rigorous diffraction theory: Topics by Science.gov

Sample records for rigorous diffraction theory

Rigorous diffraction analysis using geometrical theory of diffraction for future mask technology

NASA Astrophysics Data System (ADS)

Chua, Gek S.; Tay, Cho J.; Quan, Chenggen; Lin, Qunying

2004-05-01

Advanced lithographic techniques such as phase shift masks (PSM) and optical proximity correction (OPC) result in a more complex mask design and technology. In contrast to the binary masks, which have only transparent and nontransparent regions, phase shift masks also take into consideration transparent features with a different optical thickness and a modified phase of the transmitted light. PSM are well-known to show prominent diffraction effects, which cannot be described by the assumption of an infinitely thin mask (Kirchhoff approach) that is used in many commercial photolithography simulators. A correct prediction of sidelobe printability, process windows and linearity of OPC masks require the application of rigorous diffraction theory. The problem of aerial image intensity imbalance through focus with alternating Phase Shift Masks (altPSMs) is performed and compared between a time-domain finite-difference (TDFD) algorithm (TEMPEST) and Geometrical theory of diffraction (GTD). Using GTD, with the solution to the canonical problems, we obtained a relationship between the edge on the mask and the disturbance in image space. The main interest is to develop useful formulations that can be readily applied to solve rigorous diffraction for future mask technology. Analysis of rigorous diffraction effects for altPSMs using GTD approach will be discussed.
Rigorous Electromagnetic Analysis of the Focusing Action of Refractive Cylindrical Microlens

NASA Astrophysics Data System (ADS)

Liu, Juan; Gu, Ben-Yuan; Dong, Bi-Zhen; Yang, Guo-Zhen

The focusing action of refractive cylindrical microlens is investigated based on the rigorous electromagnetic theory with the use of the boundary element method. The focusing behaviors of these refractive microlenses with continuous and multilevel surface-envelope are characterized in terms of total electric-field patterns, the electric-field intensity distributions on the focal plane, and their diffractive efficiencies at the focal spots. The obtained results are also compared with the ones obtained by Kirchhoff's scalar diffraction theory. The present numerical and graphical results may provide useful information for the analysis and design of refractive elements in micro-optics.
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.
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.
Volume Holograms in Photopolymers: Comparison between Analytical and Rigorous Theories

PubMed Central

Gallego, Sergi; Neipp, Cristian; Estepa, Luis A.; Ortuño, Manuel; Márquez, Andrés; Francés, Jorge; Pascual, Inmaculada; Beléndez, Augusto

2012-01-01

There is no doubt that the concept of volume holography has led to an incredibly great amount of scientific research and technological applications. One of these applications is the use of volume holograms as optical memories, and in particular, the use of a photosensitive medium like a photopolymeric material to record information in all its volume. In this work we analyze the applicability of Kogelnik’s Coupled Wave theory to the study of volume holograms recorded in photopolymers. Some of the theoretical models in the literature describing the mechanism of hologram formation in photopolymer materials use Kogelnik’s theory to analyze the gratings recorded in photopolymeric materials. If Kogelnik’s theory cannot be applied is necessary to use a more general Coupled Wave theory (CW) or the Rigorous Coupled Wave theory (RCW). The RCW does not incorporate any approximation and thus, since it is rigorous, permits judging the accurateness of the approximations included in Kogelnik’s and CW theories. In this article, a comparison between the predictions of the three theories for phase transmission diffraction gratings is carried out. We have demonstrated the agreement in the prediction of CW and RCW and the validity of Kogelnik’s theory only for gratings with spatial frequencies higher than 500 lines/mm for the usual values of the refractive index modulations obtained in photopolymers.
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.
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
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.
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.
Imaging 2D optical diffuse reflectance in skeletal muscle

NASA Astrophysics Data System (ADS)

Ranasinghesagara, Janaka; Yao, Gang

2007-04-01

We discovered a unique pattern of optical reflectance from fresh prerigor skeletal muscles, which can not be described using existing theories. A numerical fitting function was developed to quantify the equiintensity contours of acquired reflectance images. Using this model, we studied the changes of reflectance profile during stretching and rigor process. We found that the prominent anisotropic features diminished after rigor completion. These results suggested that muscle sarcomere structures played important roles in modulating light propagation in whole muscle. When incorporating the sarcomere diffraction in a Monte Carlo model, we showed that the resulting reflectance profiles quantitatively resembled the experimental observation.
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.
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.
Coupled-mode theory and Fano resonances in guided-mode resonant gratings: the conical diffraction mounting.

PubMed

Bykov, Dmitry A; Doskolovich, Leonid L; Soifer, Victor A

2017-01-23

We study resonances of guided-mode resonant gratings in conical mounting. By developing 2D time-dependent coupled-mode theory we obtain simple approximations of the transmission and reflection coefficients. Being functions of the incident light's frequency and in-plane wave vector components, the obtained approximations can be considered as multi-variable generalizations of the Fano line shape. We show that the approximations are in good agreement with the rigorously calculated transmission and reflection spectra. We use the developed theory to investigate angular tolerances of the considered structures and to obtain mode excitation conditions. In particular, we obtain the cross-polarization mode excitation conditions in the case of conical mounting.
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.
Fourier optics of constant-thickness three-dimensional objects on the basis of diffraction models

NASA Astrophysics Data System (ADS)

Chugui, Yu. V.

2017-09-01

Results of investigations of diffraction phenomena on constant-thickness three-dimensional objects with flat inner surfaces (thick plates) are summarized on the basis of our constructive theory of their calculation as applied to dimensional inspection. It is based on diffraction models of 3D objects with the use of equivalent diaphragms (distributions), which allow the Kirchhoff-Fresnel approximation to be effectively used. In contrast to available rigorous and approximate methods, the present approach does not require cumbersome calculations; it is a clearly arranged method, which ensures sufficient accuracy for engineering applications. It is found that the fundamental diffraction parameter for 3D objects of constant thickness d is the critical diffraction angle {θ _{cr}} = √ {λ /d} at which the effect of three-dimensionality on the spectrum of the 3D object becomes appreciable. Calculated Fraunhofer diffraction patterns (spectra) and images of constant-thickness 3D objects with absolutely absorbing, absolutely reflecting, and gray internal faces are presented. It is demonstrated that selection of 3D object fragments can be performed by choosing an appropriate configuration of the wave illuminating the object (plane normal or inclined waves, spherical waves).
Rigorous coupled wave analysis of acousto-optics with relativistic considerations.

PubMed

Xia, Guoqiang; Zheng, Weijian; Lei, Zhenggang; Zhang, Ruolan

2015-09-01

A relativistic analysis of acousto-optics is presented, and a rigorous coupled wave analysis is generalized for the diffraction of the acousto-optical effect. An acoustic wave generates a grating with temporally and spatially modulated permittivity, hindering direct applications of the rigorous coupled wave analysis for the acousto-optical effect. In a reference frame which moves with the acoustic wave, the grating is static, the medium moves, and the coupled wave equations for the static grating may be derived. Floquet's theorem is then applied to cast these equations into an eigenproblem. Using a Lorentz transformation, the electromagnetic fields in the grating region are transformed to the lab frame where the medium is at rest, and relativistic Doppler frequency shifts are introduced into various diffraction orders. In the lab frame, the boundary conditions are considered and the diffraction efficiencies of various orders are determined. This method is rigorous and general, and the plane waves in the resulting expansion satisfy the dispersion relation of the medium and are propagation modes. Properties of various Bragg diffractions are results, rather than preconditions, of this method. Simulations of an acousto-optical tunable filter made by paratellurite, TeO(2), are given as examples.
Edge effects in phase-shifting masks for 0.25-µm lithography

NASA Astrophysics Data System (ADS)

Wong, Alfred K. K.; Neureuther, Andrew R.

1993-03-01

The impact on image quality of scattering from phase-shifter edges and of interactions between phase-shifter and chrome edges is assessed using rigorous electromagnetic simulation. Effects of edge taper in phase-shift masks, spacing between phase-shifter and chrome edges, small outrigger features with a trench phase-shifter, and of the repair of phase defects by etching to 360 degree(s) are considered. Near field distributions and diffraction efficiencies are examined and images are compared with more approximate results from the commonly used Hopkins' theory of imaging.
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.
General imaging of advanced 3D mask objects based on the fully-vectorial extended Nijboer-Zernike (ENZ) theory

NASA Astrophysics Data System (ADS)

van Haver, Sven; Janssen, Olaf T. A.; Braat, Joseph J. M.; Janssen, Augustus J. E. M.; Urbach, H. Paul; Pereira, Silvania F.

2008-03-01

In this paper we introduce a new mask imaging algorithm that is based on the source point integration method (or Abbe method). The method presented here distinguishes itself from existing methods by exploiting the through-focus imaging feature of the Extended Nijboer-Zernike (ENZ) theory of diffraction. An introduction to ENZ-theory and its application in general imaging is provided after which we describe the mask imaging scheme that can be derived from it. The remainder of the paper is devoted to illustrating the advantages of the new method over existing methods (Hopkins-based). To this extent several simulation results are included that illustrate advantages arising from: the accurate incorporation of isolated structures, the rigorous treatment of the object (mask topography) and the fully vectorial through-focus image formation of the ENZ-based algorithm.
Review of rigorous coupled-wave analysis and of homogeneous effective medium approximations for high spatial-frequency surface-relief gratings

NASA Technical Reports Server (NTRS)

Glytsis, Elias N.; Brundrett, David L.; Gaylord, Thomas K.

1993-01-01

A review of the rigorous coupled-wave analysis as applied to the diffraction of electro-magnetic waves by gratings is presented. The analysis is valid for any polarization, angle of incidence, and conical diffraction. Cascaded and/or multiplexed gratings as well as material anisotropy can be incorporated under the same formalism. Small period rectangular groove gratings can also be modeled using approximately equivalent uniaxial homogeneous layers (effective media). The ordinary and extraordinary refractive indices of these layers depend on the gratings filling factor, the refractive indices of the substrate and superstrate, and the ratio of the freespace wavelength to grating period. Comparisons of the homogeneous effective medium approximations with the rigorous coupled-wave analysis are presented. Antireflection designs (single-layer or multilayer) using the effective medium models are presented and compared. These ultra-short period antireflection gratings can also be used to produce soft x-rays. Comparisons of the rigorous coupled-wave analysis with experimental results on soft x-ray generation by gratings are also included.

An efficient hybrid technique in RCS predictions of complex targets at high frequencies

NASA Astrophysics Data System (ADS)

Algar, María-Jesús; Lozano, Lorena; Moreno, Javier; González, Iván; Cátedra, Felipe

2017-09-01

Most computer codes in Radar Cross Section (RCS) prediction use Physical Optics (PO) and Physical theory of Diffraction (PTD) combined with Geometrical Optics (GO) and Geometrical Theory of Diffraction (GTD). The latter approaches are computationally cheaper and much more accurate for curved surfaces, but not applicable for the computation of the RCS of all surfaces of a complex object due to the presence of caustic problems in the analysis of concave surfaces or flat surfaces in the far field. The main contribution of this paper is the development of a hybrid method based on a new combination of two asymptotic techniques: GTD and PO, considering the advantages and avoiding the disadvantages of each of them. A very efficient and accurate method to analyze the RCS of complex structures at high frequencies is obtained with the new combination. The proposed new method has been validated comparing RCS results obtained for some simple cases using the proposed approach and RCS using the rigorous technique of Method of Moments (MoM). Some complex cases have been examined at high frequencies contrasting the results with PO. This study shows the accuracy and the efficiency of the hybrid method and its suitability for the computation of the RCS at really large and complex targets at high frequencies.
Design, simulation, and optimization of an RGB polarization independent transmission volume hologram

NASA Astrophysics Data System (ADS)

Mahamat, Adoum Hassan

Volume phase holographic (VPH) gratings have been designed for use in many areas of science and technology such as optical communication, medical imaging, spectroscopy and astronomy. The goal of this dissertation is to design a volume phase holographic grating that provides diffraction efficiencies of at least 70% for the entire visible wavelengths and higher than 90% for red, green, and blue light when the incident light is unpolarized. First, the complete design, simulation and optimization of the volume hologram are presented. The optimization is done using a Monte Carlo analysis to solve for the index modulation needed to provide higher diffraction efficiencies. The solutions are determined by solving the diffraction efficiency equations determined by Kogelnik's two wave coupled-wave theory. The hologram is further optimized using the rigorous coupled-wave analysis to correct for effects of absorption omitted by Kogelnik's method. Second, the fabrication or recording process of the volume hologram is described in detail. The active region of the volume hologram is created by interference of two coherent beams within the thin film. Third, the experimental set up and measurement of some properties including the diffraction efficiencies of the volume hologram, and the thickness of the active region are conducted. Fourth, the polarimetric response of the volume hologram is investigated. The polarization study is developed to provide insight into the effect of the refractive index modulation onto the polarization state and diffraction efficiency of incident light.
Guided-mode resonance reflection and transmission filters in the optical and microwave spectral ranges

NASA Astrophysics Data System (ADS)

Tibuleac, Sorin

In this dissertation, new reflection and transmission filters are developed and characterized in the optical and microwave spectral regions. These guided-mode resonance (GMR) filters are implemented by integrating diffraction gratings into classical thin-film multilayers to produce high efficiency filter response and low sidebands extended over a large spectral range. Diffraction from phase-shifted gratings and gratings with different periods is analyzed using rigorous coupled-wave theory yielding a new approach to filter linewidth broadening, line-shaping, and multi-line filters at normal incidence. New single-grating transmission filters presented have narrow linewidth, high peak transmittance, and low sideband reflectance. A comparison with classical thin-film filters shows that GMR devices require significantly fewer layers to obtain narrow linewidth and high peak response. All-dielectric microwave frequency- selective surfaces operating in reflection or transmission are shown to be realizable with only a few layers using common microwave materials. Single-layer and multilayer waveguide gratings operating as reflection and transmission filters, respectively, were built and tested in the 4-20 GHz frequency range. The presence of GMR notches and peaks is clearly established by the experimental results, and their spectral location and lineshape found to be in excellent agreement with the theoretical predictions. A new computer program using genetic algorithms and rigorous coupled-wave analysis was developed for optimization of multilayer structures containing homogeneous and diffractive layers. This program was utilized to find GMR filters possessing features not previously known. Thus, numerous examples of transmission filters with peaks approaching 100%, narrow linewidths (~0.03%), and low sidebands have been found in structures containing only 1-3 layers. A new type of GMR device integrating a waveguide grating with subwavelength period on the endface of an optical fiber is developed for high-resolution biomedical or chemical sensors and spectral filtering applications. Diffraction gratings with submicron periods exhibiting high efficiencies have been recorded for the first time on coated and uncoated endfaces of single-mode and multimode fibers. Guided-mode resonance transmittance notches of ~18% were experimentally obtained with structures consisting of photoresist gratings on thin films of Si3N4 deposited on optical fiber endfaces.
A Draft Conceptual Framework of Relevant Theories to Inform Future Rigorous Research on Student Service-Learning Outcomes

ERIC Educational Resources Information Center

Whitley, Meredith A.

2014-01-01

While the quality and quantity of research on service-learning has increased considerably over the past 20 years, researchers as well as governmental and funding agencies have called for more rigor in service-learning research. One key variable in improving rigor is using relevant existing theories to improve the research. The purpose of this…
Autostereoscopic three-dimensional display by combining a single spatial light modulator and a zero-order nulled grating

NASA Astrophysics Data System (ADS)

Su, Yanfeng; Cai, Zhijian; Liu, Quan; Lu, Yifan; Guo, Peiliang; Shi, Lingyan; Wu, Jianhong

2018-04-01

In this paper, an autostereoscopic three-dimensional (3D) display system based on synthetic hologram reconstruction is proposed and implemented. The system uses a single phase-only spatial light modulator to load the synthetic hologram of the left and right stereo images, and the parallax angle between two reconstructed stereo images is enlarged by a grating to meet the split angle requirement of normal stereoscopic vision. To realize the crosstalk-free autostereoscopic 3D display with high light utilization efficiency, the groove parameters of the grating are specifically designed by the rigorous coupled-wave theory for suppressing the zero-order diffraction, and then the zero-order nulled grating is fabricated by the holographic lithography and the ion beam etching. Furthermore, the diffraction efficiency of the fabricated grating is measured under the illumination of a laser beam with a wavelength of 532 nm. Finally, the experimental verification system for the proposed autostereoscopic 3D display is presented. The experimental results prove that the proposed system is able to generate stereoscopic 3D images with good performances.
Modeling the depth-sectioning effect in reflection-mode dynamic speckle-field interferometric microscopy

PubMed Central

Zhou, Renjie; Jin, Di; Hosseini, Poorya; Singh, Vijay Raj; Kim, Yang-hyo; Kuang, Cuifang; Dasari, Ramachandra R.; Yaqoob, Zahid; So, Peter T. C.

2017-01-01

Unlike most optical coherence microscopy (OCM) systems, dynamic speckle-field interferometric microscopy (DSIM) achieves depth sectioning through the spatial-coherence gating effect. Under high numerical aperture (NA) speckle-field illumination, our previous experiments have demonstrated less than 1 μm depth resolution in reflection-mode DSIM, while doubling the diffraction limited resolution as under structured illumination. However, there has not been a physical model to rigorously describe the speckle imaging process, in particular explaining the sectioning effect under high illumination and imaging NA settings in DSIM. In this paper, we develop such a model based on the diffraction tomography theory and the speckle statistics. Using this model, we calculate the system response function, which is used to further obtain the depth resolution limit in reflection-mode DSIM. Theoretically calculated depth resolution limit is in an excellent agreement with experiment results. We envision that our physical model will not only help in understanding the imaging process in DSIM, but also enable better designing such systems for depth-resolved measurements in biological cells and tissues. PMID:28085800
Rigorous description of holograms of particles illuminated by an astigmatic elliptical Gaussian beam

NASA Astrophysics Data System (ADS)

Yuan, Y. J.; Ren, K. F.; Coëtmellec, S.; Lebrun, D.

2009-02-01

The digital holography is a non-intrusive optical metrology and well adapted for the measurement of the size and velocity field of particles in the spray of a fluid. The simplified model of an opaque disk is often used in the treatment of the diagrams and therefore the refraction and the third dimension diffraction of the particle are not taken into account. We present in this paper a rigorous description of the holographic diagrams and evaluate the effects of the refraction and the third dimension diffraction by comparison to the opaque disk model. It is found that the effects are important when the real part of the refractive index is near unity or the imaginary part is non zero but small.
Diffraction-based overlay measurement on dedicated mark using rigorous modeling method

NASA Astrophysics Data System (ADS)

Lu, Hailiang; Wang, Fan; Zhang, Qingyun; Chen, Yonghui; Zhou, Chang

2012-03-01

Diffraction Based Overlay (DBO) is widely evaluated by numerous authors, results show DBO can provide better performance than Imaging Based Overlay (IBO). However, DBO has its own problems. As well known, Modeling based DBO (mDBO) faces challenges of low measurement sensitivity and crosstalk between various structure parameters, which may result in poor accuracy and precision. Meanwhile, main obstacle encountered by empirical DBO (eDBO) is that a few pads must be employed to gain sufficient information on overlay-induced diffraction signature variations, which consumes more wafer space and costs more measuring time. Also, eDBO may suffer from mark profile asymmetry caused by processes. In this paper, we propose an alternative DBO technology that employs a dedicated overlay mark and takes a rigorous modeling approach. This technology needs only two or three pads for each direction, which is economic and time saving. While overlay measurement error induced by mark profile asymmetry being reduced, this technology is expected to be as accurate and precise as scatterometry technologies.
Optical diffraction by ordered 2D arrays of silica microspheres

NASA Astrophysics Data System (ADS)

Shcherbakov, A. A.; Shavdina, O.; Tishchenko, A. V.; Veillas, C.; Verrier, I.; Dellea, O.; Jourlin, Y.

2017-03-01

The article presents experimental and theoretical studies of angular dependent diffraction properties of 2D monolayer arrays of silica microspheres. High-quality large area defect-free monolayers of 1 μm diameter silica microspheres were deposited by the Langmuir-Blodgett technique under an accurate optical control. Measured angular dependencies of zeroth and one of the first order diffraction efficiencies produced by deposited samples were simulated by the rigorous Generalized Source Method taking into account particle size dispersion and lattice nonideality.
Developments in optical modeling methods for metrology

NASA Astrophysics Data System (ADS)

Davidson, Mark P.

1999-06-01

Despite the fact that in recent years the scanning electron microscope has come to dominate the linewidth measurement application for wafer manufacturing, there are still many applications for optical metrology and alignment. These include mask metrology, stepper alignment, and overlay metrology. Most advanced non-optical lithographic technologies are also considering using topics for alignment. In addition, there have been a number of in-situ technologies proposed which use optical measurements to control one aspect or another of the semiconductor process. So optics is definitely not dying out in the semiconductor industry. In this paper a description of recent advances in optical metrology and alignment modeling is presented. The theory of high numerical aperture image simulation for partially coherent illumination is discussed. The implications of telecentric optics on the image simulation is also presented. Reciprocity tests are proposed as an important measure of numerical accuracy. Diffraction efficiencies for chrome gratings on reticles are one good way to test Kirchoff's approximation as compared to rigorous calculations. We find significant differences between the predictions of Kirchoff's approximation and rigorous methods. The methods for simulating brightfield, confocal, and coherence probe microscope imags are outlined, as are methods for describing aberrations such as coma, spherical aberration, and illumination aperture decentering.
Computer Analysis of Electromagnetic Field Exposure Hazard for Space Station Astronauts during Extravehicular Activity

NASA Technical Reports Server (NTRS)

Hwu, Shian U.; Kelley, James S.; Panneton, Robert B.; Arndt, G. Dickey

1995-01-01

In order to estimate the RF radiation hazards to astronauts and electronics equipment due to various Space Station transmitters, the electric fields around the various Space Station antennas are computed using the rigorous Computational Electromagnetics (CEM) techniques. The Method of Moments (MoM) was applied to the UHF and S-band low gain antennas. The Aperture Integration (AI) method and the Geometrical Theory of Diffraction (GTD) method were used to compute the electric field intensities for the S- and Ku-band high gain antennas. As a result of this study, The regions in which the electric fields exceed the specified exposure levels for the Extravehicular Mobility Unit (EMU) electronics equipment and Extravehicular Activity (EVA) astronaut are identified for various Space Station transmitters.
How to Map Theory: Reliable Methods Are Fruitless Without Rigorous Theory.

PubMed

Gray, Kurt

2017-09-01

Good science requires both reliable methods and rigorous theory. Theory allows us to build a unified structure of knowledge, to connect the dots of individual studies and reveal the bigger picture. Some have criticized the proliferation of pet "Theories," but generic "theory" is essential to healthy science, because questions of theory are ultimately those of validity. Although reliable methods and rigorous theory are synergistic, Action Identification suggests psychological tension between them: The more we focus on methodological details, the less we notice the broader connections. Therefore, psychology needs to supplement training in methods (how to design studies and analyze data) with training in theory (how to connect studies and synthesize ideas). This article provides a technique for visually outlining theory: theory mapping. Theory mapping contains five elements, which are illustrated with moral judgment and with cars. Also included are 15 additional theory maps provided by experts in emotion, culture, priming, power, stress, ideology, morality, marketing, decision-making, and more (see all at theorymaps.org ). Theory mapping provides both precision and synthesis, which helps to resolve arguments, prevent redundancies, assess the theoretical contribution of papers, and evaluate the likelihood of surprising effects.
Tri-critical behavior of the Blume-Emery-Griffiths model on a Kagomé lattice: Effective-field theory and Rigorous bounds

NASA Astrophysics Data System (ADS)

Santos, Jander P.; Sá Barreto, F. C.

2016-01-01

Spin correlation identities for the Blume-Emery-Griffiths model on Kagomé lattice are derived and combined with rigorous correlation inequalities lead to upper bounds on the critical temperature. From the spin correlation identities the mean field approximation and the effective field approximation results for the magnetization, the critical frontiers and the tricritical points are obtained. The rigorous upper bounds on the critical temperature improve over those effective-field type theories results.
Effective Field Theory on Manifolds with Boundary

NASA Astrophysics Data System (ADS)

Albert, Benjamin I.

In the monograph Renormalization and Effective Field Theory, Costello made two major advances in rigorous quantum field theory. Firstly, he gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. Secondly, he gave a rigorous formulation of quantum gauge theory within effective field theory that makes use of the BV formalism. In this work, we extend Costello's renormalization procedure to a class of manifolds with boundary and make preliminary steps towards extending his formulation of gauge theory to manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.
Solving the inverse scattering problem in reflection-mode dynamic speckle-field phase microscopy (Conference Presentation)

NASA Astrophysics Data System (ADS)

Zhou, Renjie; So, Peter T. C.; Yaqoob, Zahid; Jin, Di; Hosseini, Poorya; Kuang, Cuifang; Singh, Vijay Raj; Kim, Yang-Hyo; Dasari, Ramachandra R.

2017-02-01

Most of the quantitative phase microscopy systems are unable to provide depth-resolved information for measuring complex biological structures. Optical diffraction tomography provides a non-trivial solution to it by 3D reconstructing the object with multiple measurements through different ways of realization. Previously, our lab developed a reflection-mode dynamic speckle-field phase microscopy (DSPM) technique, which can be used to perform depth resolved measurements in a single shot. Thus, this system is suitable for measuring dynamics in a layer of interest in the sample. DSPM can be also used for tomographic imaging, which promises to solve the long-existing "missing cone" problem in 3D imaging. However, the 3D imaging theory for this type of system has not been developed in the literature. Recently, we have developed an inverse scattering model to rigorously describe the imaging physics in DSPM. Our model is based on the diffraction tomography theory and the speckle statistics. Using our model, we first precisely calculated the defocus response and the depth resolution in our system. Then, we further calculated the 3D coherence transfer function to link the 3D object structural information with the axially scanned imaging data. From this transfer function, we found that in the reflection mode excellent sectioning effect exists in the low lateral spatial frequency region, thus allowing us to solve the "missing cone" problem. Currently, we are working on using this coherence transfer function to reconstruct layered structures and complex cells.
Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment

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

Öztürk, Hande; Noyan, I. Cevdet

A rigorous study of sampling and intensity statistics applicable for a powder diffraction experiment as a function of crystallite size is presented. Our analysis yields approximate equations for the expected value, variance and standard deviations for both the number of diffracting grains and the corresponding diffracted intensity for a given Bragg peak. The classical formalism published in 1948 by Alexander, Klug & Kummer [J. Appl. Phys.(1948),19, 742–753] appears as a special case, limited to large crystallite sizes, here. It is observed that both the Lorentz probability expression and the statistics equations used in the classical formalism are inapplicable for nanocrystallinemore » powder samples.« less
Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment

DOE PAGES

Öztürk, Hande; Noyan, I. Cevdet

2017-08-24

A rigorous study of sampling and intensity statistics applicable for a powder diffraction experiment as a function of crystallite size is presented. Our analysis yields approximate equations for the expected value, variance and standard deviations for both the number of diffracting grains and the corresponding diffracted intensity for a given Bragg peak. The classical formalism published in 1948 by Alexander, Klug & Kummer [J. Appl. Phys.(1948),19, 742–753] appears as a special case, limited to large crystallite sizes, here. It is observed that both the Lorentz probability expression and the statistics equations used in the classical formalism are inapplicable for nanocrystallinemore » powder samples.« less
Design of a Binary Grating with Subwavelength Features that Acts as a Polarizing Beam Splitter.

PubMed

Pajewski, L; Borghi, R; Schettini, G; Frezza, F; Santarsiero, M

2001-11-10

A binary diffractive optical element, acting as a polarizing beam splitter, is proposed and analyzed. It behaves like a transmissive blazed grating, working on the first or the second diffraction order, depending on the polarization state of the incident radiation. The grating-phase profile required for both polarization states is obtained by means of suitably sized subwavelength groups etched in an isotropic dielectric medium. A rigorous electromagnetic analysis of the grating is presented, and numerical results concerning its performances in terms of diffraction efficiency as well as frequency and angular bandwidths are provided.
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.
Achieving a high mode count in the exact electromagnetic simulation of diffractive optical elements.

PubMed

Junker, André; Brenner, Karl-Heinz

2018-03-01

The application of rigorous optical simulation algorithms, both in the modal as well as in the time domain, is known to be limited to the nano-optical scale due to severe computing time and memory constraints. This is true even for today's high-performance computers. To address this problem, we develop the fast rigorous iterative method (FRIM), an algorithm based on an iterative approach, which, under certain conditions, allows solving also large-size problems approximation free. We achieve this in the case of a modal representation by avoiding the computationally complex eigenmode decomposition. Thereby, the numerical cost is reduced from O(N 3 ) to O(N log N), enabling a simulation of structures like certain diffractive optical elements with a significantly higher mode count than presently possible. Apart from speed, another major advantage of the iterative FRIM over standard modal methods is the possibility to trade runtime against accuracy.

Adaptive characterization of recrystallization kinetics in IF steel by electron backscatter diffraction.

PubMed

Kim, Dong-Kyu; Park, Won-Woong; Lee, Ho Won; Kang, Seong-Hoon; Im, Yong-Taek

2013-12-01

In this study, a rigorous methodology for quantifying recrystallization kinetics by electron backscatter diffraction is proposed in order to reduce errors associated with the operator's skill. An adaptive criterion to determine adjustable grain orientation spread depending on the recrystallization stage is proposed to better identify the recrystallized grains in the partially recrystallized microstructure. The proposed method was applied in characterizing the microstructure evolution during annealing of interstitial-free steel cold rolled to low and high true strain levels of 0.7 and 1.6, respectively. The recrystallization kinetics determined by the proposed method was found to be consistent with the standard method of Vickers microhardness. The application of the proposed method to the overall recrystallization stages showed that it can be used for the rigorous characterization of progressive microstructure evolution, especially for the severely deformed material. © 2013 The Authors Journal of Microscopy © 2013 Royal Microscopical Society.
Do we need methodological theory to do qualitative research?

PubMed

Avis, Mark

2003-09-01

Positivism is frequently used to stand for the epistemological assumption that empirical science based on principles of verificationism, objectivity, and reproducibility is the foundation of all genuine knowledge. Qualitative researchers sometimes feel obliged to provide methodological alternatives to positivism that recognize their different ethical, ontological, and epistemological commitments and have provided three theories: phenomenology, grounded theory, and ethnography. The author argues that positivism was a doomed attempt to define empirical foundations for knowledge through a rigorous separation of theory and evidence; offers a pragmatic, coherent view of knowledge; and suggests that rigorous, rational empirical investigation does not need methodological theory. Therefore, qualitative methodological theory is unnecessary and counterproductive because it hinders critical reflection on the relation between methodological theory and empirical evidence.
Advanced EUV mask and imaging modeling

NASA Astrophysics Data System (ADS)

Evanschitzky, Peter; Erdmann, Andreas

2017-10-01

The exploration and optimization of image formation in partially coherent EUV projection systems with complex source shapes requires flexible, accurate, and efficient simulation models. This paper reviews advanced mask diffraction and imaging models for the highly accurate and fast simulation of EUV lithography systems, addressing important aspects of the current technical developments. The simulation of light diffraction from the mask employs an extended rigorous coupled wave analysis (RCWA) approach, which is optimized for EUV applications. In order to be able to deal with current EUV simulation requirements, several additional models are included in the extended RCWA approach: a field decomposition and a field stitching technique enable the simulation of larger complex structured mask areas. An EUV multilayer defect model including a database approach makes the fast and fully rigorous defect simulation and defect repair simulation possible. A hybrid mask simulation approach combining real and ideal mask parts allows the detailed investigation of the origin of different mask 3-D effects. The image computation is done with a fully vectorial Abbe-based approach. Arbitrary illumination and polarization schemes and adapted rigorous mask simulations guarantee a high accuracy. A fully vectorial sampling-free description of the pupil with Zernikes and Jones pupils and an optimized representation of the diffraction spectrum enable the computation of high-resolution images with high accuracy and short simulation times. A new pellicle model supports the simulation of arbitrary membrane stacks, pellicle distortions, and particles/defects on top of the pellicle. Finally, an extension for highly accurate anamorphic imaging simulations is included. The application of the models is demonstrated by typical use cases.
Tactics for mechanized reasoning: a commentary on Milner (1984) ‘The use of machines to assist in rigorous proof’

PubMed Central

Gordon, M. J. C.

2015-01-01

Robin Milner's paper, ‘The use of machines to assist in rigorous proof’, introduces methods for automating mathematical reasoning that are a milestone in the development of computer-assisted theorem proving. His ideas, particularly his theory of tactics, revolutionized the architecture of proof assistants. His methodology for automating rigorous proof soundly, particularly his theory of type polymorphism in programing, led to major contributions to the theory and design of programing languages. His citation for the 1991 ACM A.M. Turing award, the most prestigious award in computer science, credits him with, among other achievements, ‘probably the first theoretically based yet practical tool for machine assisted proof construction’. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society. PMID:25750147
Focusing Leaky Waves: A Class of Electromagnetic Localized Waves with Complex Spectra

NASA Astrophysics Data System (ADS)

Fuscaldo, Walter; Comite, Davide; Boesso, Alessandro; Baccarelli, Paolo; Burghignoli, Paolo; Galli, Alessandro

2018-05-01

Localized waves, i.e., the wide class of limited-diffraction, limited-dispersion solutions to the wave equation are generally characterized by real wave numbers. We consider the role played by localized waves with generally complex "leaky" wave numbers. First, the impact of the imaginary part of the wave number (i.e., the leakage constant) on the diffractive (spatial broadening) features of monochromatic localized solutions (i.e., beams) is rigorously evaluated. Then general conditions are derived to show that only a restricted class of spectra (either real or complex) allows for generating a causal localized wave. It turns out that backward leaky waves fall into this category. On this ground, several criteria for the systematic design of wideband radiators, namely, periodic radial waveguides based on backward leaky waves, are established in the framework of leaky-wave theory. An effective design method is proposed to minimize the frequency dispersion of the proposed class of devices and the impact of the "leakage" on the dispersive (temporal broadening) features of polychromatic localized solutions (i.e., pulses) is accounted for. Numerical results corroborate the concept, clearly highlighting the advantages and limitations of the leaky-wave approach for the generation of localized pulses at millimeter-wave frequencies, where energy focusing is in high demand in modern applications.
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
Fresnel diffraction by spherical obstacles

NASA Technical Reports Server (NTRS)

Hovenac, Edward A.

1989-01-01

Lommel functions were used to solve the Fresnel-Kirchhoff diffraction integral for the case of a spherical obstacle. Comparisons were made between Fresnel diffraction theory and Mie scattering theory. Fresnel theory is then compared to experimental data. Experiment and theory typically deviated from one another by less than 10 percent. A unique experimental setup using mercury spheres suspended in a viscous fluid significantly reduced optical noise. The major source of error was due to the Gaussian-shaped laser beam.
Memory sparing, fast scattering formalism for rigorous diffraction modeling

NASA Astrophysics Data System (ADS)

Iff, W.; Kämpfe, T.; Jourlin, Y.; Tishchenko, A. V.

2017-07-01

The basics and algorithmic steps of a novel scattering formalism suited for memory sparing and fast electromagnetic calculations are presented. The formalism, called ‘S-vector algorithm’ (by analogy with the known scattering-matrix algorithm), allows the calculation of the collective scattering spectra of individual layered micro-structured scattering objects. A rigorous method of linear complexity is applied to model the scattering at individual layers; here the generalized source method (GSM) resorting to Fourier harmonics as basis functions is used as one possible method of linear complexity. The concatenation of the individual scattering events can be achieved sequentially or in parallel, both having pros and cons. The present development will largely concentrate on a consecutive approach based on the multiple reflection series. The latter will be reformulated into an implicit formalism which will be associated with an iterative solver, resulting in improved convergence. The examples will first refer to 1D grating diffraction for the sake of simplicity and intelligibility, with a final 2D application example.
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.
A re-examination of the biphasic theory of skeletal muscle growth.

PubMed Central

Levine, A S; Hegarty, P V

1977-01-01

Because of the importance of fibre diameter measurements it was decided to re-evaluate the biphasic theory of skeletal muscle growth and development. This theory proposes an initial memophasic distribution of muscle fibres which changes to a biphasic distribution during development. The theory is based on observations made on certain muscles in mice, where two distinct populations of fibre diameters (20 and 40 micronm) contribute to the biphasic distribution. In the present investigation corss sections of frozen biceps brachii of mice in rigor mortis were examined. The rigor state was used to avoid complications produced by thaw-rigor contraction. The diameters of the outermost and innermost fibres were found to be significantly different. However, if the outer and inner fibres were combined to form one group, no significant difference between this group and other random groups was found. The distributions of all groups were monophasic. The diameters of isolated fibres from mice and rats also displayed a monophasic distribution. This evidence leads to the conclusion that the biphasic theory of muscle growth is untenable. Some of the variables which may occur in fibre size and shape are discussed. Images Fig. 1 PMID:858691
A Developmental Test of Mertonian Anomie Theory.

ERIC Educational Resources Information Center

Menard, Scott

1995-01-01

Carefully reviewed Merton's writings on anomie theory to construct a more complete and rigorous test of the theory for respondents in early, middle, and late adolescence. Concluded that misspecified models of strain theory have underestimated the predictive power of strain theory in general and of anomie theory in particular. (JBJ)
Quantization of noncompact coverings and its physical applications

NASA Astrophysics Data System (ADS)

Ivankov, Petr

2018-02-01

A rigorous algebraic definition of noncommutative coverings is developed. In the case of commutative algebras this definition is equivalent to the classical definition of topological coverings of locally compact spaces. The theory has following nontrivial applications: • Coverings of continuous trace algebras, • Coverings of noncommutative tori, • Coverings of the quantum SU(2) group, • Coverings of foliations, • Coverings of isospectral deformations of Spin - manifolds. The theory supplies the rigorous definition of noncommutative Wilson lines.
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.
Diffraction efficiency calculations of polarization diffraction gratings with surface relief

NASA Astrophysics Data System (ADS)

Nazarova, D.; Sharlandjiev, P.; Berberova, N.; Blagoeva, B.; Stoykova, E.; Nedelchev, L.

2018-03-01

In this paper, we evaluate the optical response of a stack of two diffraction gratings of equal one-dimensional periodicity. The first one is a surface-relief grating structure; the second, a volume polarization grating. This model is based on our experimental results from polarization holographic recordings in azopolymer films. We used films of commercially available azopolymer (poly[1-[4-(3-carboxy-4-hydroxyphenylazo) benzenesulfonamido]-1,2-ethanediyl, sodium salt]), shortly denoted as PAZO. During the recording process, a polarization grating in the volume of the material and a relief grating on the film surface are formed simultaneously. In order to evaluate numerically the optical response of this “hybrid” diffraction structure, we used the rigorous coupled-wave approach (RCWA). It yields stable numerical solutions of Maxwell’s vector equations using the algebraic eigenvalue method.
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
Carrying capacity in a heterogeneous environment with habitat connectivity.

PubMed

Zhang, Bo; Kula, Alex; Mack, Keenan M L; Zhai, Lu; Ryce, Arrix L; Ni, Wei-Ming; DeAngelis, Donald L; Van Dyken, J David

2017-09-01

A large body of theory predicts that populations diffusing in heterogeneous environments reach higher total size than if non-diffusing, and, paradoxically, higher size than in a corresponding homogeneous environment. However, this theory and its assumptions have not been rigorously tested. Here, we extended previous theory to include exploitable resources, proving qualitatively novel results, which we tested experimentally using spatially diffusing laboratory populations of yeast. Consistent with previous theory, we predicted and experimentally observed that spatial diffusion increased total equilibrium population abundance in heterogeneous environments, with the effect size depending on the relationship between r and K. Refuting previous theory, however, we discovered that homogeneously distributed resources support higher total carrying capacity than heterogeneously distributed resources, even with species diffusion. Our results provide rigorous experimental tests of new and old theory, demonstrating how the traditional notion of carrying capacity is ambiguous for populations diffusing in spatially heterogeneous environments. © 2017 John Wiley & Sons Ltd/CNRS.
Carrying capacity in a heterogeneous environment with habitat connectivity

USGS Publications Warehouse

Zhang, Bo; Kula, Alex; Mack, Keenan M.L.; Zhai, Lu; Ryce, Arrix L.; Ni, Wei-Ming; DeAngelis, Donald L.; Van Dyken, J. David

2017-01-01

A large body of theory predicts that populations diffusing in heterogeneous environments reach higher total size than if non-diffusing, and, paradoxically, higher size than in a corresponding homogeneous environment. However, this theory and its assumptions have not been rigorously tested. Here, we extended previous theory to include exploitable resources, proving qualitatively novel results, which we tested experimentally using spatially diffusing laboratory populations of yeast. Consistent with previous theory, we predicted and experimentally observed that spatial diffusion increased total equilibrium population abundance in heterogeneous environments, with the effect size depending on the relationship between r and K. Refuting previous theory, however, we discovered that homogeneously distributed resources support higher total carrying capacity than heterogeneously distributed resources, even with species diffusion. Our results provide rigorous experimental tests of new and old theory, demonstrating how the traditional notion of carrying capacity is ambiguous for populations diffusing in spatially heterogeneous environments.

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
Investigation of possible observable e ects in a proposed theory of physics

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

Freidan, Daniel

2015-03-31

The work supported by this grant produced rigorous mathematical results on what is possible in quantum field theory. Quantum field theory is the well-established mathematical language for fundamental particle physics, for critical phenomena in condensed matter physics, and for Physical Mathematics (the numerous branches of Mathematics that have benefitted from ideas, constructions, and conjectures imported from Theoretical Physics). Proving rigorous constraints on what is possible in quantum field theories thus guides the field, puts actual constraints on what is physically possible in physical or mathematical systems described by quantum field theories, and saves the community the effort of trying tomore » do what is proved impossible. Results were obtained in two dimensional qft (describing, e.g., quantum circuits) and in higher dimensional qft. Rigorous bounds were derived on basic quantities in 2d conformal field theories, i.e., in 2d critical phenomena. Conformal field theories are the basic objects in quantum field theory, the scale invariant theories describing renormalization group fixed points from which all qfts flow. The first known lower bounds on the 2d boundary entropy were found. This is the entropy- information content- in junctions in critical quantum circuits. For dimensions d > 2, a no-go theorem was proved on the possibilities of Cauchy fields, which are the analogs of the holomorphic fields in d = 2 dimensions, which have had enormously useful applications in Physics and Mathematics over the last four decades. This closed o the possibility of finding analogously rich theories in dimensions above 2. The work of two postdoctoral research fellows was partially supported by this grant. Both have gone on to tenure track positions.« less
Fiber facet gratings for high power fiber lasers

NASA Astrophysics Data System (ADS)

Vanek, Martin; Vanis, Jan; Baravets, Yauhen; Todorov, Filip; Ctyroky, Jiri; Honzatko, Pavel

2017-12-01

We numerically investigated the properties of diffraction gratings designated for fabrication on the facet of an optical fiber. The gratings are intended to be used in high-power fiber lasers as mirrors either with a low or high reflectivity. The modal reflectance of low reflectivity polarizing grating has a value close to 3% for TE mode while it is significantly suppressed for TM mode. Such a grating can be fabricated on laser output fiber facet. The polarizing grating with high modal reflectance is designed as a leaky-mode resonant diffraction grating. The grating can be etched in a thin layer of high index dielectric which is sputtered on fiber facet. We used refractive index of Ta2O5 for such a layer. We found that modal reflectance can be close to 0.95 for TE polarization and polarization extinction ratio achieves 18 dB. Rigorous coupled wave analysis was used for fast optimization of grating parameters while aperiodic rigorous coupled wave analysis, Fourier modal method and finite difference time domain method were compared and used to compute modal reflectance of designed gratings.
A modal analysis of lamellar diffraction gratings in conical mountings

NASA Technical Reports Server (NTRS)

Li, Lifeng

1992-01-01

A rigorous modal analysis of lamellar grating, i.e., gratings having rectangular grooves, in conical mountings is presented. It is an extension of the analysis of Botten et al. which considered non-conical mountings. A key step in the extension is a decomposition of the electromagnetic field in the grating region into two orthogonal components. A computer program implementing this extended modal analysis is capable of dealing with plane wave diffraction by dielectric and metallic gratings with deep grooves, at arbitrary angles of incidence, and having arbitrary incident polarizations. Some numerical examples are included.
The role of a posteriori mathematics in physics

NASA Astrophysics Data System (ADS)

MacKinnon, Edward

2018-05-01

The calculus that co-evolved with classical mechanics relied on definitions of functions and differentials that accommodated physical intuitions. In the early nineteenth century mathematicians began the rigorous reformulation of calculus and eventually succeeded in putting almost all of mathematics on a set-theoretic foundation. Physicists traditionally ignore this rigorous mathematics. Physicists often rely on a posteriori math, a practice of using physical considerations to determine mathematical formulations. This is illustrated by examples from classical and quantum physics. A justification of such practice stems from a consideration of the role of phenomenological theories in classical physics and effective theories in contemporary physics. This relates to the larger question of how physical theories should be interpreted.
Grading Rigor in Counselor Education: A Specifications Grading Framework

ERIC Educational Resources Information Center

Bonner, Matthew W.

2016-01-01

According to accreditation and professional bodies, evaluation and grading are a high priority in counselor education. Specifications grading, an evaluative tool, can be used to increase grading rigor. This article describes the components of specifications grading and applies the framework of specifications grading to a counseling theories course.
75 FR 5291 - Office of Special Education and Rehabilitative Services; Overview Information; Technology and...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-02-02

... two phases: (1) Development and (2) research on effectiveness. Abstracts of projects funded under... approaches. Phase 2 projects must subject technology-based approaches to rigorous field-based research to... disabilities; (2) Present a justification, based on scientifically rigorous research or theory, that supports...
76 FR 12343 - Technology and Media Services for Individuals With Disabilities-Steppingstones of Technology...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-03-07

... two phases: (1) Development and (2) research on effectiveness. Abstracts of projects funded under... approaches. Phase 2 projects must subject technology-based approaches to rigorous field-based research to... scientifically rigorous research or theory, that demonstrates the potential effectiveness of the technology-based...
Systemic Planning: An Annotated Bibliography and Literature Guide. Exchange Bibliography No. 91.

ERIC Educational Resources Information Center

Catanese, Anthony James

Systemic planning is an operational approach to using scientific rigor and qualitative judgment in a complementary manner. It integrates rigorous techniques and methods from systems analysis, cybernetics, decision theory, and work programing. The annotated reference sources in this bibliography include those works that have been most influential…
A Theory of Material Spike Formation in Flow Separation

NASA Astrophysics Data System (ADS)

Serra, Mattia; Haller, George

2017-11-01

We develop a frame-invariant theory of material spike formation during flow separation over a no-slip boundary in two-dimensional flows with arbitrary time dependence. This theory identifies both fixed and moving separation, is effective also over short-time intervals, and admits a rigorous instantaneous limit. Our theory is based on topological properties of material lines, combining objectively stretching- and rotation-based kinematic quantities. The separation profile identified here serves as the theoretical backbone for the material spike from its birth to its fully developed shape, and remains hidden to existing approaches. Finally, our theory can be used to rigorously explain the perception of off-wall separation in unsteady flows, and more importantly, provide the conditions under which such a perception is justified. We illustrate our results in several examples including steady, time-periodic and unsteady analytic velocity fields with flat and curved boundaries, and an experimental dataset.
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.
Evaluation of Two Computational Techniques of Calculating Multipath Using Global Positioning System Carrier Phase Measurements

NASA Technical Reports Server (NTRS)

Gomez, Susan F.; Hood, Laura; Panneton, Robert J.; Saunders, Penny E.; Adkins, Antha; Hwu, Shian U.; Lu, Ba P.

1996-01-01

Two computational techniques are used to calculate differential phase errors on Global Positioning System (GPS) carrier war phase measurements due to certain multipath-producing objects. The two computational techniques are a rigorous computati electromagnetics technique called Geometric Theory of Diffraction (GTD) and the other is a simple ray tracing method. The GTD technique has been used successfully to predict microwave propagation characteristics by taking into account the dominant multipath components due to reflections and diffractions from scattering structures. The ray tracing technique only solves for reflected signals. The results from the two techniques are compared to GPS differential carrier phase ns taken on the ground using a GPS receiver in the presence of typical International Space Station (ISS) interference structures. The calculations produced using the GTD code compared to the measured results better than the ray tracing technique. The agreement was good, demonstrating that the phase errors due to multipath can be modeled and characterized using the GTD technique and characterized to a lesser fidelity using the DECAT technique. However, some discrepancies were observed. Most of the discrepancies occurred at lower devations and were either due to phase center deviations of the antenna, the background multipath environment, or the receiver itself. Selected measured and predicted differential carrier phase error results are presented and compared. Results indicate that reflections and diffractions caused by the multipath producers, located near the GPS antennas, can produce phase shifts of greater than 10 mm, and as high as 95 mm. It should be noted tl the field test configuration was meant to simulate typical ISS structures, but the two environments are not identical. The GZ and DECAT techniques have been used to calculate phase errors due to multipath o the ISS configuration to quantify the expected attitude determination errors.
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.
Full-potential multiple scattering theory with space-filling cells for bound and continuum states.

PubMed

Hatada, Keisuke; Hayakawa, Kuniko; Benfatto, Maurizio; Natoli, Calogero R

2010-05-12

We present a rigorous derivation of a real-space full-potential multiple scattering theory (FP-MST) that is free from the drawbacks that up to now have impaired its development (in particular the need to expand cell shape functions in spherical harmonics and rectangular matrices), valid both for continuum and bound states, under conditions for space partitioning that are not excessively restrictive and easily implemented. In this connection we give a new scheme to generate local basis functions for the truncated potential cells that is simple, fast, efficient, valid for any shape of the cell and reduces to the minimum the number of spherical harmonics in the expansion of the scattering wavefunction. The method also avoids the need for saturating 'internal sums' due to the re-expansion of the spherical Hankel functions around another point in space (usually another cell center). Thus this approach provides a straightforward extension of MST in the muffin-tin (MT) approximation, with only one truncation parameter given by the classical relation l(max) = kR(b), where k is the electron wavevector (either in the excited or ground state of the system under consideration) and R(b) is the radius of the bounding sphere of the scattering cell. Moreover, the scattering path operator of the theory can be found in terms of an absolutely convergent procedure in the l(max) --> ∞ limit. Consequently, this feature provides a firm ground for the use of FP-MST as a viable method for electronic structure calculations and makes possible the computation of x-ray spectroscopies, notably photo-electron diffraction, absorption and anomalous scattering among others, with the ease and versatility of the corresponding MT theory. Some numerical applications of the theory are presented, both for continuum and bound states.
Reconstructing Constructivism: Causal Models, Bayesian Learning Mechanisms, and the Theory Theory

ERIC Educational Resources Information Center

Gopnik, Alison; Wellman, Henry M.

2012-01-01

We propose a new version of the "theory theory" grounded in the computational framework of probabilistic causal models and Bayesian learning. Probabilistic models allow a constructivist but rigorous and detailed approach to cognitive development. They also explain the learning of both more specific causal hypotheses and more abstract framework…
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.
Applying Sociocultural Theory to Teaching Statistics for Doctoral Social Work Students

ERIC Educational Resources Information Center

Mogro-Wilson, Cristina; Reeves, Michael G.; Charter, Mollie Lazar

2015-01-01

This article describes the development of two doctoral-level multivariate statistics courses utilizing sociocultural theory, an integrative pedagogical framework. In the first course, the implementation of sociocultural theory helps to support the students through a rigorous introduction to statistics. The second course involves students…
A New Theory-to-Practice Model for Student Affairs: Integrating Scholarship, Context, and Reflection

ERIC Educational Resources Information Center

Reason, Robert D.; Kimball, Ezekiel W.

2012-01-01

In this article, we synthesize existing theory-to-practice approaches within the student affairs literature to arrive at a new model that incorporates formal and informal theory, institutional context, and reflective practice. The new model arrives at a balance between the rigor necessary for scholarly theory development and the adaptability…
Design and fabrication of continuous-profile diffractive micro-optical elements as a beam splitter.

PubMed

Feng, Di; Yan, Yingbai; Jin, Guofan; Fan, Shoushan

2004-10-10

An optimization algorithm that combines a rigorous electromagnetic computation model with an effective iterative method is utilized to design diffractive micro-optical elements that exhibit fast convergence and better design quality. The design example is a two-dimensional 1-to-2 beam splitter that can symmetrically generate two focal lines separated by 80 microm at the observation plane with a small angle separation of +/- 16 degrees. Experimental results are presented for an element with continuous profiles fabricated into a monocrystalline silicon substrate that has a width of 160 microm and a focal length of 140 microm at a free-space wavelength of 10.6 microm.
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.

A Generalizability Investigation of Cognitive Demand and Rigor Ratings of Items and Standards in an Alignment Study

ERIC Educational Resources Information Center

Lombardi, Allison; Seburn, Mary; Conley, David; Snow, Eric

2010-01-01

In alignment studies, expert raters evaluate assessment items against standards and ratings are used to compute various alignment indices. Questions about rater reliability, however, are often ignored or inadequately addressed. This paper reports the results of a generalizability theory study of cognitive demand and rigor ratings of assessment…
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.
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.
Rigorous electromagnetic simulation applied to alignment systems

NASA Astrophysics Data System (ADS)

Deng, Yunfei; Pistor, Thomas V.; Neureuther, Andrew R.

2001-09-01

Rigorous electromagnetic simulation with TEMPEST is used to provide benchmark data and understanding of key parameters in the design of topographical features of alignment marks. Periodic large silicon trenches are analyzed as a function of wavelength (530-800 nm), duty cycle, depth, slope and angle of incidence. The signals are well behaved except when the trench width becomes about 1 micrometers or smaller. Segmentation of the trenches to form 3D marks shows that a segmentation period of 2-5 wavelengths makes the diffraction in the (1,1) direction about 1/3 to 1/2 of that in the main first order (1,0). Transmission alignment marks nanoimprint lithography using the difference between the +1 and -1 reflected orders showed a sensitivity of the difference signal to misalignment of 0.7%/nm for rigorous simulation and 0.5%/nm for simple ray-tracing. The sensitivity to a slanted substrate indentation was 10 nm off-set per degree of tilt from horizontal.
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.
Topics in Computational Learning Theory and Graph Algorithms.

ERIC Educational Resources Information Center

Board, Raymond Acton

This thesis addresses problems from two areas of theoretical computer science. The first area is that of computational learning theory, which is the study of the phenomenon of concept learning using formal mathematical models. The goal of computational learning theory is to investigate learning in a rigorous manner through the use of techniques…
NORMATIVE ACCOUNTING THEORY AND THE THEORY OF DECISION,

DTIC Science & Technology

The paper discusses an approach to the construction of normative accounting theory with respect to both methodology and substance. The method of...postulation and deduction is outlined, with particular emphasis on its role in the social sciences in general and in accounting in particular. It is...suggested that a formal link must be established between the (normative) theory of decision and accounting , and that rigorous (economic) theories of the
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)
Propagation dynamics of off-axis symmetrical and asymmetrical vortices embedded in flat-topped beams

NASA Astrophysics Data System (ADS)

Zhang, Xu; Wang, Haiyan

2017-11-01

In this paper, propagation dynamics of off-axis symmetrical and asymmetrical optical vortices(OVs) embedded in flat-topped beams have been explored numerically based on rigorous scalar diffraction theory. The distribution properties of phase and intensity play an important role in driving the propagation dynamics of OVs. Numerical results show that the single off-axis vortex moves in a straight line. The displacement of the single off-axis vortex becomes smaller, when either the order of flatness N and the beam size ω0are increased or the off-axis displacement d is decreased. In addition, the phase singularities of high order vortex beams can be split after propagating a certain distance. It is also demonstrated that the movement of OVs are closely related with the spatial symmetrical or asymmetrical distribution of vortex singularities field. Multiple symmetrical and asymmetrical optical vortices(OVs) embedded in flat-topped beams can interact and rotate. The investment of the propagation dynamics of OVs may have many applications in optical micro-manipulation and optical tweezers.
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)
Machine learning in the string landscape

NASA Astrophysics Data System (ADS)

Carifio, Jonathan; Halverson, James; Krioukov, Dmitri; Nelson, Brent D.

2017-09-01

We utilize machine learning to study the string landscape. Deep data dives and conjecture generation are proposed as useful frameworks for utilizing machine learning in the landscape, and examples of each are presented. A decision tree accurately predicts the number of weak Fano toric threefolds arising from reflexive polytopes, each of which determines a smooth F-theory compactification, and linear regression generates a previously proven conjecture for the gauge group rank in an ensemble of 4/3× 2.96× {10}^{755} F-theory compactifications. Logistic regression generates a new conjecture for when E 6 arises in the large ensemble of F-theory compactifications, which is then rigorously proven. This result may be relevant for the appearance of visible sectors in the ensemble. Through conjecture generation, machine learning is useful not only for numerics, but also for rigorous results.
Quantifying falsifiability of scientific theories

NASA Astrophysics Data System (ADS)

Nemenman, Ilya

I argue that the notion of falsifiability, a key concept in defining a valid scientific theory, can be quantified using Bayesian Model Selection, which is a standard tool in modern statistics. This relates falsifiability to the quantitative version of the statistical Occam's razor, and allows transforming some long-running arguments about validity of scientific theories from philosophical discussions to rigorous mathematical calculations.
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.
A systematic review of the use of theory in the design of guideline dissemination and implementation strategies and interpretation of the results of rigorous evaluations.

PubMed

Davies, Philippa; Walker, Anne E; Grimshaw, Jeremy M

2010-02-09

There is growing interest in the use of cognitive, behavioural, and organisational theories in implementation research. However, the extent of use of theory in implementation research is uncertain. We conducted a systematic review of use of theory in 235 rigorous evaluations of guideline dissemination and implementation studies published between 1966 and 1998. Use of theory was classified according to type of use (explicitly theory based, some conceptual basis, and theoretical construct used) and stage of use (choice/design of intervention, process/mediators/moderators, and post hoc/explanation). Fifty-three of 235 studies (22.5%) were judged to have employed theories, including 14 studies that explicitly used theory. The majority of studies (n = 42) used only one theory; the maximum number of theories employed by any study was three. Twenty-five different theories were used. A small number of theories accounted for the majority of theory use including PRECEDE (Predisposing, Reinforcing, and Enabling Constructs in Educational Diagnosis and Evaluation), diffusion of innovations, information overload and social marketing (academic detailing). There was poor justification of choice of intervention and use of theory in implementation research in the identified studies until at least 1998. Future research should explicitly identify the justification for the interventions. Greater use of explicit theory to understand barriers, design interventions, and explore mediating pathways and moderators is needed to advance the science of implementation research.
Dark-field imaging based on post-processed electron backscatter diffraction patterns of bulk crystalline materials in a scanning electron microscope.

PubMed

Brodusch, Nicolas; Demers, Hendrix; Gauvin, Raynald

2015-01-01

Dark-field (DF) images were acquired in the scanning electron microscope with an offline procedure based on electron backscatter diffraction (EBSD) patterns (EBSPs). These EBSD-DF images were generated by selecting a particular reflection on the electron backscatter diffraction pattern and by reporting the intensity of one or several pixels around this point at each pixel of the EBSD-DF image. Unlike previous studies, the diffraction information of the sample is the basis of the final image contrast with a pixel scale resolution at the EBSP providing DF imaging in the scanning electron microscope. The offline facility of this technique permits the selection of any diffraction condition available in the diffraction pattern and displaying the corresponding image. The high number of diffraction-based images available allows a better monitoring of deformation structures compared to electron channeling contrast imaging (ECCI) which is generally limited to a few images of the same area. This technique was applied to steel and iron specimens and showed its high capability in describing more rigorously the deformation structures around micro-hardness indents. Due to the offline relation between the reference EBSP and the EBSD-DF images, this new technique will undoubtedly greatly improve our knowledge of deformation mechanism and help to improve our understanding of the ECCI contrast mechanisms. Copyright © 2014 Elsevier B.V. All rights reserved.
The impact of rigorous mathematical thinking as learning method toward geometry understanding

NASA Astrophysics Data System (ADS)

Nugraheni, Z.; Budiyono, B.; Slamet, I.

2018-05-01

To reach higher order thinking skill, needed to be mastered the conceptual understanding. RMT is a unique realization of the cognitive conceptual construction approach based on Mediated Learning Experience (MLE) theory by Feurstein and Vygotsky’s sociocultural theory. This was quasi experimental research which was comparing the experimental class that was given Rigorous Mathematical Thinking (RMT) as learning method and control class that was given Direct Learning (DL) as the conventional learning activity. This study examined whether there was different effect of two learning method toward conceptual understanding of Junior High School students. The data was analyzed by using Independent t-test and obtained a significant difference of mean value between experimental and control class on geometry conceptual understanding. Further, by semi-structure interview known that students taught by RMT had deeper conceptual understanding than students who were taught by conventional way. By these result known that Rigorous Mathematical Thinking (RMT) as learning method have positive impact toward Geometry conceptual understanding.
Newton's second law and the multiplication of distributions

NASA Astrophysics Data System (ADS)

Sarrico, C. O. R.; Paiva, A.

2018-01-01

Newton's second law is applied to study the motion of a particle subjected to a time dependent impulsive force containing a Dirac delta distribution. Within this setting, we prove that this problem can be rigorously solved neither by limit processes nor by using the theory of distributions (limited to the classical Schwartz products). However, using a distributional multiplication, not defined by a limit process, a rigorous solution emerges.
Tension Recovery following Ramp-Shaped Release in High-Ca and Low-Ca Rigor Muscle Fibers: Evidence for the Dynamic State of AMADP Myosin Heads in the Absence of ATP

PubMed Central

Sugi, Haruo; Yamaguchi, Maki; Ohno, Tetsuo; Kobayashi, Takakazu; Chaen, Shigeru; Okuyama, Hiroshi

2016-01-01

During muscle contraction, myosin heads (M) bound to actin (A) perform power stroke associated with reaction, AMADPPi → AM + ADP + Pi. In this scheme, A • M is believed to be a high-affinity complex after removal of ATP. Biochemical studies on extracted protein samples show that, in the AM complex, actin-binding sites are located at both sides of junctional peptide between 50K and 20K segments of myosin heavy chain. Recently, we found that a monoclonal antibody (IgG) to the junctional peptide had no effect on both in vitro actin-myosin sliding and skinned muscle fiber contraction, though it covers the actin-binding sites on myosin. It follows from this that, during muscle contraction, myosin heads do not pass through the static rigor AM configuration, determined biochemically and electron microscopically using extracted protein samples. To study the nature of AM and AMADP myosin heads, actually existing in muscle, we examined mechanical responses to ramp-shaped releases (0.5% of Lo, complete in 5ms) in single skinned rabbit psoas muscle fibers in high-Ca (pCa, 4) and low-Ca (pCa, >9) rigor states. The fibers exhibited initial elastic tension drop and subsequent small but definite tension recovery to a steady level. The tension recovery was present over many minutes in high-Ca rigor fibers, while it tended to decrease quickly in low-Ca rigor fibers. EDTA (10mM, with MgCl2 removed) had no appreciable effect on the tension recovery in high-Ca rigor fibers, while it completely eliminated the tension recovery in low-Ca rigor fibers. These results suggest that the AMADP myosin heads in rigor muscle have long lifetimes and dynamic properties, which show up as the tension recovery following applied release. Possible AM linkage structure in muscle is discussed in connection with the X-ray diffraction pattern from contracting muscle, which is intermediate between resting and rigor muscles. PMID:27583360
Tension Recovery following Ramp-Shaped Release in High-Ca and Low-Ca Rigor Muscle Fibers: Evidence for the Dynamic State of AMADP Myosin Heads in the Absence of ATP.

PubMed

Sugi, Haruo; Yamaguchi, Maki; Ohno, Tetsuo; Kobayashi, Takakazu; Chaen, Shigeru; Okuyama, Hiroshi

2016-01-01

During muscle contraction, myosin heads (M) bound to actin (A) perform power stroke associated with reaction, AMADPPi → AM + ADP + Pi. In this scheme, A • M is believed to be a high-affinity complex after removal of ATP. Biochemical studies on extracted protein samples show that, in the AM complex, actin-binding sites are located at both sides of junctional peptide between 50K and 20K segments of myosin heavy chain. Recently, we found that a monoclonal antibody (IgG) to the junctional peptide had no effect on both in vitro actin-myosin sliding and skinned muscle fiber contraction, though it covers the actin-binding sites on myosin. It follows from this that, during muscle contraction, myosin heads do not pass through the static rigor AM configuration, determined biochemically and electron microscopically using extracted protein samples. To study the nature of AM and AMADP myosin heads, actually existing in muscle, we examined mechanical responses to ramp-shaped releases (0.5% of Lo, complete in 5ms) in single skinned rabbit psoas muscle fibers in high-Ca (pCa, 4) and low-Ca (pCa, >9) rigor states. The fibers exhibited initial elastic tension drop and subsequent small but definite tension recovery to a steady level. The tension recovery was present over many minutes in high-Ca rigor fibers, while it tended to decrease quickly in low-Ca rigor fibers. EDTA (10mM, with MgCl2 removed) had no appreciable effect on the tension recovery in high-Ca rigor fibers, while it completely eliminated the tension recovery in low-Ca rigor fibers. These results suggest that the AMADP myosin heads in rigor muscle have long lifetimes and dynamic properties, which show up as the tension recovery following applied release. Possible AM linkage structure in muscle is discussed in connection with the X-ray diffraction pattern from contracting muscle, which is intermediate between resting and rigor muscles.

Optimal design and evaluation of a color separation grating using rigorous coupled wave analysis

NASA Astrophysics Data System (ADS)

Nagayoshi, Mayumi; Oka, Keiko; Klaus, Werner; Komai, Yuki; Kodate, Kashiko

2006-02-01

In recent years, the technology which separates white light into the three primary colors of Red (R), Green (G) and Blue (B) and adjusts each optical intensity and composites R, G and B to display various colors is required in the development and spread of color visual equipments. Various color separation devices have been proposed and have been put to practical use in color visual equipments. We have focused on a small and light grating-type device which has the possibility of reduction in cost and large-scale production and generates only the three primary colors of R, G and B so that a high saturation level can be obtained. To perform a rigorous analysis and design of color separation gratings, our group has developed a program that is based on the Rigorous Coupled Wave Analysis (RCWA). We then calculated the parameters to obtain a diffraction efficiency of higher than 70% and the color gamut of about 70%. We will report on the design, fabrication and evaluation of color separation gratings that have been optimized for fabrication by laser drawing.
Increased scientific rigor will improve reliability of research and effectiveness of management

USGS Publications Warehouse

Sells, Sarah N.; Bassing, Sarah B.; Barker, Kristin J.; Forshee, Shannon C.; Keever, Allison; Goerz, James W.; Mitchell, Michael S.

2018-01-01

Rigorous science that produces reliable knowledge is critical to wildlife management because it increases accurate understanding of the natural world and informs management decisions effectively. Application of a rigorous scientific method based on hypothesis testing minimizes unreliable knowledge produced by research. To evaluate the prevalence of scientific rigor in wildlife research, we examined 24 issues of the Journal of Wildlife Management from August 2013 through July 2016. We found 43.9% of studies did not state or imply a priori hypotheses, which are necessary to produce reliable knowledge. We posit that this is due, at least in part, to a lack of common understanding of what rigorous science entails, how it produces more reliable knowledge than other forms of interpreting observations, and how research should be designed to maximize inferential strength and usefulness of application. Current primary literature does not provide succinct explanations of the logic behind a rigorous scientific method or readily applicable guidance for employing it, particularly in wildlife biology; we therefore synthesized an overview of the history, philosophy, and logic that define scientific rigor for biological studies. A rigorous scientific method includes 1) generating a research question from theory and prior observations, 2) developing hypotheses (i.e., plausible biological answers to the question), 3) formulating predictions (i.e., facts that must be true if the hypothesis is true), 4) designing and implementing research to collect data potentially consistent with predictions, 5) evaluating whether predictions are consistent with collected data, and 6) drawing inferences based on the evaluation. Explicitly testing a priori hypotheses reduces overall uncertainty by reducing the number of plausible biological explanations to only those that are logically well supported. Such research also draws inferences that are robust to idiosyncratic observations and unavoidable human biases. Offering only post hoc interpretations of statistical patterns (i.e., a posteriorihypotheses) adds to uncertainty because it increases the number of plausible biological explanations without determining which have the greatest support. Further, post hocinterpretations are strongly subject to human biases. Testing hypotheses maximizes the credibility of research findings, makes the strongest contributions to theory and management, and improves reproducibility of research. Management decisions based on rigorous research are most likely to result in effective conservation of wildlife resources.
Understanding information exchange during disaster response: Methodological insights from infocentric analysis

Treesearch

Toddi A. Steelman; Branda Nowell; Deena Bayoumi; Sarah McCaffrey

2014-01-01

We leverage economic theory, network theory, and social network analytical techniques to bring greater conceptual and methodological rigor to understand how information is exchanged during disasters. We ask, "How can information relationships be evaluated more systematically during a disaster response?" "Infocentric analysis"a term and...
Towards a wave theory of charged beam transport: A collection of thoughts

NASA Technical Reports Server (NTRS)

Dattoli, G.; Mari, C.; Torre, A.

1992-01-01

We formulate in a rigorous way a wave theory of charged beam linear transport. The Wigner distribution function is introduced and provides the link with classical mechanics. Finally, the von Neumann equation is shown to coincide with the Liouville equation for the nonlinear transport.
Bayesian Decision Theory Guiding Educational Decision-Making: Theories, Models and Application

ERIC Educational Resources Information Center

Pan, Yilin

2016-01-01

Given the importance of education and the growing public demand for improving education quality under tight budget constraints, there has been an emerging movement to call for research-informed decisions in educational resource allocation. Despite the abundance of rigorous studies on the effectiveness, cost, and implementation of educational…
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.
The DOZZ formula from the path integral

NASA Astrophysics Data System (ADS)

Kupiainen, Antti; Rhodes, Rémi; Vargas, Vincent

2018-05-01

We present a rigorous proof of the Dorn, Otto, Zamolodchikov, Zamolodchikov formula (the DOZZ formula) for the 3 point structure constants of Liouville Conformal Field Theory (LCFT) starting from a rigorous probabilistic construction of the functional integral defining LCFT given earlier by the authors and David. A crucial ingredient in our argument is a probabilistic derivation of the reflection relation in LCFT based on a refined tail analysis of Gaussian multiplicative chaos measures.
Predicting surface scatter using a linear systems formulation of non-paraxial scalar diffraction

NASA Astrophysics Data System (ADS)

Krywonos, Andrey

Scattering effects from rough surfaces are non-paraxial diffraction phenomena resulting from random phase variations in the reflected wavefront. The ability to predict these effects is important in a variety of applications including x-ray and EUV imaging, the design of stray light rejection systems, and reflection modeling for rendering realistic scenes and animations of physical objects in computer graphics. Rayleigh-Rice (small perturbation method) and Beckmann-Kirchoff (Kirchhoff approximation) theories are commonly used to predict surface scatter effects. In addition, Harvey and Shack developed a linear systems formulation of surface scatter phenomena in which the scattering behavior is characterized by a surface transfer function. This treatment provided insight and understanding not readily gleaned from the two previous theories, and has been incorporated into a variety of computer software packages (ASAP, Zemax, Tracepro). However, smooth surface and paraxial approximations have severely limited the range of applicability of each of the above theoretical treatments. In this dissertation, a linear systems formulation of non-paraxial scalar diffraction theory is first developed and then applied to sinusoidal phase gratings, resulting in diffraction efficiency predictions far more accurate than those provided by classical scalar theories. The application of the theory to these gratings was motivated by the fact that rough surfaces are frequently modeled as a superposition of sinusoidal surfaces of different amplitudes, periods, and orientations. The application of the non-paraxial scalar diffraction theory to surface scatter phenomena resulted first in a modified Beckmann-Kirchhoff surface scattering model, then a generalized Harvey-Shack theory, both of which produce accurate results for rougher surfaces than the Rayleigh-Rice theory and for larger incident and scattering angles than the classical Beckmann-Kirchhoff theory. These new developments enable the analysis and simplify the understanding of wide-angle scattering behavior from rough surfaces illuminated at large incident angles. In addition, they provide an improved BRDF (Bidirectional Reflectance Distribution Function) model, particularly for the smooth surface inverse scattering problem of determining surface power spectral density (PSD) curves from BRDF measurements.
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
Survey of Intermediate Microeconomic Textbooks.

ERIC Educational Resources Information Center

Goulet, Janet C.

1986-01-01

Surveys nine undergraduate microeconomic theory textbooks comprising a representing sample those available. Criteria used were quantity and quality of examples, mathematical rigor, and level of abstraction. (JDH)
David crighton, 1942-2000: a commentary on his career and his influence on aeroacoustic theory

NASA Astrophysics Data System (ADS)

Ffowcs Williams, John E.

David Crighton, a greatly admired figure in fluid mechanics, Head of the Department of Applied Mathematics and Theoretical Physics at Cambridge, and Master of Jesus College, Cambridge, died at the peak of his career. He had made important contributions to the theory of waves generated by unsteady flow. Crighton's work was always characterized by the application of rigorous mathematical approximations to fluid mechanical idealizations of practically relevant problems. At the time of his death, he was certainly the most influential British applied mathematical figure, and his former collaborators and students form a strong school that continues his special style of mathematical application. Rigorous analysis of well-posed aeroacoustical problems was transformed by David Crighton.
Investigations into phase effects from diffracted Gaussian beams for high-precision interferometry

NASA Astrophysics Data System (ADS)

Lodhia, Deepali

Gravitational wave detectors are a new class of observatories aiming to detect gravitational waves from cosmic sources. All-reflective interferometer configurations have been proposed for future detectors, replacing transmissive optics with diffractive elements, thereby reducing thermal issues associated with power absorption. However, diffraction gratings introduce additional phase noise, creating more stringent conditions for alignment stability, and further investigations are required into all-reflective interferometers. A suitable mathematical framework using Gaussian modes is required for analysing the alignment stability using diffraction gratings. Such a framework was created, whereby small beam displacements are modelled using a modal technique. It was confirmed that the original modal-based model does not contain the phase changes associated with grating displacements. Experimental tests verified that the phase of a diffracted Gaussian beam is independent of the beam shape. Phase effects were further examined using a rigorous time-domain simulation tool. These findings show that the perceived phase difference is based on an intrinsic change of coordinate system within the modal-based model, and that the extra phase can be added manually to the modal expansion. This thesis provides a well-tested and detailed mathematical framework that can be used to develop simulation codes to model more complex layouts of all-reflective interferometers.
Measurement system for diffraction efficiency of convex gratings

NASA Astrophysics Data System (ADS)

Liu, Peng; Chen, Xin-hua; Zhou, Jian-kang; Zhao, Zhi-cheng; Liu, Quan; Luo, Chao; Wang, Xiao-feng; Tang, Min-xue; Shen, Wei-min

2017-08-01

A measurement system for diffraction efficiency of convex gratings is designed. The measurement system mainly includes four components as a light source, a front system, a dispersing system that contains a convex grating, and a detector. Based on the definition and measuring principle of diffraction efficiency, the optical scheme of the measurement system is analyzed and the design result is given. Then, in order to validate the feasibility of the designed system, the measurement system is set up and the diffraction efficiency of a convex grating with the aperture of 35 mm, the curvature-radius of 72mm, the blazed angle of 6.4°, the grating period of 2.5μm and the working waveband of 400nm-900nm is tested. Based on GUM (Guide to the Expression of Uncertainty in Measurement), the uncertainties in the measuring results are evaluated. The measured diffraction efficiency data are compared to the theoretical ones, which are calculated based on the grating groove parameters got by an atomic force microscope and Rigorous Couple Wave Analysis, and the reliability of the measurement system is illustrated. Finally, the measurement performance of the system is analyzed and tested. The results show that, the testing accuracy, the testing stability and the testing repeatability are 2.5%, 0.085% and 3.5% , respectively.
Modeling of profilometry with laser focus sensors

NASA Astrophysics Data System (ADS)

Bischoff, Jörg; Manske, Eberhard; Baitinger, Henner

2011-05-01

Metrology is of paramount importance in submicron patterning. Particularly, line width and overlay have to be measured very accurately. Appropriated metrology techniques are scanning electron microscopy and optical scatterometry. The latter is non-invasive, highly accurate and enables optical cross sections of layer stacks but it requires periodic patterns. Scanning laser focus sensors are a viable alternative enabling the measurement of non-periodic features. Severe limitations are imposed by the diffraction limit determining the edge location accuracy. It will be shown that the accuracy can be greatly improved by means of rigorous modeling. To this end, a fully vectorial 2.5-dimensional model has been developed based on rigorous Maxwell solvers and combined with models for the scanning and various autofocus principles. The simulations are compared with experimental results. Moreover, the simulations are directly utilized to improve the edge location accuracy.
High-Efficiency, Near-Diffraction Limited, Dielectric Metasurface Lenses Based on Crystalline Titanium Dioxide at Visible Wavelengths.

PubMed

Liang, Yaoyao; Liu, Hongzhan; Wang, Faqiang; Meng, Hongyun; Guo, Jianping; Li, Jinfeng; Wei, Zhongchao

2018-04-28

Metasurfaces are planar optical elements that hold promise for overcoming the limitations of refractive and conventional diffractive optics. Previous metasurfaces have been limited to transparency windows at infrared wavelengths because of significant optical absorption and loss at visible wavelengths. Here we report a polarization-insensitive, high-contrast transmissive metasurface composed of crystalline titanium dioxide pillars in the form of metalens at the wavelength of 633 nm. The focal spots are as small as 0.54 λ d , which is very close to the optical diffraction limit of 0.5 λ d . The simulation focusing efficiency is up to 88.5%. A rigorous method for metalens design, the phase realization mechanism and the trade-off between high efficiency and small spot size (or large numerical aperture) are discussed. Besides, the metalenses can work well with an imaging point source up to ±15° off axis. The proposed design is relatively systematic and can be applied to various applications such as visible imaging, ranging and sensing systems.
You've Shown the Program Model Is Effective. Now What?

ERIC Educational Resources Information Center

Ellickson, Phyllis L.

2014-01-01

Rigorous tests of theory-based programs require faithful implementation. Otherwise, lack of results might be attributable to faulty program delivery, faulty theory, or both. However, once the evidence indicates the model works and merits broader dissemination, implementation issues do not fade away. How can developers enhance the likelihood that…
Louis Guttman's Contributions to Classical Test Theory

ERIC Educational Resources Information Center

Zimmerman, Donald W.; Williams, Richard H.; Zumbo, Bruno D.; Ross, Donald

2005-01-01

This article focuses on Louis Guttman's contributions to the classical theory of educational and psychological tests, one of the lesser known of his many contributions to quantitative methods in the social sciences. Guttman's work in this field provided a rigorous mathematical basis for ideas that, for many decades after Spearman's initial work,…
International Christian Schoolteachers' Traits, Characteristics, and Qualities Valued by Third Culture Kids

ERIC Educational Resources Information Center

Linton, Dale B.

2015-01-01

In this qualitative grounded theory study, 24 participants, referred to as "third culture kids" (or TCKs), ages 18-30 years, who had previously attended international Christian schools were interviewed to determine the dispositions they valued in their teachers. Incorporating principles of grounded theory, a series of rigorous steps were…
Rate Coefficient for the (4)Heμ + CH4 Reaction at 500 K: Comparison between Theory and Experiment.

PubMed

Arseneau, Donald J; Fleming, Donald G; Li, Yongle; Li, Jun; Suleimanov, Yury V; Guo, Hua

2016-03-03

The rate constant for the H atom abstraction reaction from methane by the muonic helium atom, Heμ + CH4 → HeμH + CH3, is reported at 500 K and compared with theory, providing an important test of both the potential energy surface (PES) and reaction rate theory for the prototypical polyatomic CH5 reaction system. The theory used to characterize this reaction includes both variational transition-state (CVT/μOMT) theory (VTST) and ring polymer molecular dynamics (RPMD) calculations on a recently developed PES, which are compared as well with earlier calculations on different PESs for the H, D, and Mu + CH4 reactions, the latter, in particular, providing for a variation in atomic mass by a factor of 36. Though rigorous quantum calculations have been carried out for the H + CH4 reaction, these have not yet been extended to the isotopologues of this reaction (in contrast to H3), so it is important to provide tests of less rigorous theories in comparison with kinetic isotope effects measured by experiment. In this regard, the agreement between the VTST and RPMD calculations and experiment for the rate constant of the Heμ + CH4 reaction at 500 K is excellent, within 10% in both cases, which overlaps with experimental error.
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)

Tunable natural nano-arrays: controlling surface properties and light reflectance

NASA Astrophysics Data System (ADS)

Watson, Jolanta A.; Myhra, Sverre; Watson, Gregory S.

2006-01-01

The general principles of optical design based on the theories of reflection, refraction and diffraction have been rigorously developed and optimized over the last three centuries. Of increasing importance has been the ability to predict and devise new optical technologies designed for specific functions. A key design feature of many of today's optical materials is the control of reflection and light transmittance through the medium. A sudden transition or impedance mismatch from one optical medium to another can result in unwanted reflections from the surface plane. Modification of a surface by creation of a gradual change in refractive index over a significant portion of a wavelength range will result in a reduction in reflection. An alternative surface modification to the multi layered stack coating (gradient index coating) is to produce a surface with structures having a period and height shorter than the light wavelength. These structures act like a pseudo-gradient index coating and can be described by the effective medium theory. Bernhard and Miller some forty years ago were the first to observe such structures found on the surface of insects. These were found in the form of hexagonally close packed nanometre sized protrusions on the corneal surface of certain moths. In this study we report on similar structures which we have found on certain species of cicada wings demonstrating that the reflective/transmission properties of these natural nano-structures can be tuned by controlled removal of the structure height using Atomic Force Microscopy (AFM).
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.
On the convergence of the coupled-wave approach for lamellar diffraction gratings

NASA Technical Reports Server (NTRS)

Li, Lifeng; Haggans, Charles W.

1992-01-01

Among the many existing rigorous methods for analyzing diffraction of electromagnetic waves by diffraction gratings, the coupled-wave approach stands out because of its versatility and simplicity. It can be applied to volume gratings and surface relief gratings, and its numerical implementation is much simpler than others. In addition, its predictions were experimentally validated in several cases. These facts explain the popularity of the coupled-wave approach among many optical engineers in the field of diffractive optics. However, a comprehensive analysis of the convergence of the model predictions has never been presented, although several authors have recently reported convergence difficulties with the model when it is used for metallic gratings in TM polarization. Herein, three points are made: (1) in the TM case, the coupled-wave approach converges much slower than the modal approach of Botten et al; (2) the slow convergence is caused by the use of Fourier expansions for the permittivity and the fields in the grating region; and (3) is manifested by the slow convergence of the eigenvalues and the associated modal fields. The reader is assumed to be familiar with the mathematical formulations of the coupled-wave approach and the modal approach.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Tregillis, Ian Lee

This document examines the performance of a generic flat-mirror multimonochromatic imager (MMI), with special emphasis on existing instruments at NIF and Omega. We begin by deriving the standard equation for the mean number of photons detected per resolution element. The pinhole energy bandwidth is a contributing factor; this is dominated by the finite size of the source and may be considerable. The most common method for estimating the spatial resolution of such a system (quadrature addition) is, technically, mathematically invalid for this case. However, under the proper circumstances it may produce good estimates compared to a rigorous calculation based onmore » the convolution of point-spread functions. Diffraction is an important contribution to the spatial resolution. Common approximations based on Fraunhofer (farfield) diffraction may be inappropriate and misleading, as the instrument may reside in multiple regimes depending upon its configuration or the energy of interest. It is crucial to identify the correct diffraction regime; Fraunhofer and Fresnel (near-field) diffraction profiles are substantially different, the latter being considerably wider. Finally, we combine the photonics and resolution analyses to derive an expression for the minimum signal level such that the resulting images are not dominated by photon statistics. This analysis is consistent with observed performance of the NIF MMI.« less
Interaction of surface plasmon polaritons in heavily doped GaN microstructures with terahertz radiation

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

Melentev, G. A., E-mail: gamelen@spbstu.ru; Shalygin, V. A.; Vorobjev, L. E.

2016-03-07

We present the results of experimental and theoretical studies of the surface plasmon polariton excitations in heavily doped GaN epitaxial layers. Reflection and emission of radiation in the frequency range of 2–20 THz including the Reststrahlen band were investigated for samples with grating etched on the sample surface, as well as for samples with flat surface. The reflectivity spectrum for p-polarized radiation measured for the sample with the surface-relief grating demonstrates a set of resonances associated with excitations of different surface plasmon polariton modes. Spectral peculiarities due to the diffraction effect have been also revealed. The characteristic features of themore » reflectivity spectrum, namely, frequencies, amplitudes, and widths of the resonance dips, are well described theoretically by a modified technique of rigorous coupled-wave analysis of Maxwell equations. The emissivity spectra of the samples were measured under epilayer temperature modulation by pulsed electric field. The emissivity spectrum of the sample with surface-relief grating shows emission peaks in the frequency ranges corresponding to the decay of the surface plasmon polariton modes. Theoretical analysis based on the blackbody-like radiation theory well describes the main peculiarities of the observed THz emission.« less
Dual-function beam splitter of a subwavelength fused-silica grating.

PubMed

Feng, Jijun; Zhou, Changhe; Zheng, Jiangjun; Cao, Hongchao; Lv, Peng

2009-05-10

We present the design and fabrication of a novel dual-function subwavelength fused-silica grating that can be used as a polarization-selective beam splitter. For TM polarization, the grating can be used as a two-port beam splitter at a wavelength of 1550 nm with a total diffraction efficiency of 98%. For TE polarization, the grating can function as a high-efficiency grating, and the diffraction efficiency of the -1st order is 95% under Littrow mounting. This dual-function grating design is based on a simplified modal method. By using the rigorous coupled-wave analysis, the optimum grating parameters can be determined. Holographic recording technology and inductively coupled plasma etching are used to manufacture the fused-silica grating. Experimental results are in agreement with the theoretical values.
EUV phase-shifting masks and aberration monitors

NASA Astrophysics Data System (ADS)

Deng, Yunfei; Neureuther, Andrew R.

2002-07-01

Rigorous electromagnetic simulation with TEMPEST is used to examine the use of phase-shifting masks in EUV lithography. The effects of oblique incident illumination and mask patterning by ion-mixing of multilayers are analyzed. Oblique incident illumination causes streamers at absorber edges and causes position shifting in aerial images. The diffraction waves between ion-mixed and pristine multilayers are observed. The phase-shifting caused by stepped substrates is simulated and images show that it succeeds in creation of phase-shifting effects. The diffraction process at the phase boundary is also analyzed. As an example of EUV phase-shifting masks, a coma pattern and probe based aberration monitor is simulated and aerial images are formed under different levels of coma aberration. The probe signal rises quickly as coma increases as designed.
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.
Research into Theory into Practice: An Overview of Family Based Interventions for Child Antisocial Behavior Developed at the Oregon Social Learning Center

PubMed Central

Fisher, Philip A.; Gilliam, Kathryn S.

2017-01-01

Although many psychotherapeutic approaches exist for treating troubled children and their families, not all have been evaluated to be effective through research. Moreover, among those that have been determined to be “evidence-based,” few have followed as coherent and rigorous a path of rigorous scientific investigation as the interventions that have been developed at the Oregon Social Learning Center. As such, these interventions serve as a model of “research to theory to practice” that may not only be employed to support families with children in need of treatment, but may also guide other programs of treatment development. This is the story of how this work has unfolded over the past four decades. PMID:29225459
Bootstrapping the (A1, A2) Argyres-Douglas theory

NASA Astrophysics Data System (ADS)

Cornagliotto, Martina; Lemos, Madalena; Liendo, Pedro

2018-03-01

We apply bootstrap techniques in order to constrain the CFT data of the ( A 1 , A 2) Argyres-Douglas theory, which is arguably the simplest of the Argyres-Douglas models. We study the four-point function of its single Coulomb branch chiral ring generator and put numerical bounds on the low-lying spectrum of the theory. Of particular interest is an infinite family of semi-short multiplets labeled by the spin ℓ. Although the conformal dimensions of these multiplets are protected, their three-point functions are not. Using the numerical bootstrap we impose rigorous upper and lower bounds on their values for spins up to ℓ = 20. Through a recently obtained inversion formula, we also estimate them for sufficiently large ℓ, and the comparison of both approaches shows consistent results. We also give a rigorous numerical range for the OPE coefficient of the next operator in the chiral ring, and estimates for the dimension of the first R-symmetry neutral non-protected multiplet for small spin.
Hybrid Theory of Electron-Hydrogenic Systems Elastic Scattering

NASA Technical Reports Server (NTRS)

Bhatia, A. K.

2007-01-01

Accurate electron-hydrogen and electron-hydrogenic cross sections are required to interpret fusion experiments, laboratory plasma physics and properties of the solar and astrophysical plasmas. We have developed a method in which the short-range and long-range correlations can be included at the same time in the scattering equations. The phase shifts have rigorous lower bounds and the scattering lengths have rigorous upper bounds. The phase shifts in the resonance region can be used to calculate very accurately the resonance parameters.
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.
Group Theory and Crystal Field Theory: A Simple and Rigorous Derivation of the Spectroscopic Terms Generated by the t[subscript 2g][superscript 2] Electronic Configuration in a Strong Octahedral Field

ERIC Educational Resources Information Center

Morpurgo, Simone

2007-01-01

The principles of symmetry and group theory are applied to the zero-order wavefunctions associated with the strong-field t[subscript 2g][superscript 2] configuration and their symmetry-adapted linear combinations (SALC) associated with the generated energy terms are derived. This approach will enable students to better understand the use of…
Enhancing Validity When Researching the "Other": Insights from Pierre Bourdieu's Theory of Social Science Research Practice

ERIC Educational Resources Information Center

Naidoo, Devika

2014-01-01

This article explores aspects of Pierre Bourdieu's theory of social science research practice and discusses their relevance for enhancing validity when researching the "other." Aspects such as: a relational way of thinking about concepts, epistemology and methodology; the rigorous construction of the object of research; and…
Education in Emergencies: A Review of Theory and Research

ERIC Educational Resources Information Center

Burde, Dana; Kapit, Amy; Wahl, Rachel L.; Guven, Ozen; Skarpeteig, Margot Igland

2017-01-01

In this article, we conduct an integrative and rigorous review of theory and research on education in emergencies programs and interventions as international agencies implement them in areas of armed conflict. We ask several questions. How did this subfield emerge and what are the key conceptual frameworks that shape it today? How do education in…
What Can Graph Theory Tell Us about Word Learning and Lexical Retrieval?

ERIC Educational Resources Information Center

Vitevitch, Michael S.

2008-01-01

Purpose: Graph theory and the new science of networks provide a mathematically rigorous approach to examine the development and organization of complex systems. These tools were applied to the mental lexicon to examine the organization of words in the lexicon and to explore how that structure might influence the acquisition and retrieval of…
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%.

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.
A study on high NA and evanescent imaging with polarized illumination

NASA Astrophysics Data System (ADS)

Yang, Seung-Hune

Simulation techniques are developed for high NA polarized microscopy with Babinet's principle, partial coherence and vector diffraction for non-periodic geometries. A mathematical model for the Babinet approach is developed and interpreted. Simulation results of the Babinet's principle approach are compared with those of Rigorous Coupled Wave Theory (RCWT) for periodic structures to investigate the accuracy of this approach and its limitations. A microscope system using a special solid immersion lens (SIL) is introduced to image Blu-Ray (BD) optical disc samples without removing the protective cover layer. Aberration caused by the cover layer is minimized with a truncated SIL. Sub-surface imaging simulation is achieved by RCWT, partial coherence, vector diffraction and Babinet's Principle. Simulated results are compared with experimental images and atomic force microscopy (AFM) measurement. A technique for obtaining native and induced using a significant amount of evanescent energy is described for a solid immersion lens (SIL) microscope. Characteristics of native and induced polarization images for different object structures and materials are studied in detail. Experiments are conducted with a NA = 1.48 at lambda = 550nm microscope. Near-field images are simulated and analyzed with an RCWT approach. Contrast curve versus object spatial frequency calculations are compared with experimental measurements. Dependencies of contrast versus source polarization angles and air gap for native and induced polarization image profiles are evaluated. By using the relationship between induced polarization and topographical structure, an induced polarization image of an alternating phase shift mask (PSM) is converted into a topographical image, which shows very good agreement with AFM measurement. Images of other material structures include a dielectric grating, chrome-on-glass grating, silicon CPU structure, BD-R and BD-ROM.
Upgrading geometry conceptual understanding and strategic competence through implementing rigorous mathematical thinking (RMT)

NASA Astrophysics Data System (ADS)

Nugraheni, Z.; Budiyono, B.; Slamet, I.

2018-03-01

To reach higher order thinking skill, needed to be mastered the conceptual understanding and strategic competence as they are two basic parts of high order thinking skill (HOTS). RMT is a unique realization of the cognitive conceptual construction approach based on Feurstein with his theory of Mediated Learning Experience (MLE) and Vygotsky’s sociocultural theory. This was quasi-experimental research which compared the experimental class that was given Rigorous Mathematical Thinking (RMT) as learning method and the control class that was given Direct Learning (DL) as the conventional learning activity. This study examined whether there was different effect of two learning model toward conceptual understanding and strategic competence of Junior High School Students. The data was analyzed by using Multivariate Analysis of Variance (MANOVA) and obtained a significant difference between experimental and control class when considered jointly on the mathematics conceptual understanding and strategic competence (shown by Wilk’s Λ = 0.84). Further, by independent t-test is known that there was significant difference between two classes both on mathematical conceptual understanding and strategic competence. By this result is known that Rigorous Mathematical Thinking (RMT) had positive impact toward Mathematics conceptual understanding and strategic competence.
Remarks on a New Possible Discretization Scheme for Gauge Theories

NASA Astrophysics Data System (ADS)

Magnot, Jean-Pierre

2018-03-01

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.
Broadband polarizing beam splitter based on the form birefringence of a subwavelength grating in the quasi-static domain.

PubMed

Yi, Deer; Yan, Yingbai; Liu, Haitao; Lu, Si; Jin, Guofan

2004-04-01

We propose a novel broadband polarizing beam splitter with a compact sandwich structure that has a subwavelength grating in the quasi-static domain as the filling. The design is based on effective-medium theory an anisotropic thin-film theory, and the performance is investigated with rigorous coupled-wave theory. The design results show that the structure can provide a high polarization extinction ratio in a broad spectral range.
Remarks on a New Possible Discretization Scheme for Gauge Theories

NASA Astrophysics Data System (ADS)

Magnot, Jean-Pierre

2018-07-01

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.
On the equivalence between Young's double-slit and crystal double-refraction interference experiments.

PubMed

Ossikovski, Razvigor; Arteaga, Oriol; Vizet, Jérémy; Garcia-Caurel, Enric

2017-08-01

We show, both analytically and experimentally, that under common experimental conditions the interference pattern produced in a classic Young's double-slit experiment is indistinguishable from that generated by means of a doubly refracting uniaxial crystal whose optic axis makes a skew angle with the light propagation direction. The equivalence between diffraction and crystal optics interference experiments, taken for granted by Arago and Fresnel in their pioneering research on the interference of polarized light beams, is thus rigorously proven.
Towards a framework for the elicitation of dilemmas.

PubMed

Burger, Marc J C

2008-08-01

This paper covers the main findings of the doctoral research that was concerned with seeking to extend aspects of dilemma theory. In professional practice, the Trompenaars Hampden-Turner Dilemma Reconciliation Process(TM) is a vehicle delivering dilemma theory in application. It informs a manager or leader on how to explore the dilemmas they face, how to reconcile the tensions that result, and how to structure the action steps for implementing the reconciled solutions. This vehicle forms the professional practice of the author who seeks to bring more rigor to consulting practice and thereby also contribute to theory development in the domain. The critical review of dilemma theory reveals that previous authors are inconsistent and variously invalid in their use of the terms 'dilemma theory,' 'dilemma methodology,' 'dilemma process,' 'dilemma reconciliation,' etc., and therefore an attempt is made to resolve these inconsistencies by considering whether 'dilemmaism' at the meta-level might be positioned as a new paradigm of inquiry for (management) research that embodies ontological, epistemological, and methodical premises that frame an approach to the resolution of real world business problems in (multi) disciplinary; (multi) functional and (multi) cultural business environments. This research offers contributions to knowledge, professional practice and theory development from the exploration of the SPID model as a way to make the elicitation of dilemmas more rigorous and structured and in the broader context of exploring 'dilemmaism' as a new paradigm of inquiry.
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.
Business Language Studies in the United States: On Nomenclature, Context, Theory, and Method

ERIC Educational Resources Information Center

Doyle, Michael Scott

2012-01-01

Although it has existed for many decades in the national curriculum of U.S. higher education, the study of languages for business purposes has lacked a more serviceable and academically communal name--a more rigorous toponymic identity--by which to identify itself as a theory-based field of scholarship. The intention here is to propose for…
An Assessment of Character and Leadership Development Latent Factor Structures through Confirmatory Factor, Item Response Theory, and Latent Class Analyses

ERIC Educational Resources Information Center

Higginbotham, David L.

2013-01-01

This study leveraged the complementary nature of confirmatory factor (CFA), item response theory (IRT), and latent class (LCA) analyses to strengthen the rigor and sophistication of evaluation of two new measures of the Air Force Academy's "leader of character" definition--the Character Mosaic Virtues (CMV) and the Leadership Mosaic…
Testing adaptive toolbox models: a Bayesian hierarchical approach.

PubMed

Scheibehenne, Benjamin; Rieskamp, Jörg; Wagenmakers, Eric-Jan

2013-01-01

Many theories of human cognition postulate that people are equipped with a repertoire of strategies to solve the tasks they face. This theoretical framework of a cognitive toolbox provides a plausible account of intra- and interindividual differences in human behavior. Unfortunately, it is often unclear how to rigorously test the toolbox framework. How can a toolbox model be quantitatively specified? How can the number of toolbox strategies be limited to prevent uncontrolled strategy sprawl? How can a toolbox model be formally tested against alternative theories? The authors show how these challenges can be met by using Bayesian inference techniques. By means of parameter recovery simulations and the analysis of empirical data across a variety of domains (i.e., judgment and decision making, children's cognitive development, function learning, and perceptual categorization), the authors illustrate how Bayesian inference techniques allow toolbox models to be quantitatively specified, strategy sprawl to be contained, and toolbox models to be rigorously tested against competing theories. The authors demonstrate that their approach applies at the individual level but can also be generalized to the group level with hierarchical Bayesian procedures. The suggested Bayesian inference techniques represent a theoretical and methodological advancement for toolbox theories of cognition and behavior.
Theory of the Decoherence Effect in Finite and Infinite Open Quantum Systems Using the Algebraic Approach

NASA Astrophysics Data System (ADS)

Blanchard, Philippe; Hellmich, Mario; Ługiewicz, Piotr; Olkiewicz, Robert

Quantum mechanics is the greatest revision of our conception of the character of the physical world since Newton. Consequently, David Hilbert was very interested in quantum mechanics. He and John von Neumann discussed it frequently during von Neumann's residence in Göttingen. He published in 1932 his book Mathematical Foundations of Quantum Mechanics. In Hilbert's opinion it was the first exposition of quantum mechanics in a mathematically rigorous way. The pioneers of quantum mechanics, Heisenberg and Dirac, neither had use for rigorous mathematics nor much interest in it. Conceptually, quantum theory as developed by Bohr and Heisenberg is based on the positivism of Mach as it describes only observable quantities. It first emerged as a result of experimental data in the form of statistical observations of quantum noise, the basic concept of quantum probability.
Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles

NASA Astrophysics Data System (ADS)

Katsoulakis, Markos A.; Vlachos, Dionisios G.

2003-11-01

We derive a hierarchy of successively coarse-grained stochastic processes and associated coarse-grained Monte Carlo (CGMC) algorithms directly from the microscopic processes as approximations in larger length scales for the case of diffusion of interacting particles on a lattice. This hierarchy of models spans length scales between microscopic and mesoscopic, satisfies a detailed balance, and gives self-consistent fluctuation mechanisms whose noise is asymptotically identical to the microscopic MC. Rigorous, detailed asymptotics justify and clarify these connections. Gradient continuous time microscopic MC and CGMC simulations are compared under far from equilibrium conditions to illustrate the validity of our theory and delineate the errors obtained by rigorous asymptotics. Information theory estimates are employed for the first time to provide rigorous error estimates between the solutions of microscopic MC and CGMC, describing the loss of information during the coarse-graining process. Simulations under periodic boundary conditions are used to verify the information theory error estimates. It is shown that coarse-graining in space leads also to coarse-graining in time by q2, where q is the level of coarse-graining, and overcomes in part the hydrodynamic slowdown. Operation counting and CGMC simulations demonstrate significant CPU savings in continuous time MC simulations that vary from q3 for short potentials to q4 for long potentials. Finally, connections of the new coarse-grained stochastic processes to stochastic mesoscopic and Cahn-Hilliard-Cook models are made.
Sound diffraction at wall impedance discontinuities in a circular cylinder, investigated using Wiener-Hopf technique

NASA Technical Reports Server (NTRS)

Cho, Y. C.

1983-01-01

Rigorous solutions are presented for sound diffraction in a circular cylinder with axial discontinuities of the wall admittance (or impedance). Analytical expressions are derived for the reflection and the transmission coefficients for duct modes. The results are discussed quantitatively in the limits of small admittance shifts (delta) and of low frequencies (ka). One of the results is the low frequency behavior of the reflection coefficient R(o) sub 00 of the fundamental mode. For the mode of a hardwall duct reflected from the junction with a softwall duct, (R(o) sub oo yields - (1-square root of (ka) square root of (2/i delta)); this result is in contrast to the frequency dependence of the reflection from the open end of a hardwall duct, for which R(o) sub oo yields - 1-(ka) squared/2 .
Wide-field-of-view nanoscale Bragg liquid crystal polarization gratings

NASA Astrophysics Data System (ADS)

Xiang, Xiao; Kim, Jihwan; Escuti, Michael J.

2018-02-01

Here, we demonstrate a liquid crystal (LC) polymer Bragg polarization grating (PG) with large angular band- width and high efficiency in transmission-mode for 532 nm wavelength and 400 nm period. The field-of-view (FOV ) is increased significantly while preserving high diffraction efficiency by realizing a monolithic grating comprising two different slants. Using rigorous coupled-wave analysis simulation, we identified a structure with 48° FOV and 70% average first-order efficiency. We then experimentally fabricated and characterized the grating with a photo-aligned LC polymer network, also known as reactive mesogens. We measured 40° FOV and nearly 80% average diffraction efficiency. With this broadened and fairly uniform angular response, this wide FOV Bragg PG is a compelling option for large deflection-angle applications, including near-eye display in augmented reality systems, waveguide based illumination, and beam steering.
Role of coherence in microsphere-assisted nanoscopy

NASA Astrophysics Data System (ADS)

Perrin, Stephane; Lecler, Sylvain; Leong-Hoi, Audrey; Montgomery, Paul C.

2017-06-01

The loss of the information, due to the diffraction and the evanescent waves, limits the resolving power of classical optical microscopy. In air, the lateral resolution of an optical microscope can approximated at half of the wavelength using a low-coherence illumination. Recently, several methods have been developed in order to overcome this limitation and, in 2011, a new far-field and full-field imaging technique was proposed where a sub-diffraction-limit resolution has been achieved using a transparent microsphere. In this article, the phenomenon of super-resolution using microsphere-assisted microscopy is analysed through rigorous electro-magnetic simulations. The performances of the imaging technique are estimated as function of optical and geometrical parameters. Furthermore, the role of coherence is introduced through the temporal coherence of the light source and the phase response of the object.

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.}
Comparison of the GHSSmooth and the Rayleigh-Rice surface scatter theories

NASA Astrophysics Data System (ADS)

Harvey, James E.; Pfisterer, Richard N.

2016-09-01

The scalar-based GHSSmooth surface scatter theory results in an expression for the BRDF in terms of the surface PSD that is very similar to that provided by the rigorous Rayleigh-Rice (RR) vector perturbation theory. However it contains correction factors for two extreme situations not shared by the RR theory: (i) large incident or scattered angles that result in some portion of the scattered radiance distribution falling outside of the unit circle in direction cosine space, and (ii) the situation where the relevant rms surface roughness, σrel, is less than the total intrinsic rms roughness of the scattering surface. Also, the RR obliquity factor has been discovered to be an approximation of the more general GHSSmooth obliquity factor due to a little-known (or long-forgotten) implicit assumption in the RR theory that the surface autocovariance length is longer than the wavelength of the scattered radiation. This assumption allowed retaining only quadratic terms and lower in the series expansion for the cosine function, and results in reducing the validity of RR predictions for scattering angles greater than 60°. This inaccurate obliquity factor in the RR theory is also the cause of a complementary unrealistic "hook" at the high spatial frequency end of the predicted surface PSD when performing the inverse scattering problem. Furthermore, if we empirically substitute the polarization reflectance, Q, from the RR expression for the scalar reflectance, R, in the GHSSmooth expression, it inherits all of the polarization capabilities of the rigorous RR vector perturbation theory.
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.
Design and fabrication of sub-wavelength anti-reflection grating

NASA Astrophysics Data System (ADS)

Zou, Wenlong; Li, Chaoming; Chen, Xinrong; Cai, Zhijian; Wu, Jianhong

2018-01-01

In the high power laser system, the reflection of optical surface has a strong impact on the efficiency for luminous energy utilization. Fresnel reflection can be effectively suppressed by antireflection film. For that, the anti-reflection film is one of the important optical elements in high power laser system. The common preparation methods of anti-reflection film include monolayer film, multilayer film and sub-wavelength grating. The effectiveness of monolayer is unsatisfactory, and its application spectrum bandwidth is very narrow. The preparation process of multilayer film is complex and it is very expensive. The emerging technology of fabrication anti-reflection film is sub-wavelength grating. The zero order transmission diffraction efficiency depends on the period, etching depth and duty cycle of the grating. The structure parameters of antireflection grating were designed and optimized under small angle incidence of 351nm based on rigorous coupled wave analysis method. The impaction of zero order reflection diffraction and zero order transmission diffraction efficiency on period, duty cycle and etching depth of grating was discussed in detail in this paper. The sub-wavelength anti-reflection grating was fabricated by holographic and ion etching method.
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.
Radiometry rocks

NASA Astrophysics Data System (ADS)

Harvey, James E.

2012-10-01

Professor Bill Wolfe was an exceptional mentor for his graduate students, and he made a major contribution to the field of optical engineering by teaching the (largely ignored) principles of radiometry for over forty years. This paper describes an extension of Bill's work on surface scatter behavior and the application of the BRDF to practical optical engineering problems. Most currently-available image analysis codes require the BRDF data as input in order to calculate the image degradation from residual optical fabrication errors. This BRDF data is difficult to measure and rarely available for short EUV wavelengths of interest. Due to a smooth-surface approximation, the classical Rayleigh-Rice surface scatter theory cannot be used to calculate BRDFs from surface metrology data for even slightly rough surfaces. The classical Beckmann-Kirchhoff theory has a paraxial limitation and only provides a closed-form solution for Gaussian surfaces. Recognizing that surface scatter is a diffraction process, and by utilizing sound radiometric principles, we first developed a linear systems theory of non-paraxial scalar diffraction in which diffracted radiance is shift-invariant in direction cosine space. Since random rough surfaces are merely a superposition of sinusoidal phase gratings, it was a straightforward extension of this non-paraxial scalar diffraction theory to develop a unified surface scatter theory that is valid for moderately rough surfaces at arbitrary incident and scattered angles. Finally, the above two steps are combined to yield a linear systems approach to modeling image quality for systems suffering from a variety of image degradation mechanisms. A comparison of image quality predictions with experimental results taken from on-orbit Solar X-ray Imager (SXI) data is presented.
Cooperative interactions in dense thermal Rb vapour confined in nm-scale cells

NASA Astrophysics Data System (ADS)

Keaveney, James

Gravitational wave detectors are a new class of observatories aiming to detect gravitational waves from cosmic sources. All-reflective interferometer configurations have been proposed for future detectors, replacing transmissive optics with diffractive elements, thereby reducing thermal issues associated with power absorption. However, diffraction gratings introduce additional phase noise, creating more stringent conditions for alignment stability, and further investigations are required into all-reflective interferometers. A suitable mathematical framework using Gaussian modes is required for analysing the alignment stability using diffraction gratings. Such a framework was created, whereby small beam displacements are modelled using a modal technique. It was confirmed that the original modal-based model does not contain the phase changes associated with grating displacements. Experimental tests verified that the phase of a diffracted Gaussian beam is independent of the beam shape. Phase effects were further examined using a rigorous time-domain simulation tool. These findings show that the perceived phase difference is based on an intrinsic change of coordinate system within the modal-based model, and that the extra phase can be added manually to the modal expansion. This thesis provides a well-tested and detailed mathematical framework that can be used to develop simulation codes to model more complex layouts of all-reflective interferometers.
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.
Linear system theory

NASA Technical Reports Server (NTRS)

Callier, Frank M.; Desoer, Charles A.

1991-01-01

The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.
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.
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.
Attitude stability of spinning satellites

NASA Technical Reports Server (NTRS)

Caughey, T. K.

1980-01-01

Some problems of attitude stability of spinning satellites are treated in a rigorous manner. With certain restrictions, linearized stability analysis correctly predicts the attitude stability of spinning satellites, even in the critical cases of the Liapunov-Poincare stability theory.
Measuring coherence with entanglement concurrence

NASA Astrophysics Data System (ADS)

Qi, Xianfei; Gao, Ting; Yan, Fengli

2017-07-01

Quantum coherence is a fundamental manifestation of the quantum superposition principle. Recently, Baumgratz et al (2014 Phys. Rev. Lett. 113 140401) presented a rigorous framework to quantify coherence from the view of theory of physical resource. Here we propose a new valid quantum coherence measure which is a convex roof measure, for a quantum system of arbitrary dimension, essentially using the generalized Gell-Mann matrices. Rigorous proof shows that the proposed coherence measure, coherence concurrence, fulfills all the requirements dictated by the resource theory of quantum coherence measures. Moreover, strong links between the resource frameworks of coherence concurrence and entanglement concurrence is derived, which shows that any degree of coherence with respect to some reference basis can be converted to entanglement via incoherent operations. Our work provides a clear quantitative and operational connection between coherence and entanglement based on two kinds of concurrence. This new coherence measure, coherence concurrence, may also be beneficial to the study of quantum coherence.
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.
Question 6: coevolution theory of the genetic code: a proven theory.

PubMed

Wong, Jeffrey Tze-Fei

2007-10-01

The coevolution theory proposes that primordial proteins consisted only of those amino acids readily obtainable from the prebiotic environment, representing about half the twenty encoded amino acids of today, and the missing amino acids entered the system as the code expanded along with pathways of amino acid biosynthesis. The isolation of genetic code mutants, and the antiquity of pretran synthesis revealed by the comparative genomics of tRNAs and aminoacyl-tRNA synthetases, have combined to provide a rigorous proof of the four fundamental tenets of the theory, thus solving the riddle of the structure of the universal genetic code.
Reconsideration of the sequence of rigor mortis through postmortem changes in adenosine nucleotides and lactic acid in different rat muscles.

PubMed

Kobayashi, M; Takatori, T; Iwadate, K; Nakajima, M

1996-10-25

We examined the changes in adenosine triphosphate (ATP), lactic acid, adenosine diphosphate (ADP) and adenosine monophosphate (AMP) in five different rat muscles after death. Rigor mortis has been thought to occur simultaneously in dead muscles and hence to start in small muscles sooner than in large muscles. In this study we found that the rate of decrease in ATP was significantly different in each muscle. The greatest drop in ATP was observed in the masseter muscle. These findings contradict the conventional theory of rigor mortis. Similarly, the rates of change in ADP and lactic acid, which are thought to be related to the consumption or production of ATP, were different in each muscle. However, the rate of change of AMP was the same in each muscle.

Polarizing beam splitter of deep-etched triangular-groove fused-silica gratings.

PubMed

Zheng, Jiangjun; Zhou, Changhe; Feng, Jijun; Wang, Bo

2008-07-15

We investigated the use of a deep-etched fused-silica grating with triangular-shaped grooves as a highly efficient polarizing beam splitter (PBS). A triangular-groove PBS grating is designed at a wavelength of 1550 nm to be used in optical communication. When it is illuminated in Littrow mounting, the transmitted TE- and TM-polarized waves are mainly diffracted in the minus-first and zeroth orders, respectively. The design condition is based on the average differences of the grating mode indices, which is verified by using rigorous coupled-wave analysis. The designed PBS grating is highly efficient over the C+L band range for both TE and TM polarizations (>97.68%). It is shown that such a triangular-groove PBS grating can exhibit a higher diffraction efficiency, a larger extinction ratio, and less reflection loss than the binary-phase fused-silica PBS grating.
Fabrication of the polarization independent spectral beam combining grating

NASA Astrophysics Data System (ADS)

Liu, Quan; Jin, Yunxia; Wu, Jianhong; Guo, Peiliang

2016-03-01

Owing to damage, thermal issues, and nonlinear optical effects, the output power of fiber laser has been proven to be limited. Beam combining techniques are the attractive solutions to achieve high-power high-brightness fiber laser output. The spectral beam combining (SBC) is a promising method to achieve high average power output without influencing the beam quality. A polarization independent spectral beam combining grating is one of the key elements in the SBC. In this paper the diffraction efficiency of the grating is investigated by rigorous coupled-wave analysis (RCWA). The theoretical -1st order diffraction efficiency of the grating is more than 95% from 1010nm to 1080nm for both TE and TM polarizations. The fabrication tolerance is analyzed. The polarization independent spectral beam combining grating with the period of 1.04μm has been fabricated by holographic lithography - ion beam etching, which are within the fabrication tolerance.
Design and analysis of a fast, two-mirror soft-x-ray microscope

NASA Technical Reports Server (NTRS)

Shealy, D. L.; Wang, C.; Jiang, W.; Jin, L.; Hoover, R. B.

1992-01-01

During the past several years, a number of investigators have addressed the design, analysis, fabrication, and testing of spherical Schwarzschild microscopes for soft-x-ray applications using multilayer coatings. Some of these systems have demonstrated diffraction limited resolution for small numerical apertures. Rigorously aplanatic, two-aspherical mirror Head microscopes can provide near diffraction limited resolution for very large numerical apertures. The relationships between the numerical aperture, mirror radii and diameters, magnifications, and total system length for Schwarzschild microscope configurations are summarized. Also, an analysis of the characteristics of the Head-Schwarzschild surfaces will be reported. The numerical surface data predicted by the Head equations were fit by a variety of functions and analyzed by conventional optical design codes. Efforts have been made to determine whether current optical substrate and multilayer coating technologies will permit construction of a very fast Head microscope which can provide resolution approaching that of the wavelength of the incident radiation.
Parent Management Training-Oregon Model: Adapting Intervention with Rigorous Research.

PubMed

Forgatch, Marion S; Kjøbli, John

2016-09-01

Parent Management Training-Oregon Model (PMTO(®) ) is a set of theory-based parenting programs with status as evidence-based treatments. PMTO has been rigorously tested in efficacy and effectiveness trials in different contexts, cultures, and formats. Parents, the presumed agents of change, learn core parenting practices, specifically skill encouragement, limit setting, monitoring/supervision, interpersonal problem solving, and positive involvement. The intervention effectively prevents and ameliorates children's behavior problems by replacing coercive interactions with positive parenting practices. Delivery format includes sessions with individual families in agencies or families' homes, parent groups, and web-based and telehealth communication. Mediational models have tested parenting practices as mechanisms of change for children's behavior and found support for the theory underlying PMTO programs. Moderating effects include children's age, maternal depression, and social disadvantage. The Norwegian PMTO implementation is presented as an example of how PMTO has been tailored to reach diverse populations as delivered by multiple systems of care throughout the nation. An implementation and research center in Oslo provides infrastructure and promotes collaboration between practitioners and researchers to conduct rigorous intervention research. Although evidence-based and tested within a wide array of contexts and populations, PMTO must continue to adapt to an ever-changing world. © 2016 Family Process Institute.
Digital morphogenesis via Schelling segregation

NASA Astrophysics Data System (ADS)

Barmpalias, George; Elwes, Richard; Lewis-Pye, Andrew

2018-04-01

Schelling’s model of segregation looks to explain the way in which particles or agents of two types may come to arrange themselves spatially into configurations consisting of large homogeneous clusters, i.e. connected regions consisting of only one type. As one of the earliest agent based models studied by economists and perhaps the most famous model of self-organising behaviour, it also has direct links to areas at the interface between computer science and statistical mechanics, such as the Ising model and the study of contagion and cascading phenomena in networks. While the model has been extensively studied it has largely resisted rigorous analysis, prior results from the literature generally pertaining to variants of the model which are tweaked so as to be amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory. In Brandt et al (2012 Proc. 44th Annual ACM Symp. on Theory of Computing) provided the first rigorous analysis of the unperturbed model, for a specific set of input parameters. Here we provide a rigorous analysis of the model’s behaviour much more generally and establish some surprising forms of threshold behaviour, notably the existence of situations where an increased level of intolerance for neighbouring agents of opposite type leads almost certainly to decreased segregation.
The 1,5-H-shift in 1-butoxy: A case study in the rigorous implementation of transition state theory for a multirotamer system

NASA Astrophysics Data System (ADS)

Vereecken, Luc; Peeters, Jozef

2003-09-01

The rigorous implementation of transition state theory (TST) for a reaction system with multiple reactant rotamers and multiple transition state conformers is discussed by way of a statistical rate analysis of the 1,5-H-shift in 1-butoxy radicals, a prototype reaction for the important class of H-shift reactions in atmospheric chemistry. Several approaches for deriving a multirotamer TST expression are treated: oscillator versus (hindered) internal rotor models; distinguishable versus indistinguishable atoms; and direct count methods versus degeneracy factors calculated by (simplified) direct count methods or from symmetry numbers and number of enantiomers, where applicable. It is shown that the various treatments are fully consistent, even if the TST expressions themselves appear different. The 1-butoxy H-shift reaction is characterized quantum chemically using B3LYP-DFT; the performance of this level of theory is compared to other methods. Rigorous application of the multirotamer TST methodology in an harmonic oscillator approximation based on this data yields a rate coefficient of k(298 K,1 atm)=1.4×105 s-1, and an Arrhenius expression k(T,1 atm)=1.43×1011 exp(-8.17 kcal mol-1/RT) s-1, which both closely match the experimental recommendations in the literature. The T-dependence is substantially influenced by the multirotamer treatment, as well as by the tunneling and fall-off corrections. The present results are compared to those of simplified TST calculations based solely on the properties of the lowest energy 1-butoxy rotamer.
Chain representations of Open Quantum Systems and Lieb-Robinson like bounds for the dynamics

NASA Astrophysics Data System (ADS)

Woods, Mischa

2013-03-01

This talk is concerned with the mapping of the Hamiltonian of open quantum systems onto chain representations, which forms the basis for a rigorous theory of the interaction of a system with its environment. This mapping progresses as an interaction which gives rise to a sequence of residual spectral densities of the system. The rigorous mathematical properties of this mapping have been unknown so far. Here we develop the theory of secondary measures to derive an analytic, expression for the sequence solely in terms of the initial measure and its associated orthogonal polynomials of the first and second kind. These mappings can be thought of as taking a highly nonlocal Hamiltonian to a local Hamiltonian. In the latter, a Lieb-Robinson like bound for the dynamics of the open quantum system makes sense. We develop analytical bounds on the error to observables of the system as a function of time when the semi-infinite chain in truncated at some finite length. The fact that this is possible shows that there is a finite ``Speed of sound'' in these chain representations. This has many implications of the simulatability of open quantum systems of this type and demonstrates that a truncated chain can faithfully reproduce the dynamics at shorter times. These results make a significant and mathematically rigorous contribution to the understanding of the theory of open quantum systems; and pave the way towards the efficient simulation of these systems, which within the standard methods, is often an intractable problem. EPSRC CDT in Controlled Quantum Dynamics, EU STREP project and Alexander von Humboldt Foundation
Mode-splitting of a non-polarizing guided mode resonance filter by substrate overetching effect

NASA Astrophysics Data System (ADS)

Saleem, Muhammad Rizwan; Honkanen, Seppo; Turunen, Jari

2014-03-01

We investigate substrate overetch effect on resonance properties of sub-wavelength titanium oxide (TiO2) Guided Mode Resonance Filters (TiO2-GMRFs). The TiO2-GMRF is designed and fabricated to possess a non-polarizing behavior, which is strongly dependent on substrate (fused silica) overetch depth. For non-polarizing gratings at resonance, TE- and TM-modes have the same propagation constants. However, an overetch substrate effect results in splitting of the degenerate modes, which is studied theoretically and experimentally. The TiO2-SiO2 GMRFs are designed by Fourier Modal method (FMM) based on the rigorous calculation of electromagnetic diffraction theory at a designed wavelength of 850 nm. The TiO2-SiO2 gratings are fabricated by Atomic Layer Deposition (ALD), Electron Beam Lithography (EBL), and Reactive Ion Etching (RIE), and they are subsequently characterized structurally by Scanning Electron Microscopy (SEM) and optically by a spectroscopic ellipsometer. Several grating samples are fabricated by gradually increasing the overetch depth into fused silica and measuring the extent of TE- and TM-mode-splitting. A close agreement between the calculated and experimentally measured resonance wavelength spectral shift is found to describe the mode splitting of non-polarizing gratings.
Engineering the on-axis intensity of Bessel beam by a feedback tuning loop

NASA Astrophysics Data System (ADS)

Li, Runze; Yu, Xianghua; Yang, Yanlong; Peng, Tong; Yao, Baoli; Zhang, Chunmin; Ye, Tong

2018-02-01

The Bessel beam belongs to a typical class of non-diffractive optical fields that are characterized by their invariant focal profiles along the propagation direction. However, ideal Bessel beams only rigorously exist in theory; Bessel beams generated in the lab are quasi-Bessel beams with finite focal extensions and varying intensity profiles along the propagation axis. The ability to engineer the on-axis intensity profile to the desired shape is essential for many applications. Here we demonstrate an iterative optimization-based approach to engineering the on-axis intensity of Bessel beams. The genetic algorithm is used to demonstrate this approach. Starting with a traditional axicon phase mask, in the design process, the computed on-axis beam profile is fed into a feedback tuning loop of an iterative optimization process, which searches for an optimal radial phase distribution that can generate a generalized Bessel beam with the desired onaxis intensity profile. The experimental implementation involves a fine-tuning process that adjusts the originally targeted profile so that the optimization process can optimize the phase mask to yield an improved on-axis profile. Our proposed method has been demonstrated in engineering several zeroth-order Bessel beams with customized on-axis profiles. High accuracy and high energy throughput merit its use in many applications.
EVALUATION OF THE COLD PIPE PRECHARGER

EPA Science Inventory

The article gives results of an evaluation of the performance of the cold pipe precharger, taking a more rigorous approach than had been previously taken. The approach required detailed descriptions of electrical characteristics, electro-hydrodynamics, and charging theory. The co...
The Influence of Academic Rigor on Factors Related to College Student Persistence

ERIC Educational Resources Information Center

Braxton, John M.; Francis, Clay H.

2018-01-01

This chapter describes research findings that show a positive relationship between higher order examination questions and core concepts of empirically supported theories of college student persistence for both residential and commuter colleges and universities.
Understanding photon sideband statistics and correlation for determining phonon coherence

NASA Astrophysics Data System (ADS)

Ding, Ding; Yin, Xiaobo; Li, Baowen

2018-01-01

Generating and detecting coherent high-frequency heat-carrying phonons have been topics of great interest in recent years. Although there have been successful attempts in generating and observing coherent phonons, rigorous techniques to characterize and detect phonon coherence in a crystalline material have been lagging compared to what has been achieved for photons. One main challenge is a lack of detailed understanding of how detection signals for phonons can be related to coherence. The quantum theory of photoelectric detection has greatly advanced the ability to characterize photon coherence in the past century, and a similar theory for phonon detection is necessary. Here, we reexamine the optical sideband fluorescence technique that has been used to detect high-frequency phonons in materials with optically active defects. We propose a quantum theory of phonon detection using the sideband technique and found that there are distinct differences in sideband counting statistics between thermal and coherent phonons. We further propose a second-order correlation function unique to sideband signals that allows for a rigorous distinction between thermal and coherent phonons. Our theory is relevant to a correlation measurement with nontrivial response functions at the quantum level and can potentially bridge the gap of experimentally determining phonon coherence to be on par with that of photons.
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.
Diffractive Optics: Design, Fabrication, and Applications, Technical Digest Series, Volume 9, 1992

DTIC Science & Technology

1992-01-01

integration of optoelec- lens are presented and discussed. (p. 8) tronic chips with the passive glass optics. (p. 26) 10:00 am-10:30 am Coffee Break 2...optical pickup, Wai-Hon Lee, HOETRON, Inc. This paper discusses the recent pro- 3:30 pm-4:00 pm COFFEE BREAK gress in miniaturization of optical pickup...compared to 0th-order EMT and to 10:00 am-10:30 am COFFEE BREAK a rigorous coupled wave approach. (p. 44) 5:10 pm CABILDO ROOM MD4 Filter properties of
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.

BINARY CORRELATIONS IN IONIZED GASES

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

Balescu, R.; Taylor, H.S.

1961-01-01

An equation of evolution for the binary distribution function in a classical homogeneous, nonequilibrium plasma was derived. It is shown that the asymptotic (long-time) solution of this equation is the Debye distribution, thus providing a rigorous dynamical derivation of the equilibrium distribution. This proof is free from the fundamental conceptual difficulties of conventional equilibrium derivations. Out of equilibrium, a closed formula was obtained for the long living correlations, in terms of the momentum distribution function. These results should form an appropriate starting point for a rigorous theory of transport phenomena in plasmas, including the effect of molecular correlations. (auth)
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)
Rigorous vector wave propagation for arbitrary flat media

NASA Astrophysics Data System (ADS)

Bos, Steven P.; Haffert, Sebastiaan Y.; Keller, Christoph U.

2017-08-01

Precise modelling of the (off-axis) point spread function (PSF) to identify geometrical and polarization aberrations is important for many optical systems. In order to characterise the PSF of the system in all Stokes parameters, an end-to-end simulation of the system has to be performed in which Maxwell's equations are rigorously solved. We present the first results of a python code that we are developing to perform multiscale end-to-end wave propagation simulations that include all relevant physics. Currently we can handle plane-parallel near- and far-field vector diffraction effects of propagating waves in homogeneous isotropic and anisotropic materials, refraction and reflection of flat parallel surfaces, interference effects in thin films and unpolarized light. We show that the code has a numerical precision on the order of 10-16 for non-absorbing isotropic and anisotropic materials. For absorbing materials the precision is on the order of 10-8. The capabilities of the code are demonstrated by simulating a converging beam reflecting from a flat aluminium mirror at normal incidence.
Collisional damping rates for plasma waves

NASA Astrophysics Data System (ADS)

Tigik, S. F.; Ziebell, L. F.; Yoon, P. H.

2016-06-01

The distinction between the plasma dynamics dominated by collisional transport versus collective processes has never been rigorously addressed until recently. A recent paper [P. H. Yoon et al., Phys. Rev. E 93, 033203 (2016)] formulates for the first time, a unified kinetic theory in which collective processes and collisional dynamics are systematically incorporated from first principles. One of the outcomes of such a formalism is the rigorous derivation of collisional damping rates for Langmuir and ion-acoustic waves, which can be contrasted to the heuristic customary approach. However, the results are given only in formal mathematical expressions. The present brief communication numerically evaluates the rigorous collisional damping rates by considering the case of plasma particles with Maxwellian velocity distribution function so as to assess the consequence of the rigorous formalism in a quantitative manner. Comparison with the heuristic ("Spitzer") formula shows that the accurate damping rates are much lower in magnitude than the conventional expression, which implies that the traditional approach over-estimates the importance of attenuation of plasma waves by collisional relaxation process. Such a finding may have a wide applicability ranging from laboratory to space and astrophysical plasmas.
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.
Quantization of Space-like States in Lorentz-Violating Theories

NASA Astrophysics Data System (ADS)

Colladay, Don

2018-01-01

Lorentz violation frequently induces modified dispersion relations that can yield space-like states that impede the standard quantization procedures. In certain cases, an extended Hamiltonian formalism can be used to define observer-covariant normalization factors for field expansions and phase space integrals. These factors extend the theory to include non-concordant frames in which there are negative-energy states. This formalism provides a rigorous way to quantize certain theories containing space-like states and allows for the consistent computation of Cherenkov radiation rates in arbitrary frames and avoids singular expressions.
Magnetoacoustic Tomography with Magnetic Induction: A Rigorous Theory

PubMed Central

Ma, Qingyu; He, Bin

2013-01-01

We have proposed a new theory on mechanism of the magnetoacoustic signal generation with magnetic induction for an object with an arbitrary shape. An object under a static magnetic field emits acoustic signals when excited by a time-varying magnetic field, and that the acoustic waveform is mainly generated at the conductivity boundaries within the object. The proposed theory on the magnetoacoustic tomography with magnetic induction produced highly consistent results among computational and experimental paradigms in a two-layer sample phantom and suggests the potential applications for bioimpedance imaging. PMID:18270025
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.
Theory of ground state factorization in quantum cooperative systems.

PubMed

Giampaolo, Salvatore M; Adesso, Gerardo; Illuminati, Fabrizio

2008-05-16

We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows us to determine rigorously the existence, location, and exact form of separable ground states in a large variety of, generally nonexactly solvable, spin models belonging to different universality classes. The theory applies to translationally invariant systems, irrespective of spatial dimensionality, and for spin-spin interactions of arbitrary range.
Vibrations of cantilevered circular cylindrical shells Shallow versus deep shell theory

NASA Technical Reports Server (NTRS)

Lee, J. K.; Leissa, A. W.; Wang, A. J.

1983-01-01

Free vibrations of cantilevered circular cylindrical shells having rectangular planforms are studied in this paper by means of the Ritz method. The deep shell theory of Novozhilov and Goldenveizer is used and compared with the usual shallow shell theory for a wide range of shell parameters. A thorough convergence study is presented along with comparisons to previously published finite element solutions and experimental results. Accurately computed frequency parameters and mode shapes for various shell configurations are presented. The present paper appears to be the first comprehensive study presenting rigorous comparisons between the two shell theories in dealing with free vibrations of cantilevered cylindrical shells.
Graph Theory-Based Pinning Synchronization of Stochastic Complex Dynamical Networks.

PubMed

Li, Xiao-Jian; Yang, Guang-Hong

2017-02-01

This paper is concerned with the adaptive pinning synchronization problem of stochastic complex dynamical networks (CDNs). Based on algebraic graph theory and Lyapunov theory, pinning controller design conditions are derived, and the rigorous convergence analysis of synchronization errors in the probability sense is also conducted. Compared with the existing results, the topology structures of stochastic CDN are allowed to be unknown due to the use of graph theory. In particular, it is shown that the selection of nodes for pinning depends on the unknown lower bounds of coupling strengths. Finally, an example on a Chua's circuit network is given to validate the effectiveness of the theoretical results.
A novel method to fabricate silicon tubular gratings with broadband antireflection and super-hydrophobicity.

PubMed

Gao, Yang; Shi, Tielin; Tan, Xianhua; Liao, Guanglan

2014-06-01

We have developed a novel method to fabricate micro/nano structure based on the coherent diffraction lithography, and acquired periodic silicon tubular gratings with deep nano-scale tapered profiles at the top part. The optical properties of these tubular gratings were similar to an effective gradient-index antireflective surface, resulting in a broadband antireflective combining super-hydrophobic behavior. The mechanism of the method was simulated by rigorous coupled wave analysis algorithms. Then coherent diffraction lithography by use of suitable mask, in which periodic micro-scale circular opaque patters were distributed, was realized on the traditional aligner. Due to coherent diffraction, we obtained enough light intensity for photoresist exposure under the center of the opaque area in the mask together with transparent areas. The tapered line profiles and hollow photoresist gratings over large areas could be fabricated on the silicon wafer after development. The dry etching process was carried out, and high aspect ratio silicon tubular gratings with deep tapered profiles at the top were fabricated. The optical property and wettability of the structure were verified, proving that the proposed method and obtained micro/nano structure provide application potential in the future.
Nanophotonic light-trapping theory for solar cells

NASA Astrophysics Data System (ADS)

Yu, Zongfu; Raman, Aaswath; Fan, Shanhui

2011-11-01

Conventional light-trapping theory, based on a ray-optics approach, was developed for standard thick photovoltaic cells. The classical theory established an upper limit for possible absorption enhancement in this context and provided a design strategy for reaching this limit. This theory has become the foundation for light management in bulk silicon PV cells, and has had enormous influence on the optical design of solar cells in general. This theory, however, is not applicable in the nanophotonic regime. Here we develop a statistical temporal coupled-mode theory of light trapping based on a rigorous electromagnetic approach. Our theory reveals that the standard limit can be substantially surpassed when optical modes in the active layer are confined to deep-subwavelength scale, opening new avenues for highly efficient next-generation solar cells.
Study designs for identifying risk compensation behavior among users of biomedical HIV prevention technologies: balancing methodological rigor and research ethics.

PubMed

Underhill, Kristen

2013-10-01

The growing evidence base for biomedical HIV prevention interventions - such as oral pre-exposure prophylaxis, microbicides, male circumcision, treatment as prevention, and eventually prevention vaccines - has given rise to concerns about the ways in which users of these biomedical products may adjust their HIV risk behaviors based on the perception that they are prevented from infection. Known as risk compensation, this behavioral adjustment draws on the theory of "risk homeostasis," which has previously been applied to phenomena as diverse as Lyme disease vaccination, insurance mandates, and automobile safety. Little rigorous evidence exists to answer risk compensation concerns in the biomedical HIV prevention literature, in part because the field has not systematically evaluated the study designs available for testing these behaviors. The goals of this Commentary are to explain the origins of risk compensation behavior in risk homeostasis theory, to reframe risk compensation as a testable response to the perception of reduced risk, and to assess the methodological rigor and ethical justification of study designs aiming to isolate risk compensation responses. Although the most rigorous methodological designs for assessing risk compensation behavior may be unavailable due to ethical flaws, several strategies can help investigators identify potential risk compensation behavior during Phase II, Phase III, and Phase IV testing of new technologies. Where concerns arise regarding risk compensation behavior, empirical evidence about the incidence, types, and extent of these behavioral changes can illuminate opportunities to better support the users of new HIV prevention strategies. This Commentary concludes by suggesting a new way to conceptualize risk compensation behavior in the HIV prevention context. Copyright © 2013 Elsevier Ltd. All rights reserved.
Study designs for identifying risk compensation behavior among users of biomedical HIV prevention technologies: Balancing methodological rigor and research ethics

PubMed Central

Underhill, Kristen

2014-01-01

The growing evidence base for biomedical HIV prevention interventions – such as oral pre-exposure prophylaxis, microbicides, male circumcision, treatment as prevention, and eventually prevention vaccines – has given rise to concerns about the ways in which users of these biomedical products may adjust their HIV risk behaviors based on the perception that they are prevented from infection. Known as risk compensation, this behavioral adjustment draws on the theory of “risk homeostasis,” which has previously been applied to phenomena as diverse as Lyme disease vaccination, insurance mandates, and automobile safety. Little rigorous evidence exists to answer risk compensation concerns in the biomedical HIV prevention literature, in part because the field has not systematically evaluated the study designs available for testing these behaviors. The goals of this Commentary are to explain the origins of risk compensation behavior in risk homeostasis theory, to reframe risk compensation as a testable response to the perception of reduced risk, and to assess the methodological rigor and ethical justification of study designs aiming to isolate risk compensation responses. Although the most rigorous methodological designs for assessing risk compensation behavior may be unavailable due to ethical flaws, several strategies can help investigators identify potential risk compensation behavior during Phase II, Phase III, and Phase IV testing of new technologies. Where concerns arise regarding risk compensation behavior, empirical evidence about the incidence, types, and extent of these behavioral changes can illuminate opportunities to better support the users of new HIV prevention strategies. This Commentary concludes by suggesting a new way to conceptualize risk compensation behavior in the HIV prevention context. PMID:23597916
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.
Do behavioral scientists really understand HIV-related sexual risk behavior? A systematic review of longitudinal and experimental studies predicting sexual behavior.

PubMed

Huebner, David M; Perry, Nicholas S

2015-10-01

Behavioral interventions to reduce sexual risk behavior depend on strong health behavior theory. By identifying the psychosocial variables that lead causally to sexual risk, theories provide interventionists with a guide for how to change behavior. However, empirical research is critical to determining whether a particular theory adequately explains sexual risk behavior. A large body of cross-sectional evidence, which has been reviewed elsewhere, supports the notion that certain theory-based constructs (e.g., self-efficacy) are correlates of sexual behavior. However, given the limitations of inferring causality from correlational research, it is essential that we review the evidence from more methodologically rigorous studies (i.e., longitudinal and experimental designs). This systematic review identified 44 longitudinal studies in which investigators attempted to predict sexual risk from psychosocial variables over time. We also found 134 experimental studies (i.e., randomized controlled trials of HIV interventions), but of these only 9 (6.7 %) report the results of mediation analyses that might provide evidence for the validity of health behavior theories in predicting sexual behavior. Results show little convergent support across both types of studies for most traditional, theoretical predictors of sexual behavior. This suggests that the field must expand the body of empirical work that utilizes the most rigorous study designs to test our theoretical assumptions. The inconsistent results of existing research would indicate that current theoretical models of sexual risk behavior are inadequate, and may require expansion or adaptation.
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.
Resource Theory of Superposition

NASA Astrophysics Data System (ADS)

Theurer, T.; Killoran, N.; Egloff, D.; Plenio, M. B.

2017-12-01

The superposition principle lies at the heart of many nonclassical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear independent states. This theory is a generalization of resource theories of coherence. We determine the general structure of operations which do not create superposition, find a fundamental connection to unambiguous state discrimination, and propose several quantitative superposition measures. Using this theory, we show that trace decreasing operations can be completed for free which, when specialized to the theory of coherence, resolves an outstanding open question and is used to address the free probabilistic transformation between pure states. Finally, we prove that linearly independent superposition is a necessary and sufficient condition for the faithful creation of entanglement in discrete settings, establishing a strong structural connection between our theory of superposition and entanglement theory.
Discerning comb and Fourier mean frequency from an fs laser based on the principle of non-interaction of waves

NASA Astrophysics Data System (ADS)

Roychoudhuri, Chandrasekhar; Prasad, Narasimha

2012-02-01

The key objective of this article is to underscore that as engineers, we need to pay close attention in repeatedly validating and re-validating the underlying physical processes behind a working theory that models a phenomenon we are using to create tools and technologies. We use the test case, the prevailing mode-lock theory, to illustrate our views by identifying existing contradictions and showing approach towards their resolution by identifying the relevant physical processes. The current theory tells us that the Fourier summation of all the allowed cavity modes directly produces the train of pulses. It effectively assumes that electromagnetic (EM) waves are capable of re-organizing their spatial and temporal energy distribution to generate a train of temporal pulses while preserving the spatial mode energy distribution. The implication is that EM waves interact with each other by themselves. Even though the theory is working, we have three logical problems. First, in the real world, in the linear domain, waves never interact with each other. On careful analysis of all types of interference experiments, we will recognize that only in the presence of some interacting material medium can we observe the physical superposition EFFECT. In other words, detectors carryout the superposition effect we call interference phenomenon, through the summation of their multiple simultaneous linear stimulations and then absorbing energy proportional to the square modulus of the sum total stimulation. Second, a Fourier monochromatic wave, existing in all space and time, is a non-causal hypothesis. Just because our theories are working does not mean that we have understood the real physical interaction processes in nature. We need to build our theories based upon space and time finite EM wave packet containing a finite amount of energy, which is a causal approach. Third, in spite of staggering successes of Quantum Mechanics, we do not yet have a self consistent model for space and time finite model of a photon. QM only predicts that EM energy emission (spontaneous and stimulated) takes place only in a discrete amount at a time from atoms and molecules. It does not give us recipe about how to visualize a propagating photon as it expands diffractively. However, Huygens-Fresnel's classical diffraction integral gives us a rigorous model, which is the cornerstone of modeling evolution of laser cavity modes, CW or pulsed. In this paper, we highlight the contradictions that arise out of the prevailing mode-lock theory and resolve them by using causal models, already underscored above. For example, there are now a wide range of very successful technological applications of the frequency comb extracted out of fs lasers. If the Fourier summation were the correct physical process, then all the cavity modes would have been summed (converted) into a single mean frequency around the gain line center for perfectly mode-locked systems. Further, sending such fs pulses through an optical spectrometer would have always displayed a transform limited fringe, centering on the mean Fourier frequency, rather than generating the comb frequencies, albeit instrumentally broadened. Output pulse train from a phase locked laser is functionally produced due to the oscillatory time-gating behavior of the intra-cavity phase-locking devices. So, we need to pay more attention to the fast temporal behavior of the materials we use for achieving very fast time-gating, since this material imposes phase locking on the cavity modes to enhance its own high-contrast time-gating behavior.
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
The fraction of myosin motors that participate in isometric contraction of rabbit muscle fibers at near-physiological temperature.

PubMed

Tsaturyan, Andrey K; Bershitsky, Sergey Y; Koubassova, Natalia A; Fernandez, Manuel; Narayanan, Theyencheri; Ferenczi, Michael A

2011-07-20

The duty ratio, or the part of the working cycle in which a myosin molecule is strongly attached to actin, determines motor processivity and is required to evaluate the force generated by each molecule. In muscle, it is equal to the fraction of myosin heads that are strongly, or stereospecifically, bound to the thin filaments. Estimates of this fraction during isometric contraction based on stiffness measurements or the intensities of the equatorial or meridional x-ray reflections vary significantly. Here, we determined this value using the intensity of the first actin layer line, A1, in the low-angle x-ray diffraction patterns of permeable fibers from rabbit skeletal muscle. We calibrated the A1 intensity by considering that the intensity in the relaxed and rigor states corresponds to 0% and 100% of myosin heads bound to actin, respectively. The fibers maximally activated with Ca(2+) at 4°C were heated to 31-34°C with a Joule temperature jump (T-jump). Rigor and relaxed-state measurements were obtained on the same fibers. The intensity of the inner part of A1 during isometric contraction compared with that in rigor corresponds to 41-43% stereospecifically bound myosin heads at near-physiological temperature, or an average force produced by a head of ~6.3 pN. Copyright © 2011 Biophysical Society. Published by Elsevier Inc. All rights reserved.
75 FR 28287 - Final Plan for Fiscal Year 2010

Federal Register 2010, 2011, 2012, 2013, 2014

2010-05-20

... Federal agencies. In keeping with OJJDP's mission, these programs are designed to help strengthen the.../intervention based on sound theory and evaluative literature, which has yet to be evaluated rigorously. OJJDP..., and research and evaluation projects designed to improve juvenile justice systems and delinquency...
Textbook Forum: Confusion in the Expressions for Transport Coefficients.

ERIC Educational Resources Information Center

Earl, Boyd L.

1989-01-01

Notes that the rigorous kinetic theory, based on the Boltzmann equation, does not yield exact results although some texts claim this to be so. Stresses that they should be presented as approximations with an indication that refinements in the values are possible. (MVL)
Reconstructing Dewey: Dialectics and Democratic Education

ERIC Educational Resources Information Center

Jackson, Jeff

2012-01-01

This essay aims to demonstrate the theoretical purchase offered by linking Dewey's educational theory with a rigorous account of dialectical development. Drawing on recent literature which emphasizes the continuing influence of Hegel on Dewey's thought throughout the latter's career, this essay reconstructs Dewey's argument regarding the…
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.
Random Matrix Theory and the Anderson Model

NASA Astrophysics Data System (ADS)

Bellissard, Jean

2004-08-01

This paper is devoted to a discussion of possible strategies to prove rigorously the existence of a metal-insulator Anderson transition for the Anderson model in dimension d≥3. The possible criterions used to define such a transition are presented. It is argued that at low disorder the lowest order in perturbation theory is described by a random matrix model. Various simplified versions for which rigorous results have been obtained in the past are discussed. It includes a free probability approach, the Wegner n-orbital model and a class of models proposed by Disertori, Pinson, and Spencer, Comm. Math. Phys. 232:83-124 (2002). At last a recent work by Magnen, Rivasseau, and the author, Markov Process and Related Fields 9:261-278 (2003) is summarized: it gives a toy modeldescribing the lowest order approximation of Anderson model and it is proved that, for d=2, its density of states is given by the semicircle distribution. A short discussion of its extension to d≥3 follows.
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
Grounded theory in medical education research: AMEE Guide No. 70.

PubMed

Watling, Christopher J; Lingard, Lorelei

2012-01-01

Qualitative research in general and the grounded theory approach in particular, have become increasingly prominent in medical education research in recent years. In this Guide, we first provide a historical perspective on the origin and evolution of grounded theory. We then outline the principles underlying the grounded theory approach and the procedures for doing a grounded theory study, illustrating these elements with real examples. Next, we address key critiques of grounded theory, which continue to shape how the method is perceived and used. Finally, pitfalls and controversies in grounded theory research are examined to provide a balanced view of both the potential and the challenges of this approach. This Guide aims to assist researchers new to grounded theory to approach their studies in a disciplined and rigorous fashion, to challenge experienced researchers to reflect on their assumptions, and to arm readers of medical education research with an approach to critically appraising the quality of grounded theory studies.
Lower-Secondary Introductory Chemistry Course: A Novel Approach Based on Science-Education Theories, with Emphasis on the Macroscopic Approach, and the Delayed Meaningful Teaching of the Concepts of Molecule and Atom

ERIC Educational Resources Information Center

Tsaparlis, Georgios; Kolioulis, Dimitrios; Pappa, Eleni

2010-01-01

We present a programme for a novel introductory lower-secondary chemistry course (seventh or eighth grade) that aims at the application of theories of science education, and in particular of conceptual/meaningful learning and of teaching methodology that encourages active and inquiry forms of learning The approach is rigorous with careful use of…
Unperturbed Schelling Segregation in Two or Three Dimensions

NASA Astrophysics Data System (ADS)

Barmpalias, George; Elwes, Richard; Lewis-Pye, Andrew

2016-09-01

Schelling's models of segregation, first described in 1969 (Am Econ Rev 59:488-493, 1969) are among the best known models of self-organising behaviour. Their original purpose was to identify mechanisms of urban racial segregation. But his models form part of a family which arises in statistical mechanics, neural networks, social science, and beyond, where populations of agents interact on networks. Despite extensive study, unperturbed Schelling models have largely resisted rigorous analysis, prior results generally focusing on variants in which noise is introduced into the dynamics, the resulting system being amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory (Young in Individual strategy and social structure: an evolutionary theory of institutions, Princeton University Press, Princeton, 1998). A series of recent papers (Brandt et al. in: Proceedings of the 44th annual ACM symposium on theory of computing (STOC 2012), 2012); Barmpalias et al. in: 55th annual IEEE symposium on foundations of computer science, Philadelphia, 2014, J Stat Phys 158:806-852, 2015), has seen the first rigorous analyses of 1-dimensional unperturbed Schelling models, in an asymptotic framework largely unknown in statistical mechanics. Here we provide the first such analysis of 2- and 3-dimensional unperturbed models, establishing most of the phase diagram, and answering a challenge from Brandt et al. in: Proceedings of the 44th annual ACM symposium on theory of computing (STOC 2012), 2012).

Dynamic field theory and executive functions: lending explanation to current theories of development.

PubMed

Morton, J Bruce

2014-06-01

Buss and Spencer's monograph is an impressive achievement that is sure to have a lasting impact on the field of child development. The dynamic field theory (DFT) model that forms the heart of this contribution is ambitious in scope, detailed in its implementation, and rigorously tested against data, old and new. As such, the ideas contained in this fine document represent a qualitative advance in our understanding of young children's behavior, and lay a foundation for future research into the developmental origins of executive functioning. © 2014 The Society for Research in Child Development, Inc.
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
Imaging the Gouy phase shift in photonic jets with a wavefront sensor.

PubMed

Bon, Pierre; Rolly, Brice; Bonod, Nicolas; Wenger, Jérôme; Stout, Brian; Monneret, Serge; Rigneault, Hervé

2012-09-01

A wavefront sensor is used as a direct observation tool to image the Gouy phase shift in photonic nanojets created by micrometer-sized dielectric spheres. The amplitude and phase distributions of light are found in good agreement with a rigorous electromagnetic computation. Interestingly the observed phase shift when travelling through the photonic jet is a combination of the awaited π Gouy shift and a phase shift induced by the bead refraction. Such direct spatial phase shift observation using wavefront sensors would find applications in microscopy, diffractive optics, optical trapping, and point spread function engineering.
Simple design of slanted grating with simplified modal method.

PubMed

Li, Shubin; Zhou, Changhe; Cao, Hongchao; Wu, Jun

2014-02-15

A simplified modal method (SMM) is presented that offers a clear physical image for subwavelength slanted grating. The diffraction characteristic of the slanted grating under Littrow configuration is revealed by the SMM as an equivalent rectangular grating, which is in good agreement with rigorous coupled-wave analysis. Based on the equivalence, we obtained an effective analytic solution for simplifying the design and optimization of a slanted grating. It offers a new approach for design of the slanted grating, e.g., a 1×2 beam splitter can be easily designed. This method should be helpful for designing various new slanted grating devices.
Three-port beam splitter of a binary fused-silica grating.

PubMed

Feng, Jijun; Zhou, Changhe; Wang, Bo; Zheng, Jiangjun; Jia, Wei; Cao, Hongchao; Lv, Peng

2008-12-10

A deep-etched polarization-independent binary fused-silica phase grating as a three-port beam splitter is designed and manufactured. The grating profile is optimized by use of the rigorous coupled-wave analysis around the 785 nm wavelength. The physical explanation of the grating is illustrated by the modal method. Simple analytical expressions of the diffraction efficiencies and modal guidelines for the three-port beam splitter grating design are given. Holographic recording technology and inductively coupled plasma etching are used to manufacture the fused-silica grating. Experimental results are in good agreement with the theoretical values.
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.
DOE Theory Graduate Student Fellowship: Gustavo Marques Tavares

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

Schmaltz, Martin

2015-12-30

Marques Tavares was awarded a fellowship for his proposal “The ttbar asymmetry and beyond” to starting in September 2012. This is the final report summarizing the research activities and accomplishments achieved with this grant support. With support from the DOE graduate fellowship Marques Tavares, Katz and Xu at BU have investigated a new technique for obtaining quantitative results in strongly coupled field theories with broken conformal invariance. Such theories are especially interesting as they may be candidates for physics beyond the standard model with possible applications to strongly coupled electroweak symmetry breaking. However, because of the strong coupling even qualitativemore » results about the spectrum of such theories are not rigorously understood.« less
Horseshoes in a Chaotic System with Only One Stable Equilibrium

NASA Astrophysics Data System (ADS)

Huan, Songmei; Li, Qingdu; Yang, Xiao-Song

To confirm the numerically demonstrated chaotic behavior in a chaotic system with only one stable equilibrium reported by Wang and Chen, we resort to Poincaré map technique and present a rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoes theory.
Towards a Unified Theory of Engineering Education

ERIC Educational Resources Information Center

Salcedo Orozco, Oscar H.

2017-01-01

STEM education is an interdisciplinary approach to learning where rigorous academic concepts are coupled with real-world lessons and activities as students apply science, technology, engineering, and mathematics in contexts that make connections between school, community, work, and the global enterprise enabling STEM literacy (Tsupros, Kohler and…
A Commentary on Hughes: The Tension between Pragmatics and Rigor.

ERIC Educational Resources Information Center

Doll, Beth

2000-01-01

Argues against Hughes' recommendation for a comprehensive clinical case planning process since it cannot displace consumers' need for psychological practice guidelines which can be applied autonomously. Challenges the notion that theory has been omitted from current research on empirically supported treatments. Concludes the problem facing…
Extreme Response Style: Which Model Is Best?

ERIC Educational Resources Information Center

Leventhal, Brian

2017-01-01

More robust and rigorous psychometric models, such as multidimensional Item Response Theory models, have been advocated for survey applications. However, item responses may be influenced by construct-irrelevant variance factors such as preferences for extreme response options. Through empirical and simulation methods, this study evaluates the use…
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.
Diffraction of stochastic electromagnetic fields by a hole in a thin film with real optical properties

NASA Astrophysics Data System (ADS)

Dorofeyev, Illarion

2008-08-01

The classical Kirchhoff theory of diffraction is extended to the case of real optical properties of a screen and its finite thickness. A spectral power density of diffracted electromagnetic fields by a hole in a thin film with real optical properties was calculated. The problem was solved by use of the vector Green theorems and related Green function of the boundary value problem. A spectral and spatial selectivity of the considered system was demonstrated. Diffracted patterns were calculated for the coherent and incoherent incident fields in case of holes array in a screen of perfect conductivity.
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…
Beam splitting of low-contrast binary gratings under second Bragg angle incidence.

PubMed

Zheng, Jiangjun; Zhou, Changhe; Wang, Bo; Feng, Jijun

2008-05-01

Beam splitting of low-contrast rectangular gratings under second Bragg angle incidence is studied. The grating period is between lambda and 2lambda. The diffraction behaviors of the three transmitted propagating orders are illustrated by analyzing the first three propagating grating modes. From a simplified modal approach, the design conditions of gratings as a high-efficiency element with most of its energy concentrated in the -2nd transmitted order (~90%) and of gratings as a 1 x 2 beam splitter with a total efficiency over 90% are derived. The grating parameters for achieving exactly the splitting pattern by use of rigorous coupled-wave analysis verified the design method. A 1 x 3 beam splitter is also demonstrated. Moreover, the polarization-dependent diffraction behaviors are investigated, which suggest the possibility of designing polarization-selective elements under such a configuration. The proposed concept of using the second Bragg angle should be helpful for developing new grating-based devices.
Shape dynamics and Mach's principles: Gravity from conformal geometrodynamics

NASA Astrophysics Data System (ADS)

Gryb, Sean

2012-04-01

In this PhD thesis, we develop a new approach to classical gravity starting from Mach's principles and the idea that the local shape of spatial configurations is fundamental. This new theory, "shape dynamics", is equivalent to general relativity but differs in an important respect: shape dynamics is a theory of dynamic conformal 3-geometry, not a theory of spacetime. Equivalence is achieved by trading foliation invariance for local conformal invariance (up to a global scale). After the trading, what is left is a gauge theory invariant under 3d diffeomorphisms and conformal transformations that preserve the volume of space. The local canonical constraints are linear and the constraint algebra closes with structure constants. Shape dynamics, thus, provides a novel new starting point for quantum gravity. The procedure for the trading of symmetries was inspired by a technique called "best matching". We explain best matching and its relation to Mach's principles. The key features of best matching are illustrated through finite dimensional toy models. A general picture is then established where relational theories are treated as gauge theories on configuration space. Shape dynamics is then constructed by applying best matching to conformal geometry. We then study shape dynamics in more detail by computing its Hamiltonian and Hamilton-Jacobi functional perturbatively. This thesis is intended as a pedagogical but complete introduction to shape dynamics and the Machian ideas that led to its discovery. The reader is encouraged to start with the introduction, which gives a conceptual outline and links to the relevant sections in the text for a more rigorous exposition. When full rigor is lacking, references to the literature are given. It is hoped that this thesis may provide a starting point for anyone interested in learning about shape dynamics.
Ray-optical theory of broadband partially coherent emission

NASA Astrophysics Data System (ADS)

Epstein, Ariel; Tessler, Nir; Einziger, Pinchas D.

2013-04-01

We present a rigorous formulation of the effects of spectral broadening on emission of partially coherent source ensembles embedded in multilayered formations with arbitrarily shaped interfaces, provided geometrical optics is valid. The resulting ray-optical theory, applicable to a variety of optical systems from terahertz lenses to photovoltaic cells, quantifies the fundamental interplay between bandwidth and layer dimensions, and sheds light on common practices in optical analysis of statistical fields, e.g., disregarding multiple reflections or neglecting interference cross terms.
Selection theory of free dendritic growth in a potential flow.

PubMed

von Kurnatowski, Martin; Grillenbeck, Thomas; Kassner, Klaus

2013-04-01

The Kruskal-Segur approach to selection theory in diffusion-limited or Laplacian growth is extended via combination with the Zauderer decomposition scheme. This way nonlinear bulk equations become tractable. To demonstrate the method, we apply it to two-dimensional crystal growth in a potential flow. We omit the simplifying approximations used in a preliminary calculation for the same system [Fischaleck, Kassner, Europhys. Lett. 81, 54004 (2008)], thus exhibiting the capability of the method to extend mathematical rigor to more complex problems than hitherto accessible.
Residual stress determination in oxide layers at different length scales combining Raman spectroscopy and X-ray diffraction: Application to chromia-forming metallic alloys

DOE PAGES

Guerain, Mathieu; Grosseau-Poussard, Jean-Luc; Geandier, Guillaume; ...

2017-11-21

In oxidizing environments, the protection of metals and alloys against further oxidation at high temperature is provided by the oxide film itself. This protection is efficient only if the formed film adheres well to the metal (substrate), i.e., without microcracks and spalls induced by thermomechanical stresses. In this study, the residual stresses at both macroscopic and microscopic scales in the oxide film adhering to the substrate and over the damaged areas have been rigorously determined on the same samples for both techniques. Ni-30Cr and Fe-47Cr alloys have been oxidized together at 900 and 1000 °C, respectively, to create films withmore » a thickness of a few microns. A multi-scale approach was adopted: macroscopic stress was determined by conventional X-ray diffraction and Raman spectroscopy, while microscopic residual stress mappings were performed over different types of bucklings using Raman micro-spectroscopy and synchrotron micro-diffraction. A very good agreement is found at macro- and microscales between the residual stress values obtained with both techniques, giving confidence on the reliability of the measurements. In addition, relevant structural information at the interface between the metallic substrate and the oxide layer was collected by micro-diffraction, a non-destructive technique that allows mapping through the oxide layer, and both the grain size and the crystallographic orientation of the supporting polycrystalline metal located either under a buckling or not were measured.« less
Residual stress determination in oxide layers at different length scales combining Raman spectroscopy and X-ray diffraction: Application to chromia-forming metallic alloys

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

Guerain, Mathieu; Grosseau-Poussard, Jean-Luc; Geandier, Guillaume

In oxidizing environments, the protection of metals and alloys against further oxidation at high temperature is provided by the oxide film itself. This protection is efficient only if the formed film adheres well to the metal (substrate), i.e., without microcracks and spalls induced by thermomechanical stresses. In this study, the residual stresses at both macroscopic and microscopic scales in the oxide film adhering to the substrate and over the damaged areas have been rigorously determined on the same samples for both techniques. Ni-30Cr and Fe-47Cr alloys have been oxidized together at 900 and 1000 °C, respectively, to create films withmore » a thickness of a few microns. A multi-scale approach was adopted: macroscopic stress was determined by conventional X-ray diffraction and Raman spectroscopy, while microscopic residual stress mappings were performed over different types of bucklings using Raman micro-spectroscopy and synchrotron micro-diffraction. A very good agreement is found at macro- and microscales between the residual stress values obtained with both techniques, giving confidence on the reliability of the measurements. In addition, relevant structural information at the interface between the metallic substrate and the oxide layer was collected by micro-diffraction, a non-destructive technique that allows mapping through the oxide layer, and both the grain size and the crystallographic orientation of the supporting polycrystalline metal located either under a buckling or not were measured.« less
Residual stress determination in oxide layers at different length scales combining Raman spectroscopy and X-ray diffraction: Application to chromia-forming metallic alloys

NASA Astrophysics Data System (ADS)

Guerain, Mathieu; Grosseau-Poussard, Jean-Luc; Geandier, Guillaume; Panicaud, Benoit; Tamura, Nobumichi; Kunz, Martin; Dejoie, Catherine; Micha, Jean-Sebastien; Thiaudière, Dominique; Goudeau, Philippe

2017-11-01

In oxidizing environments, the protection of metals and alloys against further oxidation at high temperature is provided by the oxide film itself. This protection is efficient only if the formed film adheres well to the metal (substrate), i.e., without microcracks and spalls induced by thermomechanical stresses. In this study, the residual stresses at both macroscopic and microscopic scales in the oxide film adhering to the substrate and over the damaged areas have been rigorously determined on the same samples for both techniques. Ni-30Cr and Fe-47Cr alloys have been oxidized together at 900 and 1000 °C, respectively, to create films with a thickness of a few microns. A multi-scale approach was adopted: macroscopic stress was determined by conventional X-ray diffraction and Raman spectroscopy, while microscopic residual stress mappings were performed over different types of bucklings using Raman micro-spectroscopy and synchrotron micro-diffraction. A very good agreement is found at macro- and microscales between the residual stress values obtained with both techniques, giving confidence on the reliability of the measurements. In addition, relevant structural information at the interface between the metallic substrate and the oxide layer was collected by micro-diffraction, a non-destructive technique that allows mapping through the oxide layer, and both the grain size and the crystallographic orientation of the supporting polycrystalline metal located either under a buckling or not were measured.
Explaining the Sex Difference in Dyslexia

ERIC Educational Resources Information Center

Arnett, Anne B.; Pennington, Bruce F.; Peterson, Robin L.; Willcutt, Erik G.; DeFries, John C.; Olson, Richard K.

2017-01-01

Background: Males are diagnosed with dyslexia more frequently than females, even in epidemiological samples. This may be explained by greater variance in males' reading performance. Methods: We expand on previous research by rigorously testing the variance difference theory, and testing for mediation of the sex difference by cognitive correlates.…
Control Engineering, System Theory and Mathematics: The Teacher's Challenge

ERIC Educational Resources Information Center

Zenger, K.

2007-01-01

The principles, difficulties and challenges in control education are discussed and compared to the similar problems in the teaching of mathematics and systems science in general. The difficulties of today's students to appreciate the classical teaching of engineering disciplines, which are based on rigorous and scientifically sound grounds, are…
Full Angular Profile of the Coherent Polarization Opposition Effect

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Luck, Jean-Marc; Nieuwenhuizen, Theo M.

1999-01-01

We use the rigorous vector theory of weak photon localization for a semi-infinite medium composed of nonabsorbing Rayleigh scatterers to compute the full angular profile of the polarization opposition effect. The latter is caused by coherent backscattering of unpolarized incident light and accompanies the renowned backscattering intensity peak.
Alexander Meiklejohn in Search of Freedom and Dignity.

ERIC Educational Resources Information Center

Johnson, Tony W.

1982-01-01

Assesses the contributions of the philosopher/educator Alexander Meiklejohn. Discusses the influences of Jean-Jacques Rousseau, Immanuel Kant, and the U.S. Constitution on Meiklejohn's educational theories, which stressed that human freedom and dignity can be enhanced by rigorous examination of U.S. Supreme Court decisions and the meaning of…
Chinese Students' Satisfaction of the Study Abroad Experience

ERIC Educational Resources Information Center

Wang, Qinggang; Taplin, Ross; Brown, Alistair M.

2011-01-01

Purpose: Building upon McLeod and Wainwright's paradigm for rigorous scientific assessment of study abroad programs, this paper aims to use social learning theory to assess mainland Chinese students' satisfaction of the Chinese Curtin Student Accounting Academic Programme. Design/methodology/approach: A sample of mainland Chinese students enrolled…
Examining Multidimensional Middle Grade Outcomes after Early Elementary School Grade Retention

ERIC Educational Resources Information Center

Hwang, Sophia; Cappella, Elise; Schwartz, Kate

2016-01-01

Recently, researchers have begun to employ rigorous statistical methods and developmentally-informed theories to evaluate outcomes for students retained in non-kindergarten early elementary school. However, the majority of this research focuses on academic outcomes. Gaps remain regarding retention's effects on psychosocial outcomes important to…
Three Views of Systems Theories and Their Implications for Sustainability Education

ERIC Educational Resources Information Center

Porter, Terry; Cordoba, Jose

2009-01-01

Worldwide, there is an emerging interest in sustainability and sustainability education. A popular and promising approach is the use of systems thinking. However, the systems approach to sustainability has neither been clearly defined nor has its practical application followed any systematic rigor, resulting in confounded and underspecified…
Thermodynamic theory of intrinsic finite-size effects in PbTiO3 nanocrystals. I. Nanoparticle size-dependent tetragonal phase stability

NASA Astrophysics Data System (ADS)

Akdogan, E. K.; Safari, A.

2007-03-01

We propose a phenomenological intrinsic finite-size effect model for single domain, mechanically free, and surface charge compensated ΔG-P ⃗s-ξ space, which describes the decrease in tetragonal phase stability with decreasing ξ rigorously.
Researching the Study Abroad Experience

ERIC Educational Resources Information Center

McLeod, Mark; Wainwright, Philip

2009-01-01

The authors propose a paradigm for rigorous scientific assessment of study abroad programs, with the focus being on how study abroad experiences affect psychological constructs as opposed to looking solely at study-abroad-related outcomes. Social learning theory is used as a possible theoretical basis for making testable hypotheses and guiding…

Testing Adaptive Toolbox Models: A Bayesian Hierarchical Approach

ERIC Educational Resources Information Center

Scheibehenne, Benjamin; Rieskamp, Jorg; Wagenmakers, Eric-Jan

2013-01-01

Many theories of human cognition postulate that people are equipped with a repertoire of strategies to solve the tasks they face. This theoretical framework of a cognitive toolbox provides a plausible account of intra- and interindividual differences in human behavior. Unfortunately, it is often unclear how to rigorously test the toolbox…
Cognitive Responses of Students Who Witness Classroom Cheating

ERIC Educational Resources Information Center

Firmin, Michael W.; Burger, Amanda; Blosser, Matthew

2007-01-01

We arranged for 82 General Psychology students (51 females, 31 males) to observe peers in a course cheating situation. Individual, in-depth, qualitative interviews following the experiment we were conducting, using rigorous coding and grounded theory methodology for analysis. Results showed students to experience particular cognitive stages as…
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
Towards rigorous analysis of the Levitov-Mirlin-Evers recursion

NASA Astrophysics Data System (ADS)

Fyodorov, Y. V.; Kupiainen, A.; Webb, C.

2016-12-01

This paper aims to develop a rigorous asymptotic analysis of an approximate renormalization group recursion for inverse participation ratios P q of critical powerlaw random band matrices. The recursion goes back to the work by Mirlin and Evers (2000 Phys. Rev. B 62 7920) and earlier works by Levitov (1990 Phys. Rev. Lett. 64 547, 1999 Ann. Phys. 8 697-706) and is aimed to describe the ensuing multifractality of the eigenvectors of such matrices. We point out both similarities and dissimilarities between the LME recursion and those appearing in the theory of multiplicative cascades and branching random walks and show that the methods developed in those fields can be adapted to the present case. In particular the LME recursion is shown to exhibit a phase transition, which we expect is a freezing transition, where the role of temperature is played by the exponent q. However, the LME recursion has features that make its rigorous analysis considerably harder and we point out several open problems for further study.
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
Computer Generated Diffraction Patterns Of Rough Surfaces

NASA Astrophysics Data System (ADS)

Rakels, Jan H.

1989-03-01

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. In the Micro-Engineering Centre at the University of Warwick, an optical sensor has been devised which can measure the rms roughness, slope and wavelength of turned and precision ground surfaces. The operation of this device is based upon the Kirchhoff-Fresnel diffraction integral. Application of this theory to ideal turned surfaces is straightforward, and indeed the theoretically calculated diffraction patterns are in close agreement with patterns produced by an actual optical instrument. Since it is mathematically difficult to introduce real surface profiles 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.
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.
A philosophy of science perspective on the quantitative analysis of behavior.

PubMed

Smith, Terry L

2015-05-01

B.F. Skinner argued that the science of behavior would progress more rapidly without appealing to theories of learning. He also suggested that theories in a quite different sense were possible, but that the science of behavior as of 1950 was not ready for them. The following analysis distinguishes between Skinner's two concepts of theory. It argues that theory in the second sense has arisen in the quantitative analysis of behavior. The attempt to give a dynamic account of the static regularities of this theory, however, has produced a theory in the first sense. Within its limited domain, this theory offers a rigorous alternative to cognitive accounts of behavior. Rather than distracting attention from actual behavior, it has now led to novel predictions about it. This article is part of a Special Issue entitled 'SQAB 2014'. Copyright © 2015 Elsevier B.V. All rights reserved.
Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation

NASA Astrophysics Data System (ADS)

Castelli, Roberto; Gameiro, Marcio; Lessard, Jean-Philippe

2018-04-01

In this paper, we develop computer-assisted techniques for the analysis of periodic orbits of ill-posed partial differential equations. As a case study, our proposed method is applied to the Boussinesq equation, which has been investigated extensively because of its role in the theory of shallow water waves. The idea is to use the symmetry of the solutions and a Newton-Kantorovich type argument (the radii polynomial approach) to obtain rigorous proofs of existence of the periodic orbits in a weighted ℓ1 Banach space of space-time Fourier coefficients with exponential decay. We present several computer-assisted proofs of the existence of periodic orbits at different parameter values.
Strategies for the crystallization of viruses: using phase diagrams and gels to produce 3D crystals of Grapevine fanleaf virus.

PubMed

Schellenberger, Pascale; Demangeat, Gérard; Lemaire, Olivier; Ritzenthaler, Christophe; Bergdoll, Marc; Oliéric, Vincent; Sauter, Claude; Lorber, Bernard

2011-05-01

The small icosahedral plant RNA nepovirus Grapevine fanleaf virus (GFLV) is specifically transmitted by a nematode and causes major damage to vineyards worldwide. To elucidate the molecular mechanisms underlying the recognition between the surface of its protein capsid and cellular components of its vector, host and viral proteins synthesized upon infection, the wild type GFLV strain F13 and a natural mutant (GFLV-TD) carrying a Gly₂₉₇Asp mutation were purified, characterized and crystallized. Subsequently, the geometry and volume of their crystals was optimized by establishing phase diagrams. GFLV-TD was twice as soluble as the parent virus in the crystallization solution and its crystals diffracted X-rays to a resolution of 2.7 Å. The diffraction limit of GFLV-F13 crystals was extended from 5.5 to 3 Å by growth in agarose gel. Preliminary crystallographic analyses indicate that both types of crystals are suitable for structure determination. Keys for the successful production of GFLV crystals include the rigorous quality control of virus preparations, crystal quality improvement using phase diagrams, and crystal lattice reinforcement by growth in agarose gel. These strategies are applicable to the production of well-diffracting crystals of other viruses and macromolecular assemblies. Copyright © 2011 Elsevier Inc. All rights reserved.
Fast online inverse scattering with Reduced Basis Method (RBM) for a 3D phase grating with specific line roughness

NASA Astrophysics Data System (ADS)

Kleemann, Bernd H.; Kurz, Julian; Hetzler, Jochen; Pomplun, Jan; Burger, Sven; Zschiedrich, Lin; Schmidt, Frank

2011-05-01

Finite element methods (FEM) for the rigorous electromagnetic solution of Maxwell's equations are known to be very accurate. They possess a high convergence rate for the determination of near field and far field quantities of scattering and diffraction processes of light with structures having feature sizes in the range of the light wavelength. We are using FEM software for 3D scatterometric diffraction calculations allowing the application of a brilliant and extremely fast solution method: the reduced basis method (RBM). The RBM constructs a reduced model of the scattering problem from precalculated snapshot solutions, guided self-adaptively by an error estimator. Using RBM, we achieve an efficiency accuracy of about 10-4 compared to the direct problem with only 35 precalculated snapshots being the reduced basis dimension. This speeds up the calculation of diffraction amplitudes by a factor of about 1000 compared to the conventional solution of Maxwell's equations by FEM. This allows us to reconstruct the three geometrical parameters of our phase grating from "measured" scattering data in a 3D parameter manifold online in a minute having the full FEM accuracy available. Additionally, also a sensitivity analysis or the choice of robust measuring strategies, for example, can be done online in a few minutes.
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.
Cooperative effects in spherical spasers: Ab initio analytical model

NASA Astrophysics Data System (ADS)

Bordo, V. G.

2017-06-01

A fully analytical semiclassical theory of cooperative optical processes which occur in an ensemble of molecules embedded in a spherical core-shell nanoparticle is developed from first principles. Both the plasmonic Dicke effect and spaser generation are investigated for the designs in which a shell/core contains an arbitrarily large number of active molecules in the vicinity of a metallic core/shell. An essential aspect of the theory is an ab initio account of the feedback from the core/shell boundaries which significantly modifies the molecular dynamics. The theory provides rigorous, albeit simple and physically transparent, criteria for both plasmonic superradiance and surface plasmon generation.
WKB approximation and tunneling in theories with noncanonical kinetic terms

NASA Astrophysics Data System (ADS)

González, Mariana Carrillo; Masoumi, Ali; Solomon, Adam R.; Trodden, Mark

2017-09-01

Tunneling is a fascinating aspect of quantum mechanics that renders the local minima of a potential meta-stable, with important consequences for particle physics, for the early hot stage of the universe, and more speculatively, for the behavior of the putative multiverse. While this phenomenon has been studied extensively for systems which have canonical kinetic terms, many theories of fundamental physics contain fields with noncanonical kinetic structures. It is therefore desirable to have a detailed framework for calculating tunneling rates and initial states after tunneling for these theories. In this work we present such a rigorous formulation and illustrate its use by applying it to a number of examples.

SMD-based numerical stochastic perturbation theory

NASA Astrophysics Data System (ADS)

Dalla Brida, Mattia; Lüscher, Martin

2017-05-01

The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schrödinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit.
Social Norms: Do We Love Norms Too Much?

PubMed

Bell, David C; Cox, Mary L

2015-03-01

Social norms are often cited as the cause of many social phenomena, especially as an explanation for prosocial family and relationship behaviors. And yet maybe we love the idea of social norms too much, as suggested by our failure to subject them to rigorous test. Compared to the detail in social norms theoretical orientations, there is very little detail in tests of normative theories. To provide guidance to researchers who invoke social norms as explanations, we catalog normative orientations that have been proposed to account for consistent patterns of action. We call on researchers to conduct tests of normative theories and the processes such theories assert.
Social Norms: Do We Love Norms Too Much?

PubMed Central

Bell, David C.; Cox, Mary L.

2014-01-01

Social norms are often cited as the cause of many social phenomena, especially as an explanation for prosocial family and relationship behaviors. And yet maybe we love the idea of social norms too much, as suggested by our failure to subject them to rigorous test. Compared to the detail in social norms theoretical orientations, there is very little detail in tests of normative theories. To provide guidance to researchers who invoke social norms as explanations, we catalog normative orientations that have been proposed to account for consistent patterns of action. We call on researchers to conduct tests of normative theories and the processes such theories assert. PMID:25937833
On Pokrovskii's anisotropic gap equations in superconductivity theory

NASA Astrophysics Data System (ADS)

Yang, Yisong

2003-11-01

An existence and uniqueness theorem for Pokrovskii's zero-temperature anisotropic gap equation is proved. Furthermore, it is shown that Pokrovskii's finite-temperature equation is inconsistent with the Bardeen-Cooper-Schrieffer (BCS) theory. A reformulation of the anisotropic gap equation is presented along the line of Pokrovskii and it is shown that the new equation is consistent with the BCS theory for the whole temperature range. As an application, the Markowitz-Kadanoff model for anisotropic superconductivity is considered and a rigorous proof of the half-integer-exponent isotope effect is obtained. Furthermore, a sharp estimate of the gap solution near the transition temperature is established.
Structural reliability analysis under evidence theory using the active learning kriging model

NASA Astrophysics Data System (ADS)

Yang, Xufeng; Liu, Yongshou; Ma, Panke

2017-11-01

Structural reliability analysis under evidence theory is investigated. It is rigorously proved that a surrogate model providing only correct sign prediction of the performance function can meet the accuracy requirement of evidence-theory-based reliability analysis. Accordingly, a method based on the active learning kriging model which only correctly predicts the sign of the performance function is proposed. Interval Monte Carlo simulation and a modified optimization method based on Karush-Kuhn-Tucker conditions are introduced to make the method more efficient in estimating the bounds of failure probability based on the kriging model. Four examples are investigated to demonstrate the efficiency and accuracy of the proposed method.
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.
A generalized theory on the noise generation from supersonic shear layers.

NASA Technical Reports Server (NTRS)

Pao, S. P.

1971-01-01

A generalization is presented of Phillips' (1960) theory of noise generation by supersonic turbulent shear layers. Both Mach wave radiation and non-Mach wave noise radiation mechanisms are considered. The range of validity of Phillips' theory has been expanded to include the low supersonic and transonic ranges. These generalizations are important not only for their analytical rigor, but also for their prospective applications to practical problems in jet noise prediction and control. The noise generation mechanisms in a supersonic jet are found to differ from those in a subsonic jet. The theory is considered to offer some prospects of answering important questions in supersonic jet noise, such as noise source distribution, mean flow refraction effects, directivity, spectrum, and efficiency of noise radiation.
Beyond the Fermi liquid paradigm: Hidden Fermi liquids

PubMed Central

Jain, J. K.; Anderson, P. W.

2009-01-01

An intense investigation of possible non-Fermi liquid states of matter has been inspired by two of the most intriguing phenomena discovered in the past quarter century, namely, high-temperature superconductivity and the fractional quantum Hall effect. Despite enormous conceptual strides, these two fields have developed largely along separate paths. Two widely employed theories are the resonating valence bond theory for high-temperature superconductivity and the composite fermion theory for the fractional quantum Hall effect. The goal of this perspective article is to note that they subscribe to a common underlying paradigm: They both connect these exotic quantum liquids to certain ordinary Fermi liquids residing in unphysical Hilbert spaces. Such a relation yields numerous nontrivial experimental consequences, exposing these theories to rigorous and definitive tests. PMID:19506260
Authorizers Are Not Monolithic on School Discipline: How Charter School Authorizers Differ in School Discipline Engagement

ERIC Educational Resources Information Center

Rausch, M. K.; Conlan, S. K.

2016-01-01

In theory, authorizers play an important role in decisions regarding charter schools and student discipline, as they are the bodies responsible for protecting the public interest, while balancing school autonomy and accountability. Within public education, a rigorous debate is occurring about student discipline practices, particularly suspensions…
Memory Hazard Functions: A Vehicle for Theory Development and Test

ERIC Educational Resources Information Center

Chechile, Richard A.

2006-01-01

A framework is developed to rigorously test an entire class of memory retention functions by examining hazard properties. Evidence is provided that the memory hazard function is not monotonically decreasing. Yet most of the proposals for retention functions, which have emerged from the psychological literature, imply that memory hazard is…
Building a Higher Education Pipeline: Sociocultural and Critical Approaches to 'Internationalisation' in Teaching and Research

ERIC Educational Resources Information Center

Chang, Benjamin

2017-01-01

This article discusses the use of critical and sociocultural approaches to more dynamically 'internationalise' higher education in the Hong Kong Special Administrative Region of China. The article explores the integration of critical pedagogy and sociocultural learning theory in developing more engaging and rigorous education practices for…
Shaping Social Work Science: What Should Quantitative Researchers Do?

ERIC Educational Resources Information Center

Guo, Shenyang

2015-01-01

Based on a review of economists' debates on mathematical economics, this article discusses a key issue for shaping the science of social work--research methodology. The article describes three important tasks quantitative researchers need to fulfill in order to enhance the scientific rigor of social work research. First, to test theories using…
Closing the Achievement Gap Means Transformation

ERIC Educational Resources Information Center

Colgren, Chris; Sappington, Neil E.

2015-01-01

Educating students in public schools has never been at a higher priority. As this nation enters the informational-based economy public schools are going to be required to educate far more students at a higher and more rigorous level. Inspired by theories of educational equity, this study sought to explore the problem that not all students in…
Building a Foundation for Knowledge Management Research: Developing, Validating, and Applying the Knowledge Internalization Construct

ERIC Educational Resources Information Center

Wipawayangkool, Kamphol

2011-01-01

The notion of knowledge internalization (KI), albeit a critical link in Nonaka's (1994) organizational knowledge creation theory, has not been rigorously conceptualized and defined, let alone operationalized. To strengthen the foundation for knowledge management (KM) research, we attempt to fulfill the following research objectives in the three…
Examining Foundations of Qualitative Research: A Review of Social Work Dissertations, 2008-2010

ERIC Educational Resources Information Center

Gringeri, Christina; Barusch, Amanda; Cambron, Christopher

2013-01-01

This study examined the treatment of epistemology and methodological rigor in qualitative social work dissertations. Template-based review was conducted on a random sample of 75 dissertations completed between 2008 and 2010. For each dissertation, we noted the presence or absence of four markers of epistemology: theory, paradigm, reflexivity, and…
Risk, Protection, and Achievement Disparities among African American Males: Cross-Generation Theory, Research, and Comprehensive Intervention

ERIC Educational Resources Information Center

Rowley, Larry L.; Bowman, Phillip J.

2009-01-01

In this post-industrial global society, parental and student role strains may exacerbate social-ecological risks and academic difficulties of African American male students. Therefore, school-based interventions must ensure rigorous preparation, promote successful navigation of social-ecological risks, and mobilize cultural-ecological strengths to…
Practice as Research: A Fine Art Contextual Study

ERIC Educational Resources Information Center

Adams, Suze

2014-01-01

This paper examines the dynamic interplay between practice and theory in practice-led research in the visual arts. Building on recent debate around the issue and following appropriately rigorous models, the importance of locating a suitable methodology to adequately reflect the integrated process of research practice in written as well as visual…
Molecular and Cellular Biophysics

NASA Astrophysics Data System (ADS)

Jackson, Meyer B.

2006-01-01

Molecular and Cellular Biophysics provides advanced undergraduate and graduate students with a foundation in the basic concepts of biophysics. Students who have taken physical chemistry and calculus courses will find this book an accessible and valuable aid in learning how these concepts can be used in biological research. The text provides a rigorous treatment of the fundamental theories in biophysics and illustrates their application with examples. Conformational transitions of proteins are studied first using thermodynamics, and subsequently with kinetics. Allosteric theory is developed as the synthesis of conformational transitions and association reactions. Basic ideas of thermodynamics and kinetics are applied to topics such as protein folding, enzyme catalysis and ion channel permeation. These concepts are then used as the building blocks in a treatment of membrane excitability. Through these examples, students will gain an understanding of the general importance and broad applicability of biophysical principles to biological problems. Offers a unique synthesis of concepts across a wide range of biophysical topics Provides a rigorous theoretical treatment, alongside applications in biological systems Author has been teaching biophysics for nearly 25 years

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
Response to Burgman and Regan: the elephant in the rhetoric on info-gap decision theory.

PubMed

Sniedovich, Moshe

2014-01-01

The formal, rigorous assessment of IGDT in Sniedovich (2012) reveals that this theory's central pillar, namely its robustness model, is a reinvention of a well-established model of local robustness, known universally as radius of stability (circa 1960). As a matter of fact, this robustness model is a simple model derived from Wald's famous maximin paradigm (circa 1940). This means that had there been any gap in the state of the art that IGDT could have possibly presumed to fill, this gap had already been filled decades ago, well before IGDT was even contemplated. The conclusion therefore is that there is no gap in the state of the art that IGDT does fill, or can possibly fill, or is called upon to fill. Also, since IGDT is based on a definition of local robustness, the theory is unsuitable for the treatment of a severe uncertainty of the type that this theory claims to address. Therefore, since the theory claims to be particularly suitable for the treatment of a severe, unbounded uncertainty, the inevitable conclusion is that this theory constitutes a voodoo decision theory par excellence. Fig. 1 speaks for itself so that no amount of rhetoric can explain this fact away. The Letter's attempt to brush off valid, rigorous, well-documented criticism of IGDT as "... haggling over terminology ..." is yet another attempt to avoid dealing with the elephant in the IGDT room. Nothing will be gained from the use of misleading rhetorics to argue that ideas, models, techniques, approaches, etc., that go back to the 1940s and 1960s, are IGDT innovations. But more than this, what good can come of misapplications of these ideas in applied ecology and conservation biology? In the Appendix, I address a more intriguing question, namely: QUESTION 2: What could possibly be the rationale that motivated a search for a (nonexistent) gap in the state of the art for IGDT to fill?
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.
Nonperturbative dynamics of scalar field theories through the Feynman-Schwinger representation

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

Cetin Savkli; Franz Gross; John Tjon

2004-04-01

In this paper we present a summary of results obtained for scalar field theories using the Feynman-Schwinger (FSR) approach. Specifically, scalar QED and {chi}{sup 2}{phi} theories are considered. The motivation behind the applications discussed in this paper is to use the FSR method as a rigorous tool for testing the quality of commonly used approximations in field theory. Exact calculations in a quenched theory are presented for one-, two-, and three-body bound states. Results obtained indicate that some of the commonly used approximations, such as Bethe-Salpeter ladder summation for bound states and the rainbow summation for one body problems, producemore » significantly different results from those obtained from the FSR approach. We find that more accurate results can be obtained using other, simpler, approximation schemes.« less
Operational formulation of time reversal in quantum theory

NASA Astrophysics Data System (ADS)

Oreshkov, Ognyan; Cerf, Nicolas J.

2015-10-01

The symmetry of quantum theory under time reversal has long been a subject of controversy because the transition probabilities given by Born’s rule do not apply backward in time. Here, we resolve this problem within a rigorous operational probabilistic framework. We argue that reconciling time reversal with the probabilistic rules of the theory requires a notion of operation that permits realizations through both pre- and post-selection. We develop the generalized formulation of quantum theory that stems from this approach and give a precise definition of time-reversal symmetry, emphasizing a previously overlooked distinction between states and effects. We prove an analogue of Wigner’s theorem, which characterizes all allowed symmetry transformations in this operationally time-symmetric quantum theory. Remarkably, we find larger classes of symmetry transformations than previously assumed, suggesting a possible direction in the search for extensions of known physics.
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.
Resonant Perturbation Theory of Decoherence and Relaxation of Quantum Bits

DOE PAGES

Merkli, M.; Berman, G. P.; Sigal, I. M.

2010-01-01

We describe our recenmore » t results on the resonant perturbation theory of decoherence and relaxation for quantum systems with many qubits. The approach represents a rigorous analysis of the phenomenon of decoherence and relaxation for general N -level systems coupled to reservoirs of bosonic fields. We derive a representation of the reduced dynamics valid for all times t ≥ 0 and for small but fixed interaction strength. Our approach does not involve master equation approximations and applies to a wide variety of systems which are not explicitly solvable.« less
Scan blindness in infinite phased arrays of printed dipoles

NASA Technical Reports Server (NTRS)

Pozar, D. M.; Schaubert, D. H.

1984-01-01

A comprehensive study of infinite phased arrays of printed dipole antennas is presented, with emphasis on the scan blindness phenomenon. A rigorous and efficient moment method procedure is used to calculate the array impedance versus scan angle. Data are presented for the input reflection coefficient for various element spacings and substrate parameters. A simple theory, based on coupling from Floquet modes to surface wave modes on the substrate, is shown to predict the occurrence of scan blindness. Measurements from a waveguide simulator of a blindness condition confirm the theory.
Thermal Conductivity of the Multicomponent Neutral Atmosphere

NASA Astrophysics Data System (ADS)

Pavlov, A. V.

2017-12-01

Approximate expressions for the thermal conductivity coefficient of the multicomponent neutral atmosphere consisting of N2, O2, O, He, and H are analyzed and evaluated for the atmospheric conditions by comparing them with that given by the rigorous hydrodynamic theory. The new approximations of the thermal conductivity coefficients of simple gases N2, O2, O, He, and H are derived and used. It is proved that the modified Mason and Saxena approximation of the atmospheric thermal conductivity coefficient is more accurate in reproducing the atmospheric values of the rigorous hydrodynamic thermal conductivity coefficient in comparison with those that are generally accepted in atmospheric studies. This approximation of the thermal conductivity coefficient is recommended to use in calculations of the neutral temperature of the atmosphere.
A feminist response to Weitzer.

PubMed

Dines, Gail

2012-04-01

In his review of my book Pornland: How Porn has Hijacked our Sexuality, Ronald Weitzer claims that anti-porn feminists are incapable of objective, rigorous research because they operate within the "oppression paradigm," which he defines as "a perspective that depicts all types of sex work as exploitive, violent, and perpetuating gender inequality." (VAW, 2011, 666). This article argues that while anti-porn feminists do indeed see pornography as exploitive, such a position is rooted in the rigorous theories and methods of cultural studies developed by critical media scholars such as Stuart Hall and Antonio Gramsci. Pornland applies a cultural studies approach by exploring how porn images are part of a wider system of sexist representations that legitimize and normalize the economic, political and legal oppression of women.
Origin of the spike-timing-dependent plasticity rule

NASA Astrophysics Data System (ADS)

Cho, Myoung Won; Choi, M. Y.

2016-08-01

A biological synapse changes its efficacy depending on the difference between pre- and post-synaptic spike timings. Formulating spike-timing-dependent interactions in terms of the path integral, we establish a neural-network model, which makes it possible to predict relevant quantities rigorously by means of standard methods in statistical mechanics and field theory. In particular, the biological synaptic plasticity rule is shown to emerge as the optimal form for minimizing the free energy. It is further revealed that maximization of the entropy of neural activities gives rise to the competitive behavior of biological learning. This demonstrates that statistical mechanics helps to understand rigorously key characteristic behaviors of a neural network, thus providing the possibility of physics serving as a useful and relevant framework for probing life.
Kinetics versus thermodynamics in materials modeling: The case of the di-vacancy in iron

NASA Astrophysics Data System (ADS)

Djurabekova, F.; Malerba, L.; Pasianot, R. C.; Olsson, P.; Nordlund, K.

2010-07-01

Monte Carlo models are widely used for the study of microstructural and microchemical evolution of materials under irradiation. However, they often link explicitly the relevant activation energies to the energy difference between local equilibrium states. We provide a simple example (di-vacancy migration in iron) in which a rigorous activation energy calculation, by means of both empirical interatomic potentials and density functional theory methods, clearly shows that such a link is not granted, revealing a migration mechanism that a thermodynamics-linked activation energy model cannot predict. Such a mechanism is, however, fully consistent with thermodynamics. This example emphasizes the importance of basing Monte Carlo methods on models where the activation energies are rigorously calculated, rather than deduced from widespread heuristic equations.
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.
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.
Homogenization of Periodic Masonry Using Self-Consistent Scheme and Finite Element Method

NASA Astrophysics Data System (ADS)

Kumar, Nitin; Lambadi, Harish; Pandey, Manoj; Rajagopal, Amirtham

2016-01-01

Masonry is a heterogeneous anisotropic continuum, made up of the brick and mortar arranged in a periodic manner. Obtaining the effective elastic stiffness of the masonry structures has been a challenging task. In this study, the homogenization theory for periodic media is implemented in a very generic manner to derive the anisotropic global behavior of the masonry, through rigorous application of the homogenization theory in one step and through a full three-dimensional behavior. We have considered the periodic Eshelby self-consistent method and the finite element method. Two representative unit cells that represent the microstructure of the masonry wall exactly are considered for calibration and numerical application of the theory.
Exploring theory space with Monte Carlo reweighting

DOE PAGES

Gainer, James S.; Lykken, Joseph; Matchev, Konstantin T.; ...

2014-10-13

Theories of new physics often involve a large number of unknown parameters which need to be scanned. Additionally, a putative signal in a particular channel may be due to a variety of distinct models of new physics. This makes experimental attempts to constrain the parameter space of motivated new physics models with a high degree of generality quite challenging. We describe how the reweighting of events may allow this challenge to be met, as fully simulated Monte Carlo samples generated for arbitrary benchmark models can be effectively re-used. Specifically, we suggest procedures that allow more efficient collaboration between theorists andmore » experimentalists in exploring large theory parameter spaces in a rigorous way at the LHC.« less
Fundamental limit of nanophotonic light trapping in solar cells.

PubMed

Yu, Zongfu; Raman, Aaswath; Fan, Shanhui

2010-10-12

Establishing the fundamental limit of nanophotonic light-trapping schemes is of paramount importance and is becoming increasingly urgent for current solar cell research. The standard theory of light trapping demonstrated that absorption enhancement in a medium cannot exceed a factor of 4n(2)/sin(2)θ, where n is the refractive index of the active layer, and θ is the angle of the emission cone in the medium surrounding the cell. This theory, however, is not applicable in the nanophotonic regime. Here we develop a statistical temporal coupled-mode theory of light trapping based on a rigorous electromagnetic approach. Our theory reveals that the conventional limit can be substantially surpassed when optical modes exhibit deep-subwavelength-scale field confinement, opening new avenues for highly efficient next-generation solar cells.
An advanced kinetic theory for morphing continuum with inner structures

NASA Astrophysics Data System (ADS)

Chen, James

2017-12-01

Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing equations at equilibrium state are derived and compared with Eringen's morphing (micropolar) continuum theory derived under the framework of rational continuum thermomechanics. Although rational continuum thermomechanics has the advantages of mathematical rigor and simplicity, the presented statistical kinetic theory approach provides a clear physical picture for what the governing equations represent.
Molecular Electron Density Theory: A Modern View of Reactivity in Organic Chemistry.

PubMed

Domingo, Luis R

2016-09-30

A new theory for the study of the reactivity in Organic Chemistry, named Molecular Electron Density Theory (MEDT), is proposed herein. MEDT is based on the idea that while the electron density distribution at the ground state is responsible for physical and chemical molecular properties, as proposed by the Density Functional Theory (DFT), the capability for changes in electron density is responsible for molecular reactivity. Within MEDT, the reactivity in Organic Chemistry is studied through a rigorous quantum chemical analysis of the changes of the electron density as well as the energies associated with these changes along the reaction path in order to understand experimental outcomes. Studies performed using MEDT allow establishing a modern rationalisation and to gain insight into molecular mechanisms and reactivity in Organic Chemistry.
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.
Evidence-based Sensor Tasking for Space Domain Awareness

NASA Astrophysics Data System (ADS)

Jaunzemis, A.; Holzinger, M.; Jah, M.

2016-09-01

Space Domain Awareness (SDA) is the actionable knowledge required to predict, avoid, deter, operate through, recover from, and/or attribute cause to the loss and/or degradation of space capabilities and services. A main purpose for SDA is to provide decision-making processes with a quantifiable and timely body of evidence of behavior(s) attributable to specific space threats and/or hazards. To fulfill the promise of SDA, it is necessary for decision makers and analysts to pose specific hypotheses that may be supported or refuted by evidence, some of which may only be collected using sensor networks. While Bayesian inference may support some of these decision making needs, it does not adequately capture ambiguity in supporting evidence; i.e., it struggles to rigorously quantify 'known unknowns' for decision makers. Over the past 40 years, evidential reasoning approaches such as Dempster Shafer theory have been developed to address problems with ambiguous bodies of evidence. This paper applies mathematical theories of evidence using Dempster Shafer expert systems to address the following critical issues: 1) How decision makers can pose critical decision criteria as rigorous, testable hypotheses, 2) How to interrogate these hypotheses to reduce ambiguity, and 3) How to task a network of sensors to gather evidence for multiple competing hypotheses. This theory is tested using a simulated sensor tasking scenario balancing search versus track responsibilities.
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.
Properties of Tangential and Cyclic Polygons: An Application of Circulant Matrices

ERIC Educational Resources Information Center

Leung, Allen; Lopez-Real, Francis

2003-01-01

In this paper, the properties of tangential and cyclic polygons proposed by Lopez-Real are proved rigorously using the theory of circulant matrices. In particular, the concepts of slippable tangential polygons and conformable cyclic polygons are defined. It is shown that an n-sided tangential (or cyclic) polygon P[subscript n] with n even is…
Establishing Interventions via a Theory-Driven Single Case Design Research Cycle

ERIC Educational Resources Information Center

Kilgus, Stephen P.; Riley-Tillman, T. Chris; Kratochwill, Thomas R.

2016-01-01

Recent studies have suggested single case design (SCD) intervention research is subject to publication bias, wherein studies are more likely to be published if they possess large or statistically significant effects and use rigorous experimental methods. The nature of SCD and the purposes for which it might be used could suggest that large effects…
Pedagogy and the Intuitive Appeal of Learning Styles in Post-Compulsory Education in England

ERIC Educational Resources Information Center

Nixon, Lawrence; Gregson, Maggie; Spedding, Trish

2007-01-01

Despite the rigorous and robust evaluation of learning styles theories, models and inventories, little objective evidence in support of their effectiveness has been found. The lack of unambiguous evidence in support of these models and practices leaves the continued popularity of these models and instruments as a puzzle. Two related accounts of…
Creating Cultural Consumers: The Dynamics of Cultural Capital Acquisition

ERIC Educational Resources Information Center

Kisida, Brian; Greene, Jay P.; Bowen, Daniel H.

2014-01-01

The theories of cultural reproduction and cultural mobility have largely shaped the study of the effects of cultural capital on academic outcomes. Missing in this debate has been a rigorous examination of how children actually acquire cultural capital when it is not provided by their families. Drawing on data from a large-scale experimental study…
Mario Bunge's Materialist Theory of Mind and Contemporary Cognitive Science

ERIC Educational Resources Information Center

Slezak, Peter

2012-01-01

Bunge's writings on the mind-body problem provide a rigorous, analytical antidote to the persistent anti-materialist tendency that has characterized the history of philosophy and science. Bunge gives special attention to dualism and its shortcomings, and this attention is welcome in view of the resurgence of the doctrine today. However, I focus my…
Impacts of the Boston Prekindergarten Program on the School Readiness of Young Children with Special Needs

ERIC Educational Resources Information Center

Weiland, Christina

2016-01-01

Theory and empirical work suggest inclusion preschool improves the school readiness of young children with special needs, but only 2 studies of the model have used rigorous designs that could identify causality. The present study examined the impacts of the Boston Public prekindergarten program-which combined proven language, literacy, and…
The Stability of Kindergarten Teachers' Effectiveness: A Generalizability Study Comparing the Framework for Teaching and the Classroom Assessment Scoring System

ERIC Educational Resources Information Center

Mantzicopoulos, Panayota; French, Brian F.; Patrick, Helen; Watson, J. Samuel; Ahn, Inok

2018-01-01

To meet recent accountability mandates, school districts are implementing assessment frameworks to document teachers' effectiveness. Observational assessments play a key role in this process, albeit without compelling evidence of their psychometric rigor. Using a sample of kindergarten teachers, we employed Generalizability theory to investigate…

Integrated model development for liquid fueled rocket propulsion systems

NASA Technical Reports Server (NTRS)

Santi, L. Michael

1993-01-01

As detailed in the original statement of work, the objective of phase two of this research effort was to develop a general framework for rocket engine performance prediction that integrates physical principles, a rigorous mathematical formalism, component level test data, system level test data, and theory-observation reconciliation. Specific phase two development tasks are defined.
Towards an Engaged Campus: Measuring and Comparing Definitive Stakeholders' Perceptions of University Social Engagement in South Korea

ERIC Educational Resources Information Center

Cho, Young Ha

2017-01-01

Purpose: This paper aims to measure and rigorously compare the perceptions of South Korean university social engagement between faculty and students, two definitive stakeholders identified by stakeholder theory--but considerably heterogeneous, to understand how South Korean campus embraces social engagement in practice. To that end, this study…
Growing a Professional Identity: A Grounded Theory of the Educational Experience of Baccalaureate Nursing Students

ERIC Educational Resources Information Center

Goodolf, Dawn M.

2013-01-01

Nursing students experience high levels of stress while enrolled in baccalaureate nursing programs. Research has focused on the contributors of stress such as the responsibilities of patient care, the overwhelming amount of information, high stakes methods of evaluation, and rigorous course schedules. Little research has been found on the personal…
Free Volume of the Hard Spheres Gas

ERIC Educational Resources Information Center

Shutler, P. M. E.; Martinez, J. C.; Springham, S. V.

2007-01-01

The Enskog factor [chi] plays a central role in the theory of dense gases, quantifying how the finite size of molecules causes many physical quantities, such as the equation of state, the mean free path, and the diffusion coefficient, to deviate from those of an ideal gas. We suggest an intuitive but rigorous derivation of this fact by showing how…
Implementing principles of the integrated control concept 50 years later – current challenges in IPM for arthropod pests

USDA-ARS?s Scientific Manuscript database

Pest management theory and concepts developed fifty years ago as part of the integrated control concept remain at the foundation of IPM today. Implementation of integrated control and subsequently IPM has always been faced with the challenge of carrying out their principles in a rigorous, disciplin...
The Community College Mission: History and Theory, 1930-2000. Working Paper Series. Number 1-09

ERIC Educational Resources Information Center

Meier, Kenneth M.

2008-01-01

There is a significant omission in the literature concerning the historical origins of the community college and the social and educational forces that have shaped its mission. Rigorous historical studies are relatively rare in higher education. For community colleges, analytical histories are even less common (Ratcliff, 1987; Frye, 1991, 1992).…
The radiation from slots in truncated dielectric-covered surfaces

NASA Technical Reports Server (NTRS)

Hwang, Y. M.; Kouyoumjian, R. G.; Pathak, P. H.

1974-01-01

A theoretical approach based on the geometrical theory of diffraction is used to study the electromagnetic radiation from a narrow slot in a dielectric-covered perfectly-conducting surface terminated at an edge. The total far-zone field is composed of a geometrical optics field and a diffracted field. The geometrical optics field is the direct radiation from the slot to the field point. The slot also generates surface waves which are incident at the termination of the dielectric cover, where singly-diffracted rays and reflected surface waves are excited. The diffraction and reflection coefficients are obtained from the canonical problem of the diffraction of a surface wave by a right-angle wedge where the dielectric-covered surface is approximated by an impedance surface. This approximation is satisfactory for a very thin cover; however, the radiation from its vertical and faces cannot be neglected in treating the thicker dielectric cover. This is taken into account by using a Kirchhoff-type approximation, which contributes a second term to the diffraction coefficient previously obtained. The contributions from the geometrical optics field, the singly-diffracted rays and all significant multiply-diffracted rays are summed to give the total radiation. Calculated and measured patterns are found to be in good agreement.
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.
A Theoretical Framework for Lagrangian Descriptors

NASA Astrophysics Data System (ADS)

Lopesino, C.; Balibrea-Iniesta, F.; García-Garrido, V. J.; Wiggins, S.; Mancho, A. M.

This paper provides a theoretical background for Lagrangian Descriptors (LDs). The goal of achieving rigorous proofs that justify the ability of LDs to detect invariant manifolds is simplified by introducing an alternative definition for LDs. The definition is stated for n-dimensional systems with general time dependence, however we rigorously prove that this method reveals the stable and unstable manifolds of hyperbolic points in four particular 2D cases: a hyperbolic saddle point for linear autonomous systems, a hyperbolic saddle point for nonlinear autonomous systems, a hyperbolic saddle point for linear nonautonomous systems and a hyperbolic saddle point for nonlinear nonautonomous systems. We also discuss further rigorous results which show the ability of LDs to highlight additional invariants sets, such as n-tori. These results are just a simple extension of the ergodic partition theory which we illustrate by applying this methodology to well-known examples, such as the planar field of the harmonic oscillator and the 3D ABC flow. Finally, we provide a thorough discussion on the requirement of the objectivity (frame-invariance) property for tools designed to reveal phase space structures and their implications for Lagrangian descriptors.
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.
Two-port connecting-layer-based sandwiched grating by a polarization-independent design.

PubMed

Li, Hongtao; Wang, Bo

2017-05-02

In this paper, a two-port connecting-layer-based sandwiched beam splitter grating with polarization-independent property is reported and designed. Such the grating can separate the transmission polarized light into two diffraction orders with equal energies, which can realize the nearly 50/50 output with good uniformity. For the given wavelength of 800 nm and period of 780 nm, a simplified modal method can design a optimal duty cycle and the estimation value of the grating depth can be calculated based on it. In order to obtain the precise grating parameters, a rigorous coupled-wave analysis can be employed to optimize grating parameters by seeking for the precise grating depth and the thickness of connecting layer. Based on the optimized design, a high-efficiency two-port output grating with the wideband performances can be gained. Even more important, diffraction efficiencies are calculated by using two analytical methods, which are proved to be coincided well with each other. Therefore, the grating is significant for practical optical photonic element in engineering.
Deep-etched sinusoidal polarizing beam splitter grating.

PubMed

Feng, Jijun; Zhou, Changhe; Cao, Hongchao; Lv, Peng

2010-04-01

A sinusoidal-shaped fused-silica grating as a highly efficient polarizing beam splitter (PBS) is investigated based on the simplified modal method. The grating structure depends mainly on the ratio of groove depth to grating period and the ratio of incident wavelength to grating period. These ratios can be used as a guideline for the grating design at different wavelengths. A sinusoidal-groove PBS grating is designed at a wavelength of 1310 nm under Littrow mounting, and the transmitted TM and TE polarized waves are mainly diffracted into the zeroth order and the -1st order, respectively. The grating profile is optimized by using rigorous coupled-wave analysis. The designed PBS grating is highly efficient (>95.98%) over the O-band wavelength range (1260-1360 nm) for both TE and TM polarizations. The sinusoidal grating can exhibit higher diffraction efficiency, larger extinction ratio, and less reflection loss than the rectangular-groove PBS grating. By applying wet etching technology on the rectangular grating, which was manufactured by holographic recording and inductively coupled plasma etching technology, the sinusoidal grating can be approximately fabricated. Experimental results are in agreement with theoretical values.
Wideband two-port beam splitter of a binary fused-silica phase grating.

PubMed

Wang, Bo; Zhou, Changhe; Feng, Jijun; Ru, Huayi; Zheng, Jiangjun

2008-08-01

The usual beam splitter of multilayer-coated film with a wideband spectrum is not easy to achieve. We describe the realization of a wideband transmission two-port beam splitter based on a binary fused-silica phase grating. To achieve high efficiency and equality in the diffracted 0th and -1st orders, the grating profile parameters are optimized using rigorous coupled-wave analysis at a wavelength of 1550 nm. Holographic recording and the inductively coupled plasma dry etching technique are used to fabricate the fused-silica beam splitter grating. The measured efficiency of (45% x 2) = 90% diffracted into the both orders can be obtained with the fabricated grating under Littrow mounting. The physical mechanism of such a wideband two-port beam splitter grating can be well explained by the modal method based on two-beam interference of the modes excited by the incident wave. With the high damage threshold, low coefficient of thermal expansion, and wideband high efficiency, the presented beam splitter etched in fused silica should be a useful optical element for a variety of practical applications.
On beam shaping of the field radiated by a line source coupled to finite or infinite photonic crystals.

PubMed

Ceccuzzi, Silvio; Jandieri, Vakhtang; Baccarelli, Paolo; Ponti, Cristina; Schettini, Giuseppe

2016-04-01

Comparison of the beam-shaping effect of a field radiated by a line source, when an ideal infinite structure constituted by two photonic crystals and an actual finite one are considered, has been carried out by means of two different methods. The lattice sums technique combined with the generalized reflection matrix method is used to rigorously investigate the radiation from the infinite photonic crystals, whereas radiation from crystals composed of a finite number of rods along the layers is analyzed using the cylindrical-wave approach. A directive radiation is observed with the line source embedded in the structure. With an increased separation distance between the crystals, a significant edge diffraction appears that provides the main radiation mechanism in the finite layout. Suitable absorbers are implemented to reduce the above-mentioned diffraction and the reflections at the boundaries, thus obtaining good agreement between radiation patterns of a localized line source coupled to finite and infinite photonic crystals, when the number of periods of the finite structure is properly chosen.
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
Vortex Loops at the Superfluid Lambda Transition: An Exact Theory?

NASA Technical Reports Server (NTRS)

Williams, Gary A.

2003-01-01

A vortex-loop theory of the superfluid lambda transition has been developed over the last decade, with many results in agreement with experiments. It is a very simple theory, consisting of just three basic equations. When it was first proposed the main uncertainty in the theory was the use Flory scaling to find the fractal dimension of the random-walking vortex loops. Recent developments in high-resolution Monte Carlo simulations have now made it possible to verify the accuracy of this Flory-scaling assumption. Although the loop theory is not yet rigorously proven to be exact, the Monte Carlo results show at the least that it is an extremely good approximation. Recent loop calculations of the critical Casimir effect in helium films in the superfluid phase T < Tc will be compared with similar perturbative RG calculations in the normal phase T > Tc; the two calculations are found to match very nicely right at Tc.

Scale-free crystallization of two-dimensional complex plasmas: Domain analysis using Minkowski tensors

NASA Astrophysics Data System (ADS)

Böbel, A.; Knapek, C. A.; Räth, C.

2018-05-01

Experiments of the recrystallization processes in two-dimensional complex plasmas are analyzed to rigorously test a recently developed scale-free phase transition theory. The "fractal-domain-structure" (FDS) theory is based on the kinetic theory of Frenkel. It assumes the formation of homogeneous domains, separated by defect lines, during crystallization and a fractal relationship between domain area and boundary length. For the defect number fraction and system energy a scale-free power-law relation is predicted. The long-range scaling behavior of the bond-order correlation function shows clearly that the complex plasma phase transitions are not of the Kosterlitz, Thouless, Halperin, Nelson, and Young type. Previous preliminary results obtained by counting the number of dislocations and applying a bond-order metric for structural analysis are reproduced. These findings are supplemented by extending the use of the bond-order metric to measure the defect number fraction and furthermore applying state-of-the-art analysis methods, allowing a systematic testing of the FDS theory with unprecedented scrutiny: A morphological analysis of lattice structure is performed via Minkowski tensor methods. Minkowski tensors form a complete family of additive, motion covariant and continuous morphological measures that are sensitive to nonlinear properties. The FDS theory is rigorously confirmed and predictions of the theory are reproduced extremely well. The predicted scale-free power-law relation between defect fraction number and system energy is verified for one more order of magnitude at high energies compared to the inherently discontinuous bond-order metric. It is found that the fractal relation between crystalline domain area and circumference is independent of the experiment, the particular Minkowski tensor method, and the particular choice of parameters. Thus, the fractal relationship seems to be inherent to two-dimensional phase transitions in complex plasmas. Minkowski tensor analysis turns out to be a powerful tool for investigations of crystallization processes. It is capable of revealing nonlinear local topological properties, however, still provides easily interpretable results founded on a solid mathematical framework.
Nuclear magnetic relaxation induced by exchange-mediated orientational randomization: longitudinal relaxation dispersion for a dipole-coupled spin-1/2 pair.

PubMed

Chang, Zhiwei; Halle, Bertil

2013-10-14

In complex biological or colloidal samples, magnetic relaxation dispersion (MRD) experiments using the field-cycling technique can characterize molecular motions on time scales ranging from nanoseconds to microseconds, provided that a rigorous theory of nuclear spin relaxation is available. In gels, cross-linked proteins, and biological tissues, where an immobilized macromolecular component coexists with a mobile solvent phase, nuclear spins residing in solvent (or cosolvent) species relax predominantly via exchange-mediated orientational randomization (EMOR) of anisotropic nuclear (electric quadrupole or magnetic dipole) couplings. The physical or chemical exchange processes that dominate the MRD typically occur on a time scale of microseconds or longer, where the conventional perturbation theory of spin relaxation breaks down. There is thus a need for a more general relaxation theory. Such a theory, based on the stochastic Liouville equation (SLE) for the EMOR mechanism, is available for a single quadrupolar spin I = 1. Here, we present the corresponding theory for a dipole-coupled spin-1/2 pair. To our knowledge, this is the first treatment of dipolar MRD outside the motional-narrowing regime. Based on an analytical solution of the spatial part of the SLE, we show how the integral longitudinal relaxation rate can be computed efficiently. Both like and unlike spins, with selective or non-selective excitation, are treated. For the experimentally important dilute regime, where only a small fraction of the spin pairs are immobilized, we obtain simple analytical expressions for the auto-relaxation and cross-relaxation rates which generalize the well-known Solomon equations. These generalized results will be useful in biophysical studies, e.g., of intermittent protein dynamics. In addition, they represent a first step towards a rigorous theory of water (1)H relaxation in biological tissues, which is a prerequisite for unravelling the molecular basis of soft-tissue contrast in clinical magnetic resonance imaging.
Toward a new methodological paradigm for testing theories of health behavior and health behavior change.

PubMed

Noar, Seth M; Mehrotra, Purnima

2011-03-01

Traditional theory testing commonly applies cross-sectional (and occasionally longitudinal) survey research to test health behavior theory. Since such correlational research cannot demonstrate causality, a number of researchers have called for the increased use of experimental methods for theory testing. We introduce the multi-methodological theory-testing (MMTT) framework for testing health behavior theory. The MMTT framework introduces a set of principles that broaden the perspective of how we view evidence for health behavior theory. It suggests that while correlational survey research designs represent one method of testing theory, the weaknesses of this approach demand that complementary approaches be applied. Such approaches include randomized lab and field experiments, mediation analysis of theory-based interventions, and meta-analysis. These alternative approaches to theory testing can demonstrate causality in a much more robust way than is possible with correlational survey research methods. Such approaches should thus be increasingly applied in order to more completely and rigorously test health behavior theory. Greater application of research derived from the MMTT may lead researchers to refine and modify theory and ultimately make theory more valuable to practitioners. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.
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.
Optimization design and laser damage threshold analysis of pulse compression multilayer dielectric gratings

NASA Astrophysics Data System (ADS)

Fan, Shuwei; Bai, Liang; Chen, Nana

2016-08-01

As one of the key elements of high-power laser systems, the pulse compression multilayer dielectric grating is required for broader band, higher diffraction efficiency and higher damage threshold. In this paper, the multilayer dielectric film and the multilayer dielectric gratings(MDG) were designed by eigen matrix and optimized with the help of generic algorithm and rigorous coupled wave method. The reflectivity was close to 100% and the bandwith were over 250nm, twice compared to the unoptimized film structure. The simulation software of standing wave field distribution within MDG was developed and the electric field of the MDG was calculated. And the key parameters which affected the electric field distribution were also studied.
A Mathematical Evaluation of the Core Conductor Model

PubMed Central

Clark, John; Plonsey, Robert

1966-01-01

This paper is a mathematical evaluation of the core conductor model where its three dimensionality is taken into account. The problem considered is that of a single, active, unmyelinated nerve fiber situated in an extensive, homogeneous, conducting medium. Expressions for the various core conductor parameters have been derived in a mathematically rigorous manner according to the principles of electromagnetic theory. The purpose of employing mathematical rigor in this study is to bring to light the inherent assumptions of the one dimensional core conductor model, providing a method of evaluating the accuracy of this linear model. Based on the use of synthetic squid axon data, the conclusion of this study is that the linear core conductor model is a good approximation for internal but not external parameters. PMID:5903155
Electron-Ion Dynamics with Time-Dependent Density Functional Theory: Towards Predictive Solar Cell Modeling: Final Technical Report

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

Maitra, Neepa

2016-07-14

This project investigates the accuracy of currently-used functionals in time-dependent density functional theory, which is today routinely used to predict and design materials and computationally model processes in solar energy conversion. The rigorously-based electron-ion dynamics method developed here sheds light on traditional methods and overcomes challenges those methods have. The fundamental research undertaken here is important for building reliable and practical methods for materials discovery. The ultimate goal is to use these tools for the computational design of new materials for solar cell devices of high efficiency.
Displacive transformation of virus protein crystal

NASA Astrophysics Data System (ADS)

Celotto, S.; Pond, R. C.

2003-10-01

A crystalline protein undergoes a displacive transformation in the T-even bacteriophage. In the present work, the transformation mechanism is modelled in terms of interfacial dislocations whose motion gives rise to the observed deformation. The topological properties (Burgers vector, {b}, and `overlap' step height, h) of the dislocations involved are defined rigorously and a recent theory is used that quantifies the diffusional flux arising due to their movement. The circumstance under which passage of transformation dislocations is diffusionless is identified. Thus, dislocation modelling is used successfully to describe a diffusionless displacive transformation in a process where the phenomenological theory of martensite crystallography cannot be applied.
Theory of multicolor lattice gas - A cellular automaton Poisson solver

NASA Technical Reports Server (NTRS)

Chen, H.; Matthaeus, W. H.; Klein, L. W.

1990-01-01

The present class of models for cellular automata involving a quiescent hydrodynamic lattice gas with multiple-valued passive labels termed 'colors', the lattice collisions change individual particle colors while preserving net color. The rigorous proofs of the multicolor lattice gases' essential features are rendered more tractable by an equivalent subparticle representation in which the color is represented by underlying two-state 'spins'. Schemes for the introduction of Dirichlet and Neumann boundary conditions are described, and two illustrative numerical test cases are used to verify the theory. The lattice gas model is equivalent to a Poisson equation solution.
Quantum probability and quantum decision-making.

PubMed

Yukalov, V I; Sornette, D

2016-01-13

A rigorous general definition of quantum probability is given, which is valid not only for elementary events but also for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision-making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary. © 2015 The Author(s).
Antennas in matter: Fundamentals, theory, and applications

NASA Technical Reports Server (NTRS)

King, R. W. P.; Smith, G. S.; Owens, M.; Wu, T. T.

1981-01-01

The volume provides an introduction to antennas and probes embedded within or near material bodies such as the earth, the ocean, or a living organism. After a fundamental analysis of insulated and bare antennas, an advanced treatment of antennas in various media is presented, including a detailed study of the electromagnetic equations in homogeneous isotropic media, the complete theory of the bare dipole in a general medium, and a rigorous analysis of the insulated antenna as well as bare and insulated loop antennas. Finally, experimental models and measuring techniques related to antennas and probes in a general dissipative or dielectric medium are examined.
The path integral on the Poincaré upper half plane and for Liouville quantum mechanics

NASA Astrophysics Data System (ADS)

Grosche, C.; Steiner, F.

1987-08-01

We present a rigorous path integral treatment of free motion on the Poincaré upper half plane. The Poincaré upper half plane, as a riemannian manifold, has recently become important in string theory and in the theory of quantum chaos. The calculation is done by a time-transformation and the use of the canonical method for determining quantum corrections to the classical lagrangian. Furthermore, we shall show that the same method also works for Liouville quantum mechanics. In both cases, the energy spectrum and the normalized wavefunctions are determined.
Quantum gravity model with fundamental spinor fields

NASA Astrophysics Data System (ADS)

Obukhov, Yu. N.; Hehl, F. W.

2014-01-01

We discuss the possibility that gravitational potentials (metric, coframe and connection) may emerge as composite fields from more fundamental spinor constituents. We use the formalism of Poincaré gauge gravity as an appropriate theoretical scheme for the rigorous development of such an approach. We postulate the constitutive relations of an elastic Cosserat type continuum that models spacetime. These generalized Hooke and MacCullagh type laws consistently take into account the translational and Lorentz rotational deformations, respectively. The resulting theory extends the recently proposed Diakonov model. An intriguing feature of our theory is that in the lowest approximation it reproduces Heisenberg's nonlinear spinor model.
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.
What's with all this peer-review stuff anyway?

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

Warner, J. S.

2010-01-01

The Journal of Physical Security was ostensibly started to deal with a perceived lack of peer-reviewed journals related to the field of physical security. In fact, concerns have been expressed that the field of physical security is scarcely a field at all. A typical, well-developed field might include the following: multiple peer-reviewed journals devoted to the subject, rigor and critical thinking, metrics, fundamental principles, models and theories, effective standards and guidelines, R and D conferences, professional societies, certifications, its own academic department (or at least numerous academic experts), widespread granting of degrees in the field from 4-year research universities, mechanismsmore » for easily spotting 'snake oil' products and services, and the practice of professionals organizing to police themselves, provide quality control, and determine best practices. Physical Security seems to come up short in a number of these areas. Many of these attributes are difficult to quantify. This paper seeks to focus on one area that is quantifiable: the number of peer-reviewed journals dedicated to the field of Physical Security. In addition, I want to examine the number of overall periodicals (peer-reviewed and non-peer-reviewed) dedicated to physical security, as well as the number of papers published each year about physical security. These are potentially useful analyses because one can often infer how healthy or active a given field is by its publishing activity. For example, there are 2,754 periodicals dedicated to the (very healthy and active) field of physics. This paper concentrates on trade journal versus peer-reviewed journals. Trade journals typically focus on practice-related topics. A paper appropriate for a trade journal is usually based more on practical experience than rigorous studies or research. Models, theories, or rigorous experimental research results will usually not be included. A trade journal typically targets a specific market in an industry or trade. Such journals are often considered to be news magazines and may contain industry specific advertisements and/or job ads. A peer-reviewed journal, a.k.a 'referred journal', in contrast, contains peer-reviewed papers. A peer-reviewed paper is one that has been vetted by the peer review process. In this process, the paper is typically sent to independent experts for review and consideration. A peer-reviewed paper might cover experimental results, and/or a rigorous study, analyses, research efforts, theory, models, or one of many other scholarly endeavors.« less
Late-time cosmic acceleration: ABCD of dark energy and modified theories of gravity

NASA Astrophysics Data System (ADS)

Sami, M.; Myrzakulov, R.

2016-10-01

We briefly review the problems and prospects of the standard lore of dark energy. We have shown that scalar fields, in principle, cannot address the cosmological constant problem. Indeed, a fundamental scalar field is faced with a similar problem dubbed naturalness. In order to keep the discussion pedagogical, aimed at a wider audience, we have avoided technical complications in several places and resorted to heuristic arguments based on physical perceptions. We presented underlying ideas of modified theories based upon chameleon mechanism and Vainshtein screening. We have given a lucid illustration of recently investigated ghost-free nonlinear massive gravity. Again, we have sacrificed rigor and confined to the basic ideas that led to the formulation of the theory. The review ends with a brief discussion on the difficulties of the theory applied to cosmology.
Self-consistent quantum kinetic theory of diatomic molecule formation

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

Forrey, Robert C.

2015-07-14

A quantum kinetic theory of molecule formation is presented which includes three-body recombination and radiative association for a thermodynamically closed system which may or may not exchange energy with its surrounding at a constant temperature. The theory uses a Sturmian representation of a two-body continuum to achieve a steady-state solution of a governing master equation which is self-consistent in the sense that detailed balance between all bound and unbound states is rigorously enforced. The role of quasibound states in catalyzing the molecule formation is analyzed in complete detail. The theory is used to make three predictions which differ from conventionalmore » kinetic models. These predictions suggest significant modifications may be needed to phenomenological rate constants which are currently in wide use. Implications for models of low and high density systems are discussed.« less
EFFECT OF CORRELATIONS ON THE TRANSPORT COEFFICIENTS OF A PLASMA (in French)

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

Balescu, R.; de Gottal, Ph.

1961-01-01

A closed formula is obtained for the long-lived corre1ations in an inhomogeneous plasma; it is expressed in terms of the one particle distribution function. This forms an appropriate starting point for a rigorous theory of transport phenomena in plasmas, including the effect of molecular corrclations. An expressson is obtained for the thermal conductivity. (auth)
Controlled-Root Approach To Digital Phase-Locked Loops

NASA Technical Reports Server (NTRS)

Stephens, Scott A.; Thomas, J. Brooks

1995-01-01

Performance tailored more flexibly and directly to satisfy design requirements. Controlled-root approach improved method for analysis and design of digital phase-locked loops (DPLLs). Developed rigorously from first principles for fully digital loops, making DPLL theory and design simpler and more straightforward (particularly for third- or fourth-order DPLL) and controlling performance more accurately in case of high gain.

The Development and Implementation of a Peer-Led Intervention to Prevent Smoking among Secondary School Students Using Their Established Social Networks

ERIC Educational Resources Information Center

Audrey, Suzanne; Cordall, Kathleen; Moore, Laurence; Cohen, David; Campbell, Rona

2004-01-01

Objective: To design, implement and evaluate a peer-led intervention to reduce smoking amongst secondary school students. Design: A health promotion intervention combining peer education with diffusion of innovation theory, to be rigorously evaluated by means of a cluster randomised controlled trial with concurrent process and economic…
Phase matrix induced symmetrics for multiple scattering using the matrix operator method

NASA Technical Reports Server (NTRS)

Hitzfelder, S. J.; Kattawar, G. W.

1973-01-01

Entirely rigorous proofs of the symmetries induced by the phase matrix into the reflection and transmission operators used in the matrix operator theory are given. Results are obtained for multiple scattering in both homogeneous and inhomogeneous atmospheres. These results will be useful to researchers using the method since large savings in computer time and storage are obtainable.
Ambiguity, logic, simplicity, and dynamics: Wittgensteinian evaluative criteria in peer review of quantitative research on categorization.

PubMed

Shimp, Charles P

2004-06-30

Research on categorization has changed over time, and some of these changes resemble how Wittgenstein's views changed from his Tractatus Logico-Philosophicus to his Philosophical Investigations. Wittgenstein initially focused on unambiguous, abstract, parsimonious, logical propositions and rules, and on independent, static, "atomic facts." This approach subsequently influenced the development of logical positivism and thereby may have indirectly influenced method and theory in research on categorization: much animal research on categorization has focused on learning simple, static, logical rules unambiguously interrelating small numbers of independent features. He later rejected logical simplicity and rigor and focused instead on Gestalt ideas about figure-ground reversals and context, the ambiguity of family resemblance, and the function of details of everyday language. Contemporary contextualism has been influenced by this latter position, some features of which appear in contemporary empirical research on categorization. These developmental changes are illustrated by research on avian local and global levels of visual perceptual analysis, categorization of rectangles and moving objects, and artificial grammar learning. Implications are described for peer review of quantitative theory in which ambiguity, logical rigor, simplicity, or dynamics are designed to play important roles.
The Three-Component Defocusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions

NASA Astrophysics Data System (ADS)

Biondini, Gino; Kraus, Daniel K.; Prinari, Barbara

2016-12-01

We present a rigorous theory of the inverse scattering transform (IST) for the three-component defocusing nonlinear Schrödinger (NLS) equation with initial conditions approaching constant values with the same amplitude as {xto±∞}. The theory combines and extends to a problem with non-zero boundary conditions three fundamental ideas: (i) the tensor approach used by Beals, Deift and Tomei for the n-th order scattering problem, (ii) the triangular decompositions of the scattering matrix used by Novikov, Manakov, Pitaevski and Zakharov for the N-wave interaction equations, and (iii) a generalization of the cross product via the Hodge star duality, which, to the best of our knowledge, is used in the context of the IST for the first time in this work. The combination of the first two ideas allows us to rigorously obtain a fundamental set of analytic eigenfunctions. The third idea allows us to establish the symmetries of the eigenfunctions and scattering data. The results are used to characterize the discrete spectrum and to obtain exact soliton solutions, which describe generalizations of the so-called dark-bright solitons of the two-component NLS equation.
Jones index, secret sharing and total quantum dimension

NASA Astrophysics Data System (ADS)

Fiedler, Leander; Naaijkens, Pieter; Osborne, Tobias J.

2017-02-01

We study the total quantum dimension in the thermodynamic limit of topologically ordered systems. In particular, using the anyons (or superselection sectors) of such models, we define a secret sharing scheme, storing information invisible to a malicious party, and argue that the total quantum dimension quantifies how well we can perform this task. We then argue that this can be made mathematically rigorous using the index theory of subfactors, originally due to Jones and later extended by Kosaki and Longo. This theory provides us with a ‘relative entropy’ of two von Neumann algebras and a quantum channel, and we argue how these can be used to quantify how much classical information two parties can hide form an adversary. We also review the total quantum dimension in finite systems, in particular how it relates to topological entanglement entropy. It is known that the latter also has an interpretation in terms of secret sharing schemes, although this is shown by completely different methods from ours. Our work provides a different and independent take on this, which at the same time is completely mathematically rigorous. This complementary point of view might be beneficial, for example, when studying the stability of the total quantum dimension when the system is perturbed.
Properties of field functionals and characterization of local functionals

NASA Astrophysics Data System (ADS)

Brouder, Christian; Dang, Nguyen Viet; Laurent-Gengoux, Camille; Rejzner, Kasia

2018-02-01

Functionals (i.e., functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the proper space of test functions (smooth functions) and of the relevant concept of differential (Bastiani differential) are discussed. The relation between the multiple derivatives of a functional and the corresponding distributions is described in detail. It is proved that, in a neighborhood of every test function, the support of a smooth functional is uniformly compactly supported and the order of the corresponding distribution is uniformly bounded. Relying on a recent work by Dabrowski, several spaces of functionals are furnished with a complete and nuclear topology. In view of physical applications, it is shown that most formal manipulations can be given a rigorous meaning. A new concept of local functionals is proposed and two characterizations of them are given: the first one uses the additivity (or Hammerstein) property, the second one is a variant of Peetre's theorem. Finally, the first step of a cohomological approach to quantum field theory is carried out by proving a global Poincaré lemma and defining multi-vector fields and graded functionals within our framework.
Understanding the Relativistic Generalization of Density Functional Theory (DFT) and Completing it in Practice

NASA Astrophysics Data System (ADS)

Bagayoko, Diola

In 2014, 50 years following the introduction of density functional theory (DFT), a rigorous understanding of it was published [AIP Advances, 4, 127104 (2014)]. This understanding included necessary steps ab initio electronic structure calculations have to take if their results are to possess the full physical content of DFT. These steps guarantee the fulfillment of conditions of validity of DFT; not surprisingly, they have led to accurate descriptions of several dozens of semiconductors, from first principle, without invoking derivative discontinuity or self-interaction correction. This presentation shows the mathematically and physically rigorous understanding of the relativistic extension of DFT by Rajagopal and Callaway {Phys. Rev. B 7, 1912 (1973)]. As in the non-relativistic case, the attainment of the absolute minima of the occupied energies is a necessary condition for the corresponding current density to be that of the ground state of the system and for computational results to agree with corresponding, experimental ones. Acknowledgments:This work was funded in part by the US National Science Foundation [NSF, Award Nos. EPS-1003897, NSF (2010-2015)-RII-SUBR, and HRD-1002541], the US Department of Energy, National Nuclear Security Administration (NNSA, Award No. DE-NA0002630), LaSPACE, and LONI-SUBR.
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.
The Madelung Picture as a Foundation of Geometric Quantum Theory

NASA Astrophysics Data System (ADS)

Reddiger, Maik

2017-10-01

Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but this has not resolved the problem. In this article we argue that a quantum theory recursing to quantization algorithms is necessarily incomplete. To provide an alternative approach, we show that the Schrödinger equation is a consequence of three partial differential equations governing the time evolution of a given probability density. These equations, discovered by Madelung, naturally ground the Schrödinger theory in Newtonian mechanics and Kolmogorovian probability theory. A variety of far-reaching consequences for the projection postulate, the correspondence principle, the measurement problem, the uncertainty principle, and the modeling of particle creation and annihilation are immediate. We also give a speculative interpretation of the equations following Bohm, Vigier and Tsekov, by claiming that quantum mechanical behavior is possibly caused by gravitational background noise.
Spin-Multiplet Components and Energy Splittings by Multistate Density Functional Theory.

PubMed

Grofe, Adam; Chen, Xin; Liu, Wenjian; Gao, Jiali

2017-10-05

Kohn-Sham density functional theory has been tremendously successful in chemistry and physics. Yet, it is unable to describe the energy degeneracy of spin-multiplet components with any approximate functional. This work features two contributions. (1) We present a multistate density functional theory (MSDFT) to represent spin-multiplet components and to determine multiplet energies. MSDFT is a hybrid approach, taking advantage of both wave function theory and density functional theory. Thus, the wave functions, electron densities and energy density-functionals for ground and excited states and for different components are treated on the same footing. The method is illustrated on valence excitations of atoms and molecules. (2) Importantly, a key result is that for cases in which the high-spin components can be determined separately by Kohn-Sham density functional theory, the transition density functional in MSDFT (which describes electronic coupling) can be defined rigorously. The numerical results may be explored to design and optimize transition density functionals for configuration coupling in multiconfigurational DFT.
Theory of the amplitude-phase retrieval in any linear-transform system and its applications

NASA Astrophysics Data System (ADS)

Yang, Guozhen; Gu, Ben-Yuan; Dong, Bi-Zhen

1992-12-01

This paper is a summary of the theory of the amplitude-phase retrieval problem in any linear transform system and its applications based on our previous works in the past decade. We describe the general statement on the amplitude-phase retrieval problem in an imaging system and derive a set of equations governing the amplitude-phase distribution in terms of the rigorous mathematical derivation. We then show that, by using these equations and an iterative algorithm, a variety of amplitude-phase problems can be successfully handled. We carry out the systematic investigations and comprehensive numerical calculations to demonstrate the utilization of this new algorithm in various transform systems. For instance, we have achieved the phase retrieval from two intensity measurements in an imaging system with diffraction loss (non-unitary transform), both theoretically and experimentally, and the recovery of model real image from its Hartley-transform modulus only in one and two dimensional cases. We discuss the achievement of the phase retrieval problem from a single intensity only based on the sampling theorem and our algorithm. We also apply this algorithm to provide an optimal design of the phase-adjusted plate for a phase-adjustment focusing laser accelerator and a design approach of single phase-only element for implementing optical interconnect. In order to closely simulate the really measured data, we examine the reconstruction of image from its spectral modulus corrupted by a random noise in detail. The results show that the convergent solution can always be obtained and the quality of the recovered image is satisfactory. We also indicated the relationship and distinction between our algorithm and the original Gerchberg- Saxton algorithm. From these studies, we conclude that our algorithm shows great capability to deal with the comprehensive phase-retrieval problems in the imaging system and the inverse problem in solid state physics. It may open a new way to solve important inverse source problems extensively appearing in physics.
ERP Reliability Analysis (ERA) Toolbox: An open-source toolbox for analyzing the reliability of event-related brain potentials.

PubMed

Clayson, Peter E; Miller, Gregory A

2017-01-01

Generalizability theory (G theory) provides a flexible, multifaceted approach to estimating score reliability. G theory's approach to estimating score reliability has important advantages over classical test theory that are relevant for research using event-related brain potentials (ERPs). For example, G theory does not require parallel forms (i.e., equal means, variances, and covariances), can handle unbalanced designs, and provides a single reliability estimate for designs with multiple sources of error. This monograph provides a detailed description of the conceptual framework of G theory using examples relevant to ERP researchers, presents the algorithms needed to estimate ERP score reliability, and provides a detailed walkthrough of newly-developed software, the ERP Reliability Analysis (ERA) Toolbox, that calculates score reliability using G theory. The ERA Toolbox is open-source, Matlab software that uses G theory to estimate the contribution of the number of trials retained for averaging, group, and/or event types on ERP score reliability. The toolbox facilitates the rigorous evaluation of psychometric properties of ERP scores recommended elsewhere in this special issue. Copyright © 2016 Elsevier B.V. All rights reserved.
Quadratic canonical transformation theory and higher order density matrices.

PubMed

Neuscamman, Eric; Yanai, Takeshi; Chan, Garnet Kin-Lic

2009-03-28

Canonical transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the effective Hamiltonian, and (ii) incorporation of the three-body reduced density matrix in the operator and density matrix decompositions. The quadratic commutator approximation improves CT's accuracy when used with a single-determinant reference, repairing the previous formal disadvantage of the single-reference linear CT theory relative to singles and doubles coupled cluster theory. Calculations on the BH and HF binding curves confirm this improvement. In multireference systems, the three-body reduced density matrix increases the overall accuracy of the CT theory. Tests on the H(2)O and N(2) binding curves yield results highly competitive with expensive state-of-the-art multireference methods, such as the multireference Davidson-corrected configuration interaction (MRCI+Q), averaged coupled pair functional, and averaged quadratic coupled cluster theories.
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.
Multipath analysis diffraction calculations

NASA Technical Reports Server (NTRS)

Statham, Richard B.

1996-01-01

This report describes extensions of the Kirchhoff diffraction equation to higher edge terms and discusses their suitability to model diffraction multipath effects of a small satellite structure. When receiving signals, at a satellite, from the Global Positioning System (GPS), reflected signals from the satellite structure result in multipath errors in the determination of the satellite position. Multipath error can be caused by diffraction of the reflected signals and a method of calculating this diffraction is required when using a facet model of the satellite. Several aspects of the Kirchhoff equation are discussed and numerical examples, in the near and far fields, are shown. The vector form of the extended Kirchhoff equation, by adding the Larmor-Tedone and Kottler edge terms, is given as a mathematical model in an appendix. The Kirchhoff equation was investigated as being easily implemented and of good accuracy in the basic form, especially in phase determination. The basic Kirchhoff can be extended for higher accuracy if desired. A brief discussion of the method of moments and the geometric theory of diffraction is included, but seems to offer no clear advantage in implementation over the Kirchhoff for facet models.
Optical system storage design with diffractive optical elements

NASA Technical Reports Server (NTRS)

Kostuk, Raymond K.; Haggans, Charles W.

1993-01-01

Optical data storage systems are gaining widespread acceptance due to their high areal density and the ability to remove the high capacity hard disk from the system. In magneto-optical read-write systems, a small rotation of the polarization state in the return signal from the MO media is the signal which must be sensed. A typical arrangement used for detecting these signals and correcting for errors in tracking and focusing on the disk is illustrated. The components required to achieve these functions are listed. The assembly and alignment of this complex system has a direct impact on cost, and also affects the size, weight, and corresponding data access rates. As a result, integrating these optical components and improving packaging techniques is an active area of research and development. Most designs of binary optic elements have been concerned with optimizing grating efficiency. However, rigorous coupled wave models for vector field diffraction from grating surfaces can be extended to determine the phase and polarization state of the diffracted field, and the design of polarization components. A typical grating geometry and the phase and polarization angles associated with the incident and diffracted fields are shown. In our current stage of work, we are examining system configurations which cascade several polarization functions on a single substrate. In this design, the beam returning from the MO disk illuminates a cascaded grating element which first couples light into the substrate, then introduces a quarter wave retardation, then a polarization rotation, and finally separates s- and p-polarized fields through a polarization beam splitter. The input coupler and polarization beam splitter are formed in volume gratings, and the two intermediate elements are zero-order elements.
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

Nuclear magnetic relaxation by the dipolar EMOR mechanism: General theory with applications to two-spin systems.

PubMed

Chang, Zhiwei; Halle, Bertil

2016-02-28

In aqueous systems with immobilized macromolecules, including biological tissue, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole-dipole couplings. We have embarked on a systematic program to develop, from the stochastic Liouville equation, a general and rigorous theory that can describe relaxation by the dipolar EMOR mechanism over the full range of exchange rates, dipole coupling strengths, and Larmor frequencies. Here, we present a general theoretical framework applicable to spin systems of arbitrary size with symmetric or asymmetric exchange. So far, the dipolar EMOR theory is only available for a two-spin system with symmetric exchange. Asymmetric exchange, when the spin system is fragmented by the exchange, introduces new and unexpected phenomena. Notably, the anisotropic dipole couplings of non-exchanging spins break the axial symmetry in spin Liouville space, thereby opening up new relaxation channels in the locally anisotropic sites, including longitudinal-transverse cross relaxation. Such cross-mode relaxation operates only at low fields; at higher fields it becomes nonsecular, leading to an unusual inverted relaxation dispersion that splits the extreme-narrowing regime into two sub-regimes. The general dipolar EMOR theory is illustrated here by a detailed analysis of the asymmetric two-spin case, for which we present relaxation dispersion profiles over a wide range of conditions as well as analytical results for integral relaxation rates and time-dependent spin modes in the zero-field and motional-narrowing regimes. The general theoretical framework presented here will enable a quantitative analysis of frequency-dependent water-proton longitudinal relaxation in model systems with immobilized macromolecules and, ultimately, will provide a rigorous link between relaxation-based magnetic resonance image contrast and molecular parameters.
A global solution to the Schrödinger equation: From Henstock to Feynman

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

Nathanson, Ekaterina S., E-mail: enathanson@ggc.edu; Jørgensen, Palle E. T., E-mail: palle-jorgensen@uiowa.edu

2015-09-15

One of the key elements of Feynman’s formulation of non-relativistic quantum mechanics is a so-called Feynman path integral. It plays an important role in the theory, but it appears as a postulate based on intuition, rather than a well-defined object. All previous attempts to supply Feynman’s theory with rigorous mathematics underpinning, based on the physical requirements, have not been satisfactory. The difficulty comes from the need to define a measure on the infinite dimensional space of paths and to create an integral that would possess all of the properties requested by Feynman. In the present paper, we consider a newmore » approach to defining the Feynman path integral, based on the theory developed by Muldowney [A Modern Theory of Random Variable: With Applications in Stochastic Calcolus, Financial Mathematics, and Feynman Integration (John Wiley & Sons, Inc., New Jersey, 2012)]. Muldowney uses the Henstock integration technique and deals with non-absolute integrability of the Fresnel integrals, in order to obtain a representation of the Feynman path integral as a functional. This approach offers a mathematically rigorous definition supporting Feynman’s intuitive derivations. But in his work, Muldowney gives only local in space-time solutions. A physical solution to the non-relativistic Schrödinger equation must be global, and it must be given in the form of a unitary one-parameter group in L{sup 2}(ℝ{sup n}). The purpose of this paper is to show that a system of one-dimensional local Muldowney’s solutions may be extended to yield a global solution. Moreover, the global extension can be represented by a unitary one-parameter group acting in L{sup 2}(ℝ{sup n})« less
Nuclear magnetic relaxation by the dipolar EMOR mechanism: General theory with applications to two-spin systems

NASA Astrophysics Data System (ADS)

Chang, Zhiwei; Halle, Bertil

2016-02-01

In aqueous systems with immobilized macromolecules, including biological tissue, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole-dipole couplings. We have embarked on a systematic program to develop, from the stochastic Liouville equation, a general and rigorous theory that can describe relaxation by the dipolar EMOR mechanism over the full range of exchange rates, dipole coupling strengths, and Larmor frequencies. Here, we present a general theoretical framework applicable to spin systems of arbitrary size with symmetric or asymmetric exchange. So far, the dipolar EMOR theory is only available for a two-spin system with symmetric exchange. Asymmetric exchange, when the spin system is fragmented by the exchange, introduces new and unexpected phenomena. Notably, the anisotropic dipole couplings of non-exchanging spins break the axial symmetry in spin Liouville space, thereby opening up new relaxation channels in the locally anisotropic sites, including longitudinal-transverse cross relaxation. Such cross-mode relaxation operates only at low fields; at higher fields it becomes nonsecular, leading to an unusual inverted relaxation dispersion that splits the extreme-narrowing regime into two sub-regimes. The general dipolar EMOR theory is illustrated here by a detailed analysis of the asymmetric two-spin case, for which we present relaxation dispersion profiles over a wide range of conditions as well as analytical results for integral relaxation rates and time-dependent spin modes in the zero-field and motional-narrowing regimes. The general theoretical framework presented here will enable a quantitative analysis of frequency-dependent water-proton longitudinal relaxation in model systems with immobilized macromolecules and, ultimately, will provide a rigorous link between relaxation-based magnetic resonance image contrast and molecular parameters.
The need to promote behaviour change at the cultural level: one factor explaining the limited impact of the MEMA kwa Vijana adolescent sexual health intervention in rural Tanzania. A process evaluation.

PubMed

Wight, Daniel; Plummer, Mary; Ross, David

2012-09-14

Few of the many behavioral sexual health interventions in Africa have been rigorously evaluated. Where biological outcomes have been measured, improvements have rarely been found. One of the most rigorous trials was of the multi-component MEMA kwa Vijana adolescent sexual health programme, which showed improvements in knowledge and reported attitudes and behaviour, but none in biological outcomes. This paper attempts to explain these outcomes by reviewing the process evaluation findings, particularly in terms of contextual factors. A large-scale, primarily qualitative process evaluation based mainly on participant observation identified the principal contextual barriers and facilitators of behavioural change. The contextual barriers involved four interrelated socio-structural factors: culture (i.e. shared practices and systems of belief), economic circumstances, social status, and gender. At an individual level they appeared to operate through the constructs of the theories underlying MEMA kwa Vijana - Social Cognitive Theory and the Theory of Reasoned Action - but the intervention was unable to substantially modify these individual-level constructs, apart from knowledge. The process evaluation suggests that one important reason for this failure is that the intervention did not operate sufficiently at a structural level, particularly in regard to culture. Recently most structural interventions have focused on gender or/and economics. Complementing these with a cultural approach could address the belief systems that justify and perpetuate gender and economic inequalities, as well as other barriers to behaviour change.
Systematic searching for theory to inform systematic reviews: is it feasible? Is it desirable?

PubMed

Booth, Andrew; Carroll, Christopher

2015-09-01

In recognising the potential value of theory in understanding how interventions work comes a challenge - how to make identification of theory less haphazard? To explore the feasibility of systematic identification of theory. We searched PubMed for published reviews (1998-2012) that had explicitly sought to identify theory. Systematic searching may be characterised by a structured question, methodological filters and an itemised search procedure. We constructed a template (BeHEMoTh - Behaviour of interest; Health context; Exclusions; Models or Theories) for use when systematically identifying theory. The authors tested the template within two systematic reviews. Of 34 systematic reviews, only 12 reviews (35%) reported a method for identifying theory. Nineteen did not specify how they identified studies containing theory. Data were unavailable for three reviews. Candidate terms include concept(s)/conceptual, framework(s), model(s), and theory/theories/theoretical. Information professionals must overcome inadequate reporting and the use of theory out of context. The review team faces an additional concern in lack of 'theory fidelity'. Based on experience with two systematic reviews, the BeHEMoTh template and procedure offers a feasible and useful approach for identification of theory. Applications include realist synthesis, framework synthesis or review of complex interventions. The procedure requires rigorous evaluation. © 2015 Health Libraries Group.
The validity and value of inclusive fitness theory

PubMed Central

Bourke, Andrew F. G.

2011-01-01

Social evolution is a central topic in evolutionary biology, with the evolution of eusociality (societies with altruistic, non-reproductive helpers) representing a long-standing evolutionary conundrum. Recent critiques have questioned the validity of the leading theory for explaining social evolution and eusociality, namely inclusive fitness (kin selection) theory. I review recent and past literature to argue that these critiques do not succeed. Inclusive fitness theory has added fundamental insights to natural selection theory. These are the realization that selection on a gene for social behaviour depends on its effects on co-bearers, the explanation of social behaviours as unalike as altruism and selfishness using the same underlying parameters, and the explanation of within-group conflict in terms of non-coinciding inclusive fitness optima. A proposed alternative theory for eusocial evolution assumes mistakenly that workers' interests are subordinate to the queen's, contains no new elements and fails to make novel predictions. The haplodiploidy hypothesis has yet to be rigorously tested and positive relatedness within diploid eusocial societies supports inclusive fitness theory. The theory has made unique, falsifiable predictions that have been confirmed, and its evidence base is extensive and robust. Hence, inclusive fitness theory deserves to keep its position as the leading theory for social evolution. PMID:21920980
The validity and value of inclusive fitness theory.

PubMed

Bourke, Andrew F G

2011-11-22

Social evolution is a central topic in evolutionary biology, with the evolution of eusociality (societies with altruistic, non-reproductive helpers) representing a long-standing evolutionary conundrum. Recent critiques have questioned the validity of the leading theory for explaining social evolution and eusociality, namely inclusive fitness (kin selection) theory. I review recent and past literature to argue that these critiques do not succeed. Inclusive fitness theory has added fundamental insights to natural selection theory. These are the realization that selection on a gene for social behaviour depends on its effects on co-bearers, the explanation of social behaviours as unalike as altruism and selfishness using the same underlying parameters, and the explanation of within-group conflict in terms of non-coinciding inclusive fitness optima. A proposed alternative theory for eusocial evolution assumes mistakenly that workers' interests are subordinate to the queen's, contains no new elements and fails to make novel predictions. The haplodiploidy hypothesis has yet to be rigorously tested and positive relatedness within diploid eusocial societies supports inclusive fitness theory. The theory has made unique, falsifiable predictions that have been confirmed, and its evidence base is extensive and robust. Hence, inclusive fitness theory deserves to keep its position as the leading theory for social evolution.
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)].
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.
Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding

NASA Technical Reports Server (NTRS)

Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.

1977-01-01

An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding.
General technique for discrete retardation-modulation polarimetry

NASA Technical Reports Server (NTRS)

Saxena, Indu

1993-01-01

The general theory and rigorous solutions of the Stokes parameters of light of a new technique in time-resolved ellipsometry are outlined. In this technique the phase of the linear retarder is stepped over three discrete values over a time interval for which the Stokes vector is determined. The technique has an advantage over synchronous detection techniques, as it can be implemented as a digitizable system.
Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data

DTIC Science & Technology

2015-09-30

Lagrangian Coastal Flow Data Dr. Pierre F.J. Lermusiaux Department of Mechanical Engineering Center for Ocean Science and Engineering Massachusetts...Develop and apply theory, schemes and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data...coastal ocean fields, both in Eulerian and Lagrangian forms. - Further develop and implement our GMM-DO schemes for robust Bayesian nonlinear estimation
Development of a dynamic computational model of social cognitive theory.

PubMed

Riley, William T; Martin, Cesar A; Rivera, Daniel E; Hekler, Eric B; Adams, Marc A; Buman, Matthew P; Pavel, Misha; King, Abby C

2016-12-01

Social cognitive theory (SCT) is among the most influential theories of behavior change and has been used as the conceptual basis of health behavior interventions for smoking cessation, weight management, and other health behaviors. SCT and other behavior theories were developed primarily to explain differences between individuals, but explanatory theories of within-person behavioral variability are increasingly needed as new technologies allow for intensive longitudinal measures and interventions adapted from these inputs. These within-person explanatory theoretical applications can be modeled as dynamical systems. SCT constructs, such as reciprocal determinism, are inherently dynamical in nature, but SCT has not been modeled as a dynamical system. This paper describes the development of a dynamical system model of SCT using fluid analogies and control systems principles drawn from engineering. Simulations of this model were performed to assess if the model performed as predicted based on theory and empirical studies of SCT. This initial model generates precise and testable quantitative predictions for future intensive longitudinal research. Dynamic modeling approaches provide a rigorous method for advancing health behavior theory development and refinement and for guiding the development of more potent and efficient interventions.
Reconstructing constructivism: causal models, Bayesian learning mechanisms, and the theory theory.

PubMed

Gopnik, Alison; Wellman, Henry M

2012-11-01

We propose a new version of the "theory theory" grounded in the computational framework of probabilistic causal models and Bayesian learning. Probabilistic models allow a constructivist but rigorous and detailed approach to cognitive development. They also explain the learning of both more specific causal hypotheses and more abstract framework theories. We outline the new theoretical ideas, explain the computational framework in an intuitive and nontechnical way, and review an extensive but relatively recent body of empirical results that supports these ideas. These include new studies of the mechanisms of learning. Children infer causal structure from statistical information, through their own actions on the world and through observations of the actions of others. Studies demonstrate these learning mechanisms in children from 16 months to 4 years old and include research on causal statistical learning, informal experimentation through play, and imitation and informal pedagogy. They also include studies of the variability and progressive character of intuitive theory change, particularly theory of mind. These studies investigate both the physical and the psychological and social domains. We conclude with suggestions for further collaborative projects between developmental and computational cognitive scientists.
Why so many "rigorous" evaluations fail to identify unintended consequences of development programs: How mixed methods can contribute.

PubMed

Bamberger, Michael; Tarsilla, Michele; Hesse-Biber, Sharlene

2016-04-01

Many widely-used impact evaluation designs, including randomized control trials (RCTs) and quasi-experimental designs (QEDs), frequently fail to detect what are often quite serious unintended consequences of development programs. This seems surprising as experienced planners and evaluators are well aware that unintended consequences frequently occur. Most evaluation designs are intended to determine whether there is credible evidence (statistical, theory-based or narrative) that programs have achieved their intended objectives and the logic of many evaluation designs, even those that are considered the most "rigorous," does not permit the identification of outcomes that were not specified in the program design. We take the example of RCTs as they are considered by many to be the most rigorous evaluation designs. We present a numbers of cases to illustrate how infusing RCTs with a mixed-methods approach (sometimes called an "RCT+" design) can strengthen the credibility of these designs and can also capture important unintended consequences. We provide a Mixed Methods Evaluation Framework that identifies 9 ways in which UCs can occur, and we apply this framework to two of the case studies. Copyright © 2016 Elsevier Ltd. All rights reserved.
Rigorous quantum limits on monitoring free masses and harmonic oscillators

NASA Astrophysics Data System (ADS)

Roy, S. M.

2018-03-01

There are heuristic arguments proposing that the accuracy of monitoring position of a free mass m is limited by the standard quantum limit (SQL): σ2( X (t ) ) ≥σ2( X (0 ) ) +(t2/m2) σ2( P (0 ) ) ≥ℏ t /m , where σ2( X (t ) ) and σ2( P (t ) ) denote variances of the Heisenberg representation position and momentum operators. Yuen [Phys. Rev. Lett. 51, 719 (1983), 10.1103/PhysRevLett.51.719] discovered that there are contractive states for which this result is incorrect. Here I prove universally valid rigorous quantum limits (RQL), viz. rigorous upper and lower bounds on σ2( X (t ) ) in terms of σ2( X (0 ) ) and σ2( P (0 ) ) , given by Eq. (12) for a free mass and by Eq. (36) for an oscillator. I also obtain the maximally contractive and maximally expanding states which saturate the RQL, and use the contractive states to set up an Ozawa-type measurement theory with accuracies respecting the RQL but beating the standard quantum limit. The contractive states for oscillators improve on the Schrödinger coherent states of constant variance and may be useful for gravitational wave detection and optical communication.
The case for integrating grounded theory and participatory action research: empowering clients to inform professional practice.

PubMed

Teram, Eli; Schachter, Candice L; Stalker, Carol A

2005-10-01

Grounded theory and participatory action research methods are distinct approaches to qualitative inquiry. Although grounded theory has been conceptualized in constructivist terms, it has elements of positivist thinking with an image of neutral search for objective truth through rigorous data collection and analysis. Participatory action research is based on a critique of this image and calls for more inclusive research processes. It questions the possibility of objective social sciences and aspires to engage people actively in all stages of generating knowledge. The authors applied both approaches in a project designed to explore the experiences of female survivors of childhood sexual abuse with physical therapy and subsequently develop a handbook on sensitive practice for clinicians that takes into consideration the needs and perspectives of these clients. Building on this experience, they argue that the integration of grounded theory and participatory action research can empower clients to inform professional practice.
QTest: Quantitative Testing of Theories of Binary Choice.

PubMed

Regenwetter, Michel; Davis-Stober, Clintin P; Lim, Shiau Hong; Guo, Ying; Popova, Anna; Zwilling, Chris; Cha, Yun-Shil; Messner, William

2014-01-01

The goal of this paper is to make modeling and quantitative testing accessible to behavioral decision researchers interested in substantive questions. We provide a novel, rigorous, yet very general, quantitative diagnostic framework for testing theories of binary choice. This permits the nontechnical scholar to proceed far beyond traditionally rather superficial methods of analysis, and it permits the quantitatively savvy scholar to triage theoretical proposals before investing effort into complex and specialized quantitative analyses. Our theoretical framework links static algebraic decision theory with observed variability in behavioral binary choice data. The paper is supplemented with a custom-designed public-domain statistical analysis package, the QTest software. We illustrate our approach with a quantitative analysis using published laboratory data, including tests of novel versions of "Random Cumulative Prospect Theory." A major asset of the approach is the potential to distinguish decision makers who have a fixed preference and commit errors in observed choices from decision makers who waver in their preferences.
Tests of Theories of Crime in Female Prisoners.

PubMed

Lindberg, Marc A; Fugett, April; Adkins, Ashtin; Cook, Kelsey

2017-02-01

Several general theories of crime were tested with path models on 293 female prisoners in a U.S. State prison. The theories tested included Social Bond and Control, Thrill/Risk Seeking, and a new attachment-based Developmental Dynamic Systems model. A large battery of different instruments ranging from measures of risk taking, to a crime addiction scale, to Childhood Adverse Events, to attachments and clinical issues were used. The older general theories of crime did not hold up well under the rigor of path modeling. The new dynamic systems model was supported that incorporated adverse childhood events leading to (a) peer crime, (b) crime addiction, and (c) a measure derived from the Attachment and Clinical Issues Questionnaire (ACIQ) that takes individual differences in attachments and clinical issues into account. The results were discussed in terms of new approaches to Research Defined Criteria of Diagnosis (RDoC) and new approaches to intervention.

Induction of depressed mood: a test of opponent-process theory.

PubMed

Ranieri, D J; Zeiss, A M

1984-12-01

Solomon's (1980) opponent-process theory of acquired motivation has been used to explain many phenomena in which affective or hedonic contrasts appear to exist, but has not been applied to the induction of depressed mood. The purpose of this study, therefore, was to determine whether opponent-process theory can be applied to this area. Velten's (1968) mood-induction procedure was used and subjects were assigned either to a depression-induction condition or to one of two control groups. Self-report measures of depressed mood were taken before, during, and at several points after the mood induction. Results were not totally consistent with a rigorous set of criteria for supporting an opponent-process interpretation. This suggests that the opponent-process model may not be applicable to induced depressed mood. Possible weaknesses in the experimental design, along with implications for opponent-process theory, are discussed.
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.
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)
How to do a grounded theory study: a worked example of a study of dental practices

PubMed Central

2011-01-01

Background Qualitative methodologies are increasingly popular in medical research. Grounded theory is the methodology most-often cited by authors of qualitative studies in medicine, but it has been suggested that many 'grounded theory' studies are not concordant with the methodology. In this paper we provide a worked example of a grounded theory project. Our aim is to provide a model for practice, to connect medical researchers with a useful methodology, and to increase the quality of 'grounded theory' research published in the medical literature. Methods We documented a worked example of using grounded theory methodology in practice. Results We describe our sampling, data collection, data analysis and interpretation. We explain how these steps were consistent with grounded theory methodology, and show how they related to one another. Grounded theory methodology assisted us to develop a detailed model of the process of adapting preventive protocols into dental practice, and to analyse variation in this process in different dental practices. Conclusions By employing grounded theory methodology rigorously, medical researchers can better design and justify their methods, and produce high-quality findings that will be more useful to patients, professionals and the research community. PMID:21902844
How to do a grounded theory study: a worked example of a study of dental practices.

PubMed

Sbaraini, Alexandra; Carter, Stacy M; Evans, R Wendell; Blinkhorn, Anthony

2011-09-09

Qualitative methodologies are increasingly popular in medical research. Grounded theory is the methodology most-often cited by authors of qualitative studies in medicine, but it has been suggested that many 'grounded theory' studies are not concordant with the methodology. In this paper we provide a worked example of a grounded theory project. Our aim is to provide a model for practice, to connect medical researchers with a useful methodology, and to increase the quality of 'grounded theory' research published in the medical literature. We documented a worked example of using grounded theory methodology in practice. We describe our sampling, data collection, data analysis and interpretation. We explain how these steps were consistent with grounded theory methodology, and show how they related to one another. Grounded theory methodology assisted us to develop a detailed model of the process of adapting preventive protocols into dental practice, and to analyse variation in this process in different dental practices. By employing grounded theory methodology rigorously, medical researchers can better design and justify their methods, and produce high-quality findings that will be more useful to patients, professionals and the research community.
Essential methodological considerations when using grounded theory.

PubMed

Achora, Susan; Matua, Gerald Amandu

2016-07-01

To suggest important methodological considerations when using grounded theory. A research method widely used in nursing research is grounded theory, at the centre of which is theory construction. However, researchers still struggle with some of its methodological issues. Although grounded theory is widely used to study and explain issues in nursing practice, many researchers are still failing to adhere to its rigorous standards. Researchers should articulate the focus of their investigations - the substantive area of interest as well as the focal population. This should be followed by a succinct explanation of the strategies used to collect and analyse data, supported by clear coding processes. Finally, the resolution of the core issues, including the core category and related categories, should be explained to advance readers' understanding. Researchers should endeavour to understand the tenets of grounded theory. This enables 'neophytes' in particular to make methodological decisions that will improve their studies' rigour and fit with grounded theory. This paper complements the current dialogue on improving the understanding of grounded theory methodology in nursing research. The paper also suggests important procedural decisions researchers need to make to preserve their studies' scientific merit and fit with grounded theory.
The tymbal muscle of cicada has flight muscle-type sarcomeric architecture and protein expression.

PubMed

Iwamoto, Hiroyuki

2017-01-01

The structural and biochemical features of the tymbal (sound-producing) muscle of cicadas were studied by X-ray diffraction and immunochemistry, and compared with those of flight muscles from the same species. The X-ray diffraction pattern of the tymbal muscle was very similar to that of the dorsal longitudinal flight muscle: In both muscles, the 2,0 equatorial reflection is much more intense than the 1,1, indicating that both muscles have a flight muscle-type myofilament lattice. In rigor, the first myosin/actin layer line reflection was finely lattice-sampled, indicating that the contractile proteins are arranged with a crystalline regularity as in asynchronous flight muscles. In contrast, the diffraction pattern from the tensor muscle, which modulates the sound by stressing the tymbal, did not show signs of such high regularity or flight muscle-type filament lattice. Electrophoretic patterns of myofibrillar proteins were also very similar in the tymbal muscle and flight muscles, but distinct from those from the tensor or leg muscles. The antibody raised against the flight muscle-specific troponin-I isoform reacted with an 80-kDa band from both tymbal and flight muscles, but with none of the bands from the tensor or leg muscles. The close similarities of the structural and biochemical profiles between the tymbal and the flight muscles suggest the possibility that a set of flight muscle-specific proteins is diverted to the tymbal muscle to meet its demand for fast, repetitive contractions.
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.
Analytic theory of orbit contraction and ballistic entry into planetary atmospheres

NASA Technical Reports Server (NTRS)

Longuski, J. M.; Vinh, N. X.

1980-01-01

A space object traveling through an atmosphere is governed by two forces: aerodynamic and gravitational. On this premise, equations of motion are derived to provide a set of universal entry equations applicable to all regimes of atmospheric flight from orbital motion under the dissipate force of drag through the dynamic phase of reentry, and finally to the point of contact with the planetary surface. Rigorous mathematical techniques such as averaging, Poincare's method of small parameters, and Lagrange's expansion, applied to obtain a highly accurate, purely analytic theory for orbit contraction and ballistic entry into planetary atmospheres. The theory has a wide range of applications to modern problems including orbit decay of artificial satellites, atmospheric capture of planetary probes, atmospheric grazing, and ballistic reentry of manned and unmanned space vehicles.
[History and biology: possible dialogues, necessary distances].

PubMed

Duarte, Regina Horta

2009-01-01

Evolution has often been rejected as a theory incompatible with proper historical reflection. While there are undoubtedly insurmountable barriers between biology and the study of man and society, a rigorous analysis of Darwinist theory demonstrates epistemological areas of contact between history and evolutionary biology. The amazing temporal perspective shared by both areas of knowledge points to some bridges of communication, like the importance of the event and of creation processes, the rejection of teleology and the idea of progress, the complexity of events between chance and necessity, and the impossibility of making predictions. This affords an opportunity for a transdisciplinary approach at a moment of various contemporary challenges.
Modeling of composite beams and plates for static and dynamic analysis

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Atilgan, Ali R.; Lee, Bok Woo

1990-01-01

A rigorous theory and corresponding computational algorithms was developed for a variety of problems regarding the analysis of composite beams and plates. The modeling approach is intended to be applicable to both static and dynamic analysis of generally anisotropic, nonhomogeneous beams and plates. Development of a theory for analysis of the local deformation of plates was the major focus. Some work was performed on global deformation of beams. Because of the strong parallel between beams and plates, the two were treated together as thin bodies, especially in cases where it will clarify the meaning of certain terminology and the motivation behind certain mathematical operations.
Orbital-dependent density functionals: Theory and applications

NASA Astrophysics Data System (ADS)

Kümmel, Stephan; Kronik, Leeor

2008-01-01

This review provides a perspective on the use of orbital-dependent functionals, which is currently considered one of the most promising avenues in modern density-functional theory. The focus here is on four major themes: the motivation for orbital-dependent functionals in terms of limitations of semilocal functionals; the optimized effective potential as a rigorous approach to incorporating orbital-dependent functionals within the Kohn-Sham framework; the rationale behind and advantages and limitations of four popular classes of orbital-dependent functionals; and the use of orbital-dependent functionals for predicting excited-state properties. For each of these issues, both formal and practical aspects are assessed.
Intrinsic measurement errors for the speed of light in vacuum

NASA Astrophysics Data System (ADS)

Braun, Daniel; Schneiter, Fabienne; Fischer, Uwe R.

2017-09-01

The speed of light in vacuum, one of the most important and precisely measured natural constants, is fixed by convention to c=299 792 458 m s-1 . Advanced theories predict possible deviations from this universal value, or even quantum fluctuations of c. Combining arguments from quantum parameter estimation theory and classical general relativity, we here establish rigorously the existence of lower bounds on the uncertainty to which the speed of light in vacuum can be determined in a given region of space-time, subject to several reasonable restrictions. They provide a novel perspective on the experimental falsifiability of predictions for the quantum fluctuations of space-time.
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.
Complex basis functions for molecular resonances: Methodology and applications

NASA Astrophysics Data System (ADS)

White, Alec; McCurdy, C. William; Head-Gordon, Martin

The computation of positions and widths of metastable electronic states is a challenge for molecular electronic structure theory because, in addition to the difficulty of the many-body problem, such states obey scattering boundary conditions. These resonances cannot be addressed with naïve application of traditional bound state electronic structure theory. Non-Hermitian electronic structure methods employing complex basis functions is one way that we may rigorously treat resonances within the framework of traditional electronic structure theory. In this talk, I will discuss our recent work in this area including the methodological extension from single determinant SCF-based approaches to highly correlated levels of wavefunction-based theory such as equation of motion coupled cluster and many-body perturbation theory. These approaches provide a hierarchy of theoretical methods for the computation of positions and widths of molecular resonances. Within this framework, we may also examine properties of resonances including the dependence of these parameters on molecular geometry. Some applications of these methods to temporary anions and dianions will also be discussed.
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.
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.
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
Study Quality in SLA: A Cumulative and Developmental Assessment of Designs, Analyses, Reporting Practices, and Outcomes in Quantitative L2 Research

ERIC Educational Resources Information Center

Plonsky, Luke

2011-01-01

I began this study with two assumptions. Assumption 1: Study quality matters. If the means by which researchers design, carry out, and report on their studies lack in rigor or transparency, theory and practice are likely to be misguided or at least decelerated. Assumption 2 is an implication of Assumption 1: Quality should be measured rather than…
Statistical hydrodynamics and related problems in spaces of probability measures

NASA Astrophysics Data System (ADS)

Dostoglou, Stamatios

2017-11-01

A rigorous theory of statistical solutions of the Navier-Stokes equations, suitable for exploring Kolmogorov's ideas, has been developed by M.I. Vishik and A.V. Fursikov, culminating in their monograph "Mathematical problems of Statistical Hydromechanics." We review some progress made in recent years following this approach, with emphasis on problems concerning the correlation of velocities and corresponding questions in the space of probability measures on Hilbert spaces.
Spectroscopy of the amide-I modes of acetanilide

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

Bigio, I.J.; Scott, A.C.; Johnston, C.T.

1989-01-01

Raman measurements were made on acetanilide (N-phenyl-acetamide). Data are presented of the integrated intensity of the 1650 cm/sup /minus/1/ band as a function of temperature. The experimental procedures and data reduction were highly rigorous and are believed to be to most reliable data available. A concise theory of polaron states is presented and used to interpret the data. 22 refs., 4 figs., 1 tab.
Gravitational Physics: the birth of a new era

NASA Astrophysics Data System (ADS)

Sakellariadou, Mairi

2017-11-01

We live the golden age of cosmology, while the era of gravitational astronomy has finally begun. Still, fundamental puzzles remain. Standard cosmology is formulated within the framework of Einstein's General theory of Relativity. Notwithstanding, General Relativity is not adequate to explain the earliest stages of cosmic existence, and cannot provide an explanation for the Big Bang itself. Modern early universe cosmology is in need of a rigorous underpinning in Quantum Gravity.
Statistical comparison of a hybrid approach with approximate and exact inference models for Fusion 2+

NASA Astrophysics Data System (ADS)

Lee, K. David; Wiesenfeld, Eric; Gelfand, Andrew

2007-04-01

One of the greatest challenges in modern combat is maintaining a high level of timely Situational Awareness (SA). In many situations, computational complexity and accuracy considerations make the development and deployment of real-time, high-level inference tools very difficult. An innovative hybrid framework that combines Bayesian inference, in the form of Bayesian Networks, and Possibility Theory, in the form of Fuzzy Logic systems, has recently been introduced to provide a rigorous framework for high-level inference. In previous research, the theoretical basis and benefits of the hybrid approach have been developed. However, lacking is a concrete experimental comparison of the hybrid framework with traditional fusion methods, to demonstrate and quantify this benefit. The goal of this research, therefore, is to provide a statistical analysis on the comparison of the accuracy and performance of hybrid network theory, with pure Bayesian and Fuzzy systems and an inexact Bayesian system approximated using Particle Filtering. To accomplish this task, domain specific models will be developed under these different theoretical approaches and then evaluated, via Monte Carlo Simulation, in comparison to situational ground truth to measure accuracy and fidelity. Following this, a rigorous statistical analysis of the performance results will be performed, to quantify the benefit of hybrid inference to other fusion tools.
Rigorous theory of molecular orientational nonlinear optics

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

Kwak, Chong Hoon, E-mail: chkwak@ynu.ac.kr; Kim, Gun Yeup

2015-01-15

Classical statistical mechanics of the molecular optics theory proposed by Buckingham [A. D. Buckingham and J. A. Pople, Proc. Phys. Soc. A 68, 905 (1955)] has been extended to describe the field induced molecular orientational polarization effects on nonlinear optics. In this paper, we present the generalized molecular orientational nonlinear optical processes (MONLO) through the calculation of the classical orientational averaging using the Boltzmann type time-averaged orientational interaction energy in the randomly oriented molecular system under the influence of applied electric fields. The focal points of the calculation are (1) the derivation of rigorous tensorial components of the effective molecularmore » hyperpolarizabilities, (2) the molecular orientational polarizations and the electronic polarizations including the well-known third-order dc polarization, dc electric field induced Kerr effect (dc Kerr effect), optical Kerr effect (OKE), dc electric field induced second harmonic generation (EFISH), degenerate four wave mixing (DFWM) and third harmonic generation (THG). We also present some of the new predictive MONLO processes. For second-order MONLO, second-order optical rectification (SOR), Pockels effect and difference frequency generation (DFG) are described in terms of the anisotropic coefficients of first hyperpolarizability. And, for third-order MONLO, third-order optical rectification (TOR), dc electric field induced difference frequency generation (EFIDFG) and pump-probe transmission are presented.« less
Benchmarking of density functionals for a soft but accurate prediction and assignment of (1) H and (13)C NMR chemical shifts in organic and biological molecules.

PubMed

Benassi, Enrico

2017-01-15

A number of programs and tools that simulate 1 H and 13 C nuclear magnetic resonance (NMR) chemical shifts using empirical approaches are available. These tools are user-friendly, but they provide a very rough (and sometimes misleading) estimation of the NMR properties, especially for complex systems. Rigorous and reliable ways to predict and interpret NMR properties of simple and complex systems are available in many popular computational program packages. Nevertheless, experimentalists keep relying on these "unreliable" tools in their daily work because, to have a sufficiently high accuracy, these rigorous quantum mechanical methods need high levels of theory. An alternative, efficient, semi-empirical approach has been proposed by Bally, Rablen, Tantillo, and coworkers. This idea consists of creating linear calibrations models, on the basis of the application of different combinations of functionals and basis sets. Following this approach, the predictive capability of a wider range of popular functionals was systematically investigated and tested. The NMR chemical shifts were computed in solvated phase at density functional theory level, using 30 different functionals coupled with three different triple-ζ basis sets. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

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
Limitations of the clump-correlation theories of shear-induced turbulence suppression

NASA Astrophysics Data System (ADS)

Zhang, Y. Z.; Mahajan, S. M.

2017-05-01

The clump theory, primarily constructed by Dupree [Phys. Fluids 15, 334 (1972)] based on the moment approach and then generalized to the correlation theory [Y. Z. Zhang and S. M. Mahajan, Phys. Fluids B 5, 2000 (1993)], has long served as a basis for constructing theories of turbulence suppression by shear flow. In order to reveal the "intrinsic approximation" invoked in the clump-correlation theory, we examine a model based on two dimensional magnetized drift waves. After a rigorous derivation of the exact response function—a key to average the Green function of the system—we show that the Dupree, Zhang-Mahajan approach is recovered as the lowest order approximation in a small dimensionless parameter ϒ which is a triple product of the correlation time, wave number, and fluctuating drift velocity. The clump-correlation theory, thus, constitutes the Gaussian and lowest order non-Markovian process for a homogeneous stationary turbulence. We also provide, especially for the tokamak community, a readily usable formula to evaluate the effectiveness of shear-flow suppression; this formula pertains regardless of the specific model of correlation time.
Invertibility of retarded response functions for Laplace transformable potentials: Application to one-body reduced density matrix functional theory.

PubMed

Giesbertz, K J H

2015-08-07

A theorem for the invertibility of arbitrary response functions is presented under the following conditions: the time dependence of the potentials should be Laplace transformable and the initial state should be a ground state, though it might be degenerate. This theorem provides a rigorous foundation for all density-functional-like theories in the time-dependent linear response regime. Especially for time-dependent one-body reduced density matrix (1RDM) functional theory, this is an important step forward, since a solid foundation has currently been lacking. The theorem is equally valid for static response functions in the non-degenerate case, so can be used to characterize the uniqueness of the potential in the ground state version of the corresponding density-functional-like theory. Such a classification of the uniqueness of the non-local potential in ground state 1RDM functional theory has been lacking for decades. With the aid of presented invertibility theorem presented here, a complete classification of the non-uniqueness of the non-local potential in 1RDM functional theory can be given for the first time.
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.
RF Exposure Analysis for Multiple Wi-Fi Devices In Enclosed Environment

NASA Technical Reports Server (NTRS)

Hwu, Shian U.; Rhodes, Bryan A.; deSilva, B. Kanishka; Sham, Catherine C.; Keiser, James R.

2013-01-01

Wi-Fi devices operated inside a metallic enclosure have been investigation in the recent years. A motivation for this study is to investigate wave propagation inside an enclosed environment such as elevator, car, aircraft, and spacecraft. There are performances and safety concerned that when the RF transmitters are used in the metallic enclosed environments. In this paper, the field distributions inside a confined room were investigated with multiple portable Wi-Fi devices. Computer simulations were performed using the rigorous computational electromagnetics (CEM). The method of moments (MoM) was used to model the mutual coupling among antennas. The geometrical theory of diffraction (GTD) was applied for the multiple reflections off the ground and walls. The prediction of the field distribution inside such environment is useful for the planning and deployment of a wireless radio and sensor system. Factors that affect the field strengths and distributions of radio waves in confined space were analyzed. The results could be used to evaluate the RF exposure safety in confined environment. By comparing the field distributions for various scenarios, it was observed that the Wi-Fi device counts, spacing and relative locations in the room are important factors in such environments. The RF Keep Out Zone (KOZ), where the electric field strengths exceed the permissible RF exposure limit, could be used to assess the RF human exposure compliance. As shown in this study, it s possible to maximize or minimize field intensity in specific area by arranging the Wi-Fi devices as a function of the relative location and spacing in a calculated manner.
Vector wavefront propagation modeling for the TPF coronagraph

NASA Astrophysics Data System (ADS)

Lieber, Michael D.; Neureuther, Andrew R.; Ceperley, Dan; Kasdin, N. Jeremy; Ter-Gabrielyan, Nikolay

2004-10-01

The TPF mission to search for exo-solar planets is extremely challenging both technically and from a performance modeling perspective. For the visible light coronagraph approach, the requirements for 1e10 rejection of star light to planet signal has not yet been achieved in laboratory testing and full-scale testing on the ground has many more obstacles and may not be possible. Therefore, end-to-end performance modeling will be relied upon to fully predict performance. One of the key technologies developed for achieving the rejection ratios uses shaped pupil masks to selectively cancel starlight in planet search regions by taking advantage of diffraction. Modeling results published to date have been based upon scalar wavefront propagation theory to compute the residual star and planet images. This ignores the 3D structure of the mask and the interaction of light with matter. In this paper we discuss previous work with a system model of the TPF coronagraph and propose an approach for coupling in a vector propagation model using the Finite Difference Time Domain (FDTD) method. This method, implemented in a software package called TEMPEST, allows us to propagate wavefronts through a mask structure to an integrated system model to explore the vector propagation aspects of the problem. We can then do rigorous mask scatter modeling to understand the effects of real physical mask structures on the magnitude, phase, polarization, and wavelength dependence of the transmitted light near edges. Shaped mask technology is reviewed, and computational aspects and interface issues to a TPF integrated system model are also discussed.
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.
Ordinary versus PT-symmetric Φ³ quantum field theory

DOE PAGES

Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele

2012-04-02

A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum fieldmore » theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.« less
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
A rigorous and simpler method of image charges

NASA Astrophysics Data System (ADS)

Ladera, C. L.; Donoso, G.

2016-07-01

The method of image charges relies on the proven uniqueness of the solution of the Laplace differential equation for an electrostatic potential which satisfies some specified boundary conditions. Granted by that uniqueness, the method of images is rightly described as nothing but shrewdly guessing which and where image charges are to be placed to solve the given electrostatics problem. Here we present an alternative image charges method that is based not on guessing but on rigorous and simpler theoretical grounds, namely the constant potential inside any conductor and the application of powerful geometric symmetries. The aforementioned required uniqueness and, more importantly, guessing are therefore both altogether dispensed with. Our two new theoretical fundaments also allow the image charges method to be introduced in earlier physics courses for engineering and sciences students, instead of its present and usual introduction in electromagnetic theory courses that demand familiarity with the Laplace differential equation and its boundary conditions.
First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

DOE PAGES

von Lilienfeld, O. Anatole

2013-02-26

A well-defined notion of chemical compound space (CCS) is essential for gaining rigorous control of properties through variation of elemental composition and atomic configurations. Here, we give an introduction to an atomistic first principles perspective on CCS. First, CCS is discussed in terms of variational nuclear charges in the context of conceptual density functional and molecular grand-canonical ensemble theory. Thereafter, we revisit the notion of compound pairs, related to each other via “alchemical” interpolations involving fractional nuclear charges in the electronic Hamiltonian. We address Taylor expansions in CCS, property nonlinearity, improved predictions using reference compound pairs, and the ounce-of-gold prizemore » challenge to linearize CCS. Finally, we turn to machine learning of analytical structure property relationships in CCS. Here, these relationships correspond to inferred, rather than derived through variational principle, solutions of the electronic Schrödinger equation.« less
The need to promote behaviour change at the cultural level: one factor explaining the limited impact of the MEMA kwa Vijana adolescent sexual health intervention in rural Tanzania. A process evaluation

PubMed Central

2012-01-01

Background Few of the many behavioral sexual health interventions in Africa have been rigorously evaluated. Where biological outcomes have been measured, improvements have rarely been found. One of the most rigorous trials was of the multi-component MEMA kwa Vijana adolescent sexual health programme, which showed improvements in knowledge and reported attitudes and behaviour, but none in biological outcomes. This paper attempts to explain these outcomes by reviewing the process evaluation findings, particularly in terms of contextual factors. Methods A large-scale, primarily qualitative process evaluation based mainly on participant observation identified the principal contextual barriers and facilitators of behavioural change. Results The contextual barriers involved four interrelated socio-structural factors: culture (i.e. shared practices and systems of belief), economic circumstances, social status, and gender. At an individual level they appeared to operate through the constructs of the theories underlying MEMA kwa Vijana - Social Cognitive Theory and the Theory of Reasoned Action – but the intervention was unable to substantially modify these individual-level constructs, apart from knowledge. Conclusion The process evaluation suggests that one important reason for this failure is that the intervention did not operate sufficiently at a structural level, particularly in regard to culture. Recently most structural interventions have focused on gender or/and economics. Complementing these with a cultural approach could address the belief systems that justify and perpetuate gender and economic inequalities, as well as other barriers to behaviour change. PMID:22978613
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.

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