and offer the potential to significantly improve our prediction and understanding of rotorcraft noise.

Analysis of all-frequency variational behavior of the Kirchhoff approximation for a classic surface-scattering model

NASA Technical Reports Server (NTRS)

Bird, J. F.

1985-01-01

In testing a stochastic variational principle at high frequencies by using a Kirchhoffean trial function in an idealized model for surface scattering - a randomly embossed plane - we have found not only the predicted high-frequency improvement but also an unexpected low-frequency improvement in the calculated scattering amplitudes. To investigate systematically the all-frequency variational behavior, we consider here the deterministic one-boss case - Rayleigh's classic model whose exact solution is available for comparison - over all wavelengths, polarizations, and configurations of incidence and scattering. We examine analytically in particular the long-wave limit of the variational-Kirchhoff amplitudes; the results demonstrate improvements in both wavelength and angle depedence for horizontal (TM) polarization and some variational improvements for vertical (TE) polarization. This low-frequency behavior in tandem with the foreseen high-frequency improvement leads to good variational-Kirchhoff results through the intermediate resonance-frequency regime for this model.

Synthetic seismic monitoring using reverse-time migration and Kirchhoff migration for CO2 sequestration in Korea

NASA Astrophysics Data System (ADS)

Kim, W.; Kim, Y.; Min, D.; Oh, J.; Huh, C.; Kang, S.

2012-12-01

During last two decades, CO2 sequestration in the subsurface has been extensively studied and progressed as a direct tool to reduce CO2 emission. Commercial projects such as Sleipner, In Salah and Weyburn that inject more than one million tons of CO2 per year are operated actively as well as test projects such as Ketzin to study the behavior of CO2 and the monitoring techniques. Korea also began the CCS (CO2 capture and storage) project. One of the prospects for CO2 sequestration in Korea is the southwestern continental margin of Ulleung basin. To monitor the behavior of CO2 underground for the evaluation of stability and safety, several geophysical monitoring techniques should be applied. Among various geophysical monitoring techniques, seismic survey is considered as the most effective tool. To verify CO2 migration in the subsurface more effectively, seismic numerical simulation is an essential process. Furthermore, the efficiency of the seismic migration techniques should be investigated for various cases because numerical seismic simulation and migration test help us accurately interpret CO2 migration. In this study, we apply the reverse-time migration and Kirchhoff migration to synthetic seismic monitoring data generated for the simplified model based on the geological structures of Ulleung basin in Korea. Synthetic seismic monitoring data are generated for various cases of CO2 migration in the subsurface. From the seismic migration images, we can investigate CO2 diffusion patterns indirectly. From seismic monitoring simulation, it is noted that while the reverse-time migration generates clear subsurface images when subsurface structures are steeply dipping, Kirchhoff migration has an advantage in imaging horizontal-layered structures such as depositional sediments appearing in the continental shelf. The reverse-time migration and Kirchhoff migration present reliable subsurface images for the potential site characterized by stratigraphical traps. In case of vertical CO2 migration at injection point, the reverse time migration yields better images than Kirchhoff migration does. On the other hand, Kirchhoff migration images horizontal CO2 migration clearer than the reverse time migration does. From these results, we can conclude that the reverse-time migration and Kirchhoff migration can complement with each other to describe the behavior of CO2 in the subsurface. Acknowledgement This work was financially supported by the Brain Korea 21 project of Energy Systems Engineering, the "Development of Technology for CO2 Marine Geological Storage" program funded by the Ministry of Land, Transport and Maritime Affairs (MLTM) of Korea and the Korea CCS R&D Center (KCRC) grant funded by the Korea government (Ministry of Education, Science and Technology) (No. 2012-0008926).

Imaging Shallow Salt With 3D Refraction Migration

NASA Astrophysics Data System (ADS)

Vanschuyver, C. J.; Hilterman, F. J.

2005-05-01

In offshore West Africa, numerous salt walls are within 200 m of sea level. Because of the shallowness of these salt walls, reflections from the salt top can be difficult to map, making it impossible to build an accurate velocity model for subsequent pre-stack depth migration. An accurate definition of salt boundaries is critical to any depth model where salt is present. Unfortunately, when a salt body is very shallow, the reflection from the upper interface can be obscured due to large offsets between the source and near receivers and also due to the interference from multiples and other near-surface noise events. A new method is described using 3D migration of the refraction waveforms which is simplified because of several constraints in the model definition. The azimuth and dip of the refractor is found by imaging with Kirchhoff theory. A Kirchhoff migration is performed where the traveltime values are adjusted to use the CMP refraction traveltime equation. I assume the sediment and salt velocities to be known such that once the image time is specified, then the dip and azimuth of the refraction path can be found. The resulting 3D refraction migrations are in excellent depth agreement with available well control. In addition, the refraction migration time picks of deeper salt events are in agreement with time picks of the same events on the reflection migration.

A COMPARISON OF TRANSIENT INFINITE ELEMENTS AND TRANSIENT KIRCHHOFF INTEGRAL METHODS FOR FAR FIELD ACOUSTIC ANALYSIS

DOE PAGES

WALSH, TIMOTHY F.; JONES, ANDREA; BHARDWAJ, MANOJ; ...

2013-04-01

Finite element analysis of transient acoustic phenomena on unbounded exterior domains is very common in engineering analysis. In these problems there is a common need to compute the acoustic pressure at points outside of the acoustic mesh, since meshing to points of interest is impractical in many scenarios. In aeroacoustic calculations, for example, the acoustic pressure may be required at tens or hundreds of meters from the structure. In these cases, a method is needed for post-processing the acoustic results to compute the response at far-field points. In this paper, we compare two methods for computing far-field acoustic pressures, onemore » derived directly from the infinite element solution, and the other from the transient version of the Kirchhoff integral. Here, we show that the infinite element approach alleviates the large storage requirements that are typical of Kirchhoff integral and related procedures, and also does not suffer from loss of accuracy that is an inherent part of computing numerical derivatives in the Kirchhoff integral. In order to further speed up and streamline the process of computing the acoustic response at points outside of the mesh, we also address the nonlinear iterative procedure needed for locating parametric coordinates within the host infinite element of far-field points, the parallelization of the overall process, linear solver requirements, and system stability considerations.« less

A software platform for phase contrast x-ray breast imaging research.

PubMed

Bliznakova, K; Russo, P; Mettivier, G; Requardt, H; Popov, P; Bravin, A; Buliev, I

2015-06-01

To present and validate a computer-based simulation platform dedicated for phase contrast x-ray breast imaging research. The software platform, developed at the Technical University of Varna on the basis of a previously validated x-ray imaging software simulator, comprises modules for object creation and for x-ray image formation. These modules were updated to take into account the refractive index for phase contrast imaging as well as implementation of the Fresnel-Kirchhoff diffraction theory of the propagating x-ray waves. Projection images are generated in an in-line acquisition geometry. To test and validate the platform, several phantoms differing in their complexity were constructed and imaged at 25 keV and 60 keV at the beamline ID17 of the European Synchrotron Radiation Facility. The software platform was used to design computational phantoms that mimic those used in the experimental study and to generate x-ray images in absorption and phase contrast modes. The visual and quantitative results of the validation process showed an overall good correlation between simulated and experimental images and show the potential of this platform for research in phase contrast x-ray imaging of the breast. The application of the platform is demonstrated in a feasibility study for phase contrast images of complex inhomogeneous and anthropomorphic breast phantoms, compared to x-ray images generated in absorption mode. The improved visibility of mammographic structures suggests further investigation and optimisation of phase contrast x-ray breast imaging, especially when abnormalities are present. The software platform can be exploited also for educational purposes. Copyright © 2015 Elsevier Ltd. All rights reserved.

Deformation of a helical filament by flow and electric or magnetic fields

NASA Astrophysics Data System (ADS)

Kim, Munju; Powers, Thomas R.

2005-02-01

Motivated by recent advances in the real-time imaging of fluorescent flagellar filaments in living bacteria [Turner, Ryu, and Berg, J. Bacteriol. 82, 2793 (2000)], we compute the deformation of a helical elastic filament due to flow and external magnetic or high-frequency electric fields. Two cases of deformation due to hydrodynamic drag are considered: the compression of a filament rotated by a stationary motor and the extension of a stationary filament due to flow along the helical axis. We use Kirchhoff rod theory for the filament, and work to linear order in the deflection. Hydrodynamic forces are described first by resistive-force theory, and then for comparison by the more accurate slender-body theory. For helices with a short pitch, the deflection in axial flow predicted by slender-body theory is significantly smaller than that computed with resistive-force theory. Therefore, our estimate of the bending stiffness of a flagellar filament is smaller than that of previous workers. In our calculation of the deformation of a polarizable helix in an external field, we show that the problem is equivalent to the classical case of a helix deformed by forces applied only at the ends.

Hydroelastic response of a floating runway to cnoidal waves

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

Ertekin, R. C., E-mail: ertekin@hawaii.edu; Xia, Dingwu

2014-02-15

The hydroelastic response of mat-type Very Large Floating Structures (VLFSs) to severe sea conditions, such as tsunamis and hurricanes, must be assessed for safety and survivability. An efficient and robust nonlinear hydroelastic model is required to predict accurately the motion of and the dynamic loads on a VLFS due to such large waves. We develop a nonlinear theory to predict the hydroelastic response of a VLFS in the presence of cnoidal waves and compare the predictions with the linear theory that is also developed here. This hydroelastic problem is formulated by directly coupling the structure with the fluid, by usemore » of the Level I Green-Naghdi theory for the fluid motion and the Kirchhoff thin plate theory for the runway. The coupled fluid structure system, together with the appropriate jump conditions are solved in two-dimensions by the finite-difference method. The numerical model is used to study the nonlinear response of a VLFS to storm waves which are modeled by use of the cnoidal-wave theory. Parametric studies show that the nonlinearity of the waves is very important in accurately predicting the dynamic bending moment and wave run-up on a VLFS in high seas.« less

On the buckling of elastic rings by external confinement.

PubMed

Hazel, Andrew L; Mullin, Tom

2017-05-13

We report the results of an experimental and numerical investigation into the buckling of thin elastic rings confined within containers of circular or regular polygonal cross section. The rings float on the surface of water held in the container and controlled removal of the fluid increases the confinement of the ring. The increased compressive forces can cause the ring to buckle into a variety of shapes. For the circular container, finite perturbations are required to induce buckling, whereas in polygonal containers the buckling occurs through a linear instability that is closely related to the canonical Euler column buckling. A model based on Kirchhoff-Love beam theory is developed and solved numerically, showing good agreement with the experiments and revealing that in polygons increasing the number of sides means that buckling occurs at reduced levels of confinement.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.' © 2017 The Author(s).

Development of Improved Surface Integral Methods for Jet Aeroacoustic Predictions

NASA Technical Reports Server (NTRS)

Pilon, Anthony R.; Lyrintzis, Anastasios S.

1997-01-01

The accurate prediction of aerodynamically generated noise has become an important goal over the past decade. Aeroacoustics must now be an integral part of the aircraft design process. The direct calculation of aerodynamically generated noise with CFD-like algorithms is plausible. However, large computer time and memory requirements often make these predictions impractical. It is therefore necessary to separate the aeroacoustics problem into two parts, one in which aerodynamic sound sources are determined, and another in which the propagating sound is calculated. This idea is applied in acoustic analogy methods. However, in the acoustic analogy, the determination of far-field sound requires the solution of a volume integral. This volume integration again leads to impractical computer requirements. An alternative to the volume integrations can be found in the Kirchhoff method. In this method, Green's theorem for the linear wave equation is used to determine sound propagation based on quantities on a surface surrounding the source region. The change from volume to surface integrals represents a tremendous savings in the computer resources required for an accurate prediction. This work is concerned with the development of enhancements of the Kirchhoff method for use in a wide variety of aeroacoustics problems. This enhanced method, the modified Kirchhoff method, is shown to be a Green's function solution of Lighthill's equation. It is also shown rigorously to be identical to the methods of Ffowcs Williams and Hawkings. This allows for development of versatile computer codes which can easily alternate between the different Kirchhoff and Ffowcs Williams-Hawkings formulations, using the most appropriate method for the problem at hand. The modified Kirchhoff method is developed primarily for use in jet aeroacoustics predictions. Applications of the method are shown for two dimensional and three dimensional jet flows. Additionally, the enhancements are generalized so that they may be used in any aeroacoustics problem.

Resistance Distances and Kirchhoff Index in Generalised Join Graphs

NASA Astrophysics Data System (ADS)

Chen, Haiyan

2017-03-01

The resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge with a unit resistor. The Kirchhoff index of a graph is defined as the sum of all the resistance distances between any pair of vertices of the graph. Let G=H[G1, G2, …, Gk ] be the generalised join graph of G1, G2, …, Gk determined by H. In this paper, we first give formulae for resistance distances and Kirchhoff index of G in terms of parameters of G'is {G'_i}s and H. Then, we show that computing resistance distances and Kirchhoff index of G can be decomposed into simpler ones. Finally, we obtain explicit formulae for resistance distances and Kirchhoff index of G when G'is {G'_i}s and H take some special graphs, such as the complete graph, the path, and the cycle.

Application of the Boundary Element Method to Elastic Wave Scattering Problems in Ultrasonic Nondestructive Evaluation.

NASA Astrophysics Data System (ADS)

Schafbuch, Paul Jay

The boundary element method (BEM) is used to numerically simulate the interaction of ultrasonic waves with material defects such as voids, inclusions, and open cracks. The time harmonic formulation is in 3D and therefore allows flaws of arbitrary shape to be modeled. The BEM makes such problems feasible because the underlying boundary integral equation only requires a surface (2D) integration and difficulties associated with the seemingly infinite extent of the host domain are not encountered. The computer code utilized in this work is built upon recent advances in elastodynamic boundary element theory such as a scheme for self adjusting integration order and singular integration regularization. Incident fields may be taken as compressional or shear plane waves or predicted by an approximate Gauss -Hermite beam model. The code is highly optimized for voids and has been coupled with computer aided engineering packages for automated flaw shape definition and mesh generation. Subsequent graphical display of intermediate results supports model refinement and physical interpretation. Final results are typically cast in a nondestructive evaluation (NDE) context as either scattering amplitudes or flaw signals (via a measurement model based on a reciprocity integral). The near field is also predicted which allows for improved physical insight into the scattering process and the evaluation of certain modeling approximations. The accuracy of the BEM approach is first examined by comparing its predictions to those of other models for single, isolated scatterers. The comparisons are with the predictions of analytical solutions for spherical defects and with MOOT and T-matrix calculations for axisymmetric flaws. Experimental comparisons are also made for volumetric shapes with different characteristic dimensions in all three directions, since no other numerical approach has yet produced results of this type. Theoretical findings regarding the fictitious eigenfrequency difficulty are substantiated through the analytical solution of a fundamental elastodynamics problem and corresponding BEM studies. Given the confidence in the BEM technique engendered by these comparisons, it is then used to investigate the modeling of "open", cracklike defects amenable to a volumetric formulation. The limits of applicability of approximate theories (e.g., quasistatic, Kirchhoff, and geometric theory of diffraction) are explored for elliptical cracks, from this basis. The problem of two interacting scatterers is then considered. Results from a fully implicit approach and from a more efficient hybrid scheme are compared with generalized Born and farfield approximate interaction theories.

Application of the boundary element method to elastic wave scattering problems in ultrasonic nondestructive evaluation

NASA Astrophysics Data System (ADS)

Schafbuch, Paul Jay

1991-02-01

The boundary element method (BEM) is used to numerically simulate the interaction of ultrasonic waves with material defects such as voids, inclusions, and open cracks. The time harmonic formulation is in 3D and therefore allows flaws of arbitrary shape to be modeled. The BEM makes such problems feasible because the underlying boundary integral equation only requires a surface (2D) integration and difficulties associated with the seemingly infinite extent of the host domain are not encountered. The computer code utilized in this work is built upon recent advances in elastodynamic boundary element theory such as a scheme for self adjusting integration order and singular integration regularization. Incident fields may be taken as compressional or shear plane waves or predicted by an approximate Gauss-Hermite beam model. The code is highly optimized for voids and has been coupled with computer aided engineering packages for automated flaw shape definition and mesh generation. Subsequent graphical display of intermediate results supports model refinement and physical interpretation. Final results are typically cast in a nondestructive evaluation (NDE) context as either scattering amplitudes or flaw signals (via a measurement model based on a reciprocity integral). The near field is also predicted which allows for improved physical insight into the scattering process and the evaluation of certain modeling approximations. The accuracy of the BEM approach is first examined by comparing its predictions to those of other models for single, isolated scatters. The comparisons are with the predictions of analytical solutions for spherical defects and with MOOT and T-matrix calculations for axisymmetric flaws. Experimental comparisons are also made for volumetric shapes with different characteristic dimensions in all three directions, since no other numerical approach has yet produced results of this type. Theoretical findings regarding the fictitious eigenfrequency difficulty are substantiated through the analytical solution of a fundamental elastodynamics problem and corresponding BEM studies. Given the confidence in the BEM technique engendered by these comparisons, it is then used to investigate the modeling of 'open', cracklike defects amenable to a volumetric formulation. The limits of applicability of approximate theories (e.g., quasistatic, Kirchhoff, and geometric theory of diffraction) are explored for elliptical cracks, from this basis. The problem of two interacting scatterers is then considered. Results from a fully implicit approach and from a more efficient hybrid scheme are compared with generalized Born and farfield approximate interaction theories.

On the convergence of a discrete Kirchhoff triangle method valid for shells of arbitrary shape

NASA Astrophysics Data System (ADS)

Bernadou, Michel; Eiroa, Pilar Mato; Trouve, Pascal

1994-10-01

In a recent paper by the same authors, we have thoroughly described how to extend to the case of general shells the well known DKT (discrete Kirchhoff triangle) methods which are now classically used to solve plate problems. In that paper we have also detailed how to realize the implementation and reported some numerical results obtained for classical benchmarks. The aim of this paper is to prove the convergence of a closely related method and to obtain corresponding error estimates.

Global existence and energy decay rates for a Kirchhoff-type wave equation with nonlinear dissipation.

PubMed

Kim, Daewook; Kim, Dojin; Hong, Keum-Shik; Jung, Il Hyo

2014-01-01

The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku'' + M(|A (1/2) u|(2))Au + g(u') = 0 under suitable assumptions on K, A, M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations in order to verify the analytical results are given.

Kirchhoff's Laws Revisited for Protein Dynamics

NASA Astrophysics Data System (ADS)

Atilgan, Alirana; Baysal, Canan

2001-03-01

We monitor the collective motions of the proteins, and relate the topological characteristics to the flexibility and stability of the protein molecule.^1,2 For modeling purposes, we follow the backbone topology of a compact globular protein and pick the C^α atom at each residue. To define the non-bonded contacts, the first coordination sphere of each C^α with 7 Åradius is considered. Now, C^α's are the nodes and the contacts are the branches; thus, we create an equivalent connected digraph from a folded protein. We accordingly consider first the equilibrium of each residue: A Δ f = 0, then the compatibility equation between the fluctuation of a residue and fluctuations of its contacting bonds: A^T Δ R = Δ r; and finally the constitutive relation for each bonded and nonbonded contact: K Δ r + C dotΔ r = Δ f. In this formulation, A is the incidence matrix of the connected digraph of the protein molecule, K and C are diagonal matrices whose entries are, respectively, the rigidities and the viscous dissipations of the contacts. In addition, the forces at each bond f, positional movements of each residue R, and the bond displacements r are analogous to the branch current vector, node-to-datum voltage vector, and branch voltage vector, respectively, of the circuit theory; and, therefore, the equilibrium and the compatibility equations are the Kirchhoff's Law of Currents and Voltages, respectively. For homogeneous, elastic interactions, the global rigidity of a protein is represented by the Kirchhoff Matrix, that is the incidence matrix multiplied by its transpose. This procedure lends a great helping hand to elucidate the structural dynamic mechanisms for biological activities.^3,4 Illustrative examples are presented and validated by experimental results, and the qualitative differences between one- and three-dimensional formulations are discussed. 1. Bahar, I., Atilgan A.R., Demirel, M.C., and Erman, B., Phys. Rev. Lett., 80, 2733, 1998. 2. Yilmaz, L.S. and Atilgan, A.R., J. Chem. Phys., 113, 4454, 2000. 3. Bahar, I., Erman, B., Jernigan, R.L., Atilgan, A.R., and Covell, D., J. Mol. Biol., 285, 1023, 1999. 4. Baysal, C. and Atilgan, A.R., Proteins, to appear, 2001.

Analysis of an Attenuator Artifact in an Experimental Attack by Gunn-Allison-Abbott Against the Kirchhoff-Law-Johnson-Noise (KLJN) Secure Key Exchange System

NASA Astrophysics Data System (ADS)

Kish, Laszlo B.; Gingl, Zoltan; Mingesz, Robert; Vadai, Gergely; Smulko, Janusz; Granqvist, Claes-Göran

2015-12-01

A recent paper by Gunn-Allison-Abbott (GAA) [L. J. Gunn et al., Scientific Reports 4 (2014) 6461] argued that the Kirchhoff-law-Johnson-noise (KLJN) secure key exchange system could experience a severe information leak. Here we refute their results and demonstrate that GAA's arguments ensue from a serious design flaw in their system. Specifically, an attenuator broke the single Kirchhoff-loop into two coupled loops, which is an incorrect operation since the single loop is essential for the security in the KLJN system, and hence GAA's asserted information leak is trivial. Another consequence is that a fully defended KLJN system would not be able to function due to its built-in current-comparison defense against active (invasive) attacks. In this paper we crack GAA's scheme via an elementary current-comparison attack which yields negligible error probability for Eve even without averaging over the correlation time of the noise.

Kirchhoff index of linear hexagonal chains

NASA Astrophysics Data System (ADS)

Yang, Yujun; Zhang, Heping

The resistance distance rij between vertices i and j of a connected (molecular) graph G is computed as the effective resistance between nodes i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices. In this work, according to the decomposition theorem of Laplacian polynomial, we obtain that the Laplacian spectrum of linear hexagonal chain Ln consists of the Laplacian spectrum of path P2n+1 and eigenvalues of a symmetric tridiagonal matrix of order 2n + 1. By applying the relationship between roots and coefficients of the characteristic polynomial of the above matrix, explicit closed-form formula for Kirchhoff index of Ln is derived in terms of Laplacian spectrum. To our surprise, the Krichhoff index of Ln is approximately to one half of its Wiener index. Finally, we show that holds for all graphs G in a class of graphs including Ln.0

Numerical Analysis of Small Deformation of Flexible Helical Flagellum of Swimming Bacteria

NASA Astrophysics Data System (ADS)

Takano, Yasunari; Goto, Tomonobu

Formulations are conducted to numerically analyze the effect of flexible flagellum of swimming bacteria. In the present model, a single-flagellate bacterium is assumed to consist of a rigid cell body of the prolate spheroidal shape and a flexible flagellum of the helical form. The resistive force theory is applied to estimate the force exerted on the flagellum. The torsional as well as the bending moments determine the curvature and the torsion of the deformed flagellum according to the Kirchhoff model for an elastic rod. The unit tangential vector along the deformed flagellum is calculated by applying evolution equations for space curves, and also a deformed shape of the flagellum is obtained.

Research on Near Field Pattern Effects.

DTIC Science & Technology

1981-01-01

block numbr) High frequency solutions Prolate spheroid mounted antennas Uniform Geometrical Theory of Diffraction Airborne antenna pattern predicti...Geometrical Theory of Diffraction solutions which were developed previously were DD 1473 EDITION OF I NOV 66 IS OBSOLETE UCASFE SECURITY CLASSIFICATION...be used later to simulate the fuselage of a general aircraft. The general uniform Geometrical Theory of Diffraction (GTD) solutions [1i which are

Computer modeling of electromagnetic problems using the geometrical theory of diffraction

NASA Technical Reports Server (NTRS)

Burnside, W. D.

1976-01-01

Some applications of the geometrical theory of diffraction (GTD), a high frequency ray optical solution to electromagnetic problems, are presented. GTD extends geometric optics, which does not take into account the diffractions occurring at edges, vertices, and various other discontinuities. Diffraction solutions, analysis of basic structures, construction of more complex structures, and coupling using GTD are discussed.

Comparison of two leading uniform theories of edge diffraction with the exact uniform asymptotic solution

NASA Technical Reports Server (NTRS)

Boersma, J.; Rahmat-Samii, Y.

1980-01-01

The diffraction of an arbitrary cylindrical wave by a half-plane has been treated by Rahmat-Samii and Mittra who used a spectral domain approach. In this paper, their exact solution for the total field is expressed in terms of a new integral representation. For large wave number k, two rigorous procedures are described for the exact uniform asymptotic expansion of the total field solution. The uniform expansions obtained are valid in the entire space, including transition regions around the shadow boundaries. The final results are compared with the formulations of two leading uniform theories of edge diffraction, namely, the uniform asymptotic theory and the uniform theory of diffraction. Some unique observations and conclusions are made in relating the two theories.

Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics

NASA Technical Reports Server (NTRS)

Farassat, F.

1994-01-01

Generalized functions have many applications in science and engineering. One useful aspect is that discontinuous functions can be handled as easily as continuous or differentiable functions and provide a powerful tool in formulating and solving many problems of aerodynamics and acoustics. Furthermore, generalized function theory elucidates and unifies many ad hoc mathematical approaches used by engineers and scientists. We define generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support, then introduce the concept of generalized differentiation. Generalized differentiation is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some results of classical analysis, are derived with the generalized function theory. Other applications of the generalized function theory in aerodynamics discussed here are the derivations of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of the finite part of divergent integrals, the derivation of the Oswatitsch integral equation of transonic flow, and the analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics include the derivation of the Kirchhoff formula for moving surfaces, the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation.

Stoichiometric network theory for nonequilibrium biochemical systems.

PubMed

Qian, Hong; Beard, Daniel A; Liang, Shou-dan

2003-02-01

We introduce the basic concepts and develop a theory for nonequilibrium steady-state biochemical systems applicable to analyzing large-scale complex isothermal reaction networks. In terms of the stoichiometric matrix, we demonstrate both Kirchhoff's flux law sigma(l)J(l)=0 over a biochemical species, and potential law sigma(l) mu(l)=0 over a reaction loop. They reflect mass and energy conservation, respectively. For each reaction, its steady-state flux J can be decomposed into forward and backward one-way fluxes J = J+ - J-, with chemical potential difference deltamu = RT ln(J-/J+). The product -Jdeltamu gives the isothermal heat dissipation rate, which is necessarily non-negative according to the second law of thermodynamics. The stoichiometric network theory (SNT) embodies all of the relevant fundamental physics. Knowing J and deltamu of a biochemical reaction, a conductance can be computed which directly reflects the level of gene expression for the particular enzyme. For sufficiently small flux a linear relationship between J and deltamu can be established as the linear flux-force relation in irreversible thermodynamics, analogous to Ohm's law in electrical circuits.

Soil emissivity and reflectance spectra measurements

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

Sobrino, Jose A.; Mattar, Cristian; Pardo, Pablo

We present an analysis of the laboratory reflectance and emissivity spectra of 11 soil samples collected on different field campaigns carried out over a diverse suite of test sites in Europe, North Africa, and South America from 2002 to 2008. Hemispherical reflectance spectra were measured from 2.0 to 14 {mu}m with a Fourier transform infrared spectrometer, and x-ray diffraction analysis (XRD) was used to determine the mineralogical phases of the soil samples. Emissivity spectra were obtained from the hemispherical reflectance measurements using Kirchhoff's law and compared with in situ radiance measurements obtained with a CIMEL Electronique CE312-2 thermal radiometer andmore » converted to emissivity using the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) temperature and emissivity separation algorithm. The CIMEL has five narrow bands at approximately the same positions as the ASTER. Results show a root mean square error typically below 0.015 between laboratory emissivity measurements and emissivity measurements derived from the field radiometer.« less

A new theory for X-ray diffraction.

PubMed

Fewster, Paul F

2014-05-01

This article proposes a new theory of X-ray scattering that has particular relevance to powder diffraction. The underlying concept of this theory is that the scattering from a crystal or crystallite is distributed throughout space: this leads to the effect that enhanced scatter can be observed at the `Bragg position' even if the `Bragg condition' is not satisfied. The scatter from a single crystal or crystallite, in any fixed orientation, has the fascinating property of contributing simultaneously to many `Bragg positions'. It also explains why diffraction peaks are obtained from samples with very few crystallites, which cannot be explained with the conventional theory. The intensity ratios for an Si powder sample are predicted with greater accuracy and the temperature factors are more realistic. Another consequence is that this new theory predicts a reliability in the intensity measurements which agrees much more closely with experimental observations compared to conventional theory that is based on `Bragg-type' scatter. The role of dynamical effects (extinction etc.) is discussed and how they are suppressed with diffuse scattering. An alternative explanation for the Lorentz factor is presented that is more general and based on the capture volume in diffraction space. This theory, when applied to the scattering from powders, will evaluate the full scattering profile, including peak widths and the `background'. The theory should provide an increased understanding of the reliability of powder diffraction measurements, and may also have wider implications for the analysis of powder diffraction data, by increasing the accuracy of intensities predicted from structural models.

Quantitative theory of diffraction by cylindrical scroll nanotubes.

PubMed

Khadiev, Azat; Khalitov, Zufar

2018-05-01

A quantitative theory of Fraunhofer diffraction by right- and left-handed multiwalled cylindrical scroll nanotubes is developed on the basis of the kinematical approach. The proposed theory is mainly dedicated to structural studies of individual nanotubes by the selected-area electron diffraction technique. Strong and diffuse reflections of the scroll nanotube were studied and explicit formulas that govern relations between the direct and reciprocal lattice of the scroll nanotube are achieved.

Spectral methods in edge-diffraction theories

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

Arnold, J.M.

Spectral methods for the construction of uniform asymptotic representations of the field diffracted by an aperture in a plane screen are reviewed. These are separated into contrasting approaches, roughly described as physical and geometrical. It is concluded that the geometrical methods provide a direct route to the construction of uniform representations that are formally identical to the equivalent-edge-current concept. Some interpretive and analytical difficulties that complicate the physical methods of obtaining uniform representations are analyzed. Spectral synthesis proceeds directly from the ray geometry and diffraction coefficients, without any intervening current representation, and the representation is uniform at shadow boundaries andmore » caustics of the diffracted field. The physical theory of diffraction postulates currents on the diffracting screen that give rise to the diffracted field. The difficulties encountered in evaluating the current integrals are throughly examined, and it is concluded that the additional data provided by the physical theory of diffraction (diffraction coefficients off the Keller diffraction cone) are not actually required for obtaining uniform asymptotics at the leading order. A new diffraction representation that generalizes to arbitrary plane-convex apertures a formula given by Knott and Senior [Proc. IEEE 62, 1468 (1974)] for circular apertures is deduced. 34 refs., 1 fig.« less

Uniform theory of the boundary diffraction wave

NASA Astrophysics Data System (ADS)

Umul, Yusuf Z.

2009-04-01

A uniform version of the potential function of the Maggi-Rubinowicz boundary diffraction wave theory is obtained by using the large argument expansion of the Fresnel integral. The derived function is obtained for the problem of diffraction of plane waves by a circular edge. The results are plotted numerically.

Unified structure theory of icosahedral quasicrystals: Evidence from neutron powder diffraction patterns that AlCrFeMnSi, AlCuLiMg, and TiNiFeSi icosahedral quasicrystals are twins of cubic crystals containing about 820 or 1012 atoms in a primitive unit cube

PubMed Central

Pauling, Linus

1988-01-01

A unified structure theory of icosahedral quasicrystals, combining the twinned-cubic-crystal theory and the Penrose-tiling-six-dimensional-projection theory, is described. Values of the primitive-cubic lattice constant for several quasicrystals are evaluated from x-ray and neutron diffraction data. The fact that the low-angle diffraction maxima can be indexed with cubic unit cells provides additional support for the twinned-cubic-crystal theory of icosahedral quasicrystals. PMID:16593990

A new theory for X-ray diffraction

PubMed Central

Fewster, Paul F.

2014-01-01

This article proposes a new theory of X-ray scattering that has particular relevance to powder diffraction. The underlying concept of this theory is that the scattering from a crystal or crystallite is distributed throughout space: this leads to the effect that enhanced scatter can be observed at the ‘Bragg position’ even if the ‘Bragg condition’ is not satisfied. The scatter from a single crystal or crystallite, in any fixed orientation, has the fascinating property of contributing simultaneously to many ‘Bragg positions’. It also explains why diffraction peaks are obtained from samples with very few crystallites, which cannot be explained with the conventional theory. The intensity ratios for an Si powder sample are predicted with greater accuracy and the temperature factors are more realistic. Another consequence is that this new theory predicts a reliability in the intensity measurements which agrees much more closely with experimental observations compared to conventional theory that is based on ‘Bragg-type’ scatter. The role of dynamical effects (extinction etc.) is discussed and how they are suppressed with diffuse scattering. An alternative explanation for the Lorentz factor is presented that is more general and based on the capture volume in diffraction space. This theory, when applied to the scattering from powders, will evaluate the full scattering profile, including peak widths and the ‘background’. The theory should provide an increased understanding of the reliability of powder diffraction measurements, and may also have wider implications for the analysis of powder diffraction data, by increasing the accuracy of intensities predicted from structural models. PMID:24815975

Helicopter noise prediction - The current status and future direction

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.; Farassat, F.

1992-01-01

The paper takes stock of the progress, assesses the current prediction capabilities, and forecasts the direction of future helicopter noise prediction research. The acoustic analogy approach, specifically, theories based on the Ffowcs Williams-Hawkings equations, are the most widely used for deterministic noise sources. Thickness and loading noise can be routinely predicted given good plane motion and blade loading inputs. Blade-vortex interaction noise can also be predicted well with measured input data, but prediction of airloads with the high spatial and temporal resolution required for BVI is still difficult. Current semiempirical broadband noise predictions are useful and reasonably accurate. New prediction methods based on a Kirchhoff formula and direct computation appear to be very promising, but are currently very demanding computationally.

A finite element analysis of viscoelastically damped sandwich plates

NASA Astrophysics Data System (ADS)

Ma, B.-A.; He, J.-F.

1992-01-01

A finite element analysis associated with an asymptotic solution method for the harmonic flexural vibration of viscoelastically damped unsymmetrical sandwich plates is given. The element formulation is based on generalization of the discrete Kirchhoff theory (DKT) element formulation. The results obtained with the first order approximation of the asymptotic solution presented here are the same as those obtained by means of the modal strain energy (MSE) method. By taking more terms of the asymptotic solution, with successive calculations and use of the Padé approximants method, accuracy can be improved. The finite element computation has been verified by comparison with an analytical exact solution for rectangular plates with simply supported edges. Results for the same plates with clamped edges are also presented.

Voxelwise Spectral Diffusional Connectivity and its Applications to Alzheimer’s Disease and Intelligence Prediction

PubMed Central

Li, Junning; Jin, Yan; Shi, Yonggang; Dinov, Ivo D.; Wang, Danny J.; Toga, Arthur W.; Thompson, Paul M.

2014-01-01

Human brain connectivity can be studied using graph theory. Many connectivity studies parcellate the brain into regions and count fibres extracted between them. The resulting network analyses require validation of the tractography, as well as region and parameter selection. Here we investigate whole brain connectivity from a different perspective. We propose a mathematical formulation based on studying the eigenvalues of the Laplacian matrix of the diffusion tensor field at the voxel level. This voxelwise matrix has over a million parameters, but we derive the Kirchhoff complexity and eigen-spectrum through elegant mathematical theorems, without heavy computation. We use these novel measures to accurately estimate the voxelwise connectivity in multiple biomedical applications such as Alzheimer’s disease and intelligence prediction. PMID:24505723

Full-spectrum multiwavelength pyrometry for nongray surfaces

NASA Technical Reports Server (NTRS)

Ng, Daniel; Williams, W. D.

1992-01-01

A full-spectrum (encompassing radiation on both sides of the Wien displacement peak) multiwavelength pyrometer was developed. It measures the surface temperature of arbitrary nongray ceramics by curve fitting a spectrum in this spectral region to a Planck function of temperature T. This function of T is modified by the surface spectral emissivity. The emissivity function was derived experimentally from additional spectra that were obtained by using an auxiliary radiation source and from application of Kirchhoff's law. This emissivity was verified by results that were obtained independently by using electromagnetic and solid-state theories. In the presence of interfering reflected radiation this general pyrometry improves the accuracy of the measured temperature by measuring an additional spectrum that characterizes the interfering radiation source.

Acoustic Radiation From Rotating Blades: The Kirchhoff Method in Aeroacoustics

NASA Technical Reports Server (NTRS)

Farassat, F.

2000-01-01

This paper reviews the current status of discrete frequency noise prediction for rotating blade machinery in the time domain. There are two major approaches both of which can be classified as the Kirchhoff method. These methods depend on the solution of two linear wave equations called the K and FW-H equations. The solutions of these equations for subsonic and supersonic surfaces are discussed and some important results of the research in the past years are presented. This paper is analytical in nature and emphasizes the work of the author and coworkers at NASA Langley Research Center.

Noise properties in the ideal Kirchhoff-Law-Johnson-Noise secure communication system.

PubMed

Gingl, Zoltan; Mingesz, Robert

2014-01-01

In this paper we determine the noise properties needed for unconditional security for the ideal Kirchhoff-Law-Johnson-Noise (KLJN) secure key distribution system using simple statistical analysis. It has already been shown using physical laws that resistors and Johnson-like noise sources provide unconditional security. However real implementations use artificial noise generators, therefore it is a question if other kind of noise sources and resistor values could be used as well. We answer this question and in the same time we provide a theoretical basis to analyze real systems as well.

Generalized Kirchhoff-Law-Johnson-Noise (KLJN) secure key exchange system using arbitrary resistors.

PubMed

Vadai, Gergely; Mingesz, Robert; Gingl, Zoltan

2015-09-03

The Kirchhoff-Law-Johnson-Noise (KLJN) secure key exchange system has been introduced as a simple, very low cost and efficient classical physical alternative to quantum key distribution systems. The ideal system uses only a few electronic components-identical resistor pairs, switches and interconnecting wires-in order to guarantee perfectly protected data transmission. We show that a generalized KLJN system can provide unconditional security even if it is used with significantly less limitations. The more universal conditions ease practical realizations considerably and support more robust protection against attacks. Our theoretical results are confirmed by numerical simulations.

Nonlinear vibrations and dynamic stability of viscoelastic orthotropic rectangular plates

NASA Astrophysics Data System (ADS)

Eshmatov, B. Kh.

2007-03-01

This paper describes the analyses of the nonlinear vibrations and dynamic stability of viscoelastic orthotropic plates. The models are based on the Kirchhoff-Love (K.L.) hypothesis and Reissner-Mindlin (R.M.) generalized theory (with the incorporation of shear deformation and rotatory inertia) in geometrically nonlinear statements. It provides justification for the choice of the weakly singular Koltunov-Rzhanitsyn type kernel, with three rheological parameters. In addition, the implication of each relaxation kernel parameter has been studied. To solve problems of viscoelastic systems with weakly singular kernels of relaxation, a numerical method has been used, based on quadrature formulae. With a combination of the Bubnov-Galerkin and the presented method, problems of nonlinear vibrations and dynamic stability in viscoelastic orthotropic rectangular plates have been solved, according to the K.L. and R.M. hypotheses. A comparison of the results obtained via these theories is also presented. In all problems, the convergence of the Bubnov-Galerkin method has been investigated. The implications of material viscoelasticity on vibration and dynamic stability are presented graphically.

Trigonometrical sums connected with the chiral Potts model, Verlinde dimension formula, two-dimensional resistor network, and number theory

NASA Astrophysics Data System (ADS)

Chair, Noureddine

2014-02-01

We have recently developed methods for obtaining exact two-point resistance of the complete graph minus N edges. We use these methods to obtain closed formulas of certain trigonometrical sums that arise in connection with one-dimensional lattice, in proving Scott's conjecture on permanent of Cauchy matrix, and in the perturbative chiral Potts model. The generalized trigonometrical sums of the chiral Potts model are shown to satisfy recursion formulas that are transparent and direct, and differ from those of Gervois and Mehta. By making a change of variables in these recursion formulas, the dimension of the space of conformal blocks of SU(2) and SO(3) WZW models may be computed recursively. Our methods are then extended to compute the corner-to-corner resistance, and the Kirchhoff index of the first non-trivial two-dimensional resistor network, 2×N. Finally, we obtain new closed formulas for variant of trigonometrical sums, some of which appear in connection with number theory.

Radiative transfer theory for active remote sensing of a forested canopy

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.

1989-01-01

A canopy is modeled as a two-layer medium above a rough interface. The upper layer stands for the forest crown, with the leaves modeled as randomly oriented and distributed disks and needles and the branches modeled as randomly oriented finite dielectric cylinders. The lower layer contains the tree trunks, modeled as randomly positioned vertical cylinders above the rough soil. Radiative-transfer theory is applied to calculate EM scattering from such a canopy, is expressed in terms of the scattering-amplitude tensors (SATs). For leaves, the generalized Rayleigh-Gans approximation is applied, whereas the branch and trunk SATs are obtained by estimating the inner field by fields inside a similar cylinder of infinite length. The Kirchhoff method is used to calculate the soil SAT. For a plane wave exciting the canopy, the radiative-transfer equations are solved by iteration to the first order in albedo of the leaves and the branches. Numerical results are illustrated as a function of the incidence angle.

A new multi-layer approach for progressive damage simulation in composite laminates based on isogeometric analysis and Kirchhoff-Love shells. Part II: impact modeling

NASA Astrophysics Data System (ADS)

Pigazzini, M. S.; Bazilevs, Y.; Ellison, A.; Kim, H.

2017-11-01

In this two-part paper we introduce a new formulation for modeling progressive damage in laminated composite structures. We adopt a multi-layer modeling approach, based on isogeometric analysis, where each ply or lamina is represented by a spline surface, and modeled as a Kirchhoff-Love thin shell. Continuum damage mechanics is used to model intralaminar damage, and a new zero-thickness cohesive-interface formulation is introduced to model delamination as well as permitting laminate-level transverse shear compliance. In Part I of this series we focus on the presentation of the modeling framework, validation of the framework using standard Mode I and Mode II delamination tests, and assessment of its suitability for modeling thick laminates. In Part II of this series we focus on the application of the proposed framework to modeling and simulation of damage in composite laminates resulting from impact. The proposed approach has significant accuracy and efficiency advantages over existing methods for modeling impact damage. These stem from the use of IGA-based Kirchhoff-Love shells to represent the individual plies of the composite laminate, while the compliant cohesive interfaces enable transverse shear deformation of the laminate. Kirchhoff-Love shells give a faithful representation of the ply deformation behavior, and, unlike solids or traditional shear-deformable shells, do not suffer from transverse-shear locking in the limit of vanishing thickness. This, in combination with higher-order accurate and smooth representation of the shell midsurface displacement field, allows us to adopt relatively coarse in-plane discretizations without sacrificing solution accuracy. Furthermore, the thin-shell formulation employed does not use rotational degrees of freedom, which gives additional efficiency benefits relative to more standard shell formulations.

Electromagnetic backscattering by corner reflectors

NASA Technical Reports Server (NTRS)

Balanis, C. A.; Griesser, T.

1986-01-01

The Geometrical Theory of Diffraction (GTD), which supplements Geometric Optics (GO), and the Physical Theory of Diffraction (PTD), which supplements Physical Optics (PO), are used to predict the backscatter cross sections of dihedral corner reflectors which have right, obtuse, or acute included angles. These theories allow individual backscattering mechanisms of the dihedral corner reflectors to be identified and provide good agreement with experimental results in the azimuthal plane. The advantages and disadvantages of the geometrical and physical theories are discussed in terms of their accuracy, usefulness, and complexity. Numerous comparisons of analytical results with experimental data are presented. While physical optics alone is more accurate and more useful than geometrical optics alone, the combination of geometrical optics and geometrical diffraction seems to out perform physical optics and physical diffraction when compared with experimental data, especially for acute angle dihedral corner reflectors.

Modeling of a piezoelectric/piezomagnetic nano energy harvester based on two dimensional theory

NASA Astrophysics Data System (ADS)

Yan, Zhi

2018-01-01

This work presents a two dimensional theory for a piezoelectric/piezomagnetic bilayer nanoplate in coupled extensional and flexural vibrations with both flexoelectric and surface effects. The magneto-electro-elastic (MEE) coupling equations are derived from three-dimensional equations and Kirchhoff plate theory. Based on the developed theory, a piezoelectric/piezomagnetic nano energy harvester is proposed, which can generate electricity under time-harmonic applied magnetic field. The approximate solutions for the mechanical responses and voltage of the energy harvester are obtained using the weighted residual method. Results show that the properties of the proposed energy harvester are size-dependent due to the flexoelectric and surface effects, and such effects are more pronounced when the bilayer thickness is reduced to dozens of nanometers. It is also found that the magnetoelectric coupling coefficient and power density of the energy harvester are sensitive to the load resistance, the thickness fraction of the piezoelectric or the piezomagnetic layer and damping ratios. Moreover, results indicate that the flexoelectric effect could be made use to build a dielectric/piezomagnetic nano energy harvester. This work provides modeling techniques and numerical methods for investigating the size-dependent properties of MEE nanoplate-based energy harvester and could be helpful for designing nano energy harvesters using the principle of flexoelectricity.

Practical aspects of prestack depth migration with finite differences

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

Ober, C.C.; Oldfield, R.A.; Womble, D.E.

1997-07-01

Finite-difference, prestack, depth migrations offers significant improvements over Kirchhoff methods in imaging near or under salt structures. The authors have implemented a finite-difference prestack depth migration algorithm for use on massively parallel computers which is discussed. The image quality of the finite-difference scheme has been investigated and suggested improvements are discussed. In this presentation, the authors discuss an implicit finite difference migration code, called Salvo, that has been developed through an ACTI (Advanced Computational Technology Initiative) joint project. This code is designed to be efficient on a variety of massively parallel computers. It takes advantage of both frequency and spatialmore » parallelism as well as the use of nodes dedicated to data input/output (I/O). Besides giving an overview of the finite-difference algorithm and some of the parallelism techniques used, migration results using both Kirchhoff and finite-difference migration will be presented and compared. The authors start out with a very simple Cartoon model where one can intuitively see the multiple travel paths and some of the potential problems that will be encountered with Kirchhoff migration. More complex synthetic models as well as results from actual seismic data from the Gulf of Mexico will be shown.« less

Inverse design of an isotropic suspended Kirchhoff rod: theoretical and numerical results on the uniqueness of the natural shape.

PubMed

Bertails-Descoubes, Florence; Derouet-Jourdan, Alexandre; Romero, Victor; Lazarus, Arnaud

2018-04-01

Solving the equations for Kirchhoff elastic rods has been widely explored for decades in mathematics, physics and computer science, with significant applications in the modelling of thin flexible structures such as DNA, hair or climbing plants. As demonstrated in previous experimental and theoretical studies, the natural curvature plays an important role in the equilibrium shape of a Kirchhoff rod, even in the simple case where the rod is isotropic and suspended under gravity. In this paper, we investigate the reverse problem: can we characterize the natural curvature of a suspended isotropic rod, given an equilibrium curve? We prove that although there exists an infinite number of natural curvatures that are compatible with the prescribed equilibrium, they are all equivalent in the sense that they correspond to a unique natural shape for the rod. This natural shape can be computed efficiently by solving in sequence three linear initial value problems, starting from any framing of the input curve. We provide several numerical experiments to illustrate this uniqueness result, and finally discuss its potential impact on non-invasive parameter estimation and inverse design of thin elastic rods.

Inverse design of an isotropic suspended Kirchhoff rod: theoretical and numerical results on the uniqueness of the natural shape

NASA Astrophysics Data System (ADS)

Bertails-Descoubes, Florence; Derouet-Jourdan, Alexandre; Romero, Victor; Lazarus, Arnaud

2018-04-01

Solving the equations for Kirchhoff elastic rods has been widely explored for decades in mathematics, physics and computer science, with significant applications in the modelling of thin flexible structures such as DNA, hair or climbing plants. As demonstrated in previous experimental and theoretical studies, the natural curvature plays an important role in the equilibrium shape of a Kirchhoff rod, even in the simple case where the rod is isotropic and suspended under gravity. In this paper, we investigate the reverse problem: can we characterize the natural curvature of a suspended isotropic rod, given an equilibrium curve? We prove that although there exists an infinite number of natural curvatures that are compatible with the prescribed equilibrium, they are all equivalent in the sense that they correspond to a unique natural shape for the rod. This natural shape can be computed efficiently by solving in sequence three linear initial value problems, starting from any framing of the input curve. We provide several numerical experiments to illustrate this uniqueness result, and finally discuss its potential impact on non-invasive parameter estimation and inverse design of thin elastic rods.

Asteroid thermal modeling in the presence of reflected sunlight

NASA Astrophysics Data System (ADS)

Myhrvold, Nathan

2018-03-01

A new derivation of simple asteroid thermal models is presented, investigating the need to account correctly for Kirchhoff's law of thermal radiation when IR observations contain substantial reflected sunlight. The framework applies to both the NEATM and related thermal models. A new parameterization of these models eliminates the dependence of thermal modeling on visible absolute magnitude H, which is not always available. Monte Carlo simulations are used to assess the potential impact of violating Kirchhoff's law on estimates of physical parameters such as diameter and IR albedo, with an emphasis on NEOWISE results. The NEOWISE papers use ten different models, applied to 12 different combinations of WISE data bands, in 47 different combinations. The most prevalent combinations are simulated and the accuracy of diameter estimates is found to be depend critically on the model and data band combination. In the best case of full thermal modeling of all four band the errors in an idealized model the 1σ (68.27%) confidence interval is -5% to +6%, but this combination is just 1.9% of NEOWISE results. Other combinations representing 42% of the NEOWISE results have about twice the CI at -10% to +12%, before accounting for errors due to irregular shape or other real world effects that are not simulated. The model and data band combinations found for the majority of NEOWISE results have much larger systematic and random errors. Kirchhoff's law violation by NEOWISE models leads to errors in estimation accuracy that are strongest for asteroids with W1, W2 band emissivity ɛ12 in both the lowest (0.605 ≤ɛ12 ≤ 0 . 780), and highest decile (0.969 ≤ɛ12 ≤ 0 . 988), corresponding to the highest and lowest deciles of near-IR albedo pIR. Systematic accuracy error between deciles ranges from a low of 5% to as much as 45%, and there are also differences in the random errors. Kirchhoff's law effects also produce large errors in NEOWISE estimates of pIR, particularly for high values. IR observations of asteroids in bands that have substantial reflected sunlight can largely avoid these problems by adopting the Kirchhoff law compliant modeling framework presented here, which is conceptually straightforward and comes without computational cost.

Scaling laws and vortex profiles in two-dimensional decaying turbulence.

PubMed

Laval, J P; Chavanis, P H; Dubrulle, B; Sire, C

2001-06-01

We use high resolution numerical simulations over several hundred of turnover times to study the influence of small scale dissipation onto vortex statistics in 2D decaying turbulence. A scaling regime is detected when the scaling laws are expressed in units of mean vorticity and integral scale, like predicted in Carnevale et al., Phys. Rev. Lett. 66, 2735 (1991), and it is observed that viscous effects spoil this scaling regime. The exponent controlling the decay of the number of vortices shows some trends toward xi=1, in agreement with a recent theory based on the Kirchhoff model [C. Sire and P. H. Chavanis, Phys. Rev. E 61, 6644 (2000)]. In terms of scaled variables, the vortices have a similar profile with a functional form related to the Fermi-Dirac distribution.

Instabilities of a rotating helical rod

NASA Astrophysics Data System (ADS)

Park, Yunyoung; Ko, William; Kim, Yongsam; Lim, Sookkyung

2016-11-01

Bacteria such as Escherichia coli and Vibrio alginolyticus have helical flagellar filament. By rotating a motor, which is located at the bottom end of the flagellar filament embedded in the cell body, CCW or CW, they swim forward or backward. We model a left-handed helix by the Kirchhoff rod theory and use regularized Stokes formulation to study an interaction between the surrounding fluid and the flagellar filament. We perform numerical studies focusing on relations between physical parameters and critical angular frequency of the motor, which separates overwhiring from twirling. We are also interested in the buckling instability of the hook, which is very flexible elastic rod. By measuring buckling angle, which is an angle between rotational axis and helical axis, we observe the effects of physical parameters on buckling of the hook.

On equivalent resistance of electrical circuits

NASA Astrophysics Data System (ADS)

Kagan, Mikhail

2015-01-01

While the standard (introductory physics) way of computing the equivalent resistance of nontrivial electrical circuits is based on Kirchhoff's rules, there is a mathematically and conceptually simpler approach, called the method of nodal potentials, whose basic variables are the values of the electric potential at the circuit's nodes. In this paper, we review the method of nodal potentials and illustrate it using the Wheatstone bridge as an example. We then derive a closed-form expression for the equivalent resistance of a generic circuit, which we apply to a few sample circuits. The result unveils a curious interplay between electrical circuits, matrix algebra, and graph theory and its applications to computer science. The paper is written at a level accessible by undergraduate students who are familiar with matrix arithmetic. Additional proofs and technical details are provided in appendices.

The Ponzano-Regge Model and Parametric Representation

NASA Astrophysics Data System (ADS)

Li, Dan

2014-04-01

We give a parametric representation of the effective noncommutative field theory derived from a -deformation of the Ponzano-Regge model and define a generalized Kirchhoff polynomial with -correction terms, obtained in a -linear approximation. We then consider the corresponding graph hypersurfaces and the question of how the presence of the correction term affects their motivic nature. We look in particular at the tetrahedron graph, which is the basic case of relevance to quantum gravity. With the help of computer calculations, we verify that the number of points over finite fields of the corresponding hypersurface does not fit polynomials with integer coefficients, hence the hypersurface of the tetrahedron is not polynomially countable. This shows that the correction term can change significantly the motivic properties of the hypersurfaces, with respect to the classical case.

Modulating DNA configuration by interfacial traction: an elastic rod model to characterize DNA folding and unfolding.

PubMed

Huang, Zaixing

2011-01-01

As a continuum model of DNA, a thin elastic rod subjected to interfacial interactions is used to investigate the equilibrium configuration of DNA in intracellular solution. The interfacial traction between the rod and the solution environment is derived in detail. Kirchhoff's theory of elastic rods is used to analyze the equilibrium configuration of a DNA segment under the action of the interfacial traction. The influences of the interfacial energy factor and bending stiffness on the toroidal spool formation of the DNA segment are discussed. The results show that the equilibrium configuration of DNA is mainly determined by competition between the interfacial energy and elastic strain energy of the DNA itself, and the interfacial traction is one of the forces that drives DNA folding and unfolding.

Effective grating theory for resonance domain surface-relief diffraction gratings.

PubMed

Golub, Michael A; Friesem, Asher A

2005-06-01

An effective grating model, which generalizes effective-medium theory to the case of resonance domain surface-relief gratings, is presented. In addition to the zero order, it takes into account the first diffraction order, which obeys the Bragg condition. Modeling the surface-relief grating as an effective grating with two diffraction orders provides closed-form analytical relationships between efficiency and grating parameters. The aspect ratio, the grating period, and the required incidence angle that would lead to high diffraction efficiencies are predicted for TE and TM polarization and verified by rigorous numerical calculations.

Numerical analysis of fundamental mode selection of a He-Ne laser by a circular aperture

NASA Astrophysics Data System (ADS)

He, Xin; Zhang, Bin

2011-11-01

In the He-Ne laser with an integrated cavity made of zerodur, the inner face performance of the gain tube is limited by the machining techniques, which tends to influence the beam propagation and transverse mode distribution. In order to improve the beam quality and select out the fundamental mode, an aperture is usually introduced in the cavity. In the process of laser design, the Fresnel-Kirchhoff diffraction integral equation is adopted to calculate the optical field distributions on each interface. The transit matrix is obtained based on self-reproducing principle and finite element method. Thus, optical field distribution on any interface and field loss of each transverse mode could be acquired by solving the eigenvalue and eigenvector of the transit matrix. For different-sized apertures in different positions, we could get different matrices and corresponding calculation results. By comparing these results, the optimal size and position of the aperture could be obtained. As a result, the feasibility of selecting fundamental mode in a zerodur He-Ne laser by a circular aperture has been verified theoretically.

Dynamic theory of neutron diffraction from a moving grating

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

Bushuev, V. A., E-mail: vabushuev@yandex.ru; Frank, A. I.; Kulin, G. V.

2016-01-15

A multiwave dynamic theory of diffraction of ultracold neutrons from a moving phase grating has been developed in the approximation of coupled slowly varying amplitudes of wavefunctions. The effect of the velocity, period, and height of grooves of the grating, as well as the spectral angular distribution of the intensity of incident neurons, on the discrete energy spectrum and the intensity of diffraction reflections of various orders has been analyzed.

Analytic theory of alternate multilayer gratings operating in single-order regime.

PubMed

Yang, Xiaowei; Kozhevnikov, Igor V; Huang, Qiushi; Wang, Hongchang; Hand, Matthew; Sawhney, Kawal; Wang, Zhanshan

2017-07-10

Using the coupled wave approach (CWA), we introduce the analytical theory for alternate multilayer grating (AMG) operating in the single-order regime, in which only one diffraction order is excited. Differing from previous study analogizing AMG to crystals, we conclude that symmetrical structure, or equal thickness of the two multilayer materials, is not the optimal design for AMG and may result in significant reduction in diffraction efficiency. The peculiarities of AMG compared with other multilayer gratings are analyzed. An influence of multilayer structure materials on diffraction efficiency is considered. The validity conditions of analytical theory are also discussed.

Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff-type equations involving the fractional p-Laplacian.

PubMed

Shen, Liejun

2018-01-01

The present study is concerned with the following fractional p -Laplacian equation involving a critical Sobolev exponent of Kirchhoff type: [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are constants, and [Formula: see text] is the fractional p -Laplacian operator with [Formula: see text] and [Formula: see text]. For suitable [Formula: see text], the above equation possesses at least two nontrivial solutions by variational method for any [Formula: see text]. Moreover, we regard [Formula: see text] and [Formula: see text] as parameters to obtain convergent properties of solutions for the given problem as [Formula: see text] and [Formula: see text], respectively.

Modelling Aerodynamically Generated Sound: Recent Advances in Rotor Noise Prediction

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.

2000-01-01

A great deal of progress has been made in the modeling of aerodynamically generated sound for rotors over the past decade. The Ffowcs Williams-Hawkings (FW-H ) equation has been the foundation for much of the development. Both subsonic and supersonic quadrupole noise formulations have been developed for the prediction of high-speed impulsive noise. In an effort to eliminate the need to compute the quadrupole contribution, the FW-H has also been utilized on permeable surfaces surrounding all physical noise sources. Comparison of the Kirchhoff formulation for moving surfaces with the FW-H equation have shown that the Kirchhoff formulation for moving surfaces can give erroneous results for aeroacoustic problems.

Study for the dispersion of double-diffraction spectrometers

NASA Astrophysics Data System (ADS)

Pang, Yajun; Zhang, Yinxin; Yang, Huaidong; Huang, Zhanhua; Xu, Mingming; Jin, Guofan

2018-01-01

Double-cascade spectrometers and double-pass spectrometers can be uniformly called double-diffraction spectrometers. In current double-diffraction spectrometers design theory, the differences of the incident angles in the second diffraction are ignored. There is a significant difference between the design in theory and the actual result. In this study, based on the geometries of the double-diffraction spectrometers, we strictly derived the theoretical formulas of their dispersion. By employing the ZEMAX simulation software, verification of our theoretical model is implemented, and the simulation results show big agreement with our theoretical formulas. Based on the conclusions, a double-pass spectrometer was set up and tested, and the experiment results agree with the theoretical model and the simulation.

An E-plane analysis of aperture-matched horn antennas using the moment method and the uniform geometrical theory of diffraction

NASA Technical Reports Server (NTRS)

Heedy, D. J.; Burnside, W. D.

1984-01-01

The moment method and the uniform geometrical theory of diffraction are utilized to obtain two separate solutions for the E-plane field pattern of an aperture-matched horn antenna. This particular horn antenna consists of a standard pyramidal horn with the following modifications: a rolled edge section attached to the aperture edges and a curved throat section. The resulting geometry provides significantly better performance in terms of the pattern, impedance, and frequency characteristics than normally obtainable. The moment method is used to calculate the E-plane pattern and BSWR of the antenna. However, at higher frequencies, large amounts of computation time are required. The uniform geometrical theory of diffraction provides a quick and efficient high frequency solution for the E-plane field pattern. In fact, the uniform geometrical theory of diffraction may be used to initially design the antenna; then, the moment method may be applied to fine tune the design. This procedure has been successfully applied to a compact range feed design.

A Novel Nonlinear Piezoelectric Energy Harvesting System Based on Linear-Element Coupling: Design, Modeling and Dynamic Analysis.

PubMed

Zhou, Shengxi; Yan, Bo; Inman, Daniel J

2018-05-09

This paper presents a novel nonlinear piezoelectric energy harvesting system which consists of linear piezoelectric energy harvesters connected by linear springs. In principle, the presented nonlinear system can improve broadband energy harvesting efficiency where magnets are forbidden. The linear spring inevitably produces the nonlinear spring force on the connected harvesters, because of the geometrical relationship and the time-varying relative displacement between two adjacent harvesters. Therefore, the presented nonlinear system has strong nonlinear characteristics. A theoretical model of the presented nonlinear system is deduced, based on Euler-Bernoulli beam theory, Kirchhoff’s law, piezoelectric theory and the relevant geometrical relationship. The energy harvesting enhancement of the presented nonlinear system (when n = 2, 3) is numerically verified by comparing with its linear counterparts. In the case study, the output power area of the presented nonlinear system with two and three energy harvesters is 268.8% and 339.8% of their linear counterparts, respectively. In addition, the nonlinear dynamic response characteristics are analyzed via bifurcation diagrams, Poincare maps of the phase trajectory, and the spectrum of the output voltage.

3D Kirchhoff depth migration algorithm: A new scalable approach for parallelization on multicore CPU based cluster

NASA Astrophysics Data System (ADS)

Rastogi, Richa; Londhe, Ashutosh; Srivastava, Abhishek; Sirasala, Kirannmayi M.; Khonde, Kiran

2017-03-01

In this article, a new scalable 3D Kirchhoff depth migration algorithm is presented on state of the art multicore CPU based cluster. Parallelization of 3D Kirchhoff depth migration is challenging due to its high demand of compute time, memory, storage and I/O along with the need of their effective management. The most resource intensive modules of the algorithm are traveltime calculations and migration summation which exhibit an inherent trade off between compute time and other resources. The parallelization strategy of the algorithm largely depends on the storage of calculated traveltimes and its feeding mechanism to the migration process. The presented work is an extension of our previous work, wherein a 3D Kirchhoff depth migration application for multicore CPU based parallel system had been developed. Recently, we have worked on improving parallel performance of this application by re-designing the parallelization approach. The new algorithm is capable to efficiently migrate both prestack and poststack 3D data. It exhibits flexibility for migrating large number of traces within the available node memory and with minimal requirement of storage, I/O and inter-node communication. The resultant application is tested using 3D Overthrust data on PARAM Yuva II, which is a Xeon E5-2670 based multicore CPU cluster with 16 cores/node and 64 GB shared memory. Parallel performance of the algorithm is studied using different numerical experiments and the scalability results show striking improvement over its previous version. An impressive 49.05X speedup with 76.64% efficiency is achieved for 3D prestack data and 32.00X speedup with 50.00% efficiency for 3D poststack data, using 64 nodes. The results also demonstrate the effectiveness and robustness of the improved algorithm with high scalability and efficiency on a multicore CPU cluster.

Limit analysis of multi-layered plates. Part I: The homogenized Love-Kirchhoff model

NASA Astrophysics Data System (ADS)

Dallot, Julien; Sab, Karam

The purpose of this paper is to determine Gphom, the overall homogenized Love-Kirchhoff strength domain of a rigid perfectly plastic multi-layered plate, and to study the relationship between the 3D and the homogenized Love-Kirchhoff plate limit analysis problems. In the Love-Kirchhoff model, the generalized stresses are the in-plane (membrane) and the out-of-plane (flexural) stress field resultants. The homogenization method proposed by Bourgeois [1997. Modélisation numérique des panneaux structuraux légers. Ph.D. Thesis, University Aix-Marseille] and Sab [2003. Yield design of thin periodic plates by a homogenization technique and an application to masonry wall. C. R. Méc. 331, 641-646] for in-plane periodic rigid perfectly plastic plates is justified using the asymptotic expansion method. For laminated plates, an explicit parametric representation of the yield surface ∂Gphom is given thanks to the π-function (the plastic dissipation power density function) that describes the local strength domain at each point of the plate. This representation also provides a localization method for the determination of the 3D stress components corresponding to every generalized stress belonging to ∂Gphom. For a laminated plate described with a yield function of the form F(x3,σ)=σu(x3)F^(σ), where σu is a positive even function of the out-of-plane coordinate x3 and F^ is a convex function of the local stress σ, two effective constants and a normalization procedure are introduced. A symmetric sandwich plate consisting of two Von-Mises materials ( σu=σ1u in the skins and σu=σ2u in the core) is studied. It is found that, for small enough contrast ratios ( r=σ1u/σ2u≤5), the normalized strength domain G^phom is close to the one corresponding to a homogeneous Von-Mises plate [Ilyushin, A.-A., 1956. Plasticité. Eyrolles, Paris].

Single-Slit Diffraction Pattern of a Thermal Atomic Potassium Beam

ERIC Educational Resources Information Center

Leavitt, John A.; Bills, Francis A.

1969-01-01

The diffraction of a full thermal atomic potassium beam by a single slit was observed. Four experimental diffraction patterns were compared with that predicted by de Brogtie's hypothesis and simple scalar Fresnel diffraction theory. Possible reasons for the differences were discussed. (LC)

Field-dependent hopping conduction

NASA Astrophysics Data System (ADS)

Hayashi, T.; Tokura, Y.; Fujiwara, A.

2018-07-01

We have numerically calculated transport characteristics on a Miller-Abraham network in a non-linear regime by solving the Kirchhoff's current law at each site. Assuming the Mott model, we obtained the relation between current density and electric field, J ∝exp(γ√{ E}) , which has often been observed in low-mobility materials and whose mechanism has been a source of controversy for over half a century. Our numerical calculation makes it possible to analyze the energy configuration of relevant hopping sites and visualize percolation networks. Following the percolation theory proposed by Shklovskii [Shklovskii, Sov. Phys. Semicond. 10, 855 (1976)], we show that the main mechanism of the field dependence is the replacement of dominating resistances accompanied by the geometrical evolution of the percolation networks. Our calculation is so general that it can be applied to hopping transport in a variety of systems.

Derivation of the out-of-plane behaviour of an English bond masonry wall through homogenization strategies

NASA Astrophysics Data System (ADS)

Silva, Luís Carlos; Milani, Gabriele; Lourenço, Paulo B.

2017-11-01

Two finite element homogenized-based strategies are presented for the out-of-plane behaviour characterization of an English bond masonry wall. A finite element micro-modelling approach using Cauchy stresses and first order movements are assumed for both strategies. The material nonlinearity is lumped on joints interfaces and bricks are considered elastic. Nevertheless, the first model is based on a Plane-stress assumption, in which the out-of-plane quantities are derived through on-thickness wall integration considering a Kirchhoff-plate theory. The second model is a tridimensional one, in which the homogenized out-of-plane quantities can be directly derived after solving the boundary value problem. The comparison is conducted by assessing the obtained out-of-plane bending- and torsion-curvature diagrams. A good agreement is found for the present study case.

Analysis of Small Deformation of Helical Flagellum of Swimming Vibrio alginolyticus

NASA Astrophysics Data System (ADS)

Takano, Yasunari; Yoshida, Kazuki; Kudo, Seishi; Nishitoba, Megumi; Magariyama, Yukio

The deformation of a flagellum of Vibrio alginolyticus, single-flagellate bacteria, is analyzed theoretically assuming the shape of the flagellum to be a circular helix. The viscous force exerted on the flagellum in aqueous fluid is estimated applying the resistive-force theory based on the Stokes flow. The moment of force in the flagellum are described in analytical expressions and also the curvature and the torsion of the deformed flagellum are expressed analytically according to the Kirchhoff rod model. The deformation of the flagellum is obtained numerically solving evolution equations which determine a space curve from the curvature and the torsion. Comparing variations of the pitch of helical flagella between the numerical solutions and the results of measurement, the flexural rigidity or the elastic bending coefficient for the flagellum of Vibrio alginolyticus is estimated.

The finite ground plane effect on the microstrip antenna radiation patterns

NASA Technical Reports Server (NTRS)

Huang, J.

1983-01-01

The uniform geometrical theory of diffraction (GTD) is employed for calculating the edge diffracted fields from the finite ground plane of a microstrip antenna. The source field from the radiating patch is calculated by two different methods: the slot theory and the modal expansion theory. Many numerical and measured results are presented to demonstrate the accuracy of the calculations and the finite ground plane edge effect.

Sound Velocity and Diffraction Intensity Measurements Based on Raman-Nath Theory of the Interaction of Light and Ultrasound

ERIC Educational Resources Information Center

Neeson, John F.; Austin, Stephen

1975-01-01

Describes a method for the measurement of the velocity of sound in various liquids based on the Raman-Nath theory of light-sound interaction. Utilizes an analog computer program to calculate the intensity of light scattered into various diffraction orders. (CP)

Absorption and scattering of light by nonspherical particles. [in atmosphere

NASA Technical Reports Server (NTRS)

Bohren, C. F.

1986-01-01

Using the example of the polarization of scattered light, it is shown that the scattering matrices for identical, randomly ordered particles and for spherical particles are unequal. The spherical assumptions of Mie theory are therefore inconsistent with the random shapes and sizes of atmospheric particulates. The implications for corrections made to extinction measurements of forward scattering light are discussed. Several analytical methods are examined as potential bases for developing more accurate models, including Rayleigh theory, Fraunhoffer Diffraction theory, anomalous diffraction theory, Rayleigh-Gans theory, the separation of variables technique, the Purcell-Pennypacker method, the T-matrix method, and finite difference calculations.

The Progress of Physics

NASA Astrophysics Data System (ADS)

Schuster, Arthur

2015-10-01

Introduction; 1. Scope of lectures. State of physics in 1875. Science of energy. Theory of gases. Elastic solid theory of light. Maxwell's theory of electricity. Training of students. Maxwell's view. Accurate measurement and discovery of Argon. German methods. Kirchhoff's laboratory. Wilhelm Weber's laboratory. The two laboratories of Berlin. Laboratory instruction at Manchester. Position of physics in mathematical tripos at Cambridge. Todhunter's views. The Cavendish laboratory. Spectrum analysis. The radiometer. Theory of vortex atom; 2. Action at a distance. Elastic solid of theory of light. Maxwell's theory of electrical action. Electro-magnetic theory. Verification of electromagnetic theory by Hertz. Electro-magnetic waves. Wireless telegraphy. First suggestion of molecular structure of electricity. Early experiments in the electric discharge through gases. Kathode rays. Works of Goldstein and Crookes. Hittorf's investigations. Own work on the discharge through gases. Ionization of gases. Magnetic deflexion of kathode rays. J. J. Thomson's experiments. Measurement of atomic charge; 3. Roentgen's discovery. Theories of Roentgen rays. Ionizing power of Roentgen rays. Conduction of electricity through ionized gases. Discovery of radio-activity. Discovery of radium. Magnetic deflexion of rays emitted by radio-active bodies. Discovery of emanations. Theory of radio-active change. Decay of the atom. Connexion between helium and the a ray. Helium produced by radium. Strutt's researches on helium accumulated in rocks. Electric inertia. Constitution of atom. J. J. Thomson's theory of Roentgen radiation. The Michelson-Morley experiment. Principle of relativity. The Zeeman effect. Other consequences of electron theory. Contrast between old and modern school of physics; 4. Observational sciences. Judgment affected by scale. Terrestrial magnetism. Existence of potential. Separation of internal and external causes. Diurnal variation. Magnetic storms. Their causes. Solar influence. Theories of secular variation. Atmospheric electricity. Negative charge of Earth. Ionization of air. Origin of atmospheric electricity. Electric charge of rain. Ebert's theory. Cause of thunderstorms. The age of the Earth. Rigidity of Earth. Displacement of axis. Gravitation. Identity of molecules of the same kind; Index.

Instability Paths in the Kirchhoff-Plateau Problem

NASA Astrophysics Data System (ADS)

Giusteri, Giulio G.; Franceschini, Paolo; Fried, Eliot

2016-08-01

The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a soap film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. Adopting a variational approach, we define an energy associated with shape deformations of the system and then derive general equilibrium and (linear) stability conditions by considering the first and second variations of the energy functional. We analyze in detail the transition to instability of flat circular configurations, which are ground states for the system in the absence of surface tension, when the latter is progressively increased. Such a theoretical study is particularly useful here, since the many different perturbations that can lead to instability make it challenging to perform an exhaustive experimental investigation. We generalize previous results, since we allow the filament to possess a curved intrinsic shape and also to display anisotropic flexural properties (as happens when the cross section of the filament is noncircular). This is accomplished by using a rod energy which is familiar from the modeling of DNA filaments. We find that the presence of intrinsic curvature is necessary to obtain a first buckling mode which is not purely tangent to the spanning surface. We also elucidate the role of twisting buckling modes, which become relevant in the presence of flexural anisotropy.

A one-dimensional model of flow in a junction of thin channels, including arterial trees

NASA Astrophysics Data System (ADS)

Kozlov, V. A.; Nazarov, S. A.

2017-08-01

We study a Stokes flow in a junction of thin channels (of diameter O(h)) for fixed flows of the fluid at the inlet cross-sections and fixed peripheral pressure at the outlet cross-sections. On the basis of the idea of the pressure drop matrix, apart from Neumann conditions (fixed flow) and Dirichlet conditions (fixed pressure) at the outer vertices, the ordinary one-dimensional Reynolds equations on the edges of the graph are equipped with transmission conditions containing a small parameter h at the inner vertices, which are transformed into the classical Kirchhoff conditions as h\\to+0. We establish that the pre-limit transmission conditions ensure an exponentially small error O(e-ρ/h), ρ>0, in the calculation of the three-dimensional solution, but the Kirchhoff conditions only give polynomially small error. For the arterial tree, under the assumption that the walls of the blood vessels are rigid, for every bifurcation node a ( 2×2)-pressure drop matrix appears, and its influence on the transmission conditions is taken into account by means of small variations of the lengths of the graph and by introducing effective lengths of the one-dimensional description of blood vessels whilst keeping the Kirchhoff conditions and exponentially small approximation errors. We discuss concrete forms of arterial bifurcation and available generalizations of the results, in particular, the Navier-Stokes system of equations. Bibliography: 59 titles.

Novel quadrilateral elements based on explicit Hermite polynomials for bending of Kirchhoff-Love plates

NASA Astrophysics Data System (ADS)

Beheshti, Alireza

2018-03-01

The contribution addresses the finite element analysis of bending of plates given the Kirchhoff-Love model. To analyze the static deformation of plates with different loadings and geometries, the principle of virtual work is used to extract the weak form. Following deriving the strain field, stresses and resultants may be obtained. For constructing four-node quadrilateral plate elements, the Hermite polynomials defined with respect to the variables in the parent space are applied explicitly. Based on the approximated field of displacement, the stiffness matrix and the load vector in the finite element method are obtained. To demonstrate the performance of the subparametric 4-node plate elements, some known, classical examples in structural mechanics are solved and there are comparisons with the analytical solutions available in the literature.

Elasto-plastic bending of cracked plates, including the effects of crack closure. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Jones, D. P.

1972-01-01

A capability for solving elasto-plastic plate bending problems is developed using assumptions consistent with Kirchhoff plate theory. Both bending and extensional modes of deformation are admitted with the two modes becoming coupled as yielding proceeds. Equilibrium solutions are obtained numerically by determination of the stationary point of a functional which is analogous to the potential strain energy. The stationary value of the functional for each load increment is efficiently obtained through use of the conjugate gradient. This technique is applied to the problem of a large centrally through cracked plate subject to remote circular bending. Comparison is drawn between two cases of the bending problem. The first neglects the possibility of crack face interference with bending, and the second includes a kinematic prohibition against the crack face from passing through the symmetry plane. Results are reported which isolate the effects of elastoplastic flow and crack closure.

Ground cross-modal impedance as a tool for analyzing ground/plate interaction and ground wave propagation.

PubMed

Grau, L; Laulagnet, B

2015-05-01

An analytical approach is investigated to model ground-plate interaction based on modal decomposition and the two-dimensional Fourier transform. A finite rectangular plate subjected to flexural vibration is coupled with the ground and modeled with the Kirchhoff hypothesis. A Navier equation represents the stratified ground, assumed infinite in the x- and y-directions and free at the top surface. To obtain an analytical solution, modal decomposition is applied to the structure and a Fourier Transform is applied to the ground. The result is a new tool for analyzing ground-plate interaction to resolve this problem: ground cross-modal impedance. It allows quantifying the added-stiffness, added-mass, and added-damping from the ground to the structure. Similarity with the parallel acoustic problem is highlighted. A comparison between the theory and the experiment shows good matching. Finally, specific cases are investigated, notably the influence of layer depth on plate vibration.

Reconstructing surface wave profiles from reflected acoustic pulses using multiple receivers.

PubMed

Walstead, Sean P; Deane, Grant B

2014-08-01

Surface wave shapes are determined by analyzing underwater reflected acoustic signals collected at multiple receivers. The transmitted signals are of nominal frequency 300 kHz and are reflected off surface gravity waves that are paddle-generated in a wave tank. An inverse processing algorithm reconstructs 50 surface wave shapes over a length span of 2.10 m. The inverse scheme uses a broadband forward scattering model based on Kirchhoff's diffraction formula to determine wave shapes. The surface reconstruction algorithm is self-starting in that source and receiver geometry and initial estimates of wave shape are determined from the same acoustic signals used in the inverse processing. A high speed camera provides ground-truth measurements of the surface wave field for comparison with the acoustically derived surface waves. Within Fresnel zone regions the statistical confidence of the inversely optimized surface profile exceeds that of the camera profile. Reconstructed surfaces are accurate to a resolution of about a quarter-wavelength of the acoustic pulse only within Fresnel zones associated with each source and receiver pair. Multiple isolated Fresnel zones from multiple receivers extend the spatial extent of accurate surface reconstruction while overlapping Fresnel zones increase confidence in the optimized profiles there.

Numerical analysis of biosonar beamforming mechanisms and strategies in bats.

PubMed

Müller, Rolf

2010-09-01

Beamforming is critical to the function of most sonar systems. The conspicuous noseleaf and pinna shapes in bats suggest that beamforming mechanisms based on diffraction of the outgoing and incoming ultrasonic waves play a major role in bat biosonar. Numerical methods can be used to investigate the relationships between baffle geometry, acoustic mechanisms, and resulting beampatterns. Key advantages of numerical approaches are: efficient, high-resolution estimation of beampatterns, spatially dense predictions of near-field amplitudes, and the malleability of the underlying shape representations. A numerical approach that combines near-field predictions based on a finite-element formulation for harmonic solutions to the Helmholtz equation with a free-field projection based on the Kirchhoff integral to obtain estimates of the far-field beampattern is reviewed. This method has been used to predict physical beamforming mechanisms such as frequency-dependent beamforming with half-open resonance cavities in the noseleaf of horseshoe bats and beam narrowing through extension of the pinna aperture with skin folds in false vampire bats. The fine structure of biosonar beampatterns is discussed for the case of the Chinese noctule and methods for assessing the spatial information conveyed by beampatterns are demonstrated for the brown long-eared bat.

Directivity pattern of the sound radiated from axisymmetric stepped plates.

PubMed

He, Xiping; Yan, Xiuli; Li, Na

2016-08-01

For the purpose of optimal design and efficient utilization of the kind of stepped plate radiator in air, in this contribution, an approach for calculation of the directivity pattern of the sound radiated from a stepped plate in flexural vibration with a free edge is developed based on Kirchhoff-Love hypothesis and Rayleigh integral principle. Experimental tests of directivity pattern for a fabricated flat plate and two fabricated plates with one and two step radiators were carried out. It shows that the configuration of the measured directivity patterns by the proposed analytic approach is similar to those of the calculated approach. Comparison of the agreement between the calculated directivity pattern of a stepped plate and its corresponding theoretical piston show that the former radiator is equivalent to the latter, and the diffraction field generated by the unbaffled upper surface may be small. It also shows that the directivity pattern of a stepped radiator is independent of the metallic material but dependent on the thickness of base plate and resonant frequency. The thicker the thickness of base plate, the more directive the radiation is. The proposed analytic approach in this work may be adopted for any other plates with multi-steps.

The Scherrer equation and the dynamical theory of X-ray diffraction.

PubMed

Muniz, Francisco Tiago Leitão; Miranda, Marcus Aurélio Ribeiro; Morilla Dos Santos, Cássio; Sasaki, José Marcos

2016-05-01

The Scherrer equation is a widely used tool to determine the crystallite size of polycrystalline samples. However, it is not clear if one can apply it to large crystallite sizes because its derivation is based on the kinematical theory of X-ray diffraction. For large and perfect crystals, it is more appropriate to use the dynamical theory of X-ray diffraction. Because of the appearance of polycrystalline materials with a high degree of crystalline perfection and large sizes, it is the authors' belief that it is important to establish the crystallite size limit for which the Scherrer equation can be applied. In this work, the diffraction peak profiles are calculated using the dynamical theory of X-ray diffraction for several Bragg reflections and crystallite sizes for Si, LaB6 and CeO2. The full width at half-maximum is then extracted and the crystallite size is computed using the Scherrer equation. It is shown that for crystals with linear absorption coefficients below 2117.3 cm(-1) the Scherrer equation is valid for crystallites with sizes up to 600 nm. It is also shown that as the size increases only the peaks at higher 2θ angles give good results, and if one uses peaks with 2θ > 60° the limit for use of the Scherrer equation would go up to 1 µm.

Theoretical study of the properties of X-ray diffraction moiré fringes. I

PubMed Central

Yoshimura, Jun-ichi

2015-01-01

A detailed and comprehensive theoretical description of X-ray diffraction moiré fringes for a bicrystal specimen is given on the basis of a calculation by plane-wave dynamical diffraction theory. Firstly, prior to discussing the main subject of the paper, a previous article [Yoshimura (1997 ▸). Acta Cryst. A53, 810–812] on the two-dimensionality of diffraction moiré patterns is restated on a thorough calculation of the moiré interference phase. Then, the properties of moiré fringes derived from the above theory are explained for the case of a plane-wave diffraction image, where the significant effect of Pendellösung intensity oscillation on the moiré pattern when the crystal is strained is described in detail with theoretically simulated moiré images. Although such plane-wave moiré images are not widely observed in a nearly pure form, knowledge of their properties is essential for the understanding of diffraction moiré fringes in general. PMID:25970298

A nonlocal continuum model for the biaxial buckling analysis of composite nanoplates with shape memory alloy nanowires

NASA Astrophysics Data System (ADS)

Farajpour, M. R.; Shahidi, A. R.; Farajpour, A.

2018-03-01

In this study, the buckling behavior of a three-layered composite nanoplate reinforced with shape memory alloy (SMA) nanowires is examined. Whereas the upper and lower layers are reinforced with typical nanowires, SMA nanoscale wires are used to strengthen the middle layer of the system. The composite nanoplate is assumed to be under the action of biaxial compressive loading. A scale-dependent mathematical model is presented with the consideration of size effects within the context of the Eringen’s nonlocal continuum mechanics. Using the one-dimensional Brinson’s theory and the Kirchhoff theory of plates, the governing partial differential equations of SMA nanowire-reinforced hybrid nanoplates are derived. Both lateral and longitudinal deflections are taken into consideration in the theoretical formulation and method of solution. In order to reduce the governing differential equations to their corresponding algebraic equations, a discretization approach based on the differential quadrature method is employed. The critical buckling loads of the hybrid nanosystem with various boundary conditions are obtained with the use of a standard eigenvalue solver. It is found that the stability response of SMA composite nanoplates is strongly sensitive to the small scale effect.

Thermo-magnetic field effects on the wave propagation behavior of smart magnetostrictive sandwich nanoplates

NASA Astrophysics Data System (ADS)

Ebrahimi, Farzad; Dabbagh, Ali

2018-03-01

In this paper, a three-variable plate model is utilized to explore the wave propagation problem of smart sandwich nanoplates made of a magnetostrictive core and ceramic face sheets while subjected to thermo-magnetic loading. Herein, the magnetostriction effect is considered and controlled via a feedback control system. The nanoplate is supposed to be embedded on a visco-Pasternak elastic substrate. The kinematic relations are derived based on the Kirchhoff plate theory; also, combining these obtained equations with Hamilton's principle, the local equations of motion are achieved. According to a nonlocal strain gradient theory (NSGT), the small-scale influences are covered precisely by introducing two scale coefficients. Afterwards, the nonlocal governing equations are derived coupling the local equations with those of the NSGT. Applying an analytical solution, the wave frequency and phase velocity of the propagated waves can be gathered solving an eigenvalue problem. On the other hand, accuracy and efficiency of the presented model are verified by setting a comparison between the obtained results with those of previous published researches. Effects of different variants are plotted in some figures and the highlights are discussed in detail.

The radar cross section of dielectric disks

NASA Technical Reports Server (NTRS)

Levine, D. M.

1982-01-01

A solution is presented for the backscatter (nonstatic) radar cross section of dielectric disks of arbitrary shape, thickness and dielectric constant. The result is obtained by employing a Kirchhoff type approximation to obtain the fields inside the disk. The internal fields induce polarization and conduction currents from which the scattered fields and the radar cross section can be computed. The solution for the radar cross section obtained in this manner is shown to agree with known results in the special cases of normal incidence, thin disks and perfect conductivity. The solution can also be written as a product of the reflection coefficient of an identically oriented slab times the physical optics solution for the backscatter cross section of a perfectly conducting disk of the same shape. This result follows directly from the Kirchhoff type approximation without additional assumptions.

Determination of Particle Size by Diffraction of Light

ERIC Educational Resources Information Center

Rinard, Phillip M.

1974-01-01

Describes a simplified diffraction experiment offered in a workshop with the purpose of illustrating to high school students the relation of science to society. The radii determined for cigarette smoke particles range from 0.2 to 0.5 micrometer in this experiment. Included is a description of the diffraction theory. (CC)

The statistical kinematical theory of X-ray diffraction as applied to reciprocal-space mapping

PubMed

Nesterets; Punegov

2000-11-01

The statistical kinematical X-ray diffraction theory is developed to describe reciprocal-space maps (RSMs) from deformed crystals with defects of the structure. The general solutions for coherent and diffuse components of the scattered intensity in reciprocal space are derived. As an example, the explicit expressions for intensity distributions in the case of spherical defects and of a mosaic crystal were obtained. The theory takes into account the instrumental function of the triple-crystal diffractometer and can therefore be used for experimental data analysis.

Scattering from a cylindrical reflector: modified theory of physical optics solution.

PubMed

Yalçin, Ugur

2007-02-01

The problem of scattering from a perfectly conducting cylindrical reflector is examined with the method of the modified theory of physical optics. In this technique the physical optics currents are modified by using a variable unit vector on the scatterer's surface. These current components are obtained for the reflector, which is fed by an offset electric line source. The scattering integral is expressed by using these currents and evaluated asymptotically with the stationary phase method. The results are compared numerically by using physical optics theory, geometrical optics diffraction theory, and the exact solution of the Helmholtz equation. It is found that the modified theory of physical optics scattering field equations agrees with the geometrical optics diffraction theory and the exact solution of the Helmholtz equation.

Catastrophe optics of sharp-edge diffraction.

PubMed

Borghi, Riccardo

2016-07-01

A classical problem of diffraction theory, namely plane wave diffraction by sharp-edge apertures, is here reformulated from the viewpoint of the fairly new subject of catastrophe optics. On using purely geometrical arguments, properly embedded into a wave optics context, uniform analytical estimates of the diffracted wavefield at points close to fold caustics are obtained, within paraxial approximation, in terms of the Airy function and its first derivative. Diffraction from parabolic apertures is proposed to test reliability and accuracy of our theoretical predictions.

Multilayer diffraction at 104 keV

NASA Technical Reports Server (NTRS)

Krieger, Allen S.; Blake, Richard L.; Siddons, D. P.

1993-01-01

We have measured the diffraction peak of a W:Si synthetic multilayer reflector at 104 keV using the High Energy Bonse-Hart Camera at the X-17B hard X-ray wiggler beam line of the National Synchrotron Light Source at Brookhaven National Laboratory. The characteristics of the diffraction peak are described and compared to theory.

Wavefront aberrations of x-ray dynamical diffraction beams.

PubMed

Liao, Keliang; Hong, Youli; Sheng, Weifan

2014-10-01

The effects of dynamical diffraction in x-ray diffractive optics with large numerical aperture render the wavefront aberrations difficult to describe using the aberration polynomials, yet knowledge of them plays an important role in a vast variety of scientific problems ranging from optical testing to adaptive optics. Although the diffraction theory of optical aberrations was established decades ago, its application in the area of x-ray dynamical diffraction theory (DDT) is still lacking. Here, we conduct a theoretical study on the aberration properties of x-ray dynamical diffraction beams. By treating the modulus of the complex envelope as the amplitude weight function in the orthogonalization procedure, we generalize the nonrecursive matrix method for the determination of orthonormal aberration polynomials, wherein Zernike DDT and Legendre DDT polynomials are proposed. As an example, we investigate the aberration evolution inside a tilted multilayer Laue lens. The corresponding Legendre DDT polynomials are obtained numerically, which represent balanced aberrations yielding minimum variance of the classical aberrations of an anamorphic optical system. The balancing of classical aberrations and their standard deviations are discussed. We also present the Strehl ratio of the primary and secondary balanced aberrations.

Electromagnetic diffraction radiation of a subwavelength-hole array excited by an electron beam.

PubMed

Liu, Shenggang; Hu, Min; Zhang, Yaxin; Li, Yuebao; Zhong, Renbin

2009-09-01

This paper explores the physics of the electromagnetic diffraction radiation of a subwavelength holes array excited by a set of evanescent waves generated by a line charge of electron beam moving parallel to the array. Activated by a uniformly moving line charge, numerous physical phenomena occur such as the diffraction radiation on both sides of the array as well as the electromagnetic penetration or transmission below or above the cut-off through the holes. As a result the subwavelength holes array becomes a radiation array. Making use of the integral equation with relevant Green's functions, an analytical theory for such a radiation system is built up. The results of the numerical calculations based on the theory agree well with that obtained by the computer simulation. The relation among the effective surface plasmon wave, the electromagnetic penetration or transmission of the holes and the diffraction radiation is revealed. The energy dependence of and the influence of the hole thickness on the diffraction radiation and the electromagnetic penetration or transmission are investigated in detail. Therefore, a distinct diffraction radiation phenomenon is discovered.

Modeling focusing characteristics of low Fnumber diffractive optical elements with continuous relief fabricated by laser direct writing.

PubMed

Shan, Mingguang; Tan, Jiubin

2007-12-10

A theoretical model is established using Rayleigh-Sommerfeld diffraction theory to describe the diffraction focusing characteristics of low F-number diffractive optical elements with continuous relief fabricated by laser direct writing, and continuous-relief diffractive optical elements with a design wavelength of 441.6nm and a F-number of F/4 are fabricated and measured to verify the validity of the diffraction focusing model. The measurements made indicate that the spot size is 1.75mum and the diffraction efficiency is 70.7% at the design wavelength, which coincide well with the theoretical results: a spot size of 1.66mum and a diffraction efficiency of 71.2%.

Quantifying Fish Backscattering using SONAR Instrument and Kirchhoff Ray Mode (KRM) Model

NASA Astrophysics Data System (ADS)

Manik, Henry M.

2016-08-01

Sonar instrument was used to study backscattering from tuna fish. Extraction of target strength, incidence angle, and frequency dependence of the backscattered signal for individual scatterer was important for biological information. For this purpose, acoustic measurement of fish backscatter was conducted in the laboratory. Characteristics and general trends of the target strength of fish with special reference to tuna fish were investigated by using a Kirchhoff Ray Mode (KRM) model. Backscattering strength were calculated for the KRM having typical morphological and physical parameters of actual fish. Those backscattering amplitudes were shown as frequency, body length, backscattering patterns, the density and sound speed dependences, and orientation dependence. These results were compared with experimentally measured target strength data and good agreement was found. Measurement and model showed the target strength from the fish are depend on the presence of swimbladder. Target Strength increase with increasing the frequency and fish length.

Near equilibrium dynamics of nonhomogeneous Kirchhoff filaments in viscous media

NASA Astrophysics Data System (ADS)

Fonseca, A. F.; de Aguiar, M. A.

2001-01-01

We study the near equilibrium dynamics of nonhomogeneous elastic filaments in viscous media using the Kirchhoff model of rods. Viscosity is incorporated in the model as an external force, which we approximate by the resistance felt by an infinite cylinder immersed in a slowly moving fluid. We use the recently developed method of Goriely and Tabor [Phys. Rev. Lett. 77, 3537 (1996); Physica D 105, 20 (1997); 105, 45 (1997)] to study the dynamics in the vicinity of the simplest equilibrium solution for a closed rod with nonhomogeneous distribution of mass, namely, the planar ring configuration. We show that small variations of the mass density along the rod are sufficient to couple the symmetric modes of the homogeneous rod problem, producing asymmetric deformations that modify substantially the dynamical coiling, even at quite low Reynolds number. The higher-density segments of the rod tend to become more rigid and less coiled. We comment on possible applications to DNA.

Near equilibrium dynamics of nonhomogeneous Kirchhoff filaments in viscous media.

PubMed

Fonseca, A F; de Aguiar, M A

2001-01-01

We study the near equilibrium dynamics of nonhomogeneous elastic filaments in viscous media using the Kirchhoff model of rods. Viscosity is incorporated in the model as an external force, which we approximate by the resistance felt by an infinite cylinder immersed in a slowly moving fluid. We use the recently developed method of Goriely and Tabor [Phys. Rev. Lett. 77, 3537 (1996); Physica D 105, 20 (1997); 105, 45 (1997)] to study the dynamics in the vicinity of the simplest equilibrium solution for a closed rod with nonhomogeneous distribution of mass, namely, the planar ring configuration. We show that small variations of the mass density along the rod are sufficient to couple the symmetric modes of the homogeneous rod problem, producing asymmetric deformations that modify substantially the dynamical coiling, even at quite low Reynolds number. The higher-density segments of the rod tend to become more rigid and less coiled. We comment on possible applications to DNA.

Existence of multi-bump solutions for a class of Kirchhoff type problems in R{sup 3}

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

Liang, Sihua, E-mail: liangsihua@126.com; College of Mathematics, Jilin University, Changchun 130012; Shi, Shaoyun, E-mail: shisy@mail.jlu.edu.cn

2013-12-15

Using variational methods, we establish existence of multi-bump solutions for a class of Kirchhoff type problems −(a+b∫{sub R{sup 3}}|∇u|{sup 2}dx)Δu+λV(x)u=f(u), where f is a continuous function with subcritical growth, V(x) is a critical frequency in the sense that inf{sub x∈R{sup 3}}V(x)=0. We show that if the zero set of V(x) has several isolated connected components Ω{sub 1}, …, Ω{sub k} such that the interior of Ω{sub i} is not empty and ∂Ω{sub i} is smooth, then for λ > 0 large there exists, for any non-empty subset J ⊂ (1, …, k), a bump solution is trapped in a neighborhoodmore » of ∪{sub j∈J}Ω{sub j}.« less

On necessary conditions for the comparison principle and the sub- and supersolution method for the stationary Kirchhoff equation

NASA Astrophysics Data System (ADS)

Iturriaga, Leonelo; Massa, Eugenio

2018-01-01

In this paper, we propose a counterexample to the validity of the comparison principle and of the sub- and supersolution method for nonlocal problems like the stationary Kirchhoff equation. This counterexample shows that in general smooth bounded domains in any dimension, these properties cannot hold true if the nonlinear nonlocal term M (∥u∥ 2 ) is somewhere increasing with respect to the H01-norm of the solution. Comparing with the existing results, this fills a gap between known conditions on M that guarantee or prevent these properties and leads to a condition that is necessary and sufficient for the validity of the comparison principle. It is worth noting that equations similar to the one considered here have gained interest recently for appearing in models of thermo-convective flows of non-Newtonian fluids or of electrorheological fluids, among others.

Large-Scale Diffraction Patterns from Circular Objects

ERIC Educational Resources Information Center

Rinard, Phillip M.

1976-01-01

Investigates quantitatively the diffractions of light by a U.S. penny and an aperture of the same size. Differences noted between the theory and measurements are discussed, with probable causes indicated. (Author/CP)

Numerical method of applying shadow theory to all regions of multilayered dielectric gratings in conical mounting.

PubMed

Wakabayashi, Hideaki; Asai, Masamitsu; Matsumoto, Keiji; Yamakita, Jiro

2016-11-01

Nakayama's shadow theory first discussed the diffraction by a perfectly conducting grating in a planar mounting. In the theory, a new formulation by use of a scattering factor was proposed. This paper focuses on the middle regions of a multilayered dielectric grating placed in conical mounting. Applying the shadow theory to the matrix eigenvalues method, we compose new transformation and improved propagation matrices of the shadow theory for conical mounting. Using these matrices and scattering factors, being the basic quantity of diffraction amplitudes, we formulate a new description of three-dimensional scattering fields which is available even for cases where the eigenvalues are degenerate in any region. Some numerical examples are given for cases where the eigenvalues are degenerate in the middle regions.

A full simulation of the Quetzal echo at the Mayan pyramid of Kukulkan at Chichen Itza in Mexico

NASA Astrophysics Data System (ADS)

Declercq, Nico F.; Degrieck, Joris; Briers, Rudy; Leroy, Oswald

2003-04-01

It is well known that a handclap in front of the staircase of the pyramid produces an echo that sounds similar to the chirp of the Quetzal bird. This phenomenon occurs due to diffraction. There exist some publications concerning this phenomenon and even some first attempts are reported to simulate it. However, no full simulation (amplitude, frequency, time) has ever been reported before. The present work presents a simulation which is based on the theory of the diffraction of plane waves and which takes into account continuity conditions. The latter theory is the building block for an extended theory that tackles the diffraction of a spherical sound pulse. By means of these principles it is possible to entirely simulate the echo following a handclap in front of the staircase. [Work supported by The Flemish Institute for the Encouragement of the Scientific and Technological Research in Industry (I.W.T.)

Experiments on the applicability of MAE techniques for predicting sound diffraction by irregular terrains. [Matched Asymptotic Expansion

NASA Technical Reports Server (NTRS)

Berthelot, Yves H.; Pierce, Allan D.; Kearns, James A.

1987-01-01

The sound field diffracted by a single smooth hill of finite impedance is studied both analytically, within the context of the theory of Matched Asymptotic Expansions (MAE), and experimentally, under laboratory scale modeling conditions. Special attention is given to the sound field on the diffracting surface and throughout the transition region between the illuminated and the shadow zones. The MAE theory yields integral equations that are amenable to numerical computations. Experimental results are obtained with a spark source producing a pulse of 42 microsec duration and about 130 Pa at 1 m. The insertion loss of the hill is inferred from measurements of the acoustic signals at two locations in the field, with subsequent Fourier analysis on an IBM PC/AT. In general, experimental results support the predictions of the MAE theory, and provide a basis for the analysis of more complicated geometries.

Efficient Helicopter Aerodynamic and Aeroacoustic Predictions on Parallel Computers

NASA Technical Reports Server (NTRS)

Wissink, Andrew M.; Lyrintzis, Anastasios S.; Strawn, Roger C.; Oliker, Leonid; Biswas, Rupak

1996-01-01

This paper presents parallel implementations of two codes used in a combined CFD/Kirchhoff methodology to predict the aerodynamics and aeroacoustics properties of helicopters. The rotorcraft Navier-Stokes code, TURNS, computes the aerodynamic flowfield near the helicopter blades and the Kirchhoff acoustics code computes the noise in the far field, using the TURNS solution as input. The overall parallel strategy adds MPI message passing calls to the existing serial codes to allow for communication between processors. As a result, the total code modifications required for parallel execution are relatively small. The biggest bottleneck in running the TURNS code in parallel comes from the LU-SGS algorithm that solves the implicit system of equations. We use a new hybrid domain decomposition implementation of LU-SGS to obtain good parallel performance on the SP-2. TURNS demonstrates excellent parallel speedups for quasi-steady and unsteady three-dimensional calculations of a helicopter blade in forward flight. The execution rate attained by the code on 114 processors is six times faster than the same cases run on one processor of the Cray C-90. The parallel Kirchhoff code also shows excellent parallel speedups and fast execution rates. As a performance demonstration, unsteady acoustic pressures are computed at 1886 far-field observer locations for a sample acoustics problem. The calculation requires over two hundred hours of CPU time on one C-90 processor but takes only a few hours on 80 processors of the SP2. The resultant far-field acoustic field is analyzed with state of-the-art audio and video rendering of the propagating acoustic signals.

Surface integral analogy approaches for predicting noise from 3D high-lift low-noise wings

NASA Astrophysics Data System (ADS)

Yao, Hua-Dong; Davidson, Lars; Eriksson, Lars-Erik; Peng, Shia-Hui; Grundestam, Olof; Eliasson, Peter E.

2014-06-01

Three surface integral approaches of the acoustic analogies are studied to predict the noise from three conceptual configurations of three-dimensional high-lift low-noise wings. The approaches refer to the Kirchhoff method, the Ffowcs Williams and Hawkings (FW-H) method of the permeable integral surface and the Curle method that is known as a special case of the FW-H method. The first two approaches are used to compute the noise generated by the core flow region where the energetic structures exist. The last approach is adopted to predict the noise specially from the pressure perturbation on the wall. A new way to construct the integral surface that encloses the core region is proposed for the first two methods. Considering the local properties of the flow around the complex object-the actual wing with high-lift devices-the integral surface based on the vorticity is constructed to follow the flow structures. The surface location is discussed for the Kirchhoff method and the FW-H method because a common surface is used for them. The noise from the core flow region is studied on the basis of the dependent integral quantities, which are indicated by the Kirchhoff formulation and by the FW-H formulation. The role of each wall component on noise contribution is analyzed using the Curle formulation. Effects of the volume integral terms of Lighthill's stress tensors on the noise prediction are then evaluated by comparing the results of the Curle method with the other two methods.

Beam propagation modeling of modified volume Fresnel zone plates fabricated by femtosecond laser direct writing.

PubMed

Srisungsitthisunti, Pornsak; Ersoy, Okan K; Xu, Xianfan

2009-01-01

Light diffraction by volume Fresnel zone plates (VFZPs) is simulated by the Hankel transform beam propagation method (Hankel BPM). The method utilizes circularly symmetric geometry and small step propagation to calculate the diffracted wave fields by VFZP layers. It is shown that fast and accurate diffraction results can be obtained with the Hankel BPM. The results show an excellent agreement with the scalar diffraction theory and the experimental results. The numerical method allows more comprehensive studies of the VFZP parameters to achieve higher diffraction efficiency.

Influence of vortex core on wake vortex sound emission

DOT National Transportation Integrated Search

2006-05-08

A consistent and presistent mechanism of sound emission from aircraft wake vortices has been identified. Both measurement data and theoretical results show that a dominant frequency of sound pressure matches the rotation frquency of a Kirchhoff vorte...

TERAHERTZ REFLECTION IMAGING USING KIRCHHOFF MIGRATION. (R827122)

EPA Science Inventory

The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...

Theory of hard diffraction and rapidity gaps

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

Del Duca, V.

1996-02-01

In this talk we review the models describing the hard diffractive production of jets or more generally high-mass states in presence of rapidity gaps in hadron-hadron and lepton-hadron collisions. By rapidity gaps we mean regions on the lego plot in (pseudo)-rapidity and azimuthal angle where no hadrons are produced, between the jet(s) and an elastically scattered hadron (single hard diffraction) or between two jets (double hard diffraction). {copyright} {ital 1996 American Institute of Physics.}

Diffraction patterns in Fresnel approximation of periodic objects for a colorimeter of two apertures

NASA Astrophysics Data System (ADS)

Cortes-Reynoso, Jose-German R.; Suarez-Romero, Jose G.; Hurtado-Ramos, Juan B.; Tepichin-Rodriguez, Eduardo; Solorio-Leyva, Juan Carlos

2004-10-01

In this work, we present a study of Fresnel diffraction of periodic structures in an optical system of two apertures. This system of two apertures was used successfully for measuring color in textile samples solving the problems of illumination and directionality that present current commercial equipments. However, the system is sensible to the spatial frequency of the periodic sample"s area enclosed in its optical field of view. The study of Fresnel diffraction allows us to establish criteria for geometrical parameters of measurements in order to assure invariance in angular rotations and spatial positions. In this work, we use the theory of partial coherence to calculate the diffraction through two continuous apertures. In the calculation process, we use the concept of point-spread function of the system for partial coherence, in this way we avoid complicated statistical processes commonly used in the partial coherence theory.

Transition operators in electromagnetic-wave diffraction theory. II - Applications to optics

NASA Technical Reports Server (NTRS)

Hahne, G. E.

1993-01-01

The theory developed by Hahne (1992) for the diffraction of time-harmonic electromagnetic waves from fixed obstacles is briefly summarized and extended. Applications of the theory are considered which comprise, first, a spherical harmonic expansion of the so-called radiation impedance operator in the theory, for a spherical surface, and second, a reconsideration of familiar short-wavelength approximation from the new standpoint, including a derivation of the so-called physical optics method on the basis of quasi-planar approximation to the radiation impedance operator, augmented by the method of stationary phase. The latter includes a rederivation of the geometrical optics approximation for the complete Green's function for the electromagnetic field in the presence of a smooth- and a convex-surfaced perfectly electrically conductive obstacle.

An analysis of the radiation from apertures in curved surfaces by the geometrical theory of diffraction. [ray technique for electromagnetic fields

NASA Technical Reports Server (NTRS)

Pathak, P. H.; Kouyoumjian, R. G.

1974-01-01

In this paper the geometrical theory of diffraction is extended to treat the radiation from apertures of slots in convex perfectly conducting surfaces. It is assumed that the tangential electric field in the aperture is known so that an equivalent infinitesimal source can be defined at each point in the aperture. Surface rays emanate from this source which is a caustic of the ray system. A launching coefficient is introduced to describe the excitation of the surface ray modes. If the field radiated from the surface is desired, the ordinary diffraction coefficients are used to determine the field of the rays shed tangentially from the surface rays. The field of the surface ray modes is not the field on the surface; hence if the mutual coupling between slots is of interest, a second coefficient related to the launching coefficient must be employed. In the region adjacent to the shadow boundary, the component of the field directly radiated from the source is represented by Fock-type functions. In the illuminated region the incident radiation from the source (this does not include the diffracted field components) is treated by geometrical optics. This extension of the geometrical theory of diffraction is applied to calculate the radiation from slots on elliptic cylinders, spheres, and spheroids.

A two-scale roughness model for the gloss of coated paper

NASA Astrophysics Data System (ADS)

Elton, N. J.

2008-08-01

A model for gloss is developed for surfaces with two-scale random roughness where one scale lies in the wavelength region (microroughness) and the other in the geometrical optics limit (macroroughness). A number of important industrial materials such as coated and printed paper and some paints exhibit such two-scale rough surfaces. Scalar Kirchhoff theory is used to describe scattering in the wavelength region and a facet model used for roughness features much greater than the wavelength. Simple analytical expressions are presented for the gloss of surfaces with Gaussian, modified and intermediate Lorentzian distributions of surface slopes, valid for gloss at high angle of incidence. In the model, gloss depends only on refractive index, rms microroughness amplitude and the FWHM of the surface slope distribution, all of which may be obtained experimentally. Model predictions are compared with experimental results for a range of coated papers and gloss standards, and found to be in fair agreement within model limitations.

Rational rates of uniform decay for strong solutions to a fluid-structure PDE system

NASA Astrophysics Data System (ADS)

Avalos, George; Bucci, Francesca

2015-06-01

In this work we investigate the uniform stability properties of solutions to a well-established partial differential equation (PDE) model for a fluid-structure interaction. The PDE system under consideration comprises a Stokes flow which evolves within a three-dimensional cavity; moreover, a Kirchhoff plate equation is invoked to describe the displacements along a (fixed) portion - say, Ω - of the cavity wall. Contact between the respective fluid and structure dynamics occurs on the boundary interface Ω. The main result in the paper is as follows: the solutions to the composite PDE system, corresponding to smooth initial data, decay at the rate of O (1 / t). Our method of proof hinges upon the appropriate invocation of a relatively recent resolvent criterion for polynomial decays of C0-semigroups. While the characterization provided by said criterion originates in the context of operator theory and functional analysis, the work entailed here is wholly within the realm of PDE.

Quantitative characterization of edge enhancement in phase contrast x-ray imaging.

PubMed

Monnin, P; Bulling, S; Hoszowska, J; Valley, J F; Meuli, R; Verdun, F R

2004-06-01

The aim of this study was to model the edge enhancement effect in in-line holography phase contrast imaging. A simple analytical approach was used to quantify refraction and interference contrasts in terms of beam energy and imaging geometry. The model was applied to predict the peak intensity and frequency of the edge enhancement for images of cylindrical fibers. The calculations were compared with measurements, and the relationship between the spatial resolution of the detector and the amplitude of the phase contrast signal was investigated. Calculations using the analytical model were in good agreement with experimental results for nylon, aluminum and copper wires of 50 to 240 microm diameter, and with numerical simulations based on Fresnel-Kirchhoff theory. A relationship between the defocusing distance and the pixel size of the image detector was established. This analytical model is a useful tool for optimizing imaging parameters in phase contrast in-line holography, including defocusing distance, detector resolution and beam energy.

Study on the criterion to determine the bottom deployment modes of a coilable mast

NASA Astrophysics Data System (ADS)

Ma, Haibo; Huang, Hai; Han, Jianbin; Zhang, Wei; Wang, Xinsheng

2017-12-01

A practical design criterion that allows the coilable mast bottom to deploy in local coil mode was proposed. The criterion was defined with initial bottom helical angle and obtained by bottom deformation analyses. Discretizing the longerons into short rods, analyses were conducted based on the cylinder assumption and Kirchhoff's kinetic analogy theory. Then, iterative calculations aiming at the bottom four rods were carried out. A critical bottom helical angle was obtained while the angle changing rate equaled to zero. The critical value was defined as a criterion for judgement of bottom deployment mode. Subsequently, micro-gravity deployment tests were carried out and bottom deployment simulations based on finite element method were developed. Through comparisons of bottom helical angles in critical state, the proposed criterion was evaluated and modified, that is, an initial bottom helical angle less than critical value with a design margin of -13.7% could ensure the mast bottom deploying in local coil mode, and further determine a successful local coil deployment of entire coilable mast.

Theoretical analysis of cross-talking signals between counter-streaming electron beams in a vacuum tube oscillator

NASA Astrophysics Data System (ADS)

Shin, Y. M.; Ryskin, N. M.; Won, J. H.; Han, S. T.; Park, G. S.

2006-03-01

The basic theory of cross-talking signals between counter-streaming electron beams in a vacuum tube oscillator consisting of two two-cavity klystron amplifiers reversely coupled through input/output slots is theoretically investigated. Application of Kirchhoff's laws to the coupled equivalent RLC circuit model of the device provides four nonlinear coupled equations, which are the first-order time-delayed differential equations. Analytical solutions obtained through linearization of the equations provide oscillation frequencies and thresholds of four fundamental eigenstates, symmetric/antisymmetric 0/π modes. Time-dependent output signals are numerically analyzed with variation of the beam current, and a self-modulation mechanism and transition to chaos scenario are examined. The oscillator shows a much stronger multistability compared to a delayed feedback klystron oscillator owing to the competitions among more diverse eigenmodes. A fully developed chaos region also appears at a relatively lower beam current, ˜3.5Ist, compared to typical vacuum tube oscillators (10-100Ist), where Ist is a start-oscillation current.

Computer models of complex multiloop branched pipeline systems

NASA Astrophysics Data System (ADS)

Kudinov, I. V.; Kolesnikov, S. V.; Eremin, A. V.; Branfileva, A. N.

2013-11-01

This paper describes the principal theoretical concepts of the method used for constructing computer models of complex multiloop branched pipeline networks, and this method is based on the theory of graphs and two Kirchhoff's laws applied to electrical circuits. The models make it possible to calculate velocities, flow rates, and pressures of a fluid medium in any section of pipeline networks, when the latter are considered as single hydraulic systems. On the basis of multivariant calculations the reasons for existing problems can be identified, the least costly methods of their elimination can be proposed, and recommendations for planning the modernization of pipeline systems and construction of their new sections can be made. The results obtained can be applied to complex pipeline systems intended for various purposes (water pipelines, petroleum pipelines, etc.). The operability of the model has been verified on an example of designing a unified computer model of the heat network for centralized heat supply of the city of Samara.

Assessing the shielding of engine noise by the wings for current aircraft using model predictions and measurements.

PubMed

Vieira, Ana; Snellen, Mirjam; Simons, Dick G

2018-01-01

Reducing aircraft noise is a major issue to be dealt with by the aerospace industry. In addition to lowering noise emissions from the engine and airframe, also the shielding of engine noise by the aircraft is considered as a promising means for reducing the perceived noise on the ground. In literature, noise shielding predictions indicate significant reductions in received noise levels for blended wing body configurations, but also for conventional aircraft with the engines placed above the wings. Little work has been done in assessing these potential shielding effects for full aircraft under real operational conditions. Therefore, in this work, noise shielding for current aircraft is investigated using both measurements and model predictions. The predictions are based on the Kirchhoff integral theory and the Modified Theory of Physical Optics. For the comparison between the predictions and measurements, Twenty Fokker 70 flyovers are considered. The data analysis approach for the extraction of shielding levels for aircraft under these operational conditions is presented. Directly under the flight path, the simulations predict an engine noise shielding of 6 dB overall sound pressure level. This is confirmed by some of the flyover data. On average, the measurements show somewhat lower shielding levels.

A network dynamics approach to chemical reaction networks

NASA Astrophysics Data System (ADS)

van der Schaft, A. J.; Rao, S.; Jayawardhana, B.

2016-04-01

A treatment of a chemical reaction network theory is given from the perspective of nonlinear network dynamics, in particular of consensus dynamics. By starting from the complex-balanced assumption, the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in the chemical reaction network theory, and which directly relates to the thermodynamics and port-Hamiltonian formulation of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This immediately leads to the characterisation of the set of equilibria and their stability. Furthermore, the assumption of complex balancedness is revisited from the point of view of Kirchhoff's matrix tree theorem. Both the form of the dynamics and the deduced behaviour are very similar to consensus dynamics, and provide additional perspectives to the latter. Finally, using the classical idea of extending the graph of chemical complexes by a 'zero' complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action kinetics outflows is given, and a unified framework is provided for structure-preserving model reduction of this important class of open reaction networks.

Calculating cellulose diffraction patterns

USDA-ARS?s Scientific Manuscript database

Although powder diffraction of cellulose is a common experiment, the patterns are not widely understood. The theory is mathematical, there are numerous different crystal forms, and the conventions are not standardized. Experience with IR spectroscopy is not directly transferable. An awful error, tha...

Aircraft noise propagation. [sound diffraction by wings

NASA Technical Reports Server (NTRS)

Hadden, W. J.; Pierce, A. D.

1978-01-01

Sound diffraction experiments conducted at NASA Langley Research Center to study the acoustical implications of the engine over wing configuration (noise-shielding by wing) and to provide a data base for assessing various theoretical approaches to the problem of aircraft noise reduction are described. Topics explored include the theory of sound diffraction around screens and wedges; the scattering of spherical waves by rectangular patches; plane wave diffraction by a wedge with finite impedence; and the effects of ambient flow and distribution sources.

Near-field diffraction from amplitude diffraction gratings: theory, simulation and results

NASA Astrophysics Data System (ADS)

Abedin, Kazi Monowar; Rahman, S. M. Mujibur

2017-08-01

We describe a computer simulation method by which the complete near-field diffract pattern of an amplitude diffraction grating can be generated. The technique uses the method of iterative Fresnel integrals to calculate and generate the diffraction images. Theoretical background as well as the techniques to perform the simulation is described. The program is written in MATLAB, and can be implemented in any ordinary PC. Examples of simulated diffraction images are presented and discussed. The generated images in the far-field where they reduce to Fraunhofer diffraction pattern are also presented for a realistic grating, and compared with the results predicted by the grating equation, which is applicable in the far-field. The method can be used as a tool to teach the complex phenomenon of diffraction in classrooms.

TM surface wave diffraction by a truncated dielectric slab recessed in a perfectly conducting surface. [considering flush mounted space shuttle antenna

NASA Technical Reports Server (NTRS)

Pathak, P. H.; Kouyoumjian, R. G.

1974-01-01

The diffraction of a TM sub o surface wave by a terminated dielectric slab which is flush mounted in a perfectly conducting surface is studied. The incident surface wave gives rise to waves reflected and diffracted by the termination; these reflected and diffracted fields may be expressed in terms of the geometrical theory of diffraction by introducing surface wave reflection and diffraction coefficients which are associated with the termination. In this investigation, the surface wave reflection and diffraction coefficients have been deduced from a formally exact solution to this canonical problem. The solution is obtained by a combination of the generalized scattering matrix technique and function theoretic methods.

Trace for Differential Pencils on a Star-Type Graph

NASA Astrophysics Data System (ADS)

Yang, Chuan-Fu

2013-07-01

In this work, we consider the spectral problem for differential pencils on a star-type graph with a Kirchhoff-type condition in the internal vertex. The regularized trace formula of this operator is established with the contour integration method in complex analysis.

Subreflector extension for improved efficiencies in Cassegrain antennas - GTD/PO analysis. [Geometrical Theory of Diffraction/Physical Optics

NASA Technical Reports Server (NTRS)

Rahmat-Samii, Yahya

1986-01-01

Both offset and symmetric Cassegrain reflector antennas are used in satellite and ground communication systems. It is known that the subreflector diffraction can degrade the performance of these reflectors. A geometrical theory of diffraction/physical optics analysis technique is used to investigate the effects of the extended subreflector, beyond its optical rim, on the reflector efficiency and far-field patterns. Representative numerical results are shown for an offset Cassegrain reflector antenna with different feed illumination tapers and subreflector extensions. It is observed that for subreflector extensions as small as one wavelength, noticeable improvements in the overall efficiencies can be expected. Useful design data are generated for the efficiency curves and far-field patterns.

Modeling thermal infrared (2-14 micrometer) reflectance spectra of frost and snow

NASA Technical Reports Server (NTRS)

Wald, Andrew E.

1994-01-01

Existing theories of radiative transfer in close-packed media assume that each particle scatters independently of its neighbors. For opaque particles, such as are common in the thermal infrared, this assumption is not valid, and these radiative transfer theories will not be accurate. A new method is proposed, called 'diffraction subtraction', which modifies the scattering cross section of close-packed large, opaque spheres to account for the effect of close packing on the diffraction cross section of a scattering particle. This method predicts the thermal infrared reflectance of coarse (greater than 50 micrometers radius), disaggregated granular snow. However, such coarse snow is typically old and metamorphosed, with adjacent grains welded together. The reflectance of such a welded block can be described as partly Fresnel in nature and cannot be predicted using Mie inputs to radiative transfer theory. Owing to the high absorption coefficient of ice in the thermal infrared, a rough surface reflectance model can be used to calculate reflectance from such a block. For very small (less than 50 micrometers), disaggregated particles, it is incorrect in principle to treat diffraction independently of reflection and refraction, and the theory fails. However, for particles larger than 50 micrometers, independent scattering is a valid assumption, and standard radiative transfer theory works.

Spectral stability of shifted states on star graphs

NASA Astrophysics Data System (ADS)

Kairzhan, Adilbek; Pelinovsky, Dmitry E.

2018-03-01

We consider the nonlinear Schrödinger (NLS) equation with the subcritical power nonlinearity on a star graph consisting of N edges and a single vertex under generalized Kirchhoff boundary conditions. The stationary NLS equation may admit a family of solitary waves parameterized by a translational parameter, which we call the shifted states. The two main examples include (i) the star graph with even N under the classical Kirchhoff boundary conditions and (ii) the star graph with one incoming edge and N  -  1 outgoing edges under a single constraint on coefficients of the generalized Kirchhoff boundary conditions. We obtain the general counting results on the Morse index of the shifted states and apply them to the two examples. In the case of (i), we prove that the shifted states with even N ≥slant 4 are saddle points of the action functional which are spectrally unstable under the NLS flow. In the case of (ii), we prove that the shifted states with the monotone profiles in the N  -  1 edges are spectrally stable, whereas the shifted states with non-monotone profiles in the N  -  1 edges are spectrally unstable, the two families intersect at the half-soliton states which are spectrally stable but nonlinearly unstable under the NLS flow. Since the NLS equation on a star graph with shifted states can be reduced to the homogeneous NLS equation on an infinite line, the spectral instability of shifted states is due to the perturbations breaking this reduction. We give a simple argument suggesting that the spectrally stable shifted states in the case of (ii) are nonlinearly unstable under the NLS flow due to the perturbations breaking the reduction to the homogeneous NLS equation.

Layered synthetic microstructures as Bragg diffractors for X rays and extreme ultraviolet - Theory and predicted performance

NASA Technical Reports Server (NTRS)

Underwood, J. H.; Barbee, T. W., Jr.

1981-01-01

The theory of X-ray diffraction by periodic structures is applied to the layered synthetic microstructures (LSMs) made possible by recent developments in thin film technology, and approximate formulas for estimating their performance are presented. A more complete computation scheme based on optical multilayer theory is also described, and it is shown that the diffracting properties may be tailored to specific applications by adjusting the refractive indices and thicknesses of the component layers. The theory may be modified to take account of imperfections in the LMS structure, and the properties of nonperiodic structures thereby computed. Structures with high integrated reflectivity constructed according to the methods defined have potential application in many areas of X-ray or EUV research and instrumentation.

A THREE-DIMENSIONAL AIR FLOW MODEL FOR SOIL VENTING: SUPERPOSITION OF ANLAYTICAL FUNCTIONS

EPA Science Inventory

A three-dimensional computer model was developed for the simulation of the soil-air pressure distribution at steady state and specific discharge vectors during soil venting with multiple wells in unsaturated soil. The Kirchhoff transformation of dependent variables and coordinate...

Finite Element Analysis of Magnetoelastic Plate Problems.

DTIC Science & Technology

1981-08-01

deformation and in the incremental large deformation analysis, respectively. The classical Kirchhoff assumption of the undeformable normal to the midsurface is...current density , is constant across the thickness of the plate and is parallel to the midsurface of the plate; (2) the normal component of the

Thermal infrared remote sensing and Kirchhoff's law: 1. Laboratory measurements

NASA Technical Reports Server (NTRS)

Salisbury, J. W.; Wald, A.; Daria, D. M.

1993-01-01

Kirchoff's Law, as originally conceived, applies only to samples in thermal equilibrium with their surroundings. Most laboratory measurements of emissivity only approach this condition and it never applies in remote sensing applications. In particular, the background is often much cooler than the radiating sample, and this has led to a long controversy about the applicability of Kirchhoff's Law under such conditions. It has also led to field and laboratory measurement techniques that use some form of the 'emissivity box' approach, which surrounds the sample with a background as close as possible to the sample temperature. In our experiments, we have heated soil samples in air on a hot plate in the laboratory to a much higher temperature than the room temperature background. Spectral emissivity was measured, except the known emissivities of both the primary and secondary Christiansen features were used, instead of assuming an emissivity of unity at these wavelengths. The results from this investigation are discussed in brief.

A Study of Supersonic Surface Sources: The Ffowcs Williams-Hawkings Equation and the Kirchhoff Formula

NASA Technical Reports Server (NTRS)

Farassat, F.; Brentner, Kenneth S.; Dunn, M. H.

2004-01-01

In this paper we address the mathematical problem of noise generation from high speed moving surfaces. The problem we are solving is the linear wave equation with sources on a moving surface. The Ffowcs Williams-Hawkings (FW-H) equation as well as the govern- ing equation for deriving the Kirchhoff formula for moving surfaces are both this type of partial differential equation. We give a new exact solution of this problem here in closed form which is valid for subsonic and supersonic motion of the surface but it is particularly suitable for supersonically moving surfaces. This new solution is the simplest of all high speed formulations of Langley and is denoted formulation 4 following the tradition of numbering of our major results for the prediction of the noise of rotating blades. We show that for a smooth surface moving at supersonic speed, our solution has only removable singularities. Thus it can be used for numerical work.

Cycle/Cocycle Oblique Projections on Oriented Graphs

NASA Astrophysics Data System (ADS)

Polettini, Matteo

2015-01-01

It is well known that the edge vector space of an oriented graph can be decomposed in terms of cycles and cocycles (alias cuts, or bonds), and that a basis for the cycle and the cocycle spaces can be generated by adding and removing edges to an arbitrarily chosen spanning tree. In this paper, we show that the edge vector space can also be decomposed in terms of cycles and the generating edges of cocycles (called cochords), or of cocycles and the generating edges of cycles (called chords). From this observation follows a construction in terms of oblique complementary projection operators. We employ this algebraic construction to prove several properties of unweighted Kirchhoff-Symanzik matrices, encoding the mutual superposition between cycles and cocycles. In particular, we prove that dual matrices of planar graphs have the same spectrum (up to multiplicities). We briefly comment on how this construction provides a refined formalization of Kirchhoff's mesh analysis of electrical circuits, which has lately been applied to generic thermodynamic networks.

Numerical simulation of mushrooms during freezing using the FEM and an enthalpy: Kirchhoff formulation

NASA Astrophysics Data System (ADS)

Santos, M. V.; Lespinard, A. R.

2011-12-01

The shelf life of mushrooms is very limited since they are susceptible to physical and microbial attack; therefore they are usually blanched and immediately frozen for commercial purposes. The aim of this work was to develop a numerical model using the finite element technique to predict freezing times of mushrooms considering the actual shape of the product. The original heat transfer equation was reformulated using a combined enthalpy-Kirchhoff formulation, therefore an own computational program using Matlab 6.5 (MathWorks, Natick, Massachusetts) was developed, considering the difficulties encountered when simulating this non-linear problem in commercial softwares. Digital images were used to generate the irregular contour and the domain discretization. The numerical predictions agreed with the experimental time-temperature curves during freezing of mushrooms (maximum absolute error <3.2°C) obtaining accurate results and minimum computer processing times. The codes were then applied to determine required processing times for different operating conditions (external fluid temperatures and surface heat transfer coefficients).

Monopolar vortices as relative equilibria and their dissipative decay

NASA Astrophysics Data System (ADS)

Vandefliert, B. W.; Vangroesen, E. W. C.

1991-11-01

Families of confined rotating monopolar vortices are characterized using a variational formulation with the angular momentum as the driving force for confinement. The characterization for positive monopolar vortices given, can be extended to negative vortices or to vortices within a rotating frame of reference. Besides the uniform Kirchhoff paths, new branches of vorticity solutions are found restricting the dynamics to levelsets of both the angular momentum and the quadratic anisotropy. The rotation rate of the smooth vorticity structures depends on the vorticity profile. This is made perceptible by considering both minimum energy vortices and minimizing vortices, rotating counterclockwise and clockwise respectively. An approximation for the decay of the vortices due to dissipation is given in terms of the dissipation of the integrals in the inviscid system. This description enables us to consider dissipation of vortices without loss of confinement. The elliptical Kirchhoff patches are found to symmetrize into circular patches. The minimum energy vortices gradually diminish while expending their support, while the maximum energy vortices are unstable for the dissipative evolution.

Experimental method for testing diffraction properties of reflection waveguide holograms.

PubMed

Xie, Yi; Kang, Ming-Wu; Wang, Bao-Ping

2014-07-01

Waveguide holograms' diffraction properties include peak wavelength and diffraction efficiency, which play an important role in determining their display performance. Based on the record and reconstruction theory of reflection waveguide holograms, a novel experimental method for testing diffraction properties is introduced and analyzed in this paper, which uses a plano-convex lens optically contacted to the surface of the substrate plate of the waveguide hologram, so that the diffracted light beam can be easily detected. Then an experiment is implemented. The designed reconstruction wavelength of the test sample is 530 nm, and its diffraction efficiency is 100%. The experimental results are a peak wavelength of 527.7 nm and a diffraction efficiency of 94.1%. It is shown that the tested value corresponds well with the designed value.

History and Solution of the Phase Problem in theTheory of Structure Determination of Crystals from X-ray Diffraction Experiments

ScienceCinema

Wolf, Emil [University of Rochester, Rochester, New York, United States

2017-12-09

Since the pioneering work of Max von Laue on interference and diffraction of x-rays, carried out almost 100 years ago, numerous attempts have been made to determine structures of crystalline media from x-ray diffraction experiments. The usefulness of all of them has been limited by the inability of measuring phases of the diffracted beams. In this talk, the most important research carried out in this field will be reviewed and a recently obtained solution of the phase problem will be presented.

An amplitude and phase hybrid modulation Fresnel diffractive optical element

NASA Astrophysics Data System (ADS)

Li, Fei; Cheng, Jiangao; Wang, Mengyu; Jin, Xueying; Wang, Keyi

2018-04-01

An Amplitude and Phase Hybrid Modulation Fresnel Diffractive Optical Element (APHMFDOE) is proposed here. We have studied the theory of APHMFDOE and simulated the focusing properties of it along the optical axis, which show that the focus can be blazed to other positions with changing the quadratic phase factor. Moreover, we design a Composite Fresnel Diffraction Optical Element (CFDOE) based on the characteristics of APHMFDOE. It greatly increases the outermost zone width without changing the F-number, which brings a lot of benefits to the design and processing of diffraction device. More importantly, the diffraction efficiency of the CFDOE is almost unchanged compared with AFZP at the same focus.

Two-photon x-ray diffraction

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

Stohr, J.

The interference pattern of a circular photon source has long been used to define the optical diffraction limit. Here we show the breakdown of conventional x-ray diffraction theory for the fundamental case of a “source”, consisting of a back-illuminated thin film in a circular aperture. When the conventional spontaneous x-ray scattering by atoms in the film is replaced at high incident intensity by stimulated resonant scattering, the film becomes the source of cloned photon twins and the diffraction pattern becomes self-focused beyond the diffraction limit. Furthermore, the case of cloned photon pairs is compared to and distinguished from entangled photonmore » pairs or biphotons.« less

Two-photon x-ray diffraction

DOE PAGES

Stohr, J.

2017-01-11

The interference pattern of a circular photon source has long been used to define the optical diffraction limit. Here we show the breakdown of conventional x-ray diffraction theory for the fundamental case of a “source”, consisting of a back-illuminated thin film in a circular aperture. When the conventional spontaneous x-ray scattering by atoms in the film is replaced at high incident intensity by stimulated resonant scattering, the film becomes the source of cloned photon twins and the diffraction pattern becomes self-focused beyond the diffraction limit. Furthermore, the case of cloned photon pairs is compared to and distinguished from entangled photonmore » pairs or biphotons.« less

Development of a diffraction imaging flow cytometer

PubMed Central

Jacobs, Kenneth M.; Lu, Jun Q.

2013-01-01

Diffraction images record angle-resolved distribution of scattered light from a particle excited by coherent light and can correlate highly with the 3D morphology of a particle. We present a jet-in-fluid design of flow chamber for acquisition of clear diffraction images in a laminar flow. Diffraction images of polystyrene spheres of different diameters were acquired and found to correlate highly with the calculated ones based on the Mie theory. Fast Fourier transform analysis indicated that the measured images can be used to extract sphere diameter values. These results demonstrate the significant potentials of high-throughput diffraction imaging flow cytometry for extracting 3D morphological features of cells. PMID:19794790

X-ray nanofocusing by kinoform lenses: A comparative study using different modeling approaches

NASA Astrophysics Data System (ADS)

Yan, Hanfei

2010-02-01

We conduct a comparative study on various kinoform lenses (KLs) for x-ray nanofocusing by using the geometrical theory, the dynamical diffraction theory, and the beam propagation method. This study shows that the geometrical theory becomes invalid to describe the performance of a KL for nanofocusing. The strong edge diffraction effect from individual lens element, which distorts the desired wave field, leads to a reduction in the effective numerical aperture and imposes a limit on how small a focus a KL can achieve. Because this effect is associated with a finite thickness of a lens, larger lens thickness depicts a stronger distortion. We find that a short KL where all lens elements are folded back to a single plane shows an illumination preference: if the illuminating geometry is in favor of the Bragg diffraction for a focusing order, its performance is enhanced and vice versa. We also find that a short KL usually outperforms its long version where all lens elements do not lie in a single plane because the short one suffers less the wave field distortion due to the edge diffraction. Simulation results suggest that for a long KL, an adaptive lens design is needed to correct the wave field distortion in order to achieve a better performance.

Optical Crystals

ERIC Educational Resources Information Center

Bergsten, Ronald

1974-01-01

Discusses the production and structure of a sequence of optical crystals which can serve as one-, two-, and three-dimensional diffraction plates to illustrate diffraction patterns by using light rather than x-rays or particles. Applications to qualitative presentations of Laue theory at the secondary and college levels are recommended. (CC)

Readout signals calculated for near-field optical pickups with land and groove recording.

PubMed

Saito, K; Kishima, K; Ichimura, I

2000-08-10

Optical disk readout signals with a solid immersion lens (SIL) and the land-groove recording technique are calculated by use of a simplified vector-diffraction theory. In this method the full vector-diffraction theory is applied to calculate the diffracted light from the initial state of the disk, and the light scattered from the recorded marks is regarded as a perturbation. Using this method, we confirmed that the land-groove recording technique is effective as a means of cross-talk reduction even when the numerical aperture is more than 1. However, the top surface of the disk under the SIL must be flat, or the readout signal from marks recorded on a groove decays when the optical depth of the groove is greater than lambda/8.

On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach

NASA Astrophysics Data System (ADS)

Gerstmayr, Johannes; Irschik, Hans

2008-12-01

In finite element methods that are based on position and slope coordinates, a representation of axial and bending deformation by means of an elastic line approach has become popular. Such beam and plate formulations based on the so-called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories. Examining the existing planar absolute nodal coordinate element, which uses a curvature proportional bending strain expression, it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and, even more serious, the normal force is incorrect. A correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived. The strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the St. Venant-Kirchhoff material: therefore, the strain energy is derived for the latter case and compared to classical nonlinear rod theories. The error in the original absolute nodal coordinate formulation is documented by numerical examples. The numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach, while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications. The numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre-curved static and dynamic problems, including buckling and eigenvalue analysis. The resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy-momentum conservation.

Statistical Limits to Super Resolution

NASA Astrophysics Data System (ADS)

Lucy, L. B.

1992-08-01

The limits imposed by photon statistics on the degree to which Rayleigh's resolution limit for diffraction-limited images can be surpassed by applying image restoration techniques are investigated. An approximate statistical theory is given for the number of detected photons required in the image of an unresolved pair of equal point sources in order that its information content allows in principle resolution by restoration. This theory is confirmed by numerical restoration experiments on synthetic images, and quantitative limits are presented for restoration of diffraction-limited images formed by slit and circular apertures.

Time-domain model of gyroklystrons with diffraction power input and output

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

Ginzburg, N. S., E-mail: ginzburg@appl.sci-nnov.ru; Rozental, R. M.; Sergeev, A. S.

A time-domain theory of gyroklystrons with diffraction input and output has been developed. The theory is based on the description of the wave excitation and propagation by a parabolic equation. The results of the simulations are in good agreement with the experimental studies of two-cavity gyroklystrons operating at the first and second cyclotron harmonics. Along with the basic characteristics of the amplification regimes, such as the gain and efficiency, the developed method makes it possible to define the conditions of spurious self-excitation and frequency-locking by an external signal.

Optical Simulation of Debye-Scherrer Crystal Diffraction

ERIC Educational Resources Information Center

Logiurato, F.; Gratton, L. M.; Oss, S.

2008-01-01

In this paper we describe and discuss simple, inexpensive optical experiments used to simulate x-ray and electron diffraction according to the Debye-Scherrer theory. The experiment can be used to address, at the high school level, important subjects related to fundamental quantum and solid-state physics.

Diffraction-induced instability of coupled dark solitary waves.

PubMed

Assanto, Gaetano; MacNeil, J Michael L; Smyth, Noel F

2015-04-15

We report on a novel instability arising from the propagation of coupled dark solitary beams governed by coupled defocusing nonlinear Schrödinger equations. Considering dark notches on backgrounds with different wavelengths, hence different diffraction coefficients, we find that the vector dark soliton solution is unstable to radiation modes. Using perturbation theory and numerical integration, we demonstrate that the component undergoing stronger diffraction radiates away, leaving a single dark soliton in the other mode/wavelength.

Circuits in the Sun: Solar Panel Physics

ERIC Educational Resources Information Center

Gfroerer, Tim

2013-01-01

Typical commercial solar panels consist of approximately 60 individual photovoltaic cells connected in series. Since the usual Kirchhoff rules apply, the current is uniform throughout the circuit, while the electric potential of the individual devices is cumulative. Hence, a solar panel is a good analog of a simple resistive series circuit, except…

Networking in the Presence of Adversaries

DTIC Science & Technology

2014-09-12

a topological graph with linear algebraic constraints. As a practical example, such a model arises from an electric power system in which the power...flow is governed by the Kirchhoff law. When an adversary launches an MiM data attack, part of the sensor data are intercepted and substituted with

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

NASA Astrophysics Data System (ADS)

Koshkarbayev, Nurbol; Kanguzhin, Baltabek

2017-09-01

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

Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram

ERIC Educational Resources Information Center

Hanley, Quentin S.

2012-01-01

Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…

Dynamical scattering in coherent hard x-ray nanobeam Bragg diffraction

NASA Astrophysics Data System (ADS)

Pateras, A.; Park, J.; Ahn, Y.; Tilka, J. A.; Holt, M. V.; Kim, H.; Mawst, L. J.; Evans, P. G.

2018-06-01

Unique intensity features arising from dynamical diffraction arise in coherent x-ray nanobeam diffraction patterns of crystals having thicknesses larger than the x-ray extinction depth or exhibiting combinations of nanoscale and mesoscale features. We demonstrate that dynamical scattering effects can be accurately predicted using an optical model combined with the Darwin theory of dynamical x-ray diffraction. The model includes the highly divergent coherent x-ray nanobeams produced by Fresnel zone plate focusing optics and accounts for primary extinction, multiple scattering, and absorption. The simulation accurately reproduces the dynamical scattering features of experimental diffraction patterns acquired from a GaAs/AlGaAs epitaxial heterostructure on a GaAs (001) substrate.

High-frequency techniques for RCS prediction of plate geometries

NASA Technical Reports Server (NTRS)

Balanis, Constantine A.; Polka, Lesley A.

1992-01-01

The principal-plane scattering from perfectly conducting and coated strips and rectangular plates is examined. Previous reports have detailed Geometrical Theory of Diffraction/Uniform Theory of Diffraction (GTD/UTD) solutions for these geometries. The GTD/UTD solution for the perfectly conducting plate yields monostatic radar cross section (RCS) results that are nearly identical to measurements and results obtained using the Moment Method (MM) and the Extended Physical Theory of Diffraction (EPTD). This was demonstrated in previous reports. The previous analysis is extended to bistatic cases. GTD/UTD results for the principal-plane scattering from a perfectly conducting, infinite strip are compared to MM and EPTD data. A comprehensive overview of the advantages and disadvantages of the GTD/UTD and of the EPTD and a detailed analysis of the results from both methods are provided. Several previous reports also presented preliminary discussions and results for a GTD/UTD model of the RCS of a coated, rectangular plate. Several approximations for accounting for the finite coating thickness, plane-wave incidence, and far-field observation were discussed. Here, these approximations are replaced by a revised wedge diffraction coefficient that implicitly accounts for a coating on a perfect conductor, plane-wave incidence, and far-field observation. This coefficient is computationally more efficient than the previous diffraction coefficient because the number of Maliuzhinets functions that must be calculated using numerical integration is reduced by a factor of 2. The derivation and the revised coefficient are presented in detail for the hard polarization case. Computations and experimental data are also included. The soft polarization case is currently under investigation.

A uniform GTD analysis of the EM diffraction by a thin dielectric/ferrite half-plane and related configurations

NASA Technical Reports Server (NTRS)

Rojas, Roberto G.

1985-01-01

A uniform geometrical theory of diffraction (UTD) solution is developed for the problem of the diffraction by a thin dielectric/ferrite half plane when it is excited by a plane, cylindrical, or surface wave field. Both transverse electric and transverse magnetic cases are considered. The solution of this problem is synthesized from the solutions to the related problems of EM diffraction by configurations involving perfectly conducting electric and magnetic walls covered by a dielectric/ferrite half-plane of one half the thickness of the original half-plane.

How many photons are needed to reconstruct random objects in coherent X-ray diffractive imaging?

PubMed

Jahn, T; Wilke, R N; Chushkin, Y; Salditt, T

2017-01-01

This paper presents an investigation of the reconstructibility of coherent X-ray diffractive imaging diffraction patterns for a class of binary random `bitmap' objects. Combining analytical results and numerical simulations, the critical fluence per bitmap pixel is determined, for arbitrary contrast values (absorption level and phase shift), both for the optical near- and far-field. This work extends previous investigations based on information theory, enabling a comparison of the amount of information carried by single photons in different diffraction regimes. The experimental results show an order-of-magnitude agreement.

Diffraction-assisted micropatterning of silicon surfaces by ns-laser irradiation

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

Haro-Poniatowski, E., E-mail: haro@xanum.uam.mx; Acosta-Zepeda, C.; Mecalco, G.

2014-06-14

Single-pulse (532 nm, 8 ns) micropatterning of silicon with nanometric surface modulation is demonstrated by irradiating through a diffracting pinhole. The irradiation results obtained at fluences above the melting threshold are characterized by scanning electron and scanning force microscopy and reveal a good agreement with Fresnel diffraction theory. The physical mechanism is identified and discussed on basis of both thermocapillary and chemicapillary induced material transport during the molten state of the surface.

Development of attenuation and diffraction corrections for linear and nonlinear Rayleigh surface waves radiating from a uniform line source

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

Jeong, Hyunjo, E-mail: hjjeong@wku.ac.kr; Cho, Sungjong; Zhang, Shuzeng

2016-04-15

In recent studies with nonlinear Rayleigh surface waves, harmonic generation measurements have been successfully employed to characterize material damage and microstructural changes, and found to be sensitive to early stages of damage process. A nonlinearity parameter of Rayleigh surface waves was derived and frequently measured to quantify the level of damage. The accurate measurement of the nonlinearity parameter generally requires making corrections for beam diffraction and medium attenuation. These effects are not generally known for nonlinear Rayleigh waves, and therefore not properly considered in most of previous studies. In this paper, the nonlinearity parameter for a Rayleigh surface wave ismore » defined from the plane wave displacement solutions. We explicitly define the attenuation and diffraction corrections for fundamental and second harmonic Rayleigh wave beams radiated from a uniform line source. Attenuation corrections are obtained from the quasilinear theory of plane Rayleigh wave equations. To obtain closed-form expressions for diffraction corrections, multi-Gaussian beam (MGB) models are employed to represent the integral solutions derived from the quasilinear theory of the full two-dimensional wave equation without parabolic approximation. Diffraction corrections are presented for a couple of transmitter-receiver geometries, and the effects of making attenuation and diffraction corrections are examined through the simulation of nonlinearity parameter determination in a solid sample.« less

Working With the Wave Equation in Aeroacoustics: The Pleasures of Generalized Functions

NASA Technical Reports Server (NTRS)

Farassat, F.; Brentner, Kenneth S.; Dunn, mark H.

2007-01-01

The theme of this paper is the applications of generalized function (GF) theory to the wave equation in aeroacoustics. We start with a tutorial on GFs with particular emphasis on viewing functions as continuous linear functionals. We next define operations on GFs. The operation of interest to us in this paper is generalized differentiation. We give many applications of generalized differentiation, particularly for the wave equation. We discuss the use of GFs in finding Green s function and some subtleties that only GF theory can clarify without ambiguities. We show how the knowledge of the Green s function of an operator L in a given domain D can allow us to solve a whole range of problems with operator L for domains situated within D by the imbedding method. We will show how we can use the imbedding method to find the Kirchhoff formulas for stationary and moving surfaces with ease and elegance without the use of the four-dimensional Green s theorem, which is commonly done. Other subjects covered are why the derivatives in conservation laws should be viewed as generalized derivatives and what are the consequences of doing this. In particular we show how we can imbed a problem in a larger domain for the identical differential equation for which the Green s function is known. The primary purpose of this paper is to convince the readers that GF theory is absolutely essential in aeroacoustics because of its powerful operational properties. Furthermore, learning the subject and using it can be fun.

A non-classical Mindlin plate model incorporating microstructure, surface energy and foundation effects.

PubMed

Gao, X-L; Zhang, G Y

2016-07-01

A non-classical model for a Mindlin plate resting on an elastic foundation is developed in a general form using a modified couple stress theory, a surface elasticity theory and a two-parameter Winkler-Pasternak foundation model. It includes all five kinematic variables possible for a Mindlin plate. The equations of motion and the complete boundary conditions are obtained simultaneously through a variational formulation based on Hamilton's principle, and the microstructure, surface energy and foundation effects are treated in a unified manner. The newly developed model contains one material length-scale parameter to describe the microstructure effect, three surface elastic constants to account for the surface energy effect, and two foundation parameters to capture the foundation effect. The current non-classical plate model reduces to its classical elasticity-based counterpart when the microstructure, surface energy and foundation effects are all suppressed. In addition, the new model includes the Mindlin plate models considering the microstructure dependence or the surface energy effect or the foundation influence alone as special cases, recovers the Kirchhoff plate model incorporating the microstructure, surface energy and foundation effects, and degenerates to the Timoshenko beam model including the microstructure effect. To illustrate the new Mindlin plate model, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulae derived.

A non-classical Mindlin plate model incorporating microstructure, surface energy and foundation effects

PubMed Central

Zhang, G. Y.

2016-01-01

A non-classical model for a Mindlin plate resting on an elastic foundation is developed in a general form using a modified couple stress theory, a surface elasticity theory and a two-parameter Winkler–Pasternak foundation model. It includes all five kinematic variables possible for a Mindlin plate. The equations of motion and the complete boundary conditions are obtained simultaneously through a variational formulation based on Hamilton's principle, and the microstructure, surface energy and foundation effects are treated in a unified manner. The newly developed model contains one material length-scale parameter to describe the microstructure effect, three surface elastic constants to account for the surface energy effect, and two foundation parameters to capture the foundation effect. The current non-classical plate model reduces to its classical elasticity-based counterpart when the microstructure, surface energy and foundation effects are all suppressed. In addition, the new model includes the Mindlin plate models considering the microstructure dependence or the surface energy effect or the foundation influence alone as special cases, recovers the Kirchhoff plate model incorporating the microstructure, surface energy and foundation effects, and degenerates to the Timoshenko beam model including the microstructure effect. To illustrate the new Mindlin plate model, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulae derived. PMID:27493578

Acoustical tweezers using single spherically focused piston, X-cut, and Gaussian beams.

PubMed

Mitri, Farid G

2015-10-01

Partial-wave series expansions (PWSEs) satisfying the Helmholtz equation in spherical coordinates are derived for circular spherically focused piston (i.e., apodized by a uniform velocity amplitude normal to its surface), X-cut (i.e., apodized by a velocity amplitude parallel to the axis of wave propagation), and Gaussian (i.e., apodized by a Gaussian distribution of the velocity amplitude) beams. The Rayleigh-Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions are used to obtain the PWSEs assuming weakly focused beams (with focusing angle α ⩽ 20°) in the Fresnel-Kirchhoff (parabolic) approximation. In contrast with previous analytical models, the derived expressions allow computing the scattering and acoustic radiation force from a sphere of radius a without restriction to either the Rayleigh (a ≪ λ, where λ is the wavelength of the incident radiation) or the ray acoustics (a ≫λ) regimes. The analytical formulations are valid for wavelengths largely exceeding the radius of the focused acoustic radiator, when the viscosity of the surrounding fluid can be neglected, and when the sphere is translated along the axis of wave propagation. Computational results illustrate the analysis with particular emphasis on the sphere's elastic properties and the axial distance to the center of the concave surface, with close connection of the emergence of negative trapping forces. Potential applications are in single-beam acoustical tweezers, acoustic levitation, and particle manipulation.

Effects of the symmetry axis orientation of a TI overburden on seismic images

NASA Astrophysics Data System (ADS)

Chang, Chih-Hsiung; Chang, Young-Fo; Tseng, Cheng-Wei

2017-07-01

In active tectonic regions, the primary formations are often tilted and subjected to the processes of folding and/or faulting. Dipping formations may be categorised as tilted transverse isotropy (TTI). While carrying out hydrocarbon exploration in areas of orogenic structures, mispositioning and defocusing effects in apparent reflections are often caused by the tilted transverse isotropy of the overburden. In this study, scaled physical modelling was carried out to demonstrate the behaviours of seismic wave propagation and imaging problems incurred by transverse isotropic (TI) overburdens that possess different orientations of the symmetry axis. To facilitate our objectives, zero-offset reflections were acquired from four stratum-fault models to image the same structures that were overlain by a TI (phenolite) slab. The symmetry axis of the TI slab was vertical, tilted or horizontal. In response to the symmetry axis orientations, spatial shifts and asymmetrical diffraction patterns in apparent reflections were observed in the acquired profiles. Given the different orientations of the symmetry axis, numerical manipulations showed that the imaged events could be well described by theoretical ray paths computed by the trial-and-error ray method and Fermat's principle (TERF) method. In addition, outputs of image restoration show that the imaging problems, i.e. spatial shift in the apparent reflections, can be properly handled by the ray-based anisotropic 2D Kirchhoff time migration (RAKTM) method.

Diffractive Scattering and Gauge/String Duality

ScienceCinema

Tan, Chung-I

2018-05-11

High-energy diffractive scattering will be discussed based on Gauge/String duality. As shown by Brower, Polchinski, Strassler and Tan, the ubiquitous Pomeron emerges naturally in gauge theories with string-theoretical descriptions. Its existence is intimately tied to gluons, and also to the energy-momentum tensor. With a confining dual background metric, the Pomeron can be interpreted as a 'massive graviton'. In a single unified step, both its infrared and ultraviolet properties are dealt with, reflecting confinement and conformal symmetry respectively. An effective field theory for high-energy scattering can be constructed. Applications based on this approach will also be described.

An application of the Braunbeck method to the Maggi-Rubinowicz field representation

NASA Technical Reports Server (NTRS)

Meneghini, R.

1982-01-01

The Braunbek method is applied to the generalized vector potential associated with the Maggi-rubinowicz representation. Under certain approximations, an asymptotic evaluation of the vector potential is obtained. For observation points away from caustics or shadow boundaries, the field derived from this quantity is the same as that determined from the geometrical theory of diffraction on a singly diffracted edge ray. An evaluation of the field for the simple case of a plane wave normally incident on a circular aperture is presented showing that the field predicted by the Maggi-Rubinowicz theory is continuous across the shadow boundary.

An application of the Braunbeck method to the Maggi-Rubinowicz field representation

NASA Astrophysics Data System (ADS)

Meneghini, R.

1982-06-01

The Braunbek method is applied to the generalized vector potential associated with the Maggi-rubinowicz representation. Under certain approximations, an asymptotic evaluation of the vector potential is obtained. For observation points away from caustics or shadow boundaries, the field derived from this quantity is the same as that determined from the geometrical theory of diffraction on a singly diffracted edge ray. An evaluation of the field for the simple case of a plane wave normally incident on a circular aperture is presented showing that the field predicted by the Maggi-Rubinowicz theory is continuous across the shadow boundary.

Dynamic diffraction effects and coherent breathing oscillations in ultrafast electron diffraction in layered 1T-TaSeTe

PubMed Central

Wei, Linlin; Sun, Shuaishuai; Guo, Cong; Li, Zhongwen; Sun, Kai; Liu, Yu; Lu, Wenjian; Sun, Yuping; Tian, Huanfang; Yang, Huaixin; Li, Jianqi

2017-01-01

Anisotropic lattice movements due to the difference between intralayer and interlayer bonding are observed in the layered transition-metal dichalcogenide 1T-TaSeTe following femtosecond laser pulse excitation. Our ultrafast electron diffraction investigations using 4D-transmission electron microscopy (4D-TEM) clearly reveal that the intensity of Bragg reflection spots often changes remarkably due to the dynamic diffraction effects and anisotropic lattice movement. Importantly, the temporal diffracted intensity from a specific crystallographic plane depends on the deviation parameter s, which is commonly used in the theoretical study of diffraction intensity. Herein, we report on lattice thermalization and structural oscillations in layered 1T-TaSeTe, analyzed by dynamic diffraction theory. Ultrafast alterations of satellite spots arising from the charge density wave in the present system are also briefly discussed. PMID:28470025

Fourier optics analysis of grating sensors with tilt errors.

PubMed

Ferhanoglu, Onur; Toy, M Fatih; Urey, Hakan

2011-06-15

Dynamic diffraction gratings can be microfabricated with precision and offer extremely sensitive displacement measurements and light intensity modulation. The effect of pure translation of the moving part of the grating on diffracted order intensities is well known. This study focuses on the parameters that limit the intensity and the contrast of the interference. The effects of grating duty cycle, mirror reflectivities, sensor tilt and detector size are investigated using Fourier optics theory and Gaussian beam optics. Analytical findings reveal that fringe visibility becomes <0.3 when the optical path variation exceeds half the wavelength within the grating interferometer. The fringe visibility can be compensated by monitoring the interfering portion of the diffracted order light only through detector size reduction in the expense of optical power. Experiments were conducted with a grating interferometer that resulted in an eightfold increase in fringe visibility with reduced detector size, which is in agreement with theory. Findings show that diffraction grating readout principle is not limited to translating sensors but also can be used for sensors with tilt or other deflection modes.

Structural dynamics of surfaces by ultrafast electron crystallography: experimental and multiple scattering theory.

PubMed

Schäfer, Sascha; Liang, Wenxi; Zewail, Ahmed H

2011-12-07

Recent studies in ultrafast electron crystallography (UEC) using a reflection diffraction geometry have enabled the investigation of a wide range of phenomena on the femtosecond and picosecond time scales. In all these studies, the analysis of the diffraction patterns and their temporal change after excitation was performed within the kinematical scattering theory. In this contribution, we address the question, to what extent dynamical scattering effects have to be included in order to obtain quantitative information about structural dynamics. We discuss different scattering regimes and provide diffraction maps that describe all essential features of scatterings and observables. The effects are quantified by dynamical scattering simulations and examined by direct comparison to the results of ultrafast electron diffraction experiments on an in situ prepared Ni(100) surface, for which structural dynamics can be well described by a two-temperature model. We also report calculations for graphite surfaces. The theoretical framework provided here allows for further UEC studies of surfaces especially at larger penetration depths and for those of heavy-atom materials. © 2011 American Institute of Physics

Uniform Geometrical Theory of Diffraction

DTIC Science & Technology

1987-06-01

synbolically by 6 0’A) elb + nrn] P e ( 55 )S... j.+sr),(.psr) where the points 0 and 0 and the distances sr and sd are indicated in Figure 10. The surface...diffracted ray caustic distance P5 iN shown in Figure 11. The quantities within brackets involving and.Cr In ( 55 ) ands~ 9A A (56) may be viewed as...gereralized dyadic coefficients for surface reflection and diffraction. respectively. It is noted that ( 55 ) and (56) are expressed inWariantly in terms of

The Gauss-Bonnet operator of an infinite graph

NASA Astrophysics Data System (ADS)

Anné, Colette; Torki-Hamza, Nabila

2015-06-01

We propose a general condition, to ensure essential self-adjointness for the Gauss-Bonnet operator , based on a notion of completeness as Chernoff. This gives essential self-adjointness of the Laplace operator both for functions and 1-forms on infinite graphs. This is used to extend Flanders result concerning solutions of Kirchhoff's laws.

The Impact of a Common MDM2 SNP on the Sensitivity of Breast Cancer to Treatment

DTIC Science & Technology

2011-06-01

Kirchhoff T, Alexe G, Bond EE, Robins H, Bartel F, Taubert H, Wuerl P, Hait W, Toppmeyer D, Offit K, and Levine A. MDM2 SNP309 accelerates tumor...the Western blot analysis corresponding to the quantification in the upper graphs . 29 Figure 5. Effect of

Scattering from very rough layers under the geometric optics approximation: further investigation.

PubMed

Pinel, Nicolas; Bourlier, Christophe

2008-06-01

Scattering from very rough homogeneous layers is studied in the high-frequency limit (under the geometric optics approximation) by taking the shadowing effect into account. To do so, the iterated Kirchhoff approximation, recently developed by Pinel et al. [Waves Random Complex Media17, 283 (2007)] and reduced to the geometric optics approximation, is used and investigated in more detail. The contributions from the higher orders of scattering inside the rough layer are calculated under the iterated Kirchhoff approximation. The method can be applied to rough layers of either very rough or perfectly flat lower interfaces, separating either lossless or lossy media. The results are compared with the PILE (propagation-inside-layer expansion) method, recently developed by Déchamps et al. [J. Opt. Soc. Am. A23, 359 (2006)], and accelerated by the forward-backward method with spectral acceleration. They highlight that there is very good agreement between the developed method and the reference numerical method for all scattering orders and that the method can be applied to root-mean-square (RMS) heights at least down to 0.25lambda.

3D receiver function Kirchhoff depth migration image of Cascadia subduction slab weak zone

NASA Astrophysics Data System (ADS)

Cheng, C.; Allen, R. M.; Bodin, T.; Tauzin, B.

2016-12-01

We have developed a highly computational efficient algorithm of applying 3D Kirchhoff depth migration to telesismic receiver function data. Combine primary PS arrival with later multiple arrivals we are able to reveal a better knowledge about the earth discontinuity structure (transmission and reflection). This method is highly useful compare with traditional CCP method when dipping structure is met during the imaging process, such as subduction slab. We apply our method to the reginal Cascadia subduction zone receiver function data and get a high resolution 3D migration image, for both primary and multiples. The image showed us a clear slab weak zone (slab hole) in the upper plate boundary under Northern California and the whole Oregon. Compare with previous 2D receiver function image from 2D array(CAFE and CASC93), the position of the weak zone shows interesting conherency. This weak zone is also conherent with local seismicity missing and heat rising, which lead us to think about and compare with the ocean plate stucture and the hydralic fluid process during the formation and migration of the subduction slab.

Isogeometric Kirchhoff-Love shell formulations for biological membranes

PubMed Central

Tepole, Adrián Buganza; Kabaria, Hardik; Bletzinger, Kai-Uwe; Kuhl, Ellen

2015-01-01

Computational modeling of thin biological membranes can aid the design of better medical devices. Remarkable biological membranes include skin, alveoli, blood vessels, and heart valves. Isogeometric analysis is ideally suited for biological membranes since it inherently satisfies the C1-requirement for Kirchhoff-Love kinematics. Yet, current isogeometric shell formulations are mainly focused on linear isotropic materials, while biological tissues are characterized by a nonlinear anisotropic stress-strain response. Here we present a thin shell formulation for thin biological membranes. We derive the equilibrium equations using curvilinear convective coordinates on NURBS tensor product surface patches. We linearize the weak form of the generic linear momentum balance without a particular choice of a constitutive law. We then incorporate the constitutive equations that have been designed specifically for collagenous tissues. We explore three common anisotropic material models: Mooney-Rivlin, May Newmann-Yin, and Gasser-Ogden-Holzapfel. Our work will allow scientists in biomechanics and mechanobiology to adopt the constitutive equations that have been developed for solid three-dimensional soft tissues within the framework of isogeometric thin shell analysis. PMID:26251556

Stabilization of time domain acoustic boundary element method for the exterior problem avoiding the nonuniqueness.

PubMed

Jang, Hae-Won; Ih, Jeong-Guon

2013-03-01

The time domain boundary element method (TBEM) to calculate the exterior sound field using the Kirchhoff integral has difficulties in non-uniqueness and exponential divergence. In this work, a method to stabilize TBEM calculation for the exterior problem is suggested. The time domain CHIEF (Combined Helmholtz Integral Equation Formulation) method is newly formulated to suppress low order fictitious internal modes. This method constrains the surface Kirchhoff integral by forcing the pressures at the additional interior points to be zero when the shortest retarded time between boundary nodes and an interior point elapses. However, even after using the CHIEF method, the TBEM calculation suffers the exponential divergence due to the remaining unstable high order fictitious modes at frequencies higher than the frequency limit of the boundary element model. For complete stabilization, such troublesome modes are selectively adjusted by projecting the time response onto the eigenspace. In a test example for a transiently pulsating sphere, the final average error norm of the stabilized response compared to the analytic solution is 2.5%.

Practical Implementation of Prestack Kirchhoff Time Migration on a General Purpose Graphics Processing Unit

NASA Astrophysics Data System (ADS)

Liu, Guofeng; Li, Chun

2016-08-01

In this study, we present a practical implementation of prestack Kirchhoff time migration (PSTM) on a general purpose graphic processing unit. First, we consider the three main optimizations of the PSTM GPU code, i.e., designing a configuration based on a reasonable execution, using the texture memory for velocity interpolation, and the application of an intrinsic function in device code. This approach can achieve a speedup of nearly 45 times on a NVIDIA GTX 680 GPU compared with CPU code when a larger imaging space is used, where the PSTM output is a common reflection point that is gathered as I[ nx][ ny][ nh][ nt] in matrix format. However, this method requires more memory space so the limited imaging space cannot fully exploit the GPU sources. To overcome this problem, we designed a PSTM scheme with multi-GPUs for imaging different seismic data on different GPUs using an offset value. This process can achieve the peak speedup of GPU PSTM code and it greatly increases the efficiency of the calculations, but without changing the imaging result.

Angle-domain common imaging gather extraction via Kirchhoff prestack depth migration based on a traveltime table in transversely isotropic media

NASA Astrophysics Data System (ADS)

Liu, Shaoyong; Gu, Hanming; Tang, Yongjie; Bingkai, Han; Wang, Huazhong; Liu, Dingjin

2018-04-01

Angle-domain common image-point gathers (ADCIGs) can alleviate the limitations of common image-point gathers in an offset domain, and have been widely used for velocity inversion and amplitude variation with angle (AVA) analysis. We propose an effective algorithm for generating ADCIGs in transversely isotropic (TI) media based on the gradient of traveltime by Kirchhoff pre-stack depth migration (KPSDM), as the dynamic programming method for computing the traveltime in TI media would not suffer from the limitation of shadow zones and traveltime interpolation. Meanwhile, we present a specific implementation strategy for ADCIG extraction via KPSDM. Three major steps are included in the presented strategy: (1) traveltime computation using a dynamic programming approach in TI media; (2) slowness vector calculation by the gradient of a traveltime table calculated previously; (3) construction of illumination vectors and subsurface angles in the migration process. Numerical examples are included to demonstrate the effectiveness of our approach, which henceforce shows its potential application for subsequent tomographic velocity inversion and AVA.

Effect of the boundary conditions and influence of the rotational inertia on the vibrational modes of an elastic ring

PubMed Central

Clauvelin, Nicolas; Olson, Wilma K.; Tobias, Irwin

2013-01-01

We present the small-amplitude vibrations of a circular elastic ring with periodic and clamped boundary conditions. We model the rod as an inextensible, isotropic, naturally straight Kirchhoff elastic rod and obtain the vibrational modes of the ring analytically for periodic boundary conditions and numerically for clamped boundary conditions. Of particular interest are the dependence of the vibrational modes on the torsional stress in the ring and the influence of the rotational inertia of the rod on the mode frequencies and amplitudes. In rescaling the Kirchhoff equations, we introduce a parameter inversely proportional to the aspect ratio of the rod. This parameter makes it possible to capture the influence of the rotational inertia of the rod. We find that the rotational inertia has a minor influence on the vibrational modes with the exception of a specific category of modes corresponding to high-frequency twisting deformations in the ring. Moreover, some of the vibrational modes over or undertwist the elastic rod depending on the imposed torsional stress in the ring. PMID:24795495

Multimodal vibration damping of a plate by piezoelectric coupling to its analogous electrical network

NASA Astrophysics Data System (ADS)

Lossouarn, B.; Deü, J.-F.; Aucejo, M.; Cunefare, K. A.

2016-11-01

Multimodal damping can be achieved by coupling a mechanical structure to an electrical network exhibiting similar modal properties. Focusing on a plate, a new topology for such an electrical analogue is found from a finite difference approximation of the Kirchhoff-Love theory and the use of the direct electromechanical analogy. Discrete models based on element dynamic stiffness matrices are proposed to simulate square plate unit cells coupled to their electrical analogues through two-dimensional piezoelectric transducers. A setup made of a clamped plate covered with an array of piezoelectric patches is built in order to validate the control strategy and the numerical models. The analogous electrical network is implemented with passive components as inductors, transformers and the inherent capacitance of the piezoelectric patches. The effect of the piezoelectric coupling on the dynamics of the clamped plate is significant as it creates the equivalent of a multimodal tuned mass damping. An adequate tuning of the network then yields a broadband vibration reduction. In the end, the use of an analogous electrical network appears as an efficient solution for the multimodal control of a plate.

Static and free-vibration analyses of cracks in thin-shell structures based on an isogeometric-meshfree coupling approach

NASA Astrophysics Data System (ADS)

Nguyen-Thanh, Nhon; Li, Weidong; Zhou, Kun

2018-03-01

This paper develops a coupling approach which integrates the meshfree method and isogeometric analysis (IGA) for static and free-vibration analyses of cracks in thin-shell structures. In this approach, the domain surrounding the cracks is represented by the meshfree method while the rest domain is meshed by IGA. The present approach is capable of preserving geometry exactness and high continuity of IGA. The local refinement is achieved by adding the nodes along the background cells in the meshfree domain. Moreover, the equivalent domain integral technique for three-dimensional problems is derived from the additional Kirchhoff-Love theory to compute the J-integral for the thin-shell model. The proposed approach is able to address the problems involving through-the-thickness cracks without using additional rotational degrees of freedom, which facilitates the enrichment strategy for crack tips. The crack tip enrichment effects and the stress distribution and displacements around the crack tips are investigated. Free vibrations of cracks in thin shells are also analyzed. Numerical examples are presented to demonstrate the accuracy and computational efficiency of the coupling approach.

Theoretical analysis of cross-talking signals between counter-streaming electron beams in a vacuum tube oscillator

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

Shin, Y.M.; Ryskin, N.M.; Won, J.H.

The basic theory of cross-talking signals between counter-streaming electron beams in a vacuum tube oscillator consisting of two two-cavity klystron amplifiers reversely coupled through input/output slots is theoretically investigated. Application of Kirchhoff's laws to the coupled equivalent RLC circuit model of the device provides four nonlinear coupled equations, which are the first-order time-delayed differential equations. Analytical solutions obtained through linearization of the equations provide oscillation frequencies and thresholds of four fundamental eigenstates, symmetric/antisymmetric 0/{pi} modes. Time-dependent output signals are numerically analyzed with variation of the beam current, and a self-modulation mechanism and transition to chaos scenario are examined. The oscillatormore » shows a much stronger multistability compared to a delayed feedback klystron oscillator owing to the competitions among more diverse eigenmodes. A fully developed chaos region also appears at a relatively lower beam current, {approx}3.5I{sub st}, compared to typical vacuum tube oscillators (10-100I{sub st}), where I{sub st} is a start-oscillation current.« less

Large Deformation of an Elastic Rod with Structural Anisotropy Subjected to Fluid Flow

NASA Astrophysics Data System (ADS)

Hassani, Masoud; Mureithi, Njuki; Gosselin, Frederick

2015-11-01

In the present work, we seek to understand the fundamental mechanisms of three-dimensional reconfiguration of plants by studying the large deformation of a flexible rod in fluid flow. Flexible rods made of Polyurethane foam and reinforced with Nylon fibers are tested in a wind tunnel. The rods have bending-torsion coupling which induces a torsional deformation during asymmetric bending. A mathematical model is also developed by coupling the Kirchhoff rod theory with a semi-empirical drag formulation. Different alignments of the material frame with respect to the flow direction and a range of structural properties are considered to study their effect on the deformation of the flexible rod and its drag scaling. Results show that twisting causes the flexible rods to reorient and bend with the minimum bending rigidity. It is also found that the drag scaling of the rod in the large deformation regime is not affected by torsion. Finally, using a proper set of dimensionless numbers, the state of a bending and twisting rod is characterized as a beam undergoing a pure bending deformation.

Novel method for measuring a dense 3D strain map of robotic flapping wings

NASA Astrophysics Data System (ADS)

Li, Beiwen; Zhang, Song

2018-04-01

Measuring dense 3D strain maps of the inextensible membranous flapping wings of robots is of vital importance to the field of bio-inspired engineering. Conventional high-speed 3D videography methods typically reconstruct the wing geometries through measuring sparse points with fiducial markers, and thus cannot obtain the full-field mechanics of the wings in detail. In this research, we propose a novel system to measure a dense strain map of inextensible membranous flapping wings by developing a superfast 3D imaging system and a computational framework for strain analysis. Specifically, first we developed a 5000 Hz 3D imaging system based on the digital fringe projection technique using the defocused binary patterns to precisely measure the dynamic 3D geometries of rapidly flapping wings. Then, we developed a geometry-based algorithm to perform point tracking on the precisely measured 3D surface data. Finally, we developed a dense strain computational method using the Kirchhoff-Love shell theory. Experiments demonstrate that our method can effectively perform point tracking and measure a highly dense strain map of the wings without many fiducial markers.

Dynamic response of a poroelastic half-space to accelerating or decelerating trains

NASA Astrophysics Data System (ADS)

Cao, Zhigang; Boström, Anders

2013-05-01

The dynamic response of a fully saturated poroelastic half-space due to accelerating or decelerating trains is investigated by a semi-analytical method. The ground is modeled as a saturated poroelastic half-space and Biot's theory is applied to characterize the soil medium, taking the coupling effects between the soil skeleton and the pore fluid into account. A detailed track system is considered incorporating rails, sleepers and embankment, which are modeled as Euler-Bernoulli beams, an anisotropic Kirchhoff plate, and an elastic layer, respectively. The acceleration or deceleration of the train is simulated by properly choosing the time history of the train speed using Fourier transforms combined with Fresnel integrals in the transformed domain. The time domain results are obtained by the fast Fourier transform (FFT). It is found that the deceleration of moving trains can cause a significant increase to the ground vibrations as well as the excess pore water pressure responses at the train speed 200 km/h. Furthermore, the single-phase elastic soil model would underestimate the vertical displacement responses caused by both the accelerating and decelerating trains at the speed 200 km/h.

A parameter-free variational coupling approach for trimmed isogeometric thin shells

NASA Astrophysics Data System (ADS)

Guo, Yujie; Ruess, Martin; Schillinger, Dominik

2017-04-01

The non-symmetric variant of Nitsche's method was recently applied successfully for variationally enforcing boundary and interface conditions in non-boundary-fitted discretizations. In contrast to its symmetric variant, it does not require stabilization terms and therefore does not depend on the appropriate estimation of stabilization parameters. In this paper, we further consolidate the non-symmetric Nitsche approach by establishing its application in isogeometric thin shell analysis, where variational coupling techniques are of particular interest for enforcing interface conditions along trimming curves. To this end, we extend its variational formulation within Kirchhoff-Love shell theory, combine it with the finite cell method, and apply the resulting framework to a range of representative shell problems based on trimmed NURBS surfaces. We demonstrate that the non-symmetric variant applied in this context is stable and can lead to the same accuracy in terms of displacements and stresses as its symmetric counterpart. Based on our numerical evidence, the non-symmetric Nitsche method is a viable parameter-free alternative to the symmetric variant in elastostatic shell analysis.

Diffraction of digital micromirror device gratings and its effect on properties of tunable fiber lasers.

PubMed

Chen, Xiao; Yan, Bin-bin; Song, Fei-jun; Wang, Yi-quan; Xiao, Feng; Alameh, Kamal

2012-10-20

A digital micromirror device (DMD) is a kind of widely used spatial light modulator. We apply DMD as wavelength selector in tunable fiber lasers. Based on the two-dimensional diffraction theory, the diffraction of DMD and its effect on properties of fiber laser parameters are analyzed in detail. The theoretical results show that the diffraction efficiency is strongly dependent upon the angle of incident light and the pixel spacing of DMD. Compared with the other models of DMDs, the 0.55 in. DMD grating is an approximate blazed state in our configuration, which makes most of the diffracted radiation concentrated into one order. It is therefore a better choice to improve the stability and reliability of tunable fiber laser systems.

Observation of sagittal X-ray diffraction by surface acoustic waves in Bragg geometry.

PubMed

Vadilonga, Simone; Zizak, Ivo; Roshchupkin, Dmitry; Evgenii, Emelin; Petsiuk, Andrei; Leitenberger, Wolfram; Erko, Alexei

2017-04-01

X-ray Bragg diffraction in sagittal geometry on a Y-cut langasite crystal (La 3 Ga 5 SiO 14 ) modulated by Λ = 3 µm Rayleigh surface acoustic waves was studied at the BESSY II synchrotron radiation facility. Owing to the crystal lattice modulation by the surface acoustic wave diffraction, satellites appear. Their intensity and angular separation depend on the amplitude and wavelength of the ultrasonic superlattice. Experimental results are compared with the corresponding theoretical model that exploits the kinematical diffraction theory. This experiment shows that the propagation of the surface acoustic waves creates a dynamical diffraction grating on the crystal surface, and this can be used for space-time modulation of an X-ray beam.

Observation of sagittal X-ray diffraction by surface acoustic waves in Bragg geometry1

PubMed Central

Vadilonga, Simone; Zizak, Ivo; Roshchupkin, Dmitry; Evgenii, Emelin; Petsiuk, Andrei; Leitenberger, Wolfram; Erko, Alexei

2017-01-01

X-ray Bragg diffraction in sagittal geometry on a Y-cut langasite crystal (La3Ga5SiO14) modulated by Λ = 3 µm Rayleigh surface acoustic waves was studied at the BESSY II synchrotron radiation facility. Owing to the crystal lattice modulation by the surface acoustic wave diffraction, satellites appear. Their intensity and angular separation depend on the amplitude and wavelength of the ultrasonic superlattice. Experimental results are compared with the corresponding theoretical model that exploits the kinematical diffraction theory. This experiment shows that the propagation of the surface acoustic waves creates a dynamical diffraction grating on the crystal surface, and this can be used for space–time modulation of an X-ray beam. PMID:28381976

Measurement of attenuation coefficients of the fundamental and second harmonic waves in water

NASA Astrophysics Data System (ADS)

Zhang, Shuzeng; Jeong, Hyunjo; Cho, Sungjong; Li, Xiongbing

2016-02-01

Attenuation corrections in nonlinear acoustics play an important role in the study of nonlinear fluids, biomedical imaging, or solid material characterization. The measurement of attenuation coefficients in a nonlinear regime is not easy because they depend on the source pressure and requires accurate diffraction corrections. In this work, the attenuation coefficients of the fundamental and second harmonic waves which come from the absorption of water are measured in nonlinear ultrasonic experiments. Based on the quasilinear theory of the KZK equation, the nonlinear sound field equations are derived and the diffraction correction terms are extracted. The measured sound pressure amplitudes are adjusted first for diffraction corrections in order to reduce the impact on the measurement of attenuation coefficients from diffractions. The attenuation coefficients of the fundamental and second harmonics are calculated precisely from a nonlinear least squares curve-fitting process of the experiment data. The results show that attenuation coefficients in a nonlinear condition depend on both frequency and source pressure, which are much different from a linear regime. In a relatively lower drive pressure, the attenuation coefficients increase linearly with frequency. However, they present the characteristic of nonlinear growth in a high drive pressure. As the diffraction corrections are obtained based on the quasilinear theory, it is important to use an appropriate source pressure for accurate attenuation measurements.

Combined Diffraction and Density Functional Theory Calculations of Halogen-Bonded Cocrystal Monolayers

PubMed Central

2013-01-01

This work describes the combined use of synchrotron X-ray diffraction and density functional theory (DFT) calculations to understand the cocrystal formation or phase separation in 2D monolayers capable of halogen bonding. The solid monolayer structure of 1,4-diiodobenzene (DIB) has been determined by X-ray synchrotron diffraction. The mixing behavior of DIB with 4,4′-bipyridyl (BPY) has also been studied and interestingly is found to phase-separate rather than form a cocrystal, as observed in the bulk. DFT calculations are used to establish the underlying origin of this interesting behavior. The DFT calculations are demonstrated to agree well with the recently proposed monolayer structure for the cocrystal of BPY and 1,4-diiodotetrafluorobenzene (DITFB) (the perfluorinated analogue of DIB), where halogen bonding has also been identified by diffraction. Here we have calculated an estimate of the halogen bond strength by DFT calculations for the DITFB/BPY cocrystal monolayer, which is found to be ∼20 kJ/mol. Computationally, we find that the nonfluorinated DIB and BPY are not expected to form a halogen-bonded cocrystal in a 2D layer; for this pair of species, phase separation of the components is calculated to be lower energy, in good agreement with the diffraction results. PMID:24215390

Combined diffraction and density functional theory calculations of halogen-bonded cocrystal monolayers.

PubMed

Sacchi, Marco; Brewer, Adam Y; Jenkins, Stephen J; Parker, Julia E; Friščić, Tomislav; Clarke, Stuart M

2013-12-03

This work describes the combined use of synchrotron X-ray diffraction and density functional theory (DFT) calculations to understand the cocrystal formation or phase separation in 2D monolayers capable of halogen bonding. The solid monolayer structure of 1,4-diiodobenzene (DIB) has been determined by X-ray synchrotron diffraction. The mixing behavior of DIB with 4,4'-bipyridyl (BPY) has also been studied and interestingly is found to phase-separate rather than form a cocrystal, as observed in the bulk. DFT calculations are used to establish the underlying origin of this interesting behavior. The DFT calculations are demonstrated to agree well with the recently proposed monolayer structure for the cocrystal of BPY and 1,4-diiodotetrafluorobenzene (DITFB) (the perfluorinated analogue of DIB), where halogen bonding has also been identified by diffraction. Here we have calculated an estimate of the halogen bond strength by DFT calculations for the DITFB/BPY cocrystal monolayer, which is found to be ∼20 kJ/mol. Computationally, we find that the nonfluorinated DIB and BPY are not expected to form a halogen-bonded cocrystal in a 2D layer; for this pair of species, phase separation of the components is calculated to be lower energy, in good agreement with the diffraction results.

Electromagnetic sensing for the monitoring of structures and infrastructures: a model for the diffraction by penetrable wedges

NASA Astrophysics Data System (ADS)

Riccio, G.; Gennarelli, G.

2012-04-01

As well-known, the observation of structures and infrastructures by radar remote sensing involves the investigation of the high-frequency electromagnetic scattering by canonical shapes, such as cylinders and wedges. For instance, the ruptures caused by natural disasters can be represented in the form of a wedge-shaped fracture [1]. They modify the electromagnetic response of the scene under investigation and the Geometrical Theory of Diffraction (GTD) can be used as efficient tool for describing this occurrence. Diffraction by a wedge is a well-covered topic in the scientific literature, but the available results mainly concern impenetrable structures. The aim of this work is to provide Uniform Asymptotic Physical Optics (UAPO) diffraction coefficients in the case of lossless penetrable wedges illuminated by plane waves having normal incidence with respect to the edge. To this end, the original problem is subdivided into two parts relevant to the internal region of the wedge and the surrounding space. For what concerns the evaluation of the field diffracted in the outer region, equivalent electric and magnetic PO surface currents are used as sources in the radiation integral. They lie on the external faces of the wedge and their expressions change in accordance with the incidence direction. As a matter of fact, they involve the reflection and transmission Fresnel's coefficients when one external face is directly illuminated, and only the reflection Fresnel's coefficients if both the external faces are considered. A useful approximation and a uniform asymptotic evaluation of the resulting radiation integrals allow one to obtain the diffraction coefficients in terms of the Geometrical Optics (GO) response and the standard transition function of the Uniform Theory of Diffraction (UTD) [2]. The evaluation of the field diffracted in the inner region is tackled and solved by using equivalent PO surface currents on the internal faces of the wedge. Once such currents are determined, the diffracted field is evaluated by using a method like that employed for the exterior problem. The UAPO solutions for the diffracted field allow one to compensate the GO field discontinuities in the interior and exterior regions. Furthermore, they are simple to handle and implement in numerical simulators for radar remote sensing. Their accuracy is well assessed by comparisons with Finite-Difference Time-Domain (FDTD) results. [1] A.I. Kozlov, L. Lighart, A.I. Logvin, "Radar reflection from surfaces with ruptures," Proc. of MIKON 2000, vol. 1, pp. 347-350. [2] R.G. Kouyoumjian, P.H. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface," Proc. of IEEE, vol. 62, pp. 1448-1461, 1974.

Task reports on developing techniques for scattering by 3D composite structures and to generate new solutions in diffraction theory using higher order boundary conditions

NASA Technical Reports Server (NTRS)

Volakis, John L.

1991-01-01

There are two tasks described in this report. First, an extension of a two dimensional formulation is presented for a three dimensional body of revolution. A Fourier series expansion of the vector electric and magnetic fields is employed to reduce the dimensionality of the system, and an exact boundary condition is employed to terminate the mesh. The mesh termination boundary is chosen such that it leads to convolutional boundary operators for low O(n) memory demand. Second, rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. Ray solutions are obtained which remain valid in the transition region and reduce uniformly those in the deep lit and shadow regions. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder.

Solution to the Phase Problem Using Multibeam X-Ray Diffraction.

NASA Astrophysics Data System (ADS)

Shen, Qun

Multi-beam x-ray diffraction, especially the asymmetry effect in the virtual Bragg scattering case, has been proved to provide useful phase information on the structure factors that are involved in the scattering process. A perturbation theory has been developed to provide an analytical expression for the diffracted wave field in virtual Bragg scattering situations, which explains the physical origin of the asymmetry effect. Two experiments on the (202) reflection of benzil, using 3.5 keV x-rays, have shown that the asymmetry effect is visible in a mosaic non-centrosymmetric organic crystal. The results do not depend on the shape of the crystal, hence proving that the method is universally applicable. A practical method to obtain arbitrary values of the phase triplet, based on the perturbation theory, has been developed and shown to work in the case of non-centrosymmetric crystals like benzil.

Highly-optimized TWSM software package for seismic diffraction modeling adapted for GPU-cluster

NASA Astrophysics Data System (ADS)

Zyatkov, Nikolay; Ayzenberg, Alena; Aizenberg, Arkady

2015-04-01

Oil producing companies concern to increase resolution capability of seismic data for complex oil-and-gas bearing deposits connected with salt domes, basalt traps, reefs, lenses, etc. Known methods of seismic wave theory define shape of hydrocarbon accumulation with nonsufficient resolution, since they do not account for multiple diffractions explicitly. We elaborate alternative seismic wave theory in terms of operators of propagation in layers and reflection-transmission at curved interfaces. Approximation of this theory is realized in the seismic frequency range as the Tip-Wave Superposition Method (TWSM). TWSM based on the operator theory allows to evaluate of wavefield in bounded domains/layers with geometrical shadow zones (in nature it can be: salt domes, basalt traps, reefs, lenses, etc.) accounting for so-called cascade diffraction. Cascade diffraction includes edge waves from sharp edges, creeping waves near concave parts of interfaces, waves of the whispering galleries near convex parts of interfaces, etc. The basic algorithm of TWSM package is based on multiplication of large-size matrices (make hundreds of terabytes in size). We use advanced information technologies for effective realization of numerical procedures of the TWSM. In particular, we actively use NVIDIA CUDA technology and GPU accelerators allowing to significantly improve the performance of the TWSM software package, that is important in using it for direct and inverse problems. The accuracy, stability and efficiency of the algorithm are justified by numerical examples with curved interfaces. TWSM package and its separate components can be used in different modeling tasks such as planning of acquisition systems, physical interpretation of laboratory modeling, modeling of individual waves of different types and in some inverse tasks such as imaging in case of laterally inhomogeneous overburden, AVO inversion.

Theory and Experiment Analysis of Two-Dimensional Acousto-Optic Interaction.

DTIC Science & Technology

1995-01-03

The universal coupled wave equation of two dimensional acousto optic effect has been deduced and the solution of normal Raman-Hath acousto optic diffraction...was derived from it. The theory was compared with the experimental results of a two dimensional acousto optic device consisting of two one dimensional modulators. The experiment results agree with the theory. (AN)

Swimming Lessons: Learning, New Materialisms, Posthumanism, and Post Qualitative Research Emerge through a Pool Poem

ERIC Educational Resources Information Center

McKnight, Lucinda

2016-01-01

This article shifts from the formal learning spaces of school and university to an Australian public swimming pool to playfully engage some of the dilemmas that recent theory poses for curriculum studies. The article enacts multiple diffractions (Barad, 2007) as theory becomes swimming and swimming becomes theory, and ideas and movements are…

Erosion Control of Scour during Construction. Report 5. Experimental Measurements of Refraction and Diffraction Downcoast of an Oblique Breakwater.

DTIC Science & Technology

1984-09-01

such as a jetty or shore-connected breakwater. The theory of water wave diffraction can be explained by Huygens’ principle . Each point of an ad...a slowly varying bottom, an asymptotic theory has been developed by Liu and Mei (1976) that accounts for the combined effects ot refraction and... Fundment i" rs t Second Third Fo :rth ,ri,- ATa rronlc Ha rmon i c Ha rme qic Gage s.__ ’ sc 0.33 sec 0.25 sec 0.20 sec 1* 0.n+ 6. .0 (-163) 0.12(-9) 0.01

Prediction of the light scattering patterns from bacteria colonies by a time-resolved reaction-diffusion model and the scalar diffraction theory

NASA Astrophysics Data System (ADS)

Bae, Euiwon; Bai, Nan; Aroonnual, Amornrat; Bhunia, Arun K.; Robinson, J. Paul; Hirleman, E. Daniel

2009-05-01

In order to maximize the utility of the optical scattering technology in the area of bacterial colony identification, it is necessary to have a thorough understanding of how bacteria species grow into different morphological aggregation and subsequently function as distinctive optical amplitude and phase modulators to alter the incoming Gaussian laser beam. In this paper, a 2-dimentional reaction-diffusion (RD) model with nutrient concentration, diffusion coefficient, and agar hardness as variables is investigated to explain the correlation between the various environmental parameters and the distinctive morphological aggregations formed by different bacteria species. More importantly, the morphological change of the bacterial colony against time is demonstrated by this model, which is able to characterize the spatio-temporal patterns formed by the bacteria colonies over their entire growth curve. The bacteria population density information obtained from the RD model is mathematically converted to the amplitude/phase modulation factor used in the scalar diffraction theory which predicts the light scattering patterns for bacterial colonies. The conclusions drawn from the RD model combined with the scalar diffraction theory are useful in guiding the design of the optical scattering instrument aiming at bacteria colony detection and classification.

Magnetic coherent tunnel junctions with periodic grating barrier

PubMed Central

Fang, Henan; Xiao, Mingwen; Rui, Wenbin; Du, Jun; Tao, Zhikuo

2016-01-01

A new spintronic theory has been developed for the magnetic tunnel junction (MTJ) with single-crystal barrier. The barrier will be treated as a diffraction grating with intralayer periodicity, the diffracted waves of tunneling electrons thus contain strong coherence, both in charge and especially in spin. The theory can answer the two basic problems present in MgO-based MTJs: (1) Why does the tunneling magnetoresistance (TMR) oscillate with the barrier thickness? (2) Why is the TMR still far away from infinity when the two electrodes are both half-metallic? Other principal features of TMR can also be explained and reproduced by the present work. It also provides possible ways to modulate the oscillation of TMR, and to enhance TMR so that it can tend to infinity. Within the theory, the barrier, as a periodic diffraction grating, can get rid of the confinement in width, it can vary from nanoscale to microscale. Based on those results, a future-generation MTJ is proposed where the three pieces can be fabricated separately and then assembled together, it is especially appropriate for the layered materials, e.g., MoS2 and graphite, and most feasible for industries. PMID:27063998

Minimization of the Total Depth of Internal Saw-Tooth Reliefs of a Two-Layer Relief-Phase Diffraction Microstructure

NASA Astrophysics Data System (ADS)

Greisukh, G. I.; Danilov, V. A.; Stepanov, S. A.; Antonov, A. I.; Usievich, B. A.

2018-01-01

Results of studying the possibility to decrease the total depth of reliefs of a two-layer microstructure having two internal saw-tooth microreliefs reducing the dependence of the diffraction efficiency of the microstructure on the radiation wavelength and angle of radiation incidence on the microstructure are presented. These results allow one to minimize the complexity of obtaining optimum microrelief depths depending on requirements applicable to the diffraction optical element in the framework of the electromagnetic-diffraction theory. Optimum depths provide in the specified spectral range and interval of angles of radiation incidence the maximum possible (for the chosen width of the narrowest zone of the saw-tooth microrelief) value of the diffraction efficiency at the point of its minimum.

Stable diffraction-management soliton in a periodic structure with alternating left-handed and right-handed media

NASA Astrophysics Data System (ADS)

Zhang, Jinggui

2017-09-01

In this paper, we first derive a modified two-dimensional non-linear Schrödinger equation including high-order diffraction (HOD) suitable for the propagation of optical beam near the low-diffraction regime in Kerr non-linear media with spatial dispersion. Then, we apply our derived physical model to a designed two-dimensional configuration filled with alternate layers of a left-handed material (LHM) and a right-handed media by employing the mean-field theory. It is found that the periodic structure including LHM may experience diminished, cancelled, and even reversed diffraction behaviours through engineering the relative thickness between both media. In particular, the variational method analytically predicts that close to the zero-diffraction regime, such periodic structure can support stable diffraction-management solitons whose beamwidth and peak amplitude evolve periodically with the help of HOD effect. Numerical simulation based on the split-step Fourier method confirms the analytical results.

Grazing-incidence X-ray diffraction from a crystal with subsurface defects

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

Gaevskii, A. Yu., E-mail: transilv@mail.ru; Golentus, I. E.

2015-03-15

The diffraction of X rays incident on a crystal surface under grazing angles under conditions of total external reflection has been investigated. An approach is proposed in which exact solutions to the dynamic problem of grazing-incidence diffraction in an ideal crystal are used as initial functions to calculate the diffuse component of diffraction in a crystal with defects. The diffuse component of diffraction is calculated for a crystal with surface defects of a dilatation-center type. Exact formulas of the continuum theory which take into account the mirror-image forces are used for defect-induced atomic displacements. Scattering intensity maps near Bragg peaksmore » are constructed for different scan modes, and the conditions for detecting primarily the diffuse component are determined. The results of dynamic calculations of grazing-incidence diffraction in defect-containing crystals are compared with calculations in the kinematic approximation.« less

A Combined FEM/MoM/GTD Technique To Analyze Elliptically Polarized Cavity-Backed Antennas With Finite Ground Plane

NASA Technical Reports Server (NTRS)

Reddy, C. J.; Deshpande, M. D.; Fralick, D. T.; Cockrell, C. R.; Beck, F. B.

1996-01-01

Radiation pattern prediction analysis of elliptically polarized cavity-backed aperture antennas in a finite ground plane is performed using a combined Finite Element Method/Method of Moments/Geometrical Theory of Diffraction (FEM/MoM/GTD) technique. The magnetic current on the cavity-backed aperture in an infinite ground plane is calculated using the combined FEM/MoM analysis. GTD, including the slope diffraction contribution, is used to calculate the diffracted fields caused by both soft and hard polarizations at the edges of the finite ground plane. Explicit expressions for regular diffraction coefficients and slope diffraction coefficients are presented. The slope of the incident magnetic field at the diffraction points is derived and analytical expressions are presented. Numerical results for the radiation patterns of a cavity-backed circular spiral microstrip patch antenna excited by a coaxial probe in a finite rectangular ground plane are computed and compared with experimental results.

Dynamical effects in Bragg coherent x-ray diffraction imaging of finite crystals

NASA Astrophysics Data System (ADS)

Shabalin, A. G.; Yefanov, O. M.; Nosik, V. L.; Bushuev, V. A.; Vartanyants, I. A.

2017-08-01

We present simulations of Bragg coherent x-ray diffractive imaging (CXDI) data from finite crystals in the frame of the dynamical theory of x-ray diffraction. The developed approach is based on a numerical solution of modified Takagi-Taupin equations and can be applied for modeling of a broad range of x-ray diffraction experiments with finite three-dimensional crystals of arbitrary shape also in the presence of strain. We performed simulations for nanocrystals of a cubic and hemispherical shape of different sizes and provided a detailed analysis of artifacts in the Bragg CXDI reconstructions introduced by the dynamical diffraction. Based on our theoretical analysis we developed an analytical procedure to treat effects of refraction and absorption in the reconstruction. Our results elucidate limitations for the kinematical approach in the Bragg CXDI and suggest a natural criterion to distinguish between kinematical and dynamical cases in coherent x-ray diffraction on a finite crystal.

Teaching Electric Fences: The Physics behind the Brainiac Video

ERIC Educational Resources Information Center

Vollmer, Michael

2016-01-01

In many states, electric fences are used to prevent animals from leaving a designated area, for example for grazing. They are quite well known by most students and can therefore serve as daily-life examples of electric circuits. Besides helping to grasp the ideas of Kirchhoff's laws for voltages and currents in circuits according to loop and…

Localization on Quantum Graphs with Random Vertex Couplings

NASA Astrophysics Data System (ADS)

Klopp, Frédéric; Pankrashkin, Konstantin

2008-05-01

We consider Schrödinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. We obtain necessary conditions for localization on quantum graphs in terms of finite volume criteria for some energy-dependent discrete Hamiltonians. These conditions hold in the strong disorder limit and at the spectral edges.

Scattering and Diffraction of Electromagnetic Radiation: An Effective Probe to Material Structure

NASA Technical Reports Server (NTRS)

Xu, Yu-Lin

2016-01-01

Scattered electromagnetic waves from material bodies of different forms contain, in an intricate way, precise information on the intrinsic, geometrical and physical properties of the objects. Scattering theories, ever deepening, aim to provide dependable interpretation and prediction to the complicated interaction of electromagnetic radiation with matter. There are well-established multiple-scattering formulations based on classical electromagnetic theories. An example is the Generalized Multi-particle Mie-solution (GMM), which has recently been extended to a special version ? the GMM-PA approach, applicable to finite periodic arrays consisting of a huge number (e.g., >>106) of identical scattering centers [1]. The framework of the GMM-PA is nearly complete. When the size of the constituent unit scatterers becomes considerably small in comparison with incident wavelength, an appropriate array of such small element volumes may well be a satisfactory representation of a material entity having an arbitrary structure. X-ray diffraction is a powerful characterization tool used in a variety of scientific and technical fields, including material science. A diffraction pattern is nothing more than the spatial distribution of scattered intensity, determined by the distribution of scattering matter by way of its Fourier transform [1]. Since all linear dimensions entered into Maxwell's equations are normalized by wavelength, an analogy exists between optical and X-ray diffraction patterns. A large set of optical diffraction patterns experimentally obtained can be found in the literature [e.g., 2,3]. Theoretical results from the GMM-PA have been scrutinized using a large collection of publically accessible, experimentally obtained Fraunhofer diffraction patterns. As far as characteristic structures of the patterns are concerned, theoretical and experimental results are in uniform agreement; no exception has been found so far. Closely connected with the spatial distribution of scattered intensities are cross sections, such as for extinction, scattering, absorption, and radiation pressure, as a critical type of key quantity addressed in most theoretical and experimental studies of radiative scattering. Cross sections predicted from different scattering theories are supposed to be in general agreement. For objects of irregular shape, the GMM-PA solutions can be compared with the highly flexible Discrete Dipole Approximation (DDA) [4,5] when dividing a target to no more than 106 unit cells. Also, there are different ways to calculate the cross sections in the GMM-PA, providing an additional means to examine the accuracy of the numerical solutions and to unveil potential issues concerning the theoretical formulations and numerical aspects. To solve multiple scattering by an assembly of material volumes through classical theories such as the GMM-PA, the radiative properties of the component scatterers, the complex refractive index in particular, must be provided as input parameters. When using a PA to characterize a material body, this involves the use of an adequate theoretical tool, an effective medium theory, to connect Maxwell's phenomenogical theory with the atomistic theory of matter. In the atomic theory, one regards matter as composed of interacting particles (atoms and molecules) embedded in the vacuum [6]. However, the radiative properties of atomic-scaled particles are known to be substantially different from bulk materials. Intensive research efforts in the fields of cluster science and nanoscience attempt to bridge the gap between bulk and atom and to understand the transition from classical to quantum physics. The GMM-PA calculations, which place virtually no restriction on the component-particle size, might help to gain certain insight into the transition.

Edge Diffraction Coefficients around Critical Rays

NASA Astrophysics Data System (ADS)

Fradkin, L.; Harmer, M.; Darmon, M.

2014-04-01

The classical GTD (Geometrical Theory of Diffraction) gives a recipe, based on high-frequency asymptotics, for calculating edge diffraction coefficients in the geometrical regions where only diffracted waves propagate. The Uniform GTD extends this recipe to transition zones between irradiated and silent regions, known as penumbra. For many industrial materials, e.g. steels, and frequencies utlized in industrial ultrasonic transducers, that is, around 5 MHz, asymptotics suggested for description of geometrical regions supporting the head waves or transition regions surrounding their boundaries, known as critical rays, prove unsatisfactory. We present a numerical extension of GTD, which is based on a regularized, variable step Simpson's method for evaluating the edge diffraction coefficients in the regions of interference between head waves, diffracted waves and/or reflected waves. In mathematical terms, these are the regions of coalescence of three critical points - a branch point, stationary point and/or pole, respectively. We show that away from the shadow boundaries, near the critical rays the GTD still produces correct values of the edge diffraction coefficients.

Fast computation algorithms for speckle pattern simulation

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

Nascov, Victor; Samoilă, Cornel; Ursuţiu, Doru

2013-11-13

We present our development of a series of efficient computation algorithms, generally usable to calculate light diffraction and particularly for speckle pattern simulation. We use mainly the scalar diffraction theory in the form of Rayleigh-Sommerfeld diffraction formula and its Fresnel approximation. Our algorithms are based on a special form of the convolution theorem and the Fast Fourier Transform. They are able to evaluate the diffraction formula much faster than by direct computation and we have circumvented the restrictions regarding the relative sizes of the input and output domains, met on commonly used procedures. Moreover, the input and output planes canmore » be tilted each to other and the output domain can be off-axis shifted.« less

Physical optics-based diffraction coefficient for a wedge with different face impedances.

PubMed

Umul, Yusuf Ziya

2018-03-20

A new diffraction field expression is introduced with the aid of the modified theory of physical optics for a wedge with different face impedances. First, the scattered geometrical optics fields are determined when both faces of the wedge are illuminated by the incident wave. The geometrical optics waves are then expressed in terms of the sum of two different fields that occur for different impedance wedges. The diffracted fields are determined for the two cases separately, and the total diffracted field is obtained as a sum of these waves. Lastly, the uniform field expressions are obtained, and the resultant fields are numerically compared with the solution of Maliuzhinets.

Crystal Structure of 17α-Dihydroequilin, C18H22O2, from Synchrotron Powder Diffraction Data and Density Functional Theory

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

Kaduk, James; Gindhart, Amy; Blanton, Thomas

The crystal structure of 17α-dihydroequilin has been solved and refined using synchrotron X-ray powder diffraction data, and optimized using density functional techniques. 17α-dihydroequilin crystallizes in space group P212121 (#19) with a = 6.76849(1) Å, b = 8.96849(1) Å, c = 23.39031(5) Å, V = 1419.915(3) Å3, and Z = 4. Both hydroxyl groups form hydrogen bonds to each other, resulting in zig-zag chains along the b-axis. The powder diffraction pattern has been submitted to ICDD for inclusion in the Powder Diffraction File™ as the entry 00-066-1608.

Talbot effect of the defective grating in deep Fresnel region

NASA Astrophysics Data System (ADS)

Teng, Shuyun; Wang, Junhong; Zhang, Wei; Cui, Yuwei

2015-02-01

Talbot effect of the grating with different defect is studied theoretically and experimentally in this paper. The defects of grating include the loss of the diffraction unit, the dislocation of the diffraction unit and the modulation of the unit separation. The exact diffraction distributions of three kinds of defective gratings are obtained according to the finite-difference time-domain (FDTD) method. The calculation results show the image of the missing or dislocating unit appears at the Talbot distance (as mentioned in K. Patorski Prog. Opt., 27, 1989, pp.1-108). This is the so-called self-repair ability of grating imaging. In addition, some more phenomena are discovered. The loss or the dislocation of diffraction unit causes the diffraction distortion within a certain radial angle. The regular modulation of unit separation changes the original diffraction, but the new periodicity of the diffraction distribution rebuilds. The self-imaging of grating with smaller random modulation still keeps the partial self-repair ability, and yet this characteristic depends on the modulation degree of defective grating. These diffraction phenomena of the defective gratings are explained by use of the diffraction theory of grating. The practical experiment is also performed and the experimental results confirm the theoretic predictions.

Free boundary problems in shock reflection/diffraction and related transonic flow problems

PubMed Central

Chen, Gui-Qiang; Feldman, Mikhail

2015-01-01

Shock waves are steep wavefronts that are fundamental in nature, especially in high-speed fluid flows. When a shock hits an obstacle, or a flying body meets a shock, shock reflection/diffraction phenomena occur. In this paper, we show how several long-standing shock reflection/diffraction problems can be formulated as free boundary problems, discuss some recent progress in developing mathematical ideas, approaches and techniques for solving these problems, and present some further open problems in this direction. In particular, these shock problems include von Neumann's problem for shock reflection–diffraction by two-dimensional wedges with concave corner, Lighthill's problem for shock diffraction by two-dimensional wedges with convex corner, and Prandtl-Meyer's problem for supersonic flow impinging onto solid wedges, which are also fundamental in the mathematical theory of multidimensional conservation laws. PMID:26261363

Refined Models for an Analysis of Internal and External Buckling Modes of a Monolayer in a Layered Composite

NASA Astrophysics Data System (ADS)

Paimushin, V. N.

2017-11-01

For an analysis of internal and external buckling modes of a monolayer inside or at the periphery of a layered composite, refined geometrically nonlinear equations are constructed. They are based on modeling the monolayer as a thin plate interacting with binder layers at the points of boundary surfaces. The binder layer is modeled as a transversely soft foundation. It is assumed the foundations, previously compressed in the transverse direction (the first loading stage), have zero displacements of its external boundary surfaces at the second loading stage, but the contact interaction of the plate with foundations occurs without slippage or delamination. The deformation of the plate at a medium flexure is described by geometrically nonlinear relations of the classical plate theory based on the Kirchhoff-Love hypothesis (the first variant) or the refined Timoshenko model with account of the transverse shear and compression (the second variant). The foundation is described by linearized 3D equations of elasticity theory, which are simplified within the framework of the model of a transversely soft layer. Integrating the linearized equations along the transverse coordinate and satisfying the kinematic joining conditions of the plate with foundations, with account of their initial compression in the thickness direction, a system of 2D geometrically nonlinear equations and appropriate boundary conditions are derived. These equations describe the contact interaction between elements of the deformable system. The relations obtained are simplified for the case of a symmetric stacking sequence.

Nano-scale mass sensor based on the vibration analysis of a magneto-electro-elastic nanoplate resting on a visco-Pasternak substrate

NASA Astrophysics Data System (ADS)

Khanmirza, E.; Jamalpoor, A.; Kiani, A.

2017-10-01

In this paper, a magneto-electro-elastic nanoplate resting on a visco-Pasternak medium with added concentrated nanoparticles is presented as a mass nanosensor according to the vibration analysis. The MEE nanoplate is supposed to be subject to external electric voltage and magnetic potential. In order to take into account the size effect on the sensitivity of the sensor, the nonlocal elasticity theory in conjunction with the Kirchhoff plate theory is applied. Partial differential equations are derived by implementing Hamilton's variational principle. Equilibrium equations were solved analytically to determine an explicit closed-form statement for both the damped frequency shift and the relative damped frequency shift using Navier's approach. A genetic algorithm (GA) is employed to achieve the optimal added nanoparticle location to gain the most sensitivity performance of the nanosensor. Numerical studies are performed to illustrate the variation of the sensitivity property corresponding to various values of the number of attached nanoparticles, the mass of each nanoparticle, the nonlocal parameter, external electric voltage and magnetic potential, the aspect ratio, and visco-Pasternak parameters. Some numerical outcomes of this paper show that the minimum value of the damped frequency shift occurs for a certain value of the length-to-thickness ratio. Also, it is shown that the external magnetic and external electric potentials have a different effect on the sensitivity property. It is anticipated that the results reported in this work can be considered as a benchmark in future micro-structures issues.

Geostrophic Vortex Dynamics

DTIC Science & Technology

1988-10-01

Generalized Kirchhoff Vortices 176 B. The 2-Level Rankine Vortex: Critical Points & Stability 181 C. Tripolar Coherent Euler Vortices 186 7...spontaneously in spectral simulations. One such example is provided by the tripolar vortex structureE which will be examined in detail in Chapter 6. It...of the tripolar coherent vortex structures that have recently been observed in very high resolution numerical simulations of two- dimensional

Concurrent MR-NIR Imaging for Breast Cancer Diagnosis

DTIC Science & Technology

2007-06-01

DISTRIBUTION / AVAILABILITY STATEMENT Approved for Public Release; Distribution Unlimited 13. SUPPLEMENTARY NOTES – Original contains colored plates ...stand-alone NIR system . This information includes hemoglobin, water and lipid concentration, optical scatter power and oxygen saturation images, and ICG...absorption coef cients of each voxel by a system of linear equations. The shape of the breast was approximated as a cylinder and the Kirchhoff

Different Paths to Some Fundamental Physical Laws: Relativistic Polarization of a Moving Magnetic Dipole

ERIC Educational Resources Information Center

Kholmetskii, Alexander L.; Yarman, T.

2010-01-01

In this paper we consider the relativistic polarization of a moving magnetic dipole and show that this effect can be understood via the relativistic generalization of Kirchhoff's first law to a moving closed circuit with a steady current. This approach allows us to better understand the law of relativistic transformation of four-current density…

Biophysical modeling of forward scattering from bacterial colonies using scalar diffraction theory

NASA Astrophysics Data System (ADS)

Bae, Euiwon; Banada, Padmapriya P.; Huff, Karleigh; Bhunia, Arun K.; Robinson, J. Paul; Hirleman, E. Daniel

2007-06-01

A model for forward scattering from bacterial colonies is presented. The colonies of interest consist of approximately 1012-1013 individual bacteria densely packed in a configuration several millimeters in diameter and approximately 0.1-0.2 mm in thickness. The model is based on scalar diffraction theory and accounts for amplitude and phase modulation created by three macroscopic properties of the colonies: phase modulation due to the surface topography, phase modulation due to the radial structure observed from some strains and species, and diffraction from the outline of the colony. Phase contrast and confocal microscopy were performed to provide quantitative information on the shape and internal structure of the colonies. The computed results showed excellent agreement with the experimental scattering data for three different Listeria species: Listeria innocua, Listeria ivanovii, and Listeria monocytogenes. The results provide a physical explanation for the unique and distinctive scattering signatures produced by colonies of closely related Listeria species and support the efficacy of forward scattering for rapid detection and classification of pathogens without tagging.

Polarization-dependent force driving the Eg mode in bismuth under optical excitation: comparison of first-principles theory with ultra-fast x-ray experiments

NASA Astrophysics Data System (ADS)

Fahy, Stephen; Murray, Eamonn

2015-03-01

Using first principles electronic structure methods, we calculate the induced force on the Eg (zone centre transverse optical) phonon mode in bismuth immediately after absorption of a ultrafast pulse of polarized light. To compare the results with recent ultra-fast, time-resolved x-ray diffraction experiments, we include the decay of the force due to carrier scattering, as measured in optical Raman scattering experiments, and simulate the optical absorption process, depth-dependent atomic driving forces, and x-ray diffraction in the experimental geometry. We find excellent agreement between the theoretical predictions and the observed oscillations of the x-ray diffraction signal, indicating that first-principles theory of optical absorption is well suited to the calculation of initial atomic driving forces in photo-excited materials following ultrafast excitation. This work is supported by Science Foundation Ireland (Grant No. 12/IA/1601) and EU Commission under the Marie Curie Incoming International Fellowships (Grant No. PIIF-GA-2012-329695).

Current developments in optical engineering and diffraction phenomena; Proceedings of the Meeting, San Diego, CA, Aug. 21, 22, 1986

NASA Astrophysics Data System (ADS)

Fischer, Robert E.; Smith, Warren J.; Harvey, James

1986-01-01

Papers dealing with current materials for gradient-index optics, an intelligent data-base system for optical designers; tilted mirror systems; a null-lens design approach for centrally obscured components; the use of the vector aberration theory to optimize an unobscured optical system; multizone bifocal contact lens design; and the concentric meniscus element are presented. Topics discussed include optical manufacturing in the Far East; the optical performance of molded-glass lenses for optical memory applications; through-wafer optical interconnects for multiwafer wafer-scale integrated architecture; optical thin-flim monitoring using optical fibers; aerooptical testing; optical inspection; and a system analysis program for a 32K microcomputer. Consideration is given to various theories, algorithms, and applications of diffraction, a vector formulation of a ray-equivalent method for Gaussian beam propagation; Fourier optical analysis of aberrations in focused laser beams; holography and moire interferometry; and phase-conjugate optical correctors for diffraction-limited applications.

Molecular structure and conformational preferences of gaseous 1-iodo-1-silacyclohexane

NASA Astrophysics Data System (ADS)

Belyakov, A. V.; Baskakov, A. A.; Berger, R. J. F.; Mitzel, N. W.; Oberhammer, H.; Arnason, I.; Wallevik, S. Ò.

2012-03-01

The molecular structure of the axial and equatorial conformers of 1-iodo-1-silacyclohexane, CH2(CH2CH2)2SiH-I, as well as thermodynamic equilibrium between these species were investigated by means of gas-phase electron diffraction (GED) and quantum chemical calculations up to MP2(full)/SDB-AUG-CC-pVTZ level of theory (MP2). According to electron diffraction data, the vapor of this compound comprises a mixture of conformers with chair conformation and Cs symmetry differing in the axial and equatorial position of the Si-I bond (axial = 73(7) mol%/equatorial = 27(7) mol%) at T = 352 K. This corresponds to a free energy difference of A = -0.59(22) kcal mol-1. The observed gas-phase electron diffraction parameters are in good agreement with those obtained from theory. NBO analysis revealed that axial conformer of 1-iodo-1-silacyclohexane is an example for electrostatic stabilization of a conformer which is unfavorable in terms of steric and conjugation interaction.

Interior sound field control using generalized singular value decomposition in the frequency domain.

PubMed

Pasco, Yann; Gauthier, Philippe-Aubert; Berry, Alain; Moreau, Stéphane

2017-01-01

The problem of controlling a sound field inside a region surrounded by acoustic control sources is considered. Inspired by the Kirchhoff-Helmholtz integral, the use of double-layer source arrays allows such a control and avoids the modification of the external sound field by the control sources by the approximation of the sources as monopole and radial dipole transducers. However, the practical implementation of the Kirchhoff-Helmholtz integral in physical space leads to large numbers of control sources and error sensors along with excessive controller complexity in three dimensions. The present study investigates the potential of the Generalized Singular Value Decomposition (GSVD) to reduce the controller complexity and separate the effect of control sources on the interior and exterior sound fields, respectively. A proper truncation of the singular basis provided by the GSVD factorization is shown to lead to effective cancellation of the interior sound field at frequencies below the spatial Nyquist frequency of the control sources array while leaving the exterior sound field almost unchanged. Proofs of concept are provided through simulations achieved for interior problems by simulations in a free field scenario with circular arrays and in a reflective environment with square arrays.

Physical Unclonable Function Hardware Keys Utilizing Kirchhoff-Law Secure Key Exchange and Noise-Based Logic

NASA Astrophysics Data System (ADS)

Kish, Laszlo B.; Kwan, Chiman

Weak unclonable function (PUF) encryption key means that the manufacturer of the hardware can clone the key but not anybody else. Strong unclonable function (PUF) encryption key means that even the manufacturer of the hardware is unable to clone the key. In this paper, first we introduce an "ultra" strong PUF with intrinsic dynamical randomness, which is not only unclonable but also gets renewed to an independent key (with fresh randomness) during each use via the unconditionally secure key exchange. The solution utilizes the Kirchhoff-law-Johnson-noise (KLJN) method for dynamical key renewal and a one-time-pad secure key for the challenge/response process. The secure key is stored in a flash memory on the chip to provide tamper-resistance and nonvolatile storage with zero power requirements in standby mode. Simplified PUF keys are shown: a strong PUF utilizing KLJN protocol during the first run and noise-based logic (NBL) hyperspace vector string verification method for the challenge/response during the rest of its life or until it is re-initialized. Finally, the simplest PUF utilizes NBL without KLJN thus it can be cloned by the manufacturer but not by anybody else.

A uniform geometrical optics and an extended uniform geometrical theory of diffraction for evaluating high frequency EM fields near smooth caustics and composite shadow boundaries

NASA Technical Reports Server (NTRS)

Constantinides, E. D.; Marhefka, R. J.

1994-01-01

A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly demonstrated and it is shown that the UGO/EUTD results remain valid and uniformly reduce to the classic results away from the transition regions. Mathematical details on the asymptotic properties and efficient numerical evaluation of the canonical functions involved in the UGO/EUTD expressions are also provided.

Universal modal radiation laws for all thermal emitters

PubMed Central

Zhu, Linxiao; Fan, Shanhui

2017-01-01

We derive four laws relating the absorptivity and emissivity of thermal emitters. Unlike the original Kirchhoff radiation law derivations, these derivations include diffraction, and so are valid also for small objects, and can also cover nonreciprocal objects. The proofs exploit two recent approaches. First, we express all fields in terms of the mode-converter basis sets of beams; these sets, which can be uniquely established for any linear optical object, give orthogonal input beams that are coupled one-by-one to orthogonal output beams. Second, we consider thought experiments using universal linear optical machines, which allow us to couple appropriate beams and black bodies. Two of these laws can be regarded as rigorous extensions of previously known laws: One gives a modal version of a radiation law for reciprocal objects—the absorptivity of any input beam equals the emissivity into the “backward” (i.e., phase-conjugated) version of that beam; another gives the overall equality of the sums of the emissivities and the absorptivities for any object, including nonreciprocal ones. The other two laws, valid for reciprocal and nonreciprocal objects, are quite different from previous relations. One shows universal equivalence of the absorptivity of each mode-converter input beam and the emissivity into its corresponding scattered output beam. The other gives unexpected equivalences of absorptivity and emissivity for broad classes of beams. Additionally, we prove these orthogonal mode-converter sets of input and output beams are the ones that maximize absorptivities and emissivities, respectively, giving these beams surprising additional physical meaning. PMID:28396436

Phase modulation due to crystal diffraction by ptychographic imaging

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

Civita, M.; Diaz, A.; Bean, R. J.

Solving the phase problem in x-ray crystallography has occupied a considerable scientific effort in the 20th century and led to great advances in structural science. Here we use x-ray ptychography to demonstrate an interference method which measures the phase of the beam transmitted through a crystal, relative to the incoming beam, when diffraction takes place. The observed phase change of the direct beam through a small gold crystal is found to agree with both a quasikinematical model and full dynamical theories of diffraction. Our discovery of a diffraction contrast mechanism will enhance the interpretation of data obtained from crystalline samplesmore » using the ptychography method, which provides some of the most accurate x-ray phase-contrast images.« less

Phase modulation due to crystal diffraction by ptychographic imaging

DOE PAGES

Civita, M.; Diaz, A.; Bean, R. J.; ...

2018-03-06

Solving the phase problem in x-ray crystallography has occupied a considerable scientific effort in the 20th century and led to great advances in structural science. Here we use x-ray ptychography to demonstrate an interference method which measures the phase of the beam transmitted through a crystal, relative to the incoming beam, when diffraction takes place. The observed phase change of the direct beam through a small gold crystal is found to agree with both a quasikinematical model and full dynamical theories of diffraction. Our discovery of a diffraction contrast mechanism will enhance the interpretation of data obtained from crystalline samplesmore » using the ptychography method, which provides some of the most accurate x-ray phase-contrast images.« less

Phase modulation due to crystal diffraction by ptychographic imaging

NASA Astrophysics Data System (ADS)

Civita, M.; Diaz, A.; Bean, R. J.; Shabalin, A. G.; Gorobtsov, O. Yu.; Vartanyants, I. A.; Robinson, I. K.

2018-03-01

Solving the phase problem in x-ray crystallography has occupied a considerable scientific effort in the 20th century and led to great advances in structural science. Here we use x-ray ptychography to demonstrate an interference method which measures the phase of the beam transmitted through a crystal, relative to the incoming beam, when diffraction takes place. The observed phase change of the direct beam through a small gold crystal is found to agree with both a quasikinematical model and full dynamical theories of diffraction. Our discovery of a diffraction contrast mechanism will enhance the interpretation of data obtained from crystalline samples using the ptychography method, which provides some of the most accurate x-ray phase-contrast images.

From quantum to classical interactions between a free electron and a surface

NASA Astrophysics Data System (ADS)

Beierle, Peter James

Quantum theory is often cited as being one of the most empirically validated theories in terms of its predictive power and precision. These attributes have led to numerous scientific discoveries and technological advancements. However, the precise relationship between quantum and classical physics remains obscure. The prevailing description is known as decoherence theory, where classical physics emerges from a more general quantum theory through environmental interaction. Sometimes referred to as the decoherence program, it does not solve the quantum measurement problem. We believe experiments performed between the microscopic and macroscopic world may help finish the program. The following considers a free electron that interacts with a surface (the environment), providing a controlled decoherence mechanism. There are non-decohering interactions to be examined and quantified before the weaker decohering effects are filtered out. In the first experiment, an electron beam passes over a surface that's illuminated by low-power laser light. This induces a surface charge redistribution causing the electron deflection. This phenomenon's parameters are investigated. This system can be well understood in terms of classical electrodynamics, and the technological applications of this electron beam switch are considered. Such phenomena may mask decoherence effects. A second experiment tests decoherence theory by introducing a nanofabricated diffraction grating before the surface. The electron undergoes diffraction through the grating, but as the electron passes over the surface it's predicted by various physical models that the electron will lose its wave interference property. Image charge based models, which predict a larger loss of contrast than what is observed, are falsified (despite experiencing an image charge force). A theoretical study demonstrates how a loss of contrast may not be due to the irreversible process decoherence, but dephasing (a reversible process due to randomization of the wavefunction's phase). To resolve this ambiguity, a correlation function on an ensemble of diffraction patterns is analyzed after an electron undergoes either process in a path integral calculation. The diffraction pattern is successfully recovered for dephasing, but not for decoherence, thus verifying it as a potential tool in experimental studies to determine the nature of the observed process.

Advantages of the incoherent uniform theory of diffraction for acoustic calculations in open-plan offices.

PubMed

Chevret, P

2015-01-01

Sound prediction in open-plan offices is a real challenge for room acoustics models because of the large dimensions involved and because of the complexity of the interior layout. For these reasons, the geometrical theory, based on a high frequency hypothesis, is often cited as an advantageous solution. Two types of approaches are, in general, developed under this hypothesis: the phase-included approach and the energy-based or "incoherent" approach. In this paper, comparisons are presented between calculations performed using these two approaches and measurements conducted in the laboratory where workstations were separated by low dividers and placed under ceilings that were absorbent to various extents. Particular attention was paid to processing diffraction using the uniform theory of diffraction. Narrow-band comparisons between calculations and measurements show that the phase-included model is flawed at low frequencies whenever the characteristic dimensions of the elements of the room (desk, low divider, etc.) are of the same order of magnitude as the wavelength. Conversely, the incoherent formulation, which removes the part played by the interference, gives results at least as accurate, be it in octave band or overall. Boasting very short computation times, the incoherent approach opens up interesting prospects for acoustic predictions in large open-plan offices.

Liquid-Crystal Point-Diffraction Interferometer for Wave-Front Measurements

NASA Technical Reports Server (NTRS)

Mercer, Carolyn R.; Creath, Katherine

1996-01-01

A new instrument, the liquid-crystal point-diffraction interferometer (LCPDI), is developed for the measurement of phase objects. This instrument maintains the compact, robust design of Linnik's point-diffraction interferometer and adds to it a phase-stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wave fronts with very high data density and with automated data reduction. We describe the theory and design of the LCPDI. A focus shift was measured with the LCPDI, and the results are compared with theoretical results,

Bistatic scattering from a cone frustum

NASA Technical Reports Server (NTRS)

Ebihara, W.; Marhefka, R. J.

1986-01-01

The bistatic scattering from a perfectly conducting cone frustum is investigated using the Geometrical Theory of Diffraction (GTD). The first-order GTD edge-diffraction solution has been extended by correcting for its failure in the specular region off the curved surface and in the rim-caustic regions of the endcaps. The corrections are accomplished by the use of transition functions which are developed and introduced into the diffraction coefficients. Theoretical results are verified in the principal plane by comparison with the moment method solution and experimental measurements. The resulting solution for the scattered fields is accurate, easy to apply, and fast to compute.

Analytical solutions with Generalized Impedance Boundary Conditions (GIBC)

NASA Technical Reports Server (NTRS)

Syed, H. H.; Volakis, John L.

1991-01-01

Rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristics to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.

Borman effect in resonant diffraction of X-rays

NASA Astrophysics Data System (ADS)

Oreshko, A. P.

2013-08-01

A dynamic theory of resonant diffraction (occurring when the energy of incident radiation is close to the energy of the absorption edge of an element in the composition of a given substance) of synchronous X-rays is developed in the two-wave approximation in the coplanar Laue geometry for large grazing angles in perfect crystals. A sharp decrease in the absorption coefficient in the substance with simultaneously satisfied diffraction conditions (Borman effect) is demonstrated, and the theoretical and first experimental results are compared. The calculations reveal the possibility of applying this approach in analyzing the quadrupole-quadrupole contribution to the absorption coefficient.

Transition operators in electromagnetic-wave diffraction theory - General theory

NASA Technical Reports Server (NTRS)

Hahne, G. E.

1992-01-01

A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.

Image degradation characteristics and restoration based on regularization for diffractive imaging

NASA Astrophysics Data System (ADS)

Zhi, Xiyang; Jiang, Shikai; Zhang, Wei; Wang, Dawei; Li, Yun

2017-11-01

The diffractive membrane optical imaging system is an important development trend of ultra large aperture and lightweight space camera. However, related investigations on physics-based diffractive imaging degradation characteristics and corresponding image restoration methods are less studied. In this paper, the model of image quality degradation for the diffraction imaging system is first deduced mathematically based on diffraction theory and then the degradation characteristics are analyzed. On this basis, a novel regularization model of image restoration that contains multiple prior constraints is established. After that, the solving approach of the equation with the multi-norm coexistence and multi-regularization parameters (prior's parameters) is presented. Subsequently, the space-variant PSF image restoration method for large aperture diffractive imaging system is proposed combined with block idea of isoplanatic region. Experimentally, the proposed algorithm demonstrates its capacity to achieve multi-objective improvement including MTF enhancing, dispersion correcting, noise and artifact suppressing as well as image's detail preserving, and produce satisfactory visual quality. This can provide scientific basis for applications and possesses potential application prospects on future space applications of diffractive membrane imaging technology.

Surface-treated self-standing curved crystals as high-efficiency elements for X- and γ-ray optics: theory and experiment.

PubMed

Bonnini, Elisa; Buffagni, Elisa; Zappettini, Andrea; Doyle, Stephen; Ferrari, Claudio

2015-06-01

The efficiency of a Laue lens for X- and γ-ray focusing in the energy range 60-600 keV is closely linked to the diffraction efficiency of the single crystals composing the lens. A powerful focusing system is crucial for applications like medical imaging and X-ray astronomy where wide beams must be focused. Mosaic crystals with a high density, such as Cu or Au, and bent crystals with curved diffracting planes (CDPs) are considered for the realization of a focusing system for γ-rays, owing to their high diffraction efficiency in a predetermined angular range. In this work, a comparison of the efficiency of CDP crystals and Cu and Au mosaic crystals was performed on the basis of the theory of X-ray diffraction. Si, GaAs and Ge CDP crystals with optimized thicknesses and moderate radii of curvature of several tens of metres demonstrate comparable or superior performance with respect to the higher atomic number mosaic crystals generally used. In order to increase the efficiency of the lens further, a stack of several CDP crystals is proposed as an optical element. CDP crystals were obtained by a surface-damage method, and a stack of two surface-damaged bent Si crystals was prepared and tested. Rocking curves of the stack were performed with synchrotron radiation at 19 keV to check the lattice alignment: they exhibited only one diffraction peak.

Robust reconstruction of time-resolved diffraction from ultrafast streak cameras

PubMed Central

Badali, Daniel S.; Dwayne Miller, R. J.

2017-01-01

In conjunction with ultrafast diffraction, streak cameras offer an unprecedented opportunity for recording an entire molecular movie with a single probe pulse. This is an attractive alternative to conventional pump-probe experiments and opens the door to studying irreversible dynamics. However, due to the “smearing” of the diffraction pattern across the detector, the streaking technique has thus far been limited to simple mono-crystalline samples and extreme care has been taken to avoid overlapping diffraction spots. In this article, this limitation is addressed by developing a general theory of streaking of time-dependent diffraction patterns. Understanding the underlying physics of this process leads to the development of an algorithm based on Bayesian analysis to reconstruct the time evolution of the two-dimensional diffraction pattern from a single streaked image. It is demonstrated that this approach works on diffraction peaks that overlap when streaked, which not only removes the necessity of carefully choosing the streaking direction but also extends the streaking technique to be able to study polycrystalline samples and materials with complex crystalline structures. Furthermore, it is shown that the conventional analysis of streaked diffraction can lead to erroneous interpretations of the data. PMID:28653022

Ultrapressure materials science

NASA Technical Reports Server (NTRS)

Ruoff, A. L.

1984-01-01

Three active areas of research at ultra pressure are pursued, i.e., diffraction studies with the Cornell High Energy Synchrotron Source (CHESS), band gap and absorption edge effects, indentor-anvil experiments and theory and research to attain higher pressures. The range over which X-ray diffraction data and absorption edge data are obtained is extended to 700 kbars. Using the indentor technique pressures of 2.1 Mbars are obtained. Research results and methods are discussed.

Research on Acoustical Scattering, Diffraction Catastrophes, Optics of Bubbles, Photoacoustics, and Acoustical Phase Conjugation.

DTIC Science & Technology

1987-09-15

optical levitation of bubbles; D. Acoustical and optical diffraction catastrophes (theory and optical simulation of transverse cusps, experiments with...35 C. Optical Levitation of Bubbles in Water by the Radiation Pressure of a Laser Beam: An Acoustically Quiet Levitator ...radiation pressure of a laser beam: an acoustically quiet levitator ," J. Acoust . Soc. Am. (submitted July 1987). C. Books (and sections thereof) Published

Color separation gratings

NASA Technical Reports Server (NTRS)

Farn, Michael W.; Knowlden, Robert E.

1993-01-01

In this paper, we describe the theory, fabrication and test of a binary optics 'echelon'. The echelon is a grating structure which separates electromagnetic radiation of different wavelengths, but it does so according to diffraction order rather than by dispersion within one diffraction order, as is the case with conventional gratings. A prototype echelon, designed for the visible spectrum, is fabricated using the binary optics process. Tests of the prototype show good agreement with theoretical predictions.

Gaussian Finite Element Method for Description of Underwater Sound Diffraction

NASA Astrophysics Data System (ADS)

Huang, Dehua

A new method for solving diffraction problems is presented in this dissertation. It is based on the use of Gaussian diffraction theory. The Rayleigh integral is used to prove the core of Gaussian theory: the diffraction field of a Gaussian is described by a Gaussian function. The parabolic approximation used by previous authors is not necessary to this proof. Comparison of the Gaussian beam expansion and Fourier series expansion reveals that the Gaussian expansion is a more general and more powerful technique. The method combines the Gaussian beam superposition technique (Wen and Breazeale, J. Acoust. Soc. Am. 83, 1752-1756 (1988)) and the Finite element solution to the parabolic equation (Huang, J. Acoust. Soc. Am. 84, 1405-1413 (1988)). Computer modeling shows that the new method is capable of solving for the sound field even in an inhomogeneous medium, whether the source is a Gaussian source or a distributed source. It can be used for horizontally layered interfaces or irregular interfaces. Calculated results are compared with experimental results by use of a recently designed and improved Gaussian transducer in a laboratory water tank. In addition, the power of the Gaussian Finite element method is demonstrated by comparing numerical results with experimental results from use of a piston transducer in a water tank.

Phonon Surface Scattering and Thermal Energy Distribution in Superlattices.

PubMed

Kothari, Kartik; Maldovan, Martin

2017-07-17

Thermal transport at small length scales has attracted significant attention in recent years and various experimental and theoretical methods have been developed to establish the reduced thermal conductivity. The fundamental understanding of how phonons move and the physical mechanisms behind nanoscale thermal transport, however, remains poorly understood. Here we move beyond thermal conductivity calculations and provide a rigorous and comprehensive physical description of thermal phonon transport in superlattices by solving the Boltzmann transport equation and using the Beckman-Kirchhoff surface scattering theory with shadowing to precisely describe phonon-surface interactions. We show that thermal transport in superlattices can be divided in two different heat transport modes having different physical properties at small length scales: layer-restricted and extended heat modes. We study how interface conditions, periodicity, and composition can be used to manipulate the distribution of thermal energy flow among such layer-restricted and extended heat modes. From predicted frequency and mean free path spectra of superlattices, we also investigate the existence of wave effects. The results and insights in this paper advance the fundamental understanding of heat transport in superlattices and the prospects of rationally designing thermal systems with tailored phonon transport properties.

Simulations of heart valves by thin shells with non-linear material properties

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Asgharzadeh, Hafez; Hedayat, Mohammadali

2016-11-01

The primary function of a heart valve is to allow blood to flow in only one direction through the heart. Triangular thin-shell finite element formulation is implemented, which considers only translational degrees of freedom, in three-dimensional domain to simulate heart valves undergoing large deformations. The formulation is based on the nonlinear Kirchhoff thin-shell theory. The developed method is intensively validated against numerical and analytical benchmarks. This method is added to previously developed membrane method to obtain more realistic results since ignoring bending forces can results in unrealistic wrinkling of heart valves. A nonlinear Fung-type constitutive relation, based on experimentally measured biaxial loading tests, is used to model the material properties for response of the in-plane motion in heart valves. Furthermore, the experimentally measured liner constitutive relation is used to model the material properties to capture the flexural motion of heart valves. The Fluid structure interaction solver adopts a strongly coupled partitioned approach that is stabilized with under-relaxation and the Aitken acceleration technique. This work was supported by American Heart Association (AHA) Grant 13SDG17220022 and the Center of Computational Research (CCR) of University at Buffalo.

Robustness of a multimodal piezoelectric damping involving the electrical analogue of a plate

NASA Astrophysics Data System (ADS)

Lossouarn, Boris; Cunefare, Kenneth A.; Aucejo, Mathieu; Deü, Jean-François

2016-04-01

Multimodal passive damping of a mechanical structure can be implemented by a coupling to a secondary structure exhibiting similar modal properties. When considering a piezoelectric coupling, the secondary structure is an electrical network. A suitable topology for such a network can be obtained by a finite difference formulation of the mechanical equations, followed by a direct electromechanical analogy. This procedure is applied to the Kirchhoff-Love theory in order to find the electrical analogue of a clamped plate. The passive electrical network is implemented with inductors, transformers and the inherent capacitance of the piezoelectric patches. The electrical resonances are tuned to approach those of several mechanical modes simultaneously. This yields a broadband reduction of the plate vibrations through the array of interconnected piezoelectric patches. The robustness of the control strategy is evaluated by introducing perturbations in the mechanical or electrical designs. A non-optimal tuning is considered by way of a uniform variation of the network inductance. Then, the effect of local or boundary modifications of the electromechanical system is observed experimentally. In the end, the use of an analogous electrical network appears as an efficient and robust solution for the multimodal control of a plate.

Discrete crack growth analysis methodology for through cracks in pressurized fuselage structures

NASA Technical Reports Server (NTRS)

Potyondy, David O.; Wawrzynek, Paul A.; Ingraffea, Anthony R.

1994-01-01

A methodology for simulating the growth of long through cracks in the skin of pressurized aircraft fuselage structures is described. Crack trajectories are allowed to be arbitrary and are computed as part of the simulation. The interaction between the mechanical loads acting on the superstructure and the local structural response near the crack tips is accounted for by employing a hierarchical modeling strategy. The structural response for each cracked configuration is obtained using a geometrically nonlinear shell finite element analysis procedure. Four stress intensity factors, two for membrane behavior and two for bending using Kirchhoff plate theory, are computed using an extension of the modified crack closure integral method. Crack trajectories are determined by applying the maximum tangential stress criterion. Crack growth results in localized mesh deletion, and the deletion regions are remeshed automatically using a newly developed all-quadrilateral meshing algorithm. The effectiveness of the methodology and its applicability to performing practical analyses of realistic structures is demonstrated by simulating curvilinear crack growth in a fuselage panel that is representative of a typical narrow-body aircraft. The predicted crack trajectory and fatigue life compare well with measurements of these same quantities from a full-scale pressurized panel test.

Exploring the resonant vibration of thin plates: Reconstruction of Chladni patterns and determination of resonant wave numbers.

PubMed

Tuan, P H; Wen, C P; Chiang, P Y; Yu, Y T; Liang, H C; Huang, K F; Chen, Y F

2015-04-01

The Chladni nodal line patterns and resonant frequencies for a thin plate excited by an electronically controlled mechanical oscillator are experimentally measured. Experimental results reveal that the resonant frequencies can be fairly obtained by means of probing the variation of the effective impedance of the exciter with and without the thin plate. The influence of the extra mass from the central exciter is confirmed to be insignificant in measuring the resonant frequencies of the present system. In the theoretical aspect, the inhomogeneous Helmholtz equation is exploited to derive the response function as a function of the driving wave number for reconstructing experimental Chladni patterns. The resonant wave numbers are theoretically identified with the maximum coupling efficiency as well as the maximum entropy principle. Substituting the theoretical resonant wave numbers into the derived response function, all experimental Chladni patterns can be excellently reconstructed. More importantly, the dispersion relationship for the flexural wave of the vibrating plate can be determined with the experimental resonant frequencies and the theoretical resonant wave numbers. The determined dispersion relationship is confirmed to agree very well with the formula of the Kirchhoff-Love plate theory.

Nonlinear dynamics of contact interaction of a size-dependent plate supported by a size-dependent beam

NASA Astrophysics Data System (ADS)

Awrejcewicz, J.; Krysko, V. A.; Yakovleva, T. V.; Pavlov, S. P.; Krysko, V. A.

2018-05-01

A mathematical model of complex vibrations exhibited by contact dynamics of size-dependent beam-plate constructions was derived by taking the account of constraints between these structural members. The governing equations were yielded by variational principles based on the moment theory of elasticity. The centre of the investigated plate was supported by a beam. The plate and the beam satisfied the Kirchhoff/Euler-Bernoulli hypotheses. The derived partial differential equations (PDEs) were reduced to the Cauchy problems by the Faedo-Galerkin method in higher approximations, whereas the Cauchy problem was solved using a few Runge-Kutta methods. Reliability of results was validated by comparing the solutions obtained by qualitatively different methods. Complex vibrations were investigated with the help of methods of nonlinear dynamics such as vibration signals, phase portraits, Fourier power spectra, wavelet analysis, and estimation of the largest Lyapunov exponents based on the Rosenstein, Kantz, and Wolf methods. The effect of size-dependent parameters of the beam and plate on their contact interaction was investigated. It was detected and illustrated that the first contact between the size-dependent structural members implies chaotic vibrations. In addition, problems of chaotic synchronization between a nanoplate and a nanobeam were addressed.

Modeling polymorphic transformation of rotating bacterial flagella in a viscous fluid

NASA Astrophysics Data System (ADS)

Ko, William; Lim, Sookkyung; Lee, Wanho; Kim, Yongsam; Berg, Howard C.; Peskin, Charles S.

2017-06-01

The helical flagella that are attached to the cell body of bacteria such as Escherichia coli and Salmonella typhimurium allow the cell to swim in a fluid environment. These flagella are capable of polymorphic transformation in that they take on various helical shapes that differ in helical pitch, radius, and chirality. We present a mathematical model of a single flagellum described by Kirchhoff rod theory that is immersed in a fluid governed by Stokes equations. We perform numerical simulations to demonstrate two mechanisms by which polymorphic transformation can occur, as observed in experiments. First, we consider a flagellar filament attached to a rotary motor in which transformations are triggered by a reversal of the direction of motor rotation [L. Turner et al., J. Bacteriol. 182, 2793 (2000), 10.1128/JB.182.10.2793-2801.2000]. We then consider a filament that is fixed on one end and immersed in an external fluid flow [H. Hotani, J. Mol. Biol. 156, 791 (1982), 10.1016/0022-2836(82)90142-5]. The detailed dynamics of the helical flagellum interacting with a viscous fluid is discussed and comparisons with experimental and theoretical results are provided.

Experimental solution for scattered imaging of the interference of plasmonic and photonic mode waves launched by metal nano-slits.

PubMed

Li, Xing; Gao, Yaru; Jiang, Shuna; Ma, Li; Liu, Chunxiang; Cheng, Chuanfu

2015-02-09

Using an L-shaped metal nanoslit to generate waves of the pure photonic and plasmonic modes simultaneously, we perform an experimental solution for the scattered imaging of the interference of the two waves. From the fringe data of interference, the amplitudes and the wavevector components of the two waves are obtained. The initial phases of the two waves are obtained from the phase map reconstructed with the interference of the scattered image and the reference wave in the interferometer. The difference in the wavevector components gives rise to an additional phase delay. We introduce the scattering theory under Kirchhoff's approximation to metal slit regime and explain the wavevector difference reasonably. The solution of the quantities is a comprehensive reflection of excitation, scattering and interference of the two waves. By decomposing the polarized incident field with respect to the slit element, the scattered image produced by slit of arbitrary shape can be solved with the nanoscale Huygens-Fresnel principle. This is demonstrated by the experimental intensity pattern and phase map produced by a ring-slit and its consistency with the calculated results.

Two-point resistance of the Möbius ladder

NASA Astrophysics Data System (ADS)

Chair, Noureddine; Dannoun, Elham Mohammed Ali

2015-03-01

Exact formulas for the two-point resistance and the Kirchhoff index of the Möbius ladder are given based on the recently developed analytical approach by Chair (2012 Ann. Phys. 327 2899). The expression for the two-point resistance is written in terms of the two-point resistance of N/2-cycle graph and the Bejaia and the Pisa numbers recently introduced by the first author.

Backscatter analysis of dihedral corner reflectors using physical optics and the physical theory of diffraction

NASA Technical Reports Server (NTRS)

Griesser, Timothy; Balanis, Constantine A.

1987-01-01

The backscatter cross-sections of dihedral corner reflectors in the azimuthal plane are presently determined by both physical optics (PO) and the physical theory of diffraction (PTD), yielding results for the vertical and horizontal polarizations. In the first analysis method used, geometrical optics is used in place of PO at initial reflections in order to maintain the planar character of the reflected wave and reduce the complexity of the analysis. In the second method, PO is used at almost every reflection in order to maximize the accuracy of the PTD solution at the expense of a rapid increase in complexity. Induced surface current densities and resulting cross section patterns are illustrated for the two methods.

Strain distribution in an Si single crystal measured by interference fringes of X-ray mirage diffraction

PubMed Central

Jongsukswat, Sukswat; Fukamachi, Tomoe; Ju, Dongying; Negishi, Riichirou; Hirano, Keiichi; Kawamura, Takaaki

2013-01-01

In X-ray interference fringes accompanied by mirage diffraction, variations have been observed in the spacing and position of the fringes from a plane-parallel Si single crystal fixed at one end as a function of distance from the incident plane of the X-rays to the free crystal end. The variations can be explained by distortion of the sample crystal due to gravity. From the variations and positions of the fringes, the strain gradient of the crystal has been determined. The distribution of the observed strain agrees with that expected from rod theory except for residual strain. When the distortion is large, the observed strain distribution does not agree with that expected from rod theory. PMID:24068841

High frequency scattering by a smooth coated cylinder simulated with generalized impedance boundary conditions

NASA Technical Reports Server (NTRS)

Syed, Hasnain H.; Volakis, John L.

1991-01-01

Rigorous uniform geometrical theory of diffraction (UGTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristic to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. As usual, the diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.

Probing Atom-Surface Interactions by Diffraction of Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Bender, Helmar; Stehle, Christian; Zimmermann, Claus; Slama, Sebastian; Fiedler, Johannes; Scheel, Stefan; Buhmann, Stefan Yoshi; Marachevsky, Valery N.

2014-01-01

In this article, we analyze the Casimir-Polder interaction of atoms with a solid grating and the repulsive interaction between the atoms and the grating in the presence of an external laser source. The Casimir-Polder potential is evaluated exactly in terms of Rayleigh reflection coefficients and via an approximate Hamaker approach. The laser-tuned repulsive interaction is given in terms of Rayleigh transmission coefficients. The combined potential landscape above the solid grating is probed locally by diffraction of Bose-Einstein condensates. Measured diffraction efficiencies reveal information about the shape of the potential landscape in agreement with the theory based on Rayleigh decompositions.

Ordered rate constitutive theories for thermoviscoelastic solids with memory in Lagrangian description using Gibbs potential

NASA Astrophysics Data System (ADS)

Surana, K. S.; Reddy, J. N.; Nunez, Daniel

2015-11-01

This paper presents ordered rate constitutive theories of orders m and n, i.e., ( m, n) for finite deformation of homogeneous, isotropic, compressible and incompressible thermoviscoelastic solids with memory in Lagrangian description using entropy inequality in Gibbs potential Ψ as an alternate approach of deriving constitutive theories using entropy inequality in terms of Helmholtz free energy density Φ. Second Piola-Kirchhoff stress σ [0] and Green's strain tensor ɛ [0] are used as conjugate pair. We consider Ψ, heat vector q, entropy density η and rates of upto orders m and n of σ [0] and ɛ [0], i.e., σ [ i]; i = 0, 1, . . . , m and ɛ [ j]; j = 0, 1, . . . , n. We choose Ψ, ɛ [ n], q and η as dependent variables in the constitutive theories with ɛ [ j]; j = 0, 1, . . . , n - 1, σ [ i]; i = 0, 1, . . . , m, temperature gradient g and temperature θ as their argument tensors. Rationale for this choice is explained in the paper. Entropy inequality, decomposition of σ [0] into equilibrium and deviatoric stresses, the conditions resulting from entropy inequality and the theory of generators and invariants are used in the derivations of ordered rate constitutive theories of orders m and n in stress and strain tensors. Constitutive theories for the heat vector q (of up to orders m and n - 1) that are consistent (in terms of the argument tensors) with the constitutive theories for ɛ [ n] (of up to orders m and n) are also derived. Many simplified forms of the rate theories of orders ( m, n) are presented. Material coefficients are derived by considering Taylor series expansions of the coefficients in the linear combinations representing ɛ [ n] and q using the combined generators of the argument tensors about a known configuration {{\\underline{\\varOmega}}} in the combined invariants of the argument tensors and temperature. It is shown that the rate constitutive theories of order one ( m = 1, n = 1) when further simplified result in constitutive theories that resemble currently used theories but are in fact different. The solid continua characterized by these theories have mechanisms of elasticity, dissipation and memory, i.e., relaxation behavior or rheology. Fourier heat conduction law is shown to be an over simplified case of the rate theory of order one ( m = 1, n = 1) for q. The paper establishes when there is equivalence between the constitutive theories derived here using Ψ and those presented in reference Surana et al. (Acta Mech. doi:10.1007/s00707-014-1173-6, 2014) that are derived using Helmholtz free energy density Φ. The fundamental differences between the two constitutive theories in terms of physics and their explicit forms using Φ and Ψ are difficult to distinguish from the ordered theories of orders ( m, n) due to complexity of expressions. However, by choosing lower ordered theories, the difference between the two approaches can be clearly seen.

Acoustic Propagation and Barrier Diffraction Over an Impedance Plane.

DTIC Science & Technology

1982-10-13

Further appreciation is extended to Dr. Eugen"J. Skudrzyk, Dr. Jiri Tichy, Dr. Alan D. Stuart, and Dr. Vernon H. Neubert for actively participating on my...10 More recent theoretical studies have expanded upon the foundations laid by Rudnick, Lawhead, and Ingard. Paul (1957) studied the two-media problem...series for functions occurring in the theory of diffraction of waves by wedges. Journal of Mathematical Physics, 1956, 34, 245-255. Paul , D. I

UTD analysis of electromagnetic scattering by flat structures. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Sikta, F. A.; Peters, L., Jr.

1981-01-01

The different scattering mechanisms that contribute to the radar cross of finite flat plates were identified and analyzed. The geometrical theory of diffraction, the equivalent current and the corner diffraction are used for this study. A study of the cross polarized field for a monopole mounted on a plate is presented, using novel edge wave mechanism in the analysis. The results are compared with moment method solutions as well as measured data.

Diffraction contrast near heterostructure boundaries--its nature and its application.

PubMed

Bangert, U; Harvey, A J

1993-03-01

Two phenomena of diffraction contrast arising at or near III-V compound heterostructure boundaries are described and quantitatively analyzed. In the first observation alpha/delta-fringe contrast at boundaries inclined to the electron beam is discussed. Theoretical fringe profiles are generated according to the theory by Gevers et al. in 1964, which are then compared with experimental profiles. Applications to the characterization of AlGaAs/GaAs and InGaAsP/InP interfaces regarding composition, abruptness, and lattice tilt are presented. In the second study a new and very sensitive characterization technique for the direct determination of the strain in strained-layer structures is described. The method uses electron microscope images of 90 degrees-wedges, which exhibit a shift in the thickness contours due to strain relaxation at the edge, and compares these to images which are obtained theoretically by implementing finite element strain calculations in wedges in the dynamical theory of diffraction contrast. The considerable potential of this method is demonstrated on the strain analysis of strained GaInAs/GaAs structures.

An extended UTD analysis for the scattering and diffraction from cubic polynomial strips

NASA Technical Reports Server (NTRS)

Constantinides, E. D.; Marhefka, R. J.

1993-01-01

Spline and polynomial type surfaces are commonly used in high frequency modeling of complex structures such as aircraft, ships, reflectors, etc. It is therefore of interest to develop an efficient and accurate solution to describe the scattered fields from such surfaces. An extended Uniform Geometrical Theory of Diffraction (UTD) solution for the scattering and diffraction from perfectly conducting cubic polynomial strips is derived and involves the incomplete Airy integrals as canonical functions. This new solution is universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave convex boundaries containing edges. The classic UTD solution fails to describe the more complicated field behavior associated with higher order phase catastrophes and therefore a new set of uniform reflection and first-order edge diffraction coefficients is derived. Also, an additional diffraction coefficient associated with a zero-curvature (inflection) point is presented. Higher order effects such as double edge diffraction, creeping waves, and whispering gallery modes are not examined. The extended UTD solution is independent of the scatterer size and also provides useful physical insight into the various scattering and diffraction processes. Its accuracy is confirmed via comparison with some reference moment method results.

Acceleration Wave Propagation in Hyperelastic Rods of Variable Cross-Section.

DTIC Science & Technology

1981-07-01

direction of propagation. Many authors have considered both static and dynamic problems for such materials, of whom we mention only Antman [2] and... Antman and Jordan [3] who studied the Kirchhoff problem for nonlinearly elastic rods and qualitative properties in general, Jeffrey and Teymur [4] and...Jeffrey and Suhubi [5] who considered shock wave formation and acceleration wave propagation through periodically layered media, and Antman and Liu [6

Visibility of quantum graph spectrum from the vertices

NASA Astrophysics Data System (ADS)

Kühn, Christian; Rohleder, Jonathan

2018-03-01

We investigate the relation between the eigenvalues of the Laplacian with Kirchhoff vertex conditions on a finite metric graph and a corresponding Titchmarsh-Weyl function (a parameter-dependent Neumann-to-Dirichlet map). We give a complete description of all real resonances, including multiplicities, in terms of the edge lengths and the connectivity of the graph, and apply it to characterize all eigenvalues which are visible for the Titchmarsh-Weyl function.

The Problem of Modeling the Elastomechanics in Engineering

DTIC Science & Technology

1990-02-01

element method by the code PROBE (McNeil Schwendler- Noetic ) and STRIPE (Aeronautical Institute of Sweden). These codes have various error checks so that...Mindlin solutions converge to the Kirchhoff solution as d--O, see eg. [12), [19]. For a detailed study of the asymptotic behavior of Reissner...of study and research for foreign students in numerical mathematics who are supported by foreign govern- ments or exchange agencies (Fulbright, etc

Bending Boundary Layers in Laminated-Composite Circular Cylindrical Shells

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Smeltzer, Stanley S., III

2000-01-01

A study of the attenuation of bending boundary layers in balanced and unbalanced, symmetrically and unsymmetrically laminated cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize the effects of laminate orthotropy and anisotropy on the bending boundary-layer decay length in a very general manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all laminates considered, the results show that the differences between results obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that, in some cases, neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and, in other cases, results in an overestimation.

Instability of hooks during bacterial flagellar swimming

NASA Astrophysics Data System (ADS)

Jabbarzadeh, Mehdi; Fu, Henry C.; Henry Fu Team

2016-11-01

In bacteria, a flexible hook transmits torque from the rotary motor at the cell body to the flagellum. Previously, the hook has been modeled as a Kirchhoff rod between the cell body and rotating flagellum. To study effects of the hook's flexibility on the bacteria's swimming speed and trajectory for wide range hook stiffnesses and flagellum configurations, we develop an efficient simplified spring model for the hook by linearizing the Kirchhoff rod. We treat the hydrodynamics of the cell body and helical flagellum using resistance matrices calculated by the method of regularized Stokeslets. We investigate flagellar and swimming dynamics for a range of hook flexibilities and flagellar orientations relative to the cell body and compare the results to models without hook flexibility. We investigate in detail parameters corresponding to E. coli and Vibrio alginolyticus. Generally, the flagellum changes orientation relative to the cell body, undergoing an orbit with the period of the motor rotation. We find that as the hook stiffness decreases, steady-state orbits of the flagellum first become unstable before the hook buckles, which may suggest a new mechanism of flick initiation in run-reverse-flick motility. We also find that for some parameter ranges, there are multiple stable steady state orbits, which may have implications for the tumbling and turning of bacteria.

Propagation of coherent light pulses with PHASE

NASA Astrophysics Data System (ADS)

Bahrdt, J.; Flechsig, U.; Grizzoli, W.; Siewert, F.

2014-09-01

The current status of the software package PHASE for the propagation of coherent light pulses along a synchrotron radiation beamline is presented. PHASE is based on an asymptotic expansion of the Fresnel-Kirchhoff integral (stationary phase approximation) which is usually truncated at the 2nd order. The limits of this approximation as well as possible extensions to higher orders are discussed. The accuracy is benchmarked against a direct integration of the Fresnel-Kirchhoff integral. Long range slope errors of optical elements can be included by means of 8th order polynomials in the optical element coordinates w and l. Only recently, a method for the description of short range slope errors has been implemented. The accuracy of this method is evaluated and examples for realistic slope errors are given. PHASE can be run either from a built-in graphical user interface or from any script language. The latter method provides substantial flexibility. Optical elements including apertures can be combined. Complete wave packages can be propagated, as well. Fourier propagators are included in the package, thus, the user may choose between a variety of propagators. Several means to speed up the computation time were tested - among them are the parallelization in a multi core environment and the parallelization on a cluster.

Limited-memory BFGS based least-squares pre-stack Kirchhoff depth migration

NASA Astrophysics Data System (ADS)

Wu, Shaojiang; Wang, Yibo; Zheng, Yikang; Chang, Xu

2015-08-01

Least-squares migration (LSM) is a linearized inversion technique for subsurface reflectivity estimation. Compared to conventional migration algorithms, it can improve spatial resolution significantly with a few iterative calculations. There are three key steps in LSM, (1) calculate data residuals between observed data and demigrated data using the inverted reflectivity model; (2) migrate data residuals to form reflectivity gradient and (3) update reflectivity model using optimization methods. In order to obtain an accurate and high-resolution inversion result, the good estimation of inverse Hessian matrix plays a crucial role. However, due to the large size of Hessian matrix, the inverse matrix calculation is always a tough task. The limited-memory BFGS (L-BFGS) method can evaluate the Hessian matrix indirectly using a limited amount of computer memory which only maintains a history of the past m gradients (often m < 10). We combine the L-BFGS method with least-squares pre-stack Kirchhoff depth migration. Then, we validate the introduced approach by the 2-D Marmousi synthetic data set and a 2-D marine data set. The results show that the introduced method can effectively obtain reflectivity model and has a faster convergence rate with two comparison gradient methods. It might be significant for general complex subsurface imaging.

Analysis of three-dimensional-cavity-backed aperture antennas using a Combined Finite Element Method/Method of Moments/Geometrical Theory of Diffraction technique

NASA Technical Reports Server (NTRS)

Reddy, C. J.; Deshpande, M. D.; Cockrell, C. R.; Beck, F. B.

1995-01-01

A combined finite element method (FEM) and method of moments (MoM) technique is presented to analyze the radiation characteristics of a cavity-fed aperture in three dimensions. Generalized feed modeling has been done using the modal expansion of fields in the feed structure. Numerical results for some feeding structures such as a rectangular waveguide, circular waveguide, and coaxial line are presented. The method also uses the geometrical theory of diffraction (GTD) to predict the effect of a finite ground plane on radiation characteristics. Input admittance calculations for open radiating structures such as a rectangular waveguide, a circular waveguide, and a coaxial line are shown. Numerical data for a coaxial-fed cavity with finite ground plane are verified with experimental data.

X-ray characterization of curved crystals for hard x-ray astronomy

NASA Astrophysics Data System (ADS)

Buffagni, Elisa; Bonnini, Elisa; Ferrari, Claudio; Virgilli, Enrico; Frontera, Filippo

2015-05-01

Among the methods to focus photons the diffraction in crystals results as one of the most effective for high energy photons. An assembling of properly oriented crystals can form a lens able to focus x-rays at high energy via Laue diffraction in transmission geometry; this is a Laue lens. The x-ray diffraction theory provides that the maximum diffraction efficiency is achieved in ideal mosaic crystals, but real mosaic crystals show diffraction efficiencies several times lower than the ideal case due to technological problems. An alternative and convenient approach is the use of curved crystals. We have recently optimized an efficient method based on the surface damage of crystals to produce self-standing uniformly curved Si, GaAs and Ge tiles of thickness up to 2-3 mm and curvature radii R down to a few meters. We show that, for curved diffracting planes, such crystals have a diffraction efficiency nearly forty times higher than the diffraction efficiency of perfect similar flat crystals, thus very close to that of ideal mosaic crystals. Moreover, in an alternative configuration where the diffracting planes are perpendicular to the curved ones, a focusing effect occurs and will be shown. These results were obtained for several energies between 17 and 120 keV with lab sources or at high energy facilities such as LARIX at Ferrara (Italy), ESRF at Grenoble (France), and ANKA at Karlsruhe (Germany).

Implementation of diffraction in a ray-tracing model for the prediction of noise in open-plan offices.

PubMed

Chevret, P; Chatillon, J

2012-11-01

Sound prediction in open-plan offices is a real challenge because of the complexity of the layout of such offices, and therefore because of the multitude of acoustic phenomena involved. One such phenomenon, of primary importance, and not the least challenging of them, is the diffraction by screens and low dividers that usually partition the workspace. This paper describes implementing the equations of the Uniform Theory of Diffraction [McNamara et al. (1990). Introduction to the Uniform Theory of Diffraction (Artech House, Boston)] in an existing ray-tracing model initially dedicated to sound prediction in industrial premises. For the purposes of validation, a series of measurements was conducted in a semi-anechoic chamber in the same manner as Wang and Bradley [(2002). Appl. Acoust. 63, 849-866] but including real desktops instead of single screens. A first phase was dedicated to controlling the quality of the installation by making comparisons with McNamara's solution for a single screen on a rigid floor. Then, the validation itself was conducted with measurements on real desktops, first without a ceiling, and then with a rigid ceiling suspended above the double desk. The results of the comparisons between calculations and measurements in this configuration have demonstrated that the model is an effective tool for predicting sound levels in an open-plan office.

X-Ray Diffraction on NIF

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

Eggert, J H; Wark, J

2012-02-15

The National Ignition Facility (NIF) is currently a 192 beam, 1.6 MJ laser. NIF Ramp-Compression Experiments have already made the relevant exo-planet pressure range from 1 to 50 Mbar accessible. We Proposed to Study Carbon Phases by X-Ray Diffraction on NIF. Just a few years ago, ultra-high pressure phase diagrams for materials were very 'simple'. New experiments and theories point out surprising and decidedly complex behavior at the highest pressures considered. High pressures phases of aluminum are also predicted to be complex. Recent metadynamics survey of carbon proposed a dynamic pathway among multiple phases. We need to develop diagnostics andmore » techniques to explore this new regime of highly compressed matter science. X-Ray Diffraction - Understand the phase diagram/EOS/strength/texture of materials to 10's of Mbar. Strategy and physics goals: (1) Powder diffraction; (2) Begin with diamond; (3) Continue with metals etc.; (4) Explore phase diagrams; (5) Develop liquid diffraction; and (6) Reduce background/improve resolution.« less

Unified aeroacoustics analysis for high speed turboprop aerodynamics and noise. Volume 2: Development of theory for wing shielding

NASA Technical Reports Server (NTRS)

Amiet, R. K.

1991-01-01

A unified theory for aerodynamics and noise of advanced turboprops is presented. The theory and a computer code developed for evaluation at the shielding benefits that might be expected by an aircraft wing in a wing-mounted propeller installation are presented. Several computed directivity patterns are presented to demonstrate the theory. Recently with the advent of the concept of using the wing of an aircraft for noise shielding, the case of diffraction by a surface in a flow has been given attention. The present analysis is based on the case of diffraction of no flow. By combining a Galilean and a Lorentz transform, the wave equation with a mean flow can be reduced to the ordinary equation. Allowance is also made in the analysis for the case of a swept wing. The same combination of Galilean and Lorentz transforms lead to a problem with no flow but a different sweep. The solution procedures for the cases of leading and trailing edges are basically the same. Two normalizations of the solution are given by the computer program. FORTRAN computer programs are presented with detailed documentation. The output from these programs compares favorably with the results of other investigators.

Diffraction of dust acoustic waves by a circular cylinder

NASA Astrophysics Data System (ADS)

Kim, S.-H.; Heinrich, J. R.; Merlino, R. L.

2008-09-01

The diffraction of dust acoustic (DA) waves around a long dielectric rod is observed using video imaging methods. The DA waves are spontaneously excited in a dusty plasma produced in a direct current glow discharge plasma. The rod acquires a negative charge that produces a coaxial dust void around it. The diameter of the void is the effective size of the "obstacle" encountered by the waves. The wavelength of the DA waves is approximately the size of the void. The observations are considered in relation to the classical problem of the diffraction of sound waves from a circular cylinder, a problem first analyzed by Lord Rayleigh [Theory of Sound, 2nd ed. (MacMillan, London, 1896)].

Beam-splitter switches based on zenithal bistable liquid-crystal gratings.

PubMed

Zografopoulos, Dimitrios C; Beccherelli, Romeo; Kriezis, Emmanouil E

2014-10-01

The tunable optical diffractive properties of zenithal bistable nematic liquid-crystal gratings are theoretically investigated. The liquid-crystal orientation is rigorously solved via a tensorial formulation of the Landau-de Gennes theory and the optical transmission properties of the gratings are investigated via full-wave finite-element frequency-domain simulations. It is demonstrated that by proper design the two stable states of the grating can provide nondiffracting and diffracting operation, the latter with equal power splitting among different diffraction orders. An electro-optic switching mechanism, based on dual-frequency nematic materials, and its temporal dynamics are further discussed. Such gratings provide a solution towards tunable beam-steering and beam-splitting components with extremely low power consumption.

Effect of multiple circular holes Fraunhofer diffraction for the infrared optical imaging

NASA Astrophysics Data System (ADS)

Lu, Chunlian; Lv, He; Cao, Yang; Cai, Zhisong; Tan, Xiaojun

2014-11-01

With the development of infrared optics, infrared optical imaging systems play an increasingly important role in modern optical imaging systems. Infrared optical imaging is used in industry, agriculture, medical, military and transportation. But in terms of infrared optical imaging systems which are exposed for a long time, some contaminations will affect the infrared optical imaging. When the contamination contaminate on the lens surface of the optical system, it would affect diffraction. The lens can be seen as complementary multiple circular holes screen happen Fraunhofer diffraction. According to Babinet principle, you can get the diffraction of the imaging system. Therefore, by studying the multiple circular holes Fraunhofer diffraction, conclusions can be drawn about the effect of infrared imaging. This paper mainly studies the effect of multiple circular holes Fraunhofer diffraction for the optical imaging. Firstly, we introduce the theory of Fraunhofer diffraction and Point Spread Function. Point Spread Function is a basic tool to evaluate the image quality of the optical system. Fraunhofer diffraction will affect Point Spread Function. Then, the results of multiple circular holes Fraunhofer diffraction are given for different hole size and hole spacing. We choose the hole size from 0.1mm to 1mm and hole spacing from 0.3mm to 0.8mm. The infrared wavebands of optical imaging are chosen from 1μm to 5μm. We use the MATLAB to simulate light intensity distribution of multiple circular holes Fraunhofer diffraction. Finally, three-dimensional diffraction maps of light intensity are given to contrast.

Theoretical astrophysics in the 19th century (Homage to Radó von Kövesligethy)

NASA Astrophysics Data System (ADS)

Balázs, Lajos G.

The nature of astronomical information is determined mostly by the incoming light. Theoretical astrophysics means basically the theory of light emission and its relation to the physical constitution of the emitting celestial bodies. The necessary physical disciplines include theory of gravitation, theory of radiation, thermodynamics, matter--radiation interaction. The most significant theoretical achievement in the 17th - 18th century was the axiomatic foundation of mechanics and the law of gravitation. In the context of the nature of light, there were two conceptions: Newton contra Huygens, i.e. particle versus wave phenomenon. Using the theory of gravitation, first speculations appeared on black holes (Michell, Laplace), cosmogony (Kant-Laplace theory), the structure of the Milky Way (Kant), and the explanation of motion of the celestial bodies. The Olbers Paradox, formulated in the 19th century, is still one of the most significant constraints on observational cosmology. The development of thermodynamics, matter-radiation interaction, development of the theory of electromagnetism became important milestones. Maxwell's theory was the classical framework of the interaction between matter and radiation. Kirchhoff and Bunsen's revolutionary discovery of spectral analysis (1859) showed that observation of spectra makes it possible to study the chemical composition of emitting bodies. Thermodynamics predicted the existence of the black body radiation. It did not succeed, however, to determine the functional form of the wavelength dependence. A combination of the thermodynamic equation of state with the equation of hydrostatics resulted in the first stellar models (Lane, Ritter, Schuster). The first successful spectral equation of black body radiation was the theory of continuous spectra of celestial bodies by Radó von Kövesligethy (published 1885 in Hungarian, 1890 in German). Kövesligethy made several assumptions on the matter-radiation interaction: radiating matter consists of interacting particles, the form of interaction is an inverse power law, the radiation field is represented by the aether, aether is made also from interacting particles, light is the propagation of the oscillation of the aether particles, there is an equipartition between the oscillations energy of material and aetheric particles. Based on these assumptions, he derived a spectral equation with the following properties: the spectral distribution of radiation depends only on the temperature, the total irradiated energy is finite (15 years before Planck!), the wavelength of the intensity maximum is inversely proportional to the temperature (eight years before Wien!). Using his spectral equation, he estimated the temperature of several celestial bodies, including the Sun.

A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations

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

Zhao, B.B.; Ertekin, R.C.; College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin

2015-02-15

This work is on the nonlinear diffraction analysis of shallow-water waves, impinging on submerged obstacles, by two related theories, namely the classical Green–Naghdi (GN) equations and the Irrotational Green–Naghdi (IGN) equations, both sets of equations being at high levels and derived for incompressible and inviscid flows. Recently, the high-level Green–Naghdi equations have been applied to some wave transformation problems. The high-level IGN equations have also been used in the last decade to study certain wave propagation problems. However, past works on these theories used different numerical methods to solve these nonlinear and unsteady sets of differential equations and at differentmore » levels. Moreover, different physical problems have been solved in the past. Therefore, it has not been possible to understand the differences produced by these two sets of theories and their range of applicability so far. We are thus motivated to make a direct comparison of the results produced by these theories by use of the same numerical method to solve physically the same wave diffraction problems. We focus on comparing these two theories by using similar codes; only the equations used are different but other parts of the codes, such as the wave-maker, damping zone, discretion method, matrix solver, etc., are exactly the same. This way, we eliminate many potential sources of differences that could be produced by the solution of different equations. The physical problems include the presence of various submerged obstacles that can be used for example as breakwaters or to represent the continental shelf. A numerical wave tank is created by placing a wavemaker on one end and a wave absorbing beach on the other. The nonlinear and unsteady sets of differential equations are solved by the finite-difference method. The results are compared with different equations as well as with the available experimental data.« less

A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations

NASA Astrophysics Data System (ADS)

Zhao, B. B.; Ertekin, R. C.; Duan, W. Y.

2015-02-01

This work is on the nonlinear diffraction analysis of shallow-water waves, impinging on submerged obstacles, by two related theories, namely the classical Green-Naghdi (GN) equations and the Irrotational Green-Naghdi (IGN) equations, both sets of equations being at high levels and derived for incompressible and inviscid flows. Recently, the high-level Green-Naghdi equations have been applied to some wave transformation problems. The high-level IGN equations have also been used in the last decade to study certain wave propagation problems. However, past works on these theories used different numerical methods to solve these nonlinear and unsteady sets of differential equations and at different levels. Moreover, different physical problems have been solved in the past. Therefore, it has not been possible to understand the differences produced by these two sets of theories and their range of applicability so far. We are thus motivated to make a direct comparison of the results produced by these theories by use of the same numerical method to solve physically the same wave diffraction problems. We focus on comparing these two theories by using similar codes; only the equations used are different but other parts of the codes, such as the wave-maker, damping zone, discretion method, matrix solver, etc., are exactly the same. This way, we eliminate many potential sources of differences that could be produced by the solution of different equations. The physical problems include the presence of various submerged obstacles that can be used for example as breakwaters or to represent the continental shelf. A numerical wave tank is created by placing a wavemaker on one end and a wave absorbing beach on the other. The nonlinear and unsteady sets of differential equations are solved by the finite-difference method. The results are compared with different equations as well as with the available experimental data.

Numerical simulation of rotating body movement in medium with various densities

NASA Astrophysics Data System (ADS)

Tenenev, Valentin A.; Korolev, Stanislav A.; Rusyak, Ivan G.

2016-10-01

The paper proposes an approach to calculate the motion of rotating bodies in resisting medium by solving the Kirchhoff equations of motion in a coordinate system moving with the body and in determination of aerodynamic characteristics of the body with a given geometry by solving the Navier-Stokes equations. We present the phase trajectories of the perturbed motion of a rotating projectile in media with different densities: gas and liquid.

A Superior Kirchhoff Method for Aeroacoustic Noise Prediction: The Ffowcs Williams-Hawkings Equation

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.

1997-01-01

The prediction of aeroacoustic noise is important; all new aircraft must meet noise certification requirements. Local noise standards can be even more stringent. The NASA noise reduction goal is to reduce perceived noise levels by a factor of two in 10 years. The objective of this viewgraph presentation is to demonstrate the superiority of the FW-H approach over the Kirchoff method for aeroacoustics, both analytically and numerically.

A Scalable Distributed Syntactic, Semantic, and Lexical Language Model

DTIC Science & Technology

2012-09-01

Here pa(τ) denotes the set of parent states of τ. If the recursive factorization refers to a graph , then we have a Bayesian network (Lauritzen 1996...Broadly speaking, however, the recursive factorization can refer to a representation more complicated than a graph with a fixed set of nodes and edges...factored language (FL) model (Bilmes and Kirchhoff 2003) is close to the smoothing technique we propose here, the major difference is that FL

Inexpensive robots used to teach dc circuits and electronics

NASA Astrophysics Data System (ADS)

Sidebottom, David L.

2017-05-01

This article describes inexpensive, autonomous robots, built without microprocessors, used in a college-level introductory physics laboratory course to motivate student learning of dc circuits. Detailed circuit descriptions are provided as well as a week-by-week course plan that can guide students from elementary dc circuits, through Kirchhoff's laws, and into simple analog integrated circuits with the motivational incentive of building an autonomous robot that can compete with others in a public arena.

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

Doug Blankenship

PDFs of seismic reflection profiles 101,110, 111 local to the West Flank FORGE site. 45 line kilometers of seismic reflection data are processed data collected in 2001 through the use of vibroseis trucks. The initial analysis and interpretation of these data was performed by Unruh et al. (2001). Optim processed these data by inverting the P-wave first arrivals to create a 2-D velocity structure. Kirchhoff images were then created for each line using velocity tomograms (Unruh et al., 2001).

Teaching Fraunhofer diffraction via experimental and simulated images in the laboratory

NASA Astrophysics Data System (ADS)

Peinado, Alba; Vidal, Josep; Escalera, Juan Carlos; Lizana, Angel; Campos, Juan; Yzuel, Maria

2012-10-01

Diffraction is an important phenomenon introduced to Physics university students in a subject of Fundamentals of Optics. In addition, in the Physics Degree syllabus of the Universitat Autònoma de Barcelona, there is an elective subject in Applied Optics. In this subject, diverse diffraction concepts are discussed in-depth from different points of view: theory, experiments in the laboratory and computing exercises. In this work, we have focused on the process of teaching Fraunhofer diffraction through laboratory training. Our approach involves students working in small groups. They visualize and acquire some important diffraction patterns with a CCD camera, such as those produced by a slit, a circular aperture or a grating. First, each group calibrates the CCD camera, that is to say, they obtain the relation between the distances in the diffraction plane in millimeters and in the computer screen in pixels. Afterwards, they measure the significant distances in the diffraction patterns and using the appropriate diffraction formalism, they calculate the size of the analyzed apertures. Concomitantly, students grasp the convolution theorem in the Fourier domain by analyzing the diffraction of 2-D gratings of elemental apertures. Finally, the learners use a specific software to simulate diffraction patterns of different apertures. They can control several parameters: shape, size and number of apertures, 1-D or 2-D gratings, wavelength, focal lens or pixel size.Therefore, the program allows them to reproduce the images obtained experimentally, and generate others by changingcertain parameters. This software has been created in our research group, and it is freely distributed to the students in order to help their learning of diffraction. We have observed that these hands on experiments help students to consolidate their theoretical knowledge of diffraction in a pedagogical and stimulating learning process.

Microscope Resolution.

ERIC Educational Resources Information Center

Higbie, J.

1981-01-01

Describes problems using the Jenkins and White approach and standard diffraction theory when dealing with the topic of finite conjugate, point-source resolution and how they may be resolved using the relatively obscure Abbe's sine theorem. (JN)

Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings.

PubMed

Márquez, Andrés; Neipp, Cristian; Beléndez, Augusto; Gallego, Sergi; Ortuño, Manuel; Pascual, Inmaculada

2003-09-01

We demonstrate edge-enhanced imaging produced by volume phase gratings recorded on a polyvinyl alcohol/acrylamide photopolymer. Bragg diffraction, exhibited by volume gratings, modifies the impulse response of the imaging system, facilitating spatial filtering operations with no need for a physical Fourier plane. We demonstrate that Kogelnik's coupled-wave theory can be used to calculate the transfer function for the transmitted and the diffracted orders. The experimental and simulated results agree, and they demonstrate the feasibility of our proposal.

X-ray diffraction and X-ray standing-wave study of the lead stearate film structure

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

Blagov, A. E.; Dyakova, Yu. A.; Kovalchuk, M. V.

2016-05-15

A new approach to the study of the structural quality of crystals is proposed. It is based on the use of X-ray standing-wave method without measuring secondary processes and considers the multiwave interaction of diffraction reflections corresponding to different harmonics of the same crystallographic reflection. A theory of multiwave X-ray diffraction is developed to calculate the rocking curves in the X-ray diffraction scheme under consideration for a long-period quasi-one-dimensional crystal. This phase-sensitive method is used to study the structure of a multilayer lead stearate film on a silicon substrate. Some specific structural features are revealed for the surface layer ofmore » the thin film, which are most likely due to the tilt of the upper layer molecules with respect to the external normal to the film surface.« less

Diffractive paths for weak localization in quantum billiards

NASA Astrophysics Data System (ADS)

Březinová, Iva; Stampfer, Christoph; Wirtz, Ludger; Rotter, Stefan; Burgdörfer, Joachim

2008-04-01

We study the weak-localization effect in quantum transport through a clean ballistic cavity with regular classical dynamics. We address the question which paths account for the suppression of conductance through a system where disorder and chaos are absent. By exploiting both quantum and semiclassical methods, we unambiguously identify paths that are diffractively backscattered into the cavity (when approaching the lead mouths from the cavity interior) to play a key role. Diffractive scattering couples transmitted and reflected paths and is thus essential to reproduce the weak-localization peak in reflection and the corresponding antipeak in transmission. A comparison of semiclassical calculations featuring these diffractive paths yields good agreement with full quantum calculations and experimental data. Our theory provides system-specific predictions for the quantum regime of few open lead modes and can be expected to be relevant also for mixed as well as chaotic systems.

Ostwald ripening and interparticle-diffraction effects for illite crystals

USGS Publications Warehouse

Eberl, D.D.; Srodon, J.

1988-01-01

The Warren-Averbach method, an X-ray diffraction (XRD) method used to measure mean particle thickness and particle-thickness distribution, is used to restudy sericite from the Silverton caldera. Apparent particle-thickness distributions indicate that the clays may have undergone Ostwald ripening and that this process has modified the K-Ar ages of the samples. The mechanism of Ostwald ripening can account for many of the features found for the hydrothermal alteration of illite. Expandabilities measured by the XRD peak-position method for illite/smectites (I/S) from various locations are smaller than expandabilities measured by transmission electron microscopy (TEM) and by the Warren-Averbach (W-A) method. This disparity is interpreted as being related to the presence of nonswelling basal surfaces that form the ends of stacks of illite particles (short-stack effect), stacks that, according to the theory of interparticle diffraction, diffract as coherent X-ray scattering domains. -from Authors

Incorporation of interfacial roughness into recursion matrix formalism of dynamical X-ray diffraction in multilayers and superlattices.

PubMed

Lobach, Ihar; Benediktovitch, Andrei; Ulyanenkov, Alexander

2017-06-01

Diffraction in multilayers in the presence of interfacial roughness is studied theoretically, the roughness being considered as a transition layer. Exact (within the framework of the two-beam dynamical diffraction theory) differential equations for field amplitudes in a crystalline structure with varying properties along its surface normal are obtained. An iterative scheme for approximate solution of the equations is developed. The presented approach to interfacial roughness is incorporated into the recursion matrix formalism in a way that obviates possible numerical problems. Fitting of the experimental rocking curve is performed in order to test the possibility of reconstructing the roughness value from a diffraction scan. The developed algorithm works substantially faster than the traditional approach to dealing with a transition layer (dividing it into a finite number of thin lamellae). Calculations by the proposed approach are only two to three times longer than calculations for corresponding structures with ideally sharp interfaces.

Nuclear surface diffuseness revealed in nucleon-nucleus diffraction

NASA Astrophysics Data System (ADS)

Hatakeyama, S.; Horiuchi, W.; Kohama, A.

2018-05-01

The nuclear surface provides useful information on nuclear radius, nuclear structure, as well as properties of nuclear matter. We discuss the relationship between the nuclear surface diffuseness and elastic scattering differential cross section at the first diffraction peak of high-energy nucleon-nucleus scattering as an efficient tool in order to extract the nuclear surface information from limited experimental data involving short-lived unstable nuclei. The high-energy reaction is described by a reliable microscopic reaction theory, the Glauber model. Extending the idea of the black sphere model, we find one-to-one correspondence between the nuclear bulk structure information and proton-nucleus elastic scattering diffraction peak. This implies that we can extract both the nuclear radius and diffuseness simultaneously, using the position of the first diffraction peak and its magnitude of the elastic scattering differential cross section. We confirm the reliability of this approach by using realistic density distributions obtained by a mean-field model.

Experimental and theoretical study of rotationally inelastic diffraction of H2(D2) from methyl-terminated Si(111)

NASA Astrophysics Data System (ADS)

Nihill, Kevin J.; Hund, Zachary M.; Muzas, Alberto; Díaz, Cristina; del Cueto, Marcos; Frankcombe, Terry; Plymale, Noah T.; Lewis, Nathan S.; Martín, Fernando; Sibener, S. J.

2016-08-01

Fundamental details concerning the interaction between H2 and CH3-Si(111) have been elucidated by the combination of diffractive scattering experiments and electronic structure and scattering calculations. Rotationally inelastic diffraction (RID) of H2 and D2 from this model hydrocarbon-decorated semiconductor interface has been confirmed for the first time via both time-of-flight and diffraction measurements, with modest j = 0 → 2 RID intensities for H2 compared to the strong RID features observed for D2 over a large range of kinematic scattering conditions along two high-symmetry azimuthal directions. The Debye-Waller model was applied to the thermal attenuation of diffraction peaks, allowing for precise determination of the RID probabilities by accounting for incoherent motion of the CH3-Si(111) surface atoms. The probabilities of rotationally inelastic diffraction of H2 and D2 have been quantitatively evaluated as a function of beam energy and scattering angle, and have been compared with complementary electronic structure and scattering calculations to provide insight into the interaction potential between H2 (D2) and hence the surface charge density distribution. Specifically, a six-dimensional potential energy surface (PES), describing the electronic structure of the H2(D2)/CH3-Si(111) system, has been computed based on interpolation of density functional theory energies. Quantum and classical dynamics simulations have allowed for an assessment of the accuracy of the PES, and subsequently for identification of the features of the PES that serve as classical turning points. A close scrutiny of the PES reveals the highly anisotropic character of the interaction potential at these turning points. This combination of experiment and theory provides new and important details about the interaction of H2 with a hybrid organic-semiconductor interface, which can be used to further investigate energy flow in technologically relevant systems.

Names in Physics: Fresnel

ERIC Educational Resources Information Center

Cooper, M. L.

1970-01-01

This short biography of Fresnel traces his early education, his work as an engineer and his theories and discoveries in optics. The importance of Fresnel's ideas on diffraction, interference and double refraction are discussed. Bibliography. (LC)

Digital focusing of OCT images based on scalar diffraction theory and information entropy.

PubMed

Liu, Guozhong; Zhi, Zhongwei; Wang, Ruikang K

2012-11-01

This paper describes a digital method that is capable of automatically focusing optical coherence tomography (OCT) en face images without prior knowledge of the point spread function of the imaging system. The method utilizes a scalar diffraction model to simulate wave propagation from out-of-focus scatter to the focal plane, from which the propagation distance between the out-of-focus plane and the focal plane is determined automatically via an image-definition-evaluation criterion based on information entropy theory. By use of the proposed approach, we demonstrate that the lateral resolution close to that at the focal plane can be recovered from the imaging planes outside the depth of field region with minimal loss of resolution. Fresh onion tissues and mouse fat tissues are used in the experiments to show the performance of the proposed method.

Ray Scattering by an Arbitrarily Oriented Spheroid: 2. Transmission and Cross-polarization Effects

NASA Technical Reports Server (NTRS)

Lock, James A.

1996-01-01

Transmission of an arbitrarily polarized plane wave by an arbitrarily oriented spheroid in the short-wavelength limit is considered in the context of ray theory. The transmitted electric field is added to the diffracted plus reflected ray-theory electric field that was previously derived to obtain an approximation to the far-zone scattered intensity in the forward hemisphere. Two different types of cross-polarization effects are found. These are: (a) a rotation of the polarization state of the transmitted rays from when they are referenced with respect to their entrance into the spheroid to when they are referenced with respect to their exit from it and (b) a rotation of the polarization state of the transmitted rays when they are referenced with respect to the polarization state of the diffracted plus reflected rays.

Leading twist nuclear shadowing phenomena in hard processes with nuclei

DOE PAGES

L. Franfurt; Guzey, V.; Strikman, M.

2012-01-08

We present and discuss the theory and phenomenology of the leading twist theory of nuclear shadowing which is based on the combination of the generalization of Gribov-Glauber theory, QCD factorization theorems, and HERA QCD analysis of diffraction in lepton-proton deep inelastic scattering (DIS). We apply this technique for the analysis of a wide range of hard processes with nuclei-inclusive DIS on deuterons, medium-range and heavy nuclei, coherent and incoherent diffractive DIS with nuclei, and hard diffraction in proton-nucleus scattering - and make predictions for the effect of nuclear shadowing in the corresponding sea quark and gluon parton distributions. We alsomore » analyze the role of the leading twist nuclear shadowing in generalized parton distributions in nuclei and certain characteristics of final states in nuclear DIS. We discuss the limits of applicability of the leading twist approximation for small x scattering off nuclei and the onset of the black disk regime and methods of detecting it. It will be possible to check many of our predictions in the near future in the studies of the ultraperipheral collisions at the Large Hadron Collider (LHC). Further checks will be possible in pA collisions at the LHC and forward hadron production at Relativistic Heavy Ion Collider (RHIC). As a result, detailed tests will be possible at an Electon-Ion Collider (EIC) in USA and at the Large Hadron-Electron Collider (LHeC) at CERN.« less

MONOCULAR DIPLOPIA DUE TO SPHEROCYLINDRICAL REFRACTIVE ERRORS (AN AMERICAN OPHTHALMOLOGICAL SOCIETY THESIS)

PubMed Central

Archer, Steven M.

2007-01-01

Purpose Ordinary spherocylindrical refractive errors have been recognized as a cause of monocular diplopia for over a century, yet explanation of this phenomenon using geometrical optics has remained problematic. This study tests the hypothesis that the diffraction theory treatment of refractive errors will provide a more satisfactory explanation of monocular diplopia. Methods Diffraction theory calculations were carried out for modulation transfer functions, point spread functions, and line spread functions under conditions of defocus, astigmatism, and mixed spherocylindrical refractive errors. Defocused photographs of inked and projected black lines were made to demonstrate the predicted consequences of the theoretical calculations. Results For certain amounts of defocus, line spread functions resulting from spherical defocus are predicted to have a bimodal intensity distribution that could provide the basis for diplopia with line targets. Multimodal intensity distributions are predicted in point spread functions and provide a basis for diplopia or polyopia of point targets under conditions of astigmatism. The predicted doubling effect is evident in defocused photographs of black lines, but the effect is not as robust as the subjective experience of monocular diplopia. Conclusions Monocular diplopia due to ordinary refractive errors can be predicted from diffraction theory. Higher-order aberrations—such as spherical aberration—are not necessary but may, under some circumstances, enhance the features of monocular diplopia. The physical basis for monocular diplopia is relatively subtle, and enhancement by neural processing is probably needed to account for the robustness of the percept. PMID:18427616

On the Use of Dynamical Diffraction Theory To Refine Crystal Structure from Electron Diffraction Data: Application to KLa5O5(VO4)2, a Material with Promising Luminescent Properties.

PubMed

Colmont, Marie; Palatinus, Lukas; Huvé, Marielle; Kabbour, Houria; Saitzek, Sébastien; Djelal, Nora; Roussel, Pascal

2016-03-07

A new lanthanum oxide, KLa5O5(VO4)2, was synthesized using a flux growth technique that involved solid-state reaction under an air atmosphere at 900 °C. The crystal structure was solved and refined using an innovative approach recently established and based on three-dimensional (3D) electron diffraction data, using precession of the electron beam and then validated against Rietveld refinement and denisty functional theory (DFT) calculations. It crystallizes in a monoclinic unit cell with space group C2/m and has unit cell parameters of a = 20.2282(14) Å, b = 5.8639(4) Å, c = 12.6060(9) Å, and β = 117.64(1)°. Its structure is built on Cresnel-like two-dimensional (2D) units (La5O5) of 4*3 (OLa4) tetrahedra, which run parallel to (001) plane, being surrounded by isolated VO4 tetrahedra. Four isolated vanadate groups create channels that host K(+) ions. Substitution of K(+) cations by another alkali metal is possible, going from lithium to rubidium. Li substitution led to a similar phase with a primitive monoclinic unit cell. A complementary selected area electron diffraction (SAED) study highlighted diffuse streaks associated with stacking faults observed on high-resolution electron microscopy (HREM) images of the lithium compound. Finally, preliminary catalytic tests for ethanol oxidation are reported, as well as luminescence evidence. This paper also describes how solid-state chemists can take advantages of recent progresses in electron crystallography, assisted by DFT calculations and powder X-ray diffraction (PXRD) refinements, to propose new structural types with potential applications to the physicist community.

Development of ultrasound transducer diffractive field theory for nonlinear propagation-based imaging

NASA Astrophysics Data System (ADS)

Kharin, Nikolay A.

2000-04-01

In nonlinear ultrasound imaging the images are formed using the second harmonic energy generated due to the nonlinear nature of finite amplitude propagation. This propagation can be modeled using the KZK wave equation. This paper presents further development of nonlinear diffractive field theory based on the KZK equation and its solution by means of the slowly changing profile method for moderate nonlinearity. The analytical expression for amplitudes and phases of sum frequency wave are obtained in addition to the second harmonic wave. Also, the analytical expression for the relative curvature of the wave fronts of fundamental and second harmonic signals are derived. The media with different nonlinear properties and absorption coefficients were investigated to characterize the diffractive field of the transducer at medical frequencies. All expressions demonstrate good agreement with experimental results. The expressions are novel and provide an easy way for prediction of amplitude and phase structure of nonlinearly distorted field of a transducer. The sum frequency signal technique could be implemented as well as second harmonic technique to improve the quality of biomedical images. The results obtained are of importance for medical diagnostic ultrasound equipment design.

Inflection point caustic problems and solutions for high-gain dual-shaped reflectors

NASA Technical Reports Server (NTRS)

Galindo-Israel, Victor; Veruttipong, Thavath; Imbriale, William; Rengarajan, Sembiam

1990-01-01

The singular nature of the uniform geometrical theory of diffraction (UTD) subreflector scattered field at the vicinity of the main reflector edge (for a high-gain antenna design) is investigated. It is shown that the singularity in the UTD edge-diffracted and slope-diffracted fields is due to the reflection distance parameter approaching infinity in the transition functions. While the geometrical optics (GO) and UTD edge-diffracted fields exhibit singularities of the same order, the edge slope-diffracted field singularity is more significant and is substantial for greater subreflector edge tapers. The diffraction analysis of such a subreflector in the vicinity of the main reflector edge has been carried out efficiently and accurately by a stationary phase evaluation of the phi-integral, whereas the theta-integral is carried out numerically. Computational results from UTD and physical optics (PO) analysis of a 34-m ground station dual-shaped reflector confirm the analytical formulations for both circularly symmetric and offset asymmetric subreflectors. It is concluded that the proposed PO(theta)GO(phi) technique can be used to study the spillover or noise temperature characteristics of a high-gain reflector antenna efficiently and accurately.

A general theory of interference fringes in x-ray phase grating imaging.

PubMed

Yan, Aimin; Wu, Xizeng; Liu, Hong

2015-06-01

The authors note that the concept of the Talbot self-image distance in x-ray phase grating interferometry is indeed not well defined for polychromatic x-rays, because both the grating phase shift and the fractional Talbot distances are all x-ray wavelength-dependent. For x-ray interferometry optimization, there is a need for a quantitative theory that is able to predict if a good intensity modulation is attainable at a given grating-to-detector distance. In this work, the authors set out to meet this need. In order to apply Fourier analysis directly to the intensity fringe patterns of two-dimensional and one-dimensional phase grating interferometers, the authors start their derivation from a general phase space theory of x-ray phase-contrast imaging. Unlike previous Fourier analyses, the authors evolved the Wigner distribution to obtain closed-form expressions of the Fourier coefficients of the intensity fringes for any grating-to-detector distance, even if it is not a fractional Talbot distance. The developed theory determines the visibility of any diffraction order as a function of the grating-to-detector distance, the phase shift of the grating, and the x-ray spectrum. The authors demonstrate that the visibilities of diffraction orders can serve as the indicators of the underlying interference intensity modulation. Applying the theory to the conventional and inverse geometry configurations of single-grating interferometers, the authors demonstrated that the proposed theory provides a quantitative tool for the grating interferometer optimization with or without the Talbot-distance constraints. In this work, the authors developed a novel theory of the interference intensity fringes in phase grating x-ray interferometry. This theory provides a quantitative tool in design optimization of phase grating x-ray interferometers.

Air transparent soundproof window

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

Kim, Sang-Hoon, E-mail: shkim@mmu.ac.kr; Lee, Seong-Hyun

2014-11-15

A soundproof window or wall which is transparent to airflow is presented. The design is based on two wave theories: the theory of diffraction and the theory of acoustic metamaterials. It consists of a three-dimensional array of strong diffraction-type resonators with many holes centered on each individual resonator. The negative effective bulk modulus of the resonators produces evanescent wave, and at the same time the air holes with subwavelength diameter existed on the surfaces of the window for macroscopic air ventilation. The acoustic performance levels of two soundproof windows with air holes of 20mm and 50mm diameters were measured. Themore » sound level was reduced by about 30 - 35dB in the frequency range of 400 - 5,000Hz with the 20mm window, and by about 20 - 35dB in the frequency range of 700 - 2,200Hz with the 50mm window. Multi stop-band was created by the multi-layers of the window. The attenuation length or the thickness of the window was limited by background noise. The effectiveness of the soundproof window with airflow was demonstrated by a real installation.« less

Talbot effect of quasi-periodic grating.

PubMed

Zhang, Chong; Zhang, Wei; Li, Furui; Wang, Junhong; Teng, Shuyun

2013-07-20

Theoretic and experimental studies of the Talbot effect of quasi-periodic gratings are performed in this paper. The diffractions of periodic and quasi-periodic square aperture arrays in Fresnel fields are analyzed according to the scalar diffraction theory. The expressions of the diffraction intensities of two types of quasi-periodic gratings are deduced. Talbot images of the quasi-periodic gratings are predicted to appear at multiple certain distances. The quasi-periodic square aperture arrays are produced with the aid of a liquid crystal light modulator, and the self-images of the quasi-periodic gratings are measured successfully in the experiment. This study indicates that even a structure in short-range disorder may take on the self-imaging effect in a Fresnel field.

Extremely asymmetric diffraction as a method of determining magneto-optical constants for X-rays near absorption edges

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

Andreeva, M. A., E-mail: Mandreeva1@yandex.ru; Repchenko, Yu. L., E-mail: kent160@mail.ru; Smekhova, A. G.

2015-06-15

The spectral dependence of the Bragg peak position under conditions of extremely asymmetric diffraction has been analyzed in the kinematical and dynamical approximations of the diffraction theory. Simulations have been performed for the L{sub 3} absorption edge of yttrium in a single-crystal YFe{sub 2} film; they have shown that the magneto-optical constants (or, equivalently, the dispersion corrections to the atomic scattering factor) for hard X-rays can be determined from this dependence. Comparison with the experimental data obtained for a Nb(4 nm)/YFe{sub 2}(40 nm〈110〉)/Fe(1.5 nm)/Nb(50 nm)/sapphire sample at the European Synchrotron Radiation Facility has been made.

Cost-Effective Experiments on the Diffraction and Interference of Light.

ERIC Educational Resources Information Center

Sprigham, S. V.

2000-01-01

Presents an alternative experimental arrangement that results in a considerable cost savings by reducing the number of sensors and other apparati required while giving excellent quantitative results for comparison with theory. (Author/CCM)

Beta value coupled wave theory for nonslanted reflection gratings.

PubMed

Neipp, Cristian; Francés, Jorge; Gallego, Sergi; Bleda, Sergio; Martínez, Francisco Javier; Pascual, Inmaculada; Beléndez, Augusto

2014-01-01

We present a modified coupled wave theory to describe the properties of nonslanted reflection volume diffraction gratings. The method is based on the beta value coupled wave theory, which will be corrected by using appropriate boundary conditions. The use of this correction allows predicting the efficiency of the reflected order for nonslanted reflection gratings embedded in two media with different refractive indices. The results obtained by using this method will be compared to those obtained using a matrix method, which gives exact solutions in terms of Mathieu functions, and also to Kogelnik's coupled wave theory. As will be demonstrated, the technique presented in this paper means a significant improvement over Kogelnik's coupled wave theory.

Beta Value Coupled Wave Theory for Nonslanted Reflection Gratings

PubMed Central

Neipp, Cristian; Francés, Jorge; Gallego, Sergi; Bleda, Sergio; Martínez, Francisco Javier; Pascual, Inmaculada; Beléndez, Augusto

2014-01-01

We present a modified coupled wave theory to describe the properties of nonslanted reflection volume diffraction gratings. The method is based on the beta value coupled wave theory, which will be corrected by using appropriate boundary conditions. The use of this correction allows predicting the efficiency of the reflected order for nonslanted reflection gratings embedded in two media with different refractive indices. The results obtained by using this method will be compared to those obtained using a matrix method, which gives exact solutions in terms of Mathieu functions, and also to Kogelnik's coupled wave theory. As will be demonstrated, the technique presented in this paper means a significant improvement over Kogelnik's coupled wave theory. PMID:24723811

Sound field reproduction as an equivalent acoustical scattering problem.

PubMed

Fazi, Filippo Maria; Nelson, Philip A

2013-11-01

Given a continuous distribution of acoustic sources, the determination of the source strength that ensures the synthesis of a desired sound field is shown to be identical to the solution of an equivalent acoustic scattering problem. The paper begins with the presentation of the general theory that underpins sound field reproduction with secondary sources continuously arranged on the boundary of the reproduction region. The process of reproduction by a continuous source distribution is modeled by means of an integral operator (the single layer potential). It is then shown how the solution of the sound reproduction problem corresponds to that of an equivalent scattering problem. Analytical solutions are computed for two specific instances of this problem, involving, respectively, the use of a secondary source distribution in spherical and planar geometries. The results are shown to be the same as those obtained with analyses based on High Order Ambisonics and Wave Field Synthesis, respectively, thus bringing to light a fundamental analogy between these two methods of sound reproduction. Finally, it is shown how the physical optics (Kirchhoff) approximation enables the derivation of a high-frequency simplification for the problem under consideration, this in turn being related to the secondary source selection criterion reported in the literature on Wave Field Synthesis.

General analytical solutions for DC/AC circuit-network analysis

NASA Astrophysics Data System (ADS)

Rubido, Nicolás; Grebogi, Celso; Baptista, Murilo S.

2017-06-01

In this work, we present novel general analytical solutions for the currents that are developed in the edges of network-like circuits when some nodes of the network act as sources/sinks of DC or AC current. We assume that Ohm's law is valid at every edge and that charge at every node is conserved (with the exception of the source/sink nodes). The resistive, capacitive, and/or inductive properties of the lines in the circuit define a complex network structure with given impedances for each edge. Our solution for the currents at each edge is derived in terms of the eigenvalues and eigenvectors of the Laplacian matrix of the network defined from the impedances. This derivation also allows us to compute the equivalent impedance between any two nodes of the circuit and relate it to currents in a closed circuit which has a single voltage generator instead of many input/output source/sink nodes. This simplifies the treatment that could be done via Thévenin's theorem. Contrary to solving Kirchhoff's equations, our derivation allows to easily calculate the redistribution of currents that occurs when the location of sources and sinks changes within the network. Finally, we show that our solutions are identical to the ones found from Circuit Theory nodal analysis.

Feasibility of using PZT actuators to study the dynamic behavior of a rotating disk due to rotor-stator interaction.

PubMed

Presas, Alexandre; Egusquiza, Eduard; Valero, Carme; Valentin, David; Seidel, Ulrich

2014-07-07

In this paper, PZT actuators are used to study the dynamic behavior of a rotating disk structure due to rotor-stator interaction excitation. The disk is studied with two different surrounding fluids-air and water. The study has been performed analytically and validated experimentally. For the theoretical analysis, the natural frequencies and the associated mode shapes of the rotating disk in air and water are obtained with the Kirchhoff-Love thin plate theory coupled with the interaction with the surrounding fluid. A model for the Rotor Stator Interaction that occurs in many rotating disk-like parts of turbomachinery such as compressors, hydraulic runners or alternators is presented. The dynamic behavior of the rotating disk due to this excitation is deduced. For the experimental analysis a test rig has been developed. It consists of a stainless steel disk (r = 198 mm and h = 8 mm) connected to a variable speed motor. Excitation and response are measured from the rotating system. For the rotating excitation four piezoelectric patches have been used. Calibrating the piezoelectric patches in amplitude and phase, different rotating excitation patterns are applied on the rotating disk in air and in water. Results show the feasibility of using PZT to control the response of the disk due to a rotor-stator interaction.

Multiple scattering and stop band characteristics of flexural waves on a thin plate with circular holes

NASA Astrophysics Data System (ADS)

Wang, Zuowei; Biwa, Shiro

2018-03-01

A numerical procedure is proposed for the multiple scattering analysis of flexural waves on a thin plate with circular holes based on the Kirchhoff plate theory. The numerical procedure utilizes the wave function expansion of the exciting as well as scattered fields, and the boundary conditions at the periphery of holes are incorporated as the relations between the expansion coefficients of exciting and scattered fields. A set of linear algebraic equations with respect to the wave expansion coefficients of the exciting field alone is established by the numerical collocation method. To demonstrate the applicability of the procedure, the stop band characteristics of flexural waves are analyzed for different arrangements and concentrations of circular holes on a steel plate. The energy transmission spectra of flexural waves are shown to capture the detailed features of the stop band formation of regular and random arrangements of holes. The increase of the concentration of holes is found to shift the dips of the energy transmission spectra toward higher frequencies as well as deepen them. The hexagonal hole arrangement can form a much broader stop band than the square hole arrangement for flexural wave transmission. It is also demonstrated that random arrangements of holes make the transmission spectrum more complicated.

Recent advances in continuum plasticity: phenomenological modeling and experimentation using X-ray diffraction

NASA Astrophysics Data System (ADS)

Edmiston, John Kearney

This work explores the field of continuum plasticity from two fronts. On the theory side, we establish a complete specification of a phenomenological theory of plasticity for single crystals. The model serves as an alternative to the popular crystal plasticity formulation. Such a model has been previously proposed in the literature; the new contribution made here is the constitutive framework and resulting simulations. We calibrate the model to available data and use a simple numerical method to explore resulting predictions in plane strain boundary value problems. Results show promise for further investigation of the plasticity model. Conveniently, this theory comes with a corresponding experimental tool in X-ray diffraction. Recent advances in hardware technology at synchrotron sources have led to an increased use of the technique for studies of plasticity in the bulk of materials. The method has been successful in qualitative observations of material behavior, but its use in quantitative studies seeking to extract material properties is open for investigation. Therefore in the second component of the thesis several contributions are made to synchrotron X-ray diffraction experiments, in terms of method development as well as the quantitative reporting of constitutive parameters. In the area of method development, analytical tools are developed to determine the available precision of this type of experiment—a crucial aspect to determine if the method is to be used for quantitative studies. We also extract kinematic information relating to intragranular inhomogeneity which is not accessible with traditional methods of data analysis. In the area of constitutive parameter identification, we use the method to extract parameters corresponding to the proposed formulation of plasticity for a titanium alloy (HCP) which is continuously sampled by X-ray diffraction during uniaxial extension. These results and the lessons learned from the efforts constitute early reporting of the quantitative profitability of undertaking such a line of experimentation for the study of plastic deformation processes.

A discrete random walk on the hypercube

NASA Astrophysics Data System (ADS)

Zhang, Jingyuan; Xiang, Yonghong; Sun, Weigang

2018-03-01

In this paper, we study the scaling for mean first-passage time (MFPT) of random walks on the hypercube and obtain a closed-form formula for the MFPT over all node pairs. We also determine the exponent of scaling efficiency characterizing the random walks and compare it with those of the existing networks. Finally we study the random walks on the hypercube with a located trap and provide a solution of the Kirchhoff index of the hypercube.

Microphone Array

NASA Astrophysics Data System (ADS)

Bader, Rolf

This chapter deals with microphone arrays. It is arranged according to the different methods available to proceed through the different problems and through the different mathematical methods. After discussing general properties of different array types, such as plane arrays, spherical arrays, or scanning arrays, it proceeds to the signal processing tools that are most used in speech processing. In the third section, backpropagating methods based on the Helmholtz-Kirchhoff integral are discussed, which result in spatial radiation patterns of vibrating bodies or air.

A method for the automated construction of the joint system of equations to solve the problem of the flow distribution in hydraulic networks

NASA Astrophysics Data System (ADS)

Novikov, A. E.

1993-10-01

There are several methods of solving the problem of the flow distribution in hydraulic networks. But all these methods have no mathematical tools for forming joint systems of equations to solve this problem. This paper suggests a method of constructing joint systems of equations to calculate hydraulic circuits of the arbitrary form. The graph concept, according to Kirchhoff, has been introduced.

The triangular kagomé lattices revisited

NASA Astrophysics Data System (ADS)

Liu, Xiaoyun; Yan, Weigen

2013-11-01

The dimer problem, Ising spins and bond percolation on the triangular kagomé lattice have been studied extensively by physicists. In this paper, based on the fact the triangular kagomé lattice with toroidal boundary condition can be regarded as the line graph of 3.12.12 lattice with toroidal boundary condition, we derive the formulae of the number of spanning trees, the energy, and the Kirchhoff index of the triangular kagomé lattice with toroidal boundary condition.

Spectral analysis for weighted tree-like fractals

NASA Astrophysics Data System (ADS)

Dai, Meifeng; Chen, Yufei; Wang, Xiaoqian; Sun, Yu; Su, Weiyi

2018-02-01

Much information about the structural properties and dynamical aspects of a network is measured by the eigenvalues of its normalized Laplacian matrix. In this paper, we aim to present a study on the spectra of the normalized Laplacian of weighted tree-like fractals. We analytically obtain the relationship between the eigenvalues and their multiplicities for two successive generations. As an example of application of these results, we then derive closed-form expressions for their multiplicative Kirchhoff index and Kemeny's constant.

Nonlinear Finite Element Analysis of a General Composite Shell

DTIC Science & Technology

1988-12-01

strain I Poisson’s ratio ix I I iI I I 1 Total potential energy a Normal stress rShear stress Rotational terms Distance from midsurface e ,Y ,0 Rotations...respectively 0 0 Subscript "e" indicates element reference Subscript "g" indicates global reference Superscript "o" indicates midsurface values...surface strains and rotations are small, and displacements away from the midsurface are restricted by the Kirchhoff-Love hypotheses [3]. With these

Multi-Mode 3D Kirchhoff Migration of Receiver Functions at Continental Scale With Applications to USArray

NASA Astrophysics Data System (ADS)

Millet, F.; Bodin, T.; Rondenay, S.

2017-12-01

The teleseismic scattered seismic wavefield contains valuable information about heterogeneities and discontinuities inside the Earth. By using fast Receiver Function (RF) migration techniques such as classic Common Conversion Point (CCP) stacks, one can easily interpret structural features down to a few hundred kilometers in the mantle. However, strong simplifying 1D assumptions limit the scope of these methods to structures that are relatively planar and sub-horizontal at local-to-regional scales, such as the Lithosphere-Asthenosphere Boundary and the Mantle Transition Zone discontinuities. Other more robust 2D and 2.5D methods rely on fewer assumptions but require considerable, sometime prohibitive, computation time. Following the ideas of Cheng (2017), we have implemented a simple fully 3D Prestack Kirchhoff RF migration scheme which uses the FM3D fast Eikonal solver to compute travel times and scattering angles. The method accounts for 3D elastic point scattering and includes free surface multiples, resulting in enhanced images of laterally varying dipping structures, such as subducted slabs. The method is tested for subduction structures using 2.5D synthetics generated with Raysum and 3D synthetics generated with specfem3D. Results show that dip angles, depths and lateral variations can be recovered almost perfectly. The approach is ideally suited for applications to dense regional datasets, including those collected across the Cascadia and Alaska subduction zones by USArray.

Diffusely scattered and transmitted elastic waves by random rough solid-solid interfaces using an elastodynamic Kirchhoff approximation

NASA Astrophysics Data System (ADS)

Shi, Fan; Lowe, Mike; Craster, Richard

2017-06-01

Elastic waves scattered by random rough interfaces separating two distinct media play an important role in modeling phonon scattering and impact upon thermal transport models, and are also integral to ultrasonic inspection. We introduce theoretical formulas for the diffuse field of elastic waves scattered by, and transmitted across, random rough solid-solid interfaces using the elastodynamic Kirchhoff approximation. The new formulas are validated by comparison with numerical Monte Carlo simulations, for a wide range of roughness (rms σ ≤λ /3 , correlation length λ0≥ wavelength λ ), demonstrating a significant improvement over the widely used small-perturbation approach, which is valid only for surfaces with small rms values. Physical analysis using the theoretical formulas derived here demonstrates that increasing the rms value leads to a considerable change of the scattering patterns for each mode. The roughness has different effects on the reflection and the transmission, with a strong dependence on the material properties. In the special case of a perfect match of the wave speed of the two solid media, the transmission is the same as the case for a flat interface. We pay particular attention to scattering in the specular direction, often used as an observable quantity, in terms of the roughness parameters, showing a peak at an intermediate value of rms; this rms value coincides with that predicted by the Rayleigh parameter.

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.

The first ANDES elements: 9-DOF plate bending triangles

NASA Technical Reports Server (NTRS)

Militello, Carmelo; Felippa, Carlos A.

1991-01-01

New elements are derived to validate and assess the assumed natural deviatoric strain (ANDES) formulation. This is a brand new variant of the assumed natural strain (ANS) formulation of finite elements, which has recently attracted attention as an effective method for constructing high-performance elements for linear and nonlinear analysis. The ANDES formulation is based on an extended parametrized variational principle developed in recent publications. The key concept is that only the deviatoric part of the strains is assumed over the element whereas the mean strain part is discarded in favor of a constant stress assumption. Unlike conventional ANS elements, ANDES elements satisfy the individual element test (a stringent form of the patch test) a priori while retaining the favorable distortion-insensitivity properties of ANS elements. The first application of this formulation is the development of several Kirchhoff plate bending triangular elements with the standard nine degrees of freedom. Linear curvature variations are sampled along the three sides with the corners as gage reading points. These sample values are interpolated over the triangle using three schemes. Two schemes merge back to conventional ANS elements, one being identical to the Discrete Kirchhoff Triangle (DKT), whereas the third one produces two new ANDES elements. Numerical experiments indicate that one of the ANDES element is relatively insensitive to distortion compared to previously derived high-performance plate-bending elements, while retaining accuracy for nondistorted elements.

Bending Boundary Layers in Laminated-Composite Circular Cylindrical Shells

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Smeltzer, Stanley S., III

2000-01-01

An analytical, parametric study of the attenuation of bending boundary layers or edge effects in balanced and unbalanced, symmetrically and unsymmetrically laminated thin cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize and quantify the effects of laminate orthotropy and laminate anisotropy on the bending boundary-layer decay length in a very general and encompassing manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all the laminate constructions considered, the results show that the differences between results that were obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that in some cases neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and in other cases it results in an overestimation.

Homogenization models for 2-D grid structures

NASA Technical Reports Server (NTRS)

Banks, H. T.; Cioranescu, D.; Rebnord, D. A.

1992-01-01

In the past several years, we have pursued efforts related to the development of accurate models for the dynamics of flexible structures made of composite materials. Rather than viewing periodicity and sparseness as obstacles to be overcome, we exploit them to our advantage. We consider a variational problem on a domain that has large, periodically distributed holes. Using homogenization techniques we show that the solution to this problem is in some topology 'close' to the solution of a similar problem that holds on a much simpler domain. We study the behavior of the solution of the variational problem as the holes increase in number, but decrease in size in such a way that the total amount of material remains constant. The result is an equation that is in general more complex, but with a domain that is simply connected rather than perforated. We study the limit of the solution as the amount of material goes to zero. This second limit will, in most cases, retrieve much of the simplicity that was lost in the first limit without sacrificing the simplicity of the domain. Finally, we show that these results can be applied to the case of a vibrating Love-Kirchhoff plate with Kelvin-Voigt damping. We rely heavily on earlier results of (Du), (CS) for the static, undamped Love-Kirchhoff equation. Our efforts here result in a modification of those results to include both time dependence and Kelvin-Voigt damping.

Geometry of complex networks and topological centrality

NASA Astrophysics Data System (ADS)

Ranjan, Gyan; Zhang, Zhi-Li

2013-09-01

We explore the geometry of complex networks in terms of an n-dimensional Euclidean embedding represented by the Moore-Penrose pseudo-inverse of the graph Laplacian (L). The squared distance of a node i to the origin in this n-dimensional space (lii+), yields a topological centrality index, defined as C∗(i)=1/lii+. In turn, the sum of reciprocals of individual node centralities, ∑i1/C∗(i)=∑ilii+, or the trace of L, yields the well-known Kirchhoff index (K), an overall structural descriptor for the network. To put into context this geometric definition of centrality, we provide alternative interpretations of the proposed indices that connect them to meaningful topological characteristics - first, as forced detour overheads and frequency of recurrences in random walks that has an interesting analogy to voltage distributions in the equivalent electrical network; and then as the average connectedness of i in all the bi-partitions of the graph. These interpretations respectively help establish the topological centrality (C∗(i)) of node i as a measure of its overall position as well as its overall connectedness in the network; thus reflecting the robustness of i to random multiple edge failures. Through empirical evaluations using synthetic and real world networks, we demonstrate how the topological centrality is better able to distinguish nodes in terms of their structural roles in the network and, along with Kirchhoff index, is appropriately sensitive to perturbations/re-wirings in the network.

Diffraction of real and virtual photons in a pyrolytic graphite crystal as source of intensive quasimonochromatic X-ray beam

NASA Astrophysics Data System (ADS)

Bogomazova, E. A.; Kalinin, B. N.; Naumenko, G. A.; Padalko, D. V.; Potylitsyn, A. P.; Sharafutdinov, A. F.; Vnukov, I. E.

2003-01-01

A series of experiments on the parametric X-rays radiation (PXR) generation and radiation soft component diffraction of relativistic electrons in pyrolytic graphite (PG) crystals have been carried out at the Tomsk synchrotron. It is shown that the experimental results with PG crystals are explained by the kinematic PXR theory if we take into account a contribution of the real photons diffraction (transition radiation, bremsstrahlung and PXR photons as well). The measurements of the emission spectrum of channeled electrons in the photon energy range much smaller than the characteristic energy of channeling radiation have been performed with a crystal-diffraction spectrometer. For electrons incident along the <1 1 0> axis of a silicon crystal, the radiation intensity in the energy range 30⩽ ω⩽360 keV exceeds the bremsstrahlung one almost by an order of magnitude. Different possibilities to create an effective source of the monochromatic X-ray beam based on the real and virtual photons diffraction in the PG crystals have been considered.

OSA Proceedings of the International Topical Meeting on Photonic Switching, Held in Salt Lake City, Utah on 6 - 8 March, 1992. Volume 8

DTIC Science & Technology

1992-05-22

Frobenius Theory : Why Hilberts Metric ?," Mathematics of Operations Research 7 (1982) pp.198-210. 11. H. S. M. Cnxeter, Regular Complex Poly- topes...can be made to perform logic functions by pre-setting the device to a given state. We can, in theory , achieve arbitrary logical functionality by using...then extrapolating on the basis of this theory , is about 2000 two diffracted spots appear in the focal plane of the channels. output lenslet array

High frequency scattering from a thin lossless dielectric slab. M.S. Thesis

NASA Technical Reports Server (NTRS)

Burgener, K. W.

1979-01-01

A solution for scattering from a thin dielectric slab is developed based on geometrical optics and the geometrical theory of diffraction with the intention of developing a model for a windshield of a small private aircraft for incorporation in an aircraft antenna code. Results of the theory are compared with experimental measurements and moment method calculations showing good agreement. Application of the solution is also addressed.

Accurate determination of lattice parameters based on Niggli reduced cell theory by using digitized electron diffraction micrograph.

PubMed

Yang, Yi; Cai, Canying; Lin, Jianguo; Gong, Lunjun; Yang, Qibin

2017-05-01

In this paper, we used Niggli reduced cell theory to determine lattice constants of a micro/nano crystal by using electron diffraction patterns. The Niggli reduced cell method enhanced the accuracy of lattice constant measurement obviously, because the lengths and the angles of lattice vectors of a primitive cell can be measured directly on the electron micrographs instead of a double tilt holder. With the aid of digitized algorithm and least square optimization by using three digitized micrographs, a valid reciprocal Niggli reduced cell number can be obtained. Thus a reciprocal and real Bravais lattices are acquired. The results of three examples, i.e., Mg 4 Zn 7 , an unknown phase (Precipitate phase in nickel-base superalloy) and Ba 4 Ti 13 O 30 showed that the maximum errors are 1.6% for lengths and are 0.3% for angles. Copyright © 2017 Elsevier Ltd. All rights reserved.

Digital focusing of OCT images based on scalar diffraction theory and information entropy

PubMed Central

Liu, Guozhong; Zhi, Zhongwei; Wang, Ruikang K.

2012-01-01

This paper describes a digital method that is capable of automatically focusing optical coherence tomography (OCT) en face images without prior knowledge of the point spread function of the imaging system. The method utilizes a scalar diffraction model to simulate wave propagation from out-of-focus scatter to the focal plane, from which the propagation distance between the out-of-focus plane and the focal plane is determined automatically via an image-definition-evaluation criterion based on information entropy theory. By use of the proposed approach, we demonstrate that the lateral resolution close to that at the focal plane can be recovered from the imaging planes outside the depth of field region with minimal loss of resolution. Fresh onion tissues and mouse fat tissues are used in the experiments to show the performance of the proposed method. PMID:23162717

Validation of missed space-group symmetry in X-ray powder diffraction structures with dispersion-corrected density functional theory.

PubMed

Hempler, Daniela; Schmidt, Martin U; van de Streek, Jacco

2017-08-01

More than 600 molecular crystal structures with correct, incorrect and uncertain space-group symmetry were energy-minimized with dispersion-corrected density functional theory (DFT-D, PBE-D3). For the purpose of determining the correct space-group symmetry the required tolerance on the atomic coordinates of all non-H atoms is established to be 0.2 Å. For 98.5% of 200 molecular crystal structures published with missed symmetry, the correct space group is identified; there are no false positives. Very small, very symmetrical molecules can end up in artificially high space groups upon energy minimization, although this is easily detected through visual inspection. If the space group of a crystal structure determined from powder diffraction data is ambiguous, energy minimization with DFT-D provides a fast and reliable method to select the correct space group.

Si Nanoribbons on Ag(110) Studied by Grazing-Incidence X-Ray Diffraction, Scanning Tunneling Microscopy, and Density-Functional Theory: Evidence of a Pentamer Chain Structure.

PubMed

Prévot, Geoffroy; Hogan, Conor; Leoni, Thomas; Bernard, Romain; Moyen, Eric; Masson, Laurence

2016-12-30

We report a combined grazing incidence x-ray diffraction (GIXD), scanning tunneling microscopy (STM), and density-functional theory (DFT) study which clearly elucidates the atomic structure of the Si nanoribbons grown on the missing-row reconstructed Ag(110) surface. Our study allows us to discriminate between the theoretical models published in the literature, including the most stable atomic configurations and those based on a missing-row reconstructed Ag(110) surface. GIXD measurements unambiguously validate the pentamer model grown on the reconstructed surface, obtained from DFT. This pentamer atomistic model accurately matches the high-resolution STM images of the Si nanoribbons adsorbed on Ag(110). Our study closes the long-debated atomic structure of the Si nanoribbons grown on Ag(110) and definitively excludes a honeycomb structure similar to that of freestanding silicene.

International Journal of Quantum Chemistry. Quantum Chemistry Symposium Number 27: Proceedings of the International Symposium on Atomic, Molecular, and Condensed Matter Theory and Computational Methods Held in St. Augustine, Florida on 13-20 March 1993

DTIC Science & Technology

1993-03-20

photochromic glasses, x - ray absorbing television glasses, extrudablc oriented ceramics, and the ultra-pure materials for optical fibers. While...quartz through the analysis of x - ray diffraction experiments. The repeating nature of the quartz crystal give, many diffraction peaks which allow the...fused silica, which serves as a backbone for most of the silicate glasses. Doris Evans, an x - ray crystallographer at Corning, built a model of fused

Terahertz reflection imaging using Kirchhoff migration.

PubMed

Dorney, T D; Johnson, J L; Van Rudd, J; Baraniuk, R G; Symes, W W; Mittleman, D M

2001-10-01

We describe a new imaging method that uses single-cycle pulses of terahertz (THz) radiation. This technique emulates data-collection and image-processing procedures developed for geophysical prospecting and is made possible by the availability of fiber-coupled THz receiver antennas. We use a simple migration procedure to solve the inverse problem; this permits us to reconstruct the location and shape of targets. These results demonstrate the feasibility of the THz system as a test-bed for the exploration of new seismic processing methods involving complex model systems.

Large amplitude vibrations of laminated hybrid composite plates

NASA Astrophysics Data System (ADS)

Sarma, M. S.; Venkateshwar Rao, A.; Pillai, S. R. R.; Nageswara Rao, B.

1992-12-01

A general equation of motion for the nonlinear vibration of a rectangular plate is formulated using Kirchhoff's hypothesis and von Karman type strain-displacement relations. The formulation includes in-plane deformations and neglects the corresponding inertia terms. The amplitudes are written under assumption that mode shapes are approximately the fundamental modes which satisfy the boundary conditions of the problem. It is shown that the method can be used to easily calculate an excellent aproximation to the periodic solutions of the nonlinear antisymmetric quadratic oscillator.

Corona graphs as a model of small-world networks

NASA Astrophysics Data System (ADS)

Lv, Qian; Yi, Yuhao; Zhang, Zhongzhi

2015-11-01

We introduce recursive corona graphs as a model of small-world networks. We investigate analytically the critical characteristics of the model, including order and size, degree distribution, average path length, clustering coefficient, and the number of spanning trees, as well as Kirchhoff index. Furthermore, we study the spectra for the adjacency matrix and the Laplacian matrix for the model. We obtain explicit results for all the quantities of the recursive corona graphs, which are similar to those observed in real-life networks.

Acoustic Inverse Scattering for Breast Cancer Microcalcification Detection. Addendum

DTIC Science & Technology

2011-12-01

the center. To conserve space, few are shown here. A graph comparing the spatial location and the error in reconstruction will follow...following graphs show the error in reconstruction as a function of position of the object along the x-axis, y-axis and the diagonal in the fourth quadrant of...the well-known Kirchhoff – Poisson formulas (see, e.g., Refs. [33,34]) allow one to rep- resent the solution p(x,t) in terms of the spherical means

Electrochemistry in Colloids and Dispersions. Volume 1. Electroanalytical Methods and Applications, Electrosynthesis and Electrocatalysis, Polymers and Latexes

DTIC Science & Technology

1992-02-04

derived from dissociation of surface acid groups of the microparticles. The surface charges of these particles are provided by sulfate groups... sulfate micellar solution as a function of electrolyte concentration3 Jon R. Kirchhoff, John D. Skelton, Jr., and Kregg T. Brooks Department of...films on the voltamnmetric curve obtained for the oxidation of benzilic acid on a platinum anode in 2M sodium hydroxide. The acid is soluble in this

Application of linearized inverse scattering methods for the inspection in steel plates embedded in concrete structures

NASA Astrophysics Data System (ADS)

Tsunoda, Takaya; Suzuki, Keigo; Saitoh, Takahiro

2018-04-01

This study develops a method to visualize the state of steel-concrete interface with ultrasonic testing. Scattered waves are obtained by the UT pitch-catch mode from the surface of the concrete. Discrete wavelet transform is applied in order to extract echoes scattered from the steel-concrete interface. Then Linearized Inverse Scattering Methods are used for imaging the interface. The results show that LISM with Born and Kirchhoff approximation provide clear images for the target.

Second-harmonic diffraction from holographic volume grating.

PubMed

Nee, Tsu-Wei

2006-10-01

The full polarization property of holographic volume-grating enhanced second-harmonic diffraction (SHD) is investigated theoretically. The nonlinear coefficient is derived from a simple atomic model of the material. By using a simple volume-grating model, the SHD fields and Mueller matrices are first derived. The SHD phase-mismatching effect for a thick sample is analytically investigated. This theory is justified by fitting with published experimental SHD data of thin-film samples. The SHD of an existing polymethyl methacrylate (PMMA) holographic 2-mm-thick volume-grating sample is investigated. This sample has two strong coupling linear diffraction peaks and five SHD peaks. The splitting of SHD peaks is due to the phase-mismatching effect. The detector sensitivity and laser power needed to measure these peak signals are quantitatively estimated.

Recent modelling advances for ultrasonic TOFD inspections

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

Darmon, Michel; Ferrand, Adrien; Dorval, Vincent

The ultrasonic TOFD (Time of Flight Diffraction) Technique is commonly used to detect and characterize disoriented cracks using their edge diffraction echoes. An overview of the models integrated in the CIVA software platform and devoted to TOFD simulation is presented. CIVA allows to predict diffraction echoes from complex 3D flaws using a PTD (Physical Theory of Diffraction) based model. Other dedicated developments have been added to simulate lateral waves in 3D on planar entry surfaces and in 2D on irregular surfaces by a ray approach. Calibration echoes from Side Drilled Holes (SDHs), specimen echoes and shadowing effects from flaws canmore » also been modelled. Some examples of theoretical validation of the models are presented. In addition, experimental validations have been performed both on planar blocks containing calibration holes and various notches and also on a specimen with an irregular entry surface and allow to draw conclusions on the validity of all the developed models.« less

Generation of individually modulated femtosecond pulse string by multilayer volume holographic gratings.

PubMed

Yan, Xiaona; Gao, Lirun; Yang, Xihua; Dai, Ye; Chen, Yuanyuan; Ma, Guohong

2014-10-20

A scheme to generate individually modulated femtosecond pulse string by multilayer volume holographic grating (MVHG) is proposed. Based on Kogelnik's coupled-wave theory and matrix optics, temporal and spectral expressions of diffracted field are given when a femtosecond pulse is diffracted by a MVHG. It is shown that the number of diffracted sub-pulses in the pulse string equals to the number of grating layers of the MVHG, peak intensity and duration of each diffracted sub-pulse depend on thickness of the corresponding grating layer, whereas pulse interval between adjacent sub-pulses is related to thickness of the corresponding buffer layer. Thus by modulating parameters of the MVHG, individually modulated femtosecond pulse string can be acquired. Based on Bragg selectivity of the volume grating and phase shift provided by the buffer layers, we give an explanation on these phenomena. The result is useful to design MVHG-based devices employed in optical communications, pulse shaping and processing.

Measurement of 3D refractive index distribution by optical diffraction tomography

NASA Astrophysics Data System (ADS)

Chi, Weining; Wang, Dayong; Wang, Yunxin; Zhao, Jie; Rong, Lu; Yuan, Yuanyuan

2018-01-01

Optical Diffraction Tomography (ODT), as a novel 3D imaging technique, can obtain a 3D refractive index (RI) distribution to reveal the important optical properties of transparent samples. According to the theory of ODT, an optical diffraction tomography setup is built based on the Mach-Zehnder interferometer. The propagation direction of object beam is controlled by a 2D translation stage, and 121 holograms based on different illumination angles are recorded by a Charge-coupled Device (CCD). In order to prove the validity and accuracy of the ODT, the 3D RI profile of microsphere with a known RI is firstly measured. An iterative constraint algorithm is employed to improve the imaging accuracy effectively. The 3D morphology and average RI of the microsphere are consistent with that of the actual situation, and the RI error is less than 0.0033. Then, an optical element fabricated by laser with a non-uniform RI is taken as the sample. Its 3D RI profile is obtained by the optical diffraction tomography system.

Crystal-Site-Selective Spectrum of Fe3BO6 by Synchrotron Mössbauer Diffraction with Pure Nuclear Bragg Scattering

NASA Astrophysics Data System (ADS)

Nakamura, Shin; Mitsui, Takaya; Fujiwara, Kosuke; Ikeda, Naoshi; Kurokuzu, Masayuki; Shimomura, Susumu

2017-08-01

We have succeeded in obtaining the crystal-site-selective spectra of the collinear antiferromagnet Fe3BO6 using a synchrotron Mössbauer diffractometer with pure nuclear Bragg scattering at SPring-8 BL11XU. Well-resolved 300, 500, and 700 reflection spectra, having asymmetric line shapes owing to the higher-order interference effect between the nuclear energy levels, were quantitatively analyzed using a formula based on the dynamical theory of diffraction. Reasonable hyperfine parameters were obtained. The intensity ratio of Fe1 to Fe2 subspectra is in accordance with the nuclear structure factor. However, when the spectrum is measured at the peak position of the rocking curve (very near the Bragg position), the value of the center shift deviates from its intrinsic value. This is also due to the dynamical effect of γ-ray diffraction. To avoid this problem, it is necessary to use diffraction angles near the foot of the rocking curve, approximately 0.02° apart from the peak position.

Rigorous theory of the diffraction of Gaussian beams by finite gratings: TM polarization.

PubMed

Mata-Mendez, O; Avendaño, J; Chavez-Rivas, F

2006-08-01

Diffraction of TM-polarized Gaussian beams by N equally spaced slits (finite grating) in a planar perfectly conducting thick screen is treated. We extend to the TM polarization case the results of a previous paper where the TE polarization was considered. The far-field diffraction patterns, the transmission coefficient tau, and the normally diffracted energy E as a function of several optogeometrical parameters are analyzed within the so-called vectorial region. The existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits is shown. In addition, the property E=Ntau/lambda, valid in the scalar region, is extended to the TM polarization case in the vectorial region, lambda being the wavelength. The coupling between slits is analyzed, giving an oscillating amplitude-decreasing function as the separation between slits increases, where the period for these oscillations is the wavelength lambda. Finally, the extraordinary optical transmission phenomena that appear when the wavelength is larger than the slit width (subwavelength regime) are analyzed.

Multiple diffraction in an icosahedral Al-Cu-Fe quasicrystal

NASA Astrophysics Data System (ADS)

Fan, C. Z.; Weber, Th.; Deloudi, S.; Steurer, W.

2011-07-01

In order to reveal its influence on quasicrystal structure analysis, multiple diffraction (MD) effects in an icosahedral Al-Cu-Fe quasicrystal have been investigated in-house on an Oxford Diffraction four-circle diffractometer equipped with an Onyx™ CCD area detector and MoKα radiation. For that purpose, an automated approach for Renninger scans (ψ-scans) has been developed. Two weak reflections were chosen as the main reflections (called P) in the present measurements. As is well known for periodic crystals, it is also observed for this quasicrystal that the intensity of the main reflection may significantly increase if the simultaneous (H) and the coupling (P-H) reflections are both strong, while there is no obvious MD effect if one of them is weak. The occurrence of MD events during ψ-scans has been studied based on an ideal structure model and the kinematical MD theory. The reliability of the approach is revealed by the good agreement between simulation and experiment. It shows that the multiple diffraction effect is quite significant.

Blazed vector grating liquid crystal cells with photocrosslinkable polymeric alignment films fabricated by one-step polarizer rotation method

NASA Astrophysics Data System (ADS)

Kawai, Kotaro; Kuzuwata, Mitsuru; Sasaki, Tomoyuki; Noda, Kohei; Kawatsuki, Nobuhiro; Ono, Hiroshi

2014-12-01

Blazed vector grating liquid crystal (LC) cells, in which the directors of low-molar-mass LCs are antisymmetrically distributed, were fabricated by one-step exposure of an empty glass cell inner-coated with a photocrosslinkable polymer LC (PCLC) to UV light. By adopting a LC cell structure, twisted nematic (TN) and homogeneous (HOMO) alignments were obtained in the blazed vector grating LC cells. Moreover, the diffraction efficiency of the blazed vector grating LC cells was greatly improved by increasing the thickness of the device in comparison with that of a blazed vector grating with a thin film structure obtained in our previous study. In addition, the diffraction efficiency and polarization states of ±1st-order diffracted beams from the resultant blazed vector grating LC cells were controlled by designing a blazed pattern in the alignment films, and these diffraction properties were well explained on the basis of Jones calculus and the elastic continuum theory of nematic LCs.

Volume phase holographic grating used for beams combination of RGB primary colors

NASA Astrophysics Data System (ADS)

Liu, Hui; Zhang, Xizhao; Tang, Minxue

2013-12-01

Volume phase holographic grating (VPHG) has the characteristics of high diffraction efficiency, high signal to noise ratio, high wavelength and angular selectivity, low scattering , low absorption and low cost. It has been widely used in high resolution spectrometer, wavelength division multiplexing and pulse compression technique. In this paper, a novel kind of RGB primary colors beams combiner which is consisted of a transmission VPHG and a reflection VPHG as core components is proposed. The design idea of the element is described in detail. Based on the principle of VPHG, the rigorous coupled wave analysis (RCWA) and Kogelnik's coupled wave theory, diffraction properties of the transmission and reflection VPHG are studied theoretically. As an example, three primary colors at wavelengths of 632.8nm, 532nm and 476.5nm are taken into account. Dichromated gelatin (DCG) is used as the holographic recording material. The grating parameters are determined by the Bragg conditions. The TE and TM wave diffraction efficiency, the wavelength selectivity and the angular selectivity of the transmission and reflection VPHG are calculated and optimized by setting the amplitude of the index modulation (Δn) and the thickness of the gelatin layer (d) by applying Kogelnik's coupled wave theory and G-solver software, respectively. The theoretical calculating results give guidance for further manufacture of the element.

Analyzation of photopolymer materials shrunken influence for thick hologram gratings

NASA Astrophysics Data System (ADS)

Li, Zhenzhen; Xiao, Xue; Chen, Wei; Kang, Guoguo; Huang, Yong; Tan, Xiaodi

2016-09-01

The photopolymer materials are good media to record thick hologram gratings, because photopolymer materials have high resolution, low cost, simple process technology and so on. According to coupled wave theory for thick hologram gratings, we know that the same object beam can be reconstructed if the same reference beam is used to retrieve a thick hologram grating. However, the shrinkage always occurs in the photopolymer materials because of environment temperature, humidity, vibration etc. For instance, the same object beam cannot be reconstructed even the same reference beam to be used. In this paper, we will analysis the shrinkage influence of photopolymer materials for thick hologram gratings. We divide the photopolymer materials into several geometry layers, and analysis the reconstructed characteristics separately basing on coupled wave theory of Kogelnik. Through gradually continuous changing the angle between gratings and the border (we call it slant angle), we can build the geometry model of gratings bending caused by shrinkage of materials. We calculate wave complex amplitude diffracted from every layer, and superpose them to compute the total diffraction efficiency. We simulate above methods to obtain the curve of diffraction efficiency with reconstruction wavelength by using Matlab software. Comparing the simulated results with the experiments results, we can deduce the probable situation of thick hologram gratings bending after photopolymer materials shrink.

Global search in photoelectron diffraction structure determination using genetic algorithms

NASA Astrophysics Data System (ADS)

Viana, M. L.; Díez Muiño, R.; Soares, E. A.; Van Hove, M. A.; de Carvalho, V. E.

2007-11-01

Photoelectron diffraction (PED) is an experimental technique widely used to perform structural determinations of solid surfaces. Similarly to low-energy electron diffraction (LEED), structural determination by PED requires a fitting procedure between the experimental intensities and theoretical results obtained through simulations. Multiple scattering has been shown to be an effective approach for making such simulations. The quality of the fit can be quantified through the so-called R-factor. Therefore, the fitting procedure is, indeed, an R-factor minimization problem. However, the topography of the R-factor as a function of the structural and non-structural surface parameters to be determined is complex, and the task of finding the global minimum becomes tough, particularly for complex structures in which many parameters have to be adjusted. In this work we investigate the applicability of the genetic algorithm (GA) global optimization method to this problem. The GA is based on the evolution of species, and makes use of concepts such as crossover, elitism and mutation to perform the search. We show results of its application in the structural determination of three different systems: the Cu(111) surface through the use of energy-scanned experimental curves; the Ag(110)-c(2 × 2)-Sb system, in which a theory-theory fit was performed; and the Ag(111) surface for which angle-scanned experimental curves were used. We conclude that the GA is a highly efficient method to search for global minima in the optimization of the parameters that best fit the experimental photoelectron diffraction intensities to the theoretical ones.

Investigation of optical information for a single micro grating device combined with MATA by SMart process

NASA Astrophysics Data System (ADS)

Tsai, Chien-Chung; Huang, Yi-Chao; Yang, Tsa-Hsien; Chen, Jen-Chieh

2006-01-01

The concentric circles type and saw-tooth type of micro grating device based upon the diffraction theory are proposed in this study. The geometry dimension of micro optical device is 200 × 200 μm2, the interval of grating is 4 μm, and the depth is 0.75 μm. The Micro Array Thermal Actuator, MATA, is applied to drive the micro grating device, and the pre-elevating structure is designed to lift the micro grating device by the residual stress of polysilicon combined with metal. The micro grating device is fabricated by Surface Micromachining for applications and research technology platform, SMart, common process. The incident ray of He-Ne laser focused by a lens which focal length is 250 mm is applied to be the light source for the experiment, and then analyzes the optical information of the outgoing ray. From the experimental results, the basic optical features are examined based upon the concentric circles type and saw-tooth type of micro grating device, respectively. The outgoing ray angle of central spot is 60° in theory. The measurements are 59.475° for the concentric circles type and 59.88° for the saw-tooth type. The outgoing ray angle of the first stripe is 46.9° in theory, and 46.81° for the concentric circles type and 46.67° for the saw-tooth type are measured from the experiment. The variation of outgoing ray angle is smaller than 1% compared the measurement results with theory of diffraction on the central spot and first stripe characteristics. The work successfully demonstrates the micro grating device with highly accurate performance by the verification of optical information. All of the efforts will be contributed to Controlled Blazed Diffraction micro grating device, CBDMG, and that will be the main device of Integrate Opto-Electronics applied on display to develop in the future.

A second order thermodynamic perturbation theory for hydrogen bond cooperativity in water

NASA Astrophysics Data System (ADS)

Marshall, Bennett D.

2017-05-01

It has been extensively demonstrated through first principles quantum mechanics calculations that water exhibits strong hydrogen bond cooperativity. Equations of state developed from statistical mechanics typically assume pairwise additivity, meaning they cannot account for these 3-body and higher cooperative effects. In this paper, we extend a second order thermodynamic perturbation theory to correct for hydrogen bond cooperativity in 4 site water. We demonstrate that the theory predicts hydrogen bonding structure consistent spectroscopy, neutron diffraction, and molecular simulation data. Finally, we implement the approach into a general equation of state for water.

Theory and Application of Auger and Photoelectron Diffraction and Holography

NASA Astrophysics Data System (ADS)

Chen, Xiang

This dissertation addresses the theories and applications of three important surface analysis techniques: Auger electron diffraction (AED), x-ray photoelectron diffraction (XPD), and Auger and photoelectron holography. A full multiple-scattering scheme for the calculations of XPD, AED, and Kikuchi electron diffraction pattern from a surface cluster is described. It is used to simulate 64 eV M_{2,3}VV and 913 eV L_3VV AED patterns from Cu(001) surfaces, in order to test assertions in the literature that they are explicable by a classical "blocking" and channeling model. We find that this contention is not valid, and that only a quantum mechanical multiple-scattering calculation is able to simulate these patterns well. The same multiple scattering simulation scheme is also used to investigate the anomalous phenomena of peak shifts off the forward-scattering directions in photo -electron diffraction patterns of Mg KLL (1180 eV) and O 1s (955 eV) from MgO(001) surfaces. These shifts are explained by calculations assuming a short electron mean free path. Similar simulations of XPD from a CoSi_2(111) surface for Co-3p and Si-2p normal emission agree well with experimental diffraction patterns. A filtering process aimed at eliminating the self -interference effect in photoelectron holography is developed. A better reconstructed image from Si-2p XPD from a Si(001) (2 times 1) surface is seen at atomic resolution. A reconstruction algorithm which corrects for the anisotropic emitter waves as well as the anisotropic atomic scattering factors is used for holographic reconstruction from a Co-3p XPD pattern from a CoSi_2 surface. This new algorithm considerably improves the reconstructed image. Finally, a new reconstruction algorithm called "atomic position recovery by iterative optimization of reconstructed intensities" (APRIORI), which takes account of the self-interference terms omitted by the other holographic algorithms, is developed. Tests on a Ni-C-O chain and Si(111)(sqrt{3} times sqrt{3})B surface suggest that this new method may overcome the twin image problem in the traditional holographic methods, reduce the artifacts in real space, and even separately identify the chemical species of the scatterers.

Experimental and theoretical study of rotationally inelastic diffraction of H{sub 2}(D{sub 2}) from methyl-terminated Si(111)

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

Nihill, Kevin J.; Hund, Zachary M.; Sibener, S. J., E-mail: s-sibener@uchicago.edu

2016-08-28

Fundamental details concerning the interaction between H{sub 2} and CH{sub 3}–Si(111) have been elucidated by the combination of diffractive scattering experiments and electronic structure and scattering calculations. Rotationally inelastic diffraction (RID) of H{sub 2} and D{sub 2} from this model hydrocarbon-decorated semiconductor interface has been confirmed for the first time via both time-of-flight and diffraction measurements, with modest j = 0 → 2 RID intensities for H{sub 2} compared to the strong RID features observed for D{sub 2} over a large range of kinematic scattering conditions along two high-symmetry azimuthal directions. The Debye-Waller model was applied to the thermal attenuationmore » of diffraction peaks, allowing for precise determination of the RID probabilities by accounting for incoherent motion of the CH{sub 3}–Si(111) surface atoms. The probabilities of rotationally inelastic diffraction of H{sub 2} and D{sub 2} have been quantitatively evaluated as a function of beam energy and scattering angle, and have been compared with complementary electronic structure and scattering calculations to provide insight into the interaction potential between H{sub 2} (D{sub 2}) and hence the surface charge density distribution. Specifically, a six-dimensional potential energy surface (PES), describing the electronic structure of the H{sub 2}(D{sub 2})/CH{sub 3}−Si(111) system, has been computed based on interpolation of density functional theory energies. Quantum and classical dynamics simulations have allowed for an assessment of the accuracy of the PES, and subsequently for identification of the features of the PES that serve as classical turning points. A close scrutiny of the PES reveals the highly anisotropic character of the interaction potential at these turning points. This combination of experiment and theory provides new and important details about the interaction of H{sub 2} with a hybrid organic-semiconductor interface, which can be used to further investigate energy flow in technologically relevant systems.« less

Ionospheric irregularity characteristics from quasiperiodic structure in the radio wave scintillation

NASA Astrophysics Data System (ADS)

Chen, K. Y.; Su, S. Y.; Liu, C. H.; Basu, S.

2005-06-01

Quasiperiodic (QP) diffraction pattern in scintillation patches has been known to highly correlate with the edge structures of a plasma bubble (Franke et al., 1984). A new time-frequency analysis method of Hilbert-Huang transform (HHT) has been applied to analyze the scintillation data taken at Ascension Island to understand the characteristics of corresponding ionosphere irregularities. The HHT method enables us to extract the quasiperiodic diffraction signals embedded inside the scintillation data and to obtain the characteristics of such diffraction signals. The cross correlation of the two sets of diffraction signals received by two stations at each end of Ascension Island indicates that the density irregularity pattern that causes the diffraction pattern should have an eastward drift velocity of ˜130 m/s. The HHT analysis of the instantaneous frequency in the QP diffraction patterns also reveals some frequency shifts in their peak frequencies. For the QP diffraction pattern caused by the leading edge of the large density gradient at the east wall of a structured bubble, an ascending note in the peak frequency is observed, and for the trailing edge a descending note is observed. The linear change in the transient of the peak frequency in the QP diffraction pattern is consistent with the theory and the simulation result of Franke et al. Estimate of the slope in the transient frequency provides us the information that allows us to identify the locations of plasma walls, and the east-west scale of the irregularity can be estimated. In our case we obtain about 24 km in the east-west scale. Furthermore, the height location of density irregularities that cause the diffraction pattern is estimated to be between 310 and 330 km, that is, around the F peak during observation.

X-ray diffraction from nonuniformly stretched helical molecules

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

Prodanovic, Momcilo; Irving, Thomas C.; Mijailovich, Srboljub M.

2016-04-18

The fibrous proteins in living cells are exposed to mechanical forces interacting with other subcellular structures. X-ray fiber diffraction is often used to assess deformation and movement of these proteins, but the analysis has been limited to the theory for fibrous molecular systems that exhibit helical symmetry. However, this approach cannot adequately interpret X-ray data from fibrous protein assemblies where the local strain varies along the fiber length owing to interactions of its molecular constituents with their binding partners. To resolve this problem a theoretical formulism has been developed for predicting the diffraction from individual helical molecular structures nonuniformly strainedmore » along their lengths. This represents a critical first step towards modeling complex dynamical systems consisting of multiple helical structures using spatially explicit, multi-scale Monte Carlo simulations where predictions are compared with experimental data in a `forward' process to iteratively generate ever more realistic models. Here the effects of nonuniform strains and the helix length on the resulting magnitude and phase of diffraction patterns are quantitatively assessed. Examples of the predicted diffraction patterns of nonuniformly deformed double-stranded DNA and actin filaments in contracting muscle are presented to demonstrate the feasibly of this theoretical approach.« less

A study of angular spectrum and limited diffraction beams for calculation of field of array transducers

NASA Astrophysics Data System (ADS)

Cheng, Jiqi; Lu, Jian-Yu

2002-05-01

Angular spectrum is one of the most powerful tools for field calculation. It is based on linear system theory and the Fourier transform and is used for the calculation of propagating sound fields at different distances. In this report, the generalization and interpretation of the angular spectrum and its intrinsic relationship with limited diffraction beams are studied. With an angular spectrum, the field at the surface of a transducer is decomposed into limited diffractions beams. For an array transducer, a linear relationship between the quantized fields at the surface of elements of the array and the propagating field at any point in space can be established. For an annular array, the field is decomposed into limited diffraction Bessel beams [P. D. Fox and S. Holm, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 85-93 (2002)], while for a two-dimensional (2-D) array the field is decomposed into limited diffraction array beams [J-y. Lu and J. Cheng, J. Acoust. Soc. Am. 109, 2397-2398 (2001)]. The angular spectrum reveals the intrinsic link between these decompositions. [Work supported in part by Grant 5RO1 HL60301 from NIH.