Achieving Predictive Description of Negative Differential Resistance in Molecular Junctions Using a Range-Separated Hybrid Functional
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Results for “Green function”
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Electromagnetic and scalar diffraction by a right-angled wedge with a uniform surface impedance
The diffraction of an electromagnetic wave by a perfectly-conducting right-angled wedge with one surface covered by a dielectric slab or absorber is considered. The effect of the coated surface is approximated by a uniform surface impedance. The solution of the normally incident electromagnetic problem is facilitated by introducing two scalar fields which satisfy a mixed boundary condition on one surface of the wedge and a Neumann of Dirichlet boundary condition on the other. A functional transformation is employed to simplify the boundary conditions so that eigenfunction expansions can be obtained for the resulting Green's functions. The eigenfunction expansions are transformed into the integral representations which then are evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. A far zone approximation is made to obtain the scattered field from which the diffraction coefficient is found for scalar plane, cylindrical or sperical wave incident on the edge. With the introduction of a ray-fixed coordinate system, the dyadic diffraction coefficient for plane or cylindrical EM waves normally indicent on the edge is reduced to the sum of two dyads which can be written alternatively as a 2 X 2 diagonal matrix.
Hwang, Y. M.↗
The control and estimation of large space structures
A shape control or estimation problem for a large space structure can be modeled by a partial differential equation which represents changes in shape with respect to space and time, together with spatially discrete forcing functions or observations which represent the placement of actuators or sensors at discrete points along the structure. The use of Green's functions to convert boundary value problems into integral equations provides a convenient treatment of this mixture of continuous and discrete mathematics. Control and estimation algorithms are developed for the one-dimensional static beam to illustrate this technique.
Weeks, C.↗
Resonance frequency shift of an acoustic chamber containing a rigid sphere
The resonance frequency shift of an acoustic rectangular chamber due to the presence of a rigid sphere has been measured for l = 1,2 modes as a function of sphere size and position. The frequency shift is the results of volume exclusion and wave scattering. An analytical Green's function calculation was used to explain the data, providing excellent agreement between the measured and the calculated values. Also reported are similar measurements for a thin disk and the ratio of second harmonic to fundamental pressure as a function of sphere position. The measurement shows that the sphere reduces the first harmonic content, with sharply peaked suppression minima at specific sphere positions.
Leung, E.↗
The effects of earth model uncertainty on the inversion of seismic data for seismic source functions
SUMMARY We use Monte Carlo simulations to explore the effects of earth model uncertainty on the estimation of the seismic source time functions that correspond to the six independent components of the point source seismic moment tensor. Specifically, we invert synthetic data using Green’s functions estimated from a suite of earth models that contain stochastic density and seismic wave-speed heterogeneities. We find that the primary effect of earth model uncertainty on the data is that the amplitude of the first-arriving seismic energy is reduced, and that this amplitude reduction is proportional to the magnitude of the stochastic heterogeneities. Also, we find that the amplitude of the estimated seismic source functions can be under- or overestimated, depending on the stochastic earth model used to create the data. This effect is totally unpredictable, meaning that uncertainty in the earth model can lead to unpredictable biases in the amplitude of the estimated seismic source functions.
58 GEOSCIENCES↗
$S$ Hmax orientation in the Alpine region from observations of stress-induced anisotropy of nonlinear elasticity
The orientation of $S$ Hmax is commonly estimated from in situ borehole breakouts and earthquake focal mechanisms. Borehole measurements are expensive, and therefore sparse, and earthquake measurements can only be made in regions with many well-characterized earthquakes. Here, we derive the stress-field orientation using stress-induced anisotropy in nonlinear elasticity. In this method, we measure the strain derivative of velocity as a function of azimuth. We use a natural pump-probe (NPP) approach which consists of measuring elastic wave speed using empirical Green’s functions (probe) at different points of the earth tidal strain cycle (pump). The approach is validated using a larger data set in the Northern Alpine Foreland region where the orientation of maximum horizontal compressive stress is known from borehole breakouts and drilling-induced fractures. The technique resolves NNW-SSW to N-S directed $S$ Hmax which is in good agreement with conventional methods and the recent crustal stress model. We confirm that the NPP method can be applied to dense large-scale seismic arrays. The technique is then applied to the Southern Alps to understand the contemporary stress pattern associated with the ongoing deformation due to counterclockwise rotation of the Adriatic plate with respect to the European plate. Our results explain why the two major faults in Northeastern Italy, the Giudicarie Fault and the Periadriatic Line (Pustertal–Gailtal Fault) are currently inactive, while the currently acting stress field allows faults in Slovenia to deform actively. We have demonstrated that the pump-probe method has the potential to fill in the measurement gap left by conventional approaches, both in terms of regional coverage and in depth.
58 GEOSCIENCES↗
Examination of the sensitivity of quasifree reactions to details of the bound-state overlap functions
It is often stated that heavy-ion nucleon knockout reactions are mostly sensitive to the tails of the bound-state wave functions. In contrast, (p,2p) and (p,pn) reactions are known to access information on the full overlap functions within the nucleus. We analyze the oxygen isotopic chain and explore the differences between single-particle wave functions generated with potential models, used in the experimental analysis of knockout reactions, and ab initio computations from self-consistent Green's function theory. Contrary to common belief, we find that not only the tail of the overlap functions, but also their internal part is assessed in both reaction mechanisms, which are crucial to yield accurately determined spectroscopic information.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
MMIC devices for active phased array antennas
The study of printed circuit discontinuities is necessary in order to design, for example, transitions between rectangular waveguides and printed circuits. New developments with respect to the analytical approaches to this problem are discussed. A summary of the progress in the experimental approach is presented. The accurate solution for the modes in various millimeter-wave waveguides is essential in the analysis of many integrated circuit components, such as filters and impedance transformers. Problems associated with the numerical computation of these modes in two frequently used waveguide forms, namely, the finline and microstrip, are presented. The spectral domain method of formulation, with a moment method solution, is considered. This approach can be readily extended to analyze an arbitrary configuration of dielectric and metallized regions in a shielded enclosure. Galerkin's method is used, where the testing and basic functions are the same. It is shown that the mode functions, or eigenfunctions, are more sensitive to errors than the phase constants, or eigenvalues. The approximate mode functions do not satisfy the orthogonality relationship well, resulting in difficulties when these modal solutions are used to form an approximate Green's function or are used in a mode matching analysis.
Mittra, R.↗
Experimental and theoretical study of Rayleigh-Lamb waves in a plate containing a surface-breaking crack
Scattering of Rayleigh-Lamb waves by a normal surface-breaking crack in a plate has been studied both theoretically and experimentally. The two-dimensionality of the far field, generated by a ball impact source, is exploited to characterize the source function using a direct integration technique. The scattering of waves generated by this impact source by the crack is subsequently solved by employing a Green's function integral expression for the scattered field coupled with a finite element representation of the near field. It is shown that theoretical results of plate response, both in frequency and time, are similar to those obtained experimentally. Additionally, implication for practical applications are discussed.
Paffenholz, Joseph↗
Equation of motion coupled-cluster cumulant approach for intrinsic losses in x-ray spectra
We present an equation of motion coupled cluster approach for calculating and understanding intrinsic inelastic losses in core level x-ray absorption spectra (XAS). The method is based on a factorization of the transition amplitude in the time-domain, which leads to a convolution of an effective one-body spectrum and the core-hole spectral function. The spectral function characterizes these losses in terms of shake-up excitations and satellites, and is calculated using a cumulant representation of the core-hole Green’s function that includes non-linear corrections. The one-body spectrum also includes orthogonality corrections that enhance the XAS at the edge.
Rehr, John J.↗
Remote sensing of earth terrain
In remote sensing, the encountered geophysical media such as agricultural canopy, forest, snow, or ice are inhomogeneous and contain scatters in a random manner. Furthermore, weather conditions such as fog, mist, or snow cover can intervene the electromagnetic observation of the remotely sensed media. In the modelling of such media accounting for the weather effects, a multi-layer random medium model has been developed. The scattering effects of the random media are described by three-dimensional correlation functions with variances and correlation lengths corresponding to the fluctuation strengths and the physical geometry of the inhomogeneities, respectively. With proper consideration of the dyadic Green's function and its singularities, the strong fluctuation theory is used to calculate the effective permittivities which account for the modification of the wave speed and attenuation in the presence of the scatters. The distorted Born approximation is then applied to obtain the correlations of the scattered fields. From the correlation of the scattered field, calculated is the complete set of scattering coefficients for polarimetric radar observation or brightness temperature in passive radiometer applications. In the remote sensing of terrestrial ecosystems, the development of microwave remote sensing technology and the potential of SAR to measure vegetation structure and biomass have increased effort to conduct experimental and theoretical researches on the interactions between microwave and vegetation canopies. The overall objective is to develop inversion algorithms to retrieve biophysical parameters from radar data. In this perspective, theoretical models and experimental data are methodically interconnected in the following manner: Due to the complexity of the interactions involved, all theoretical models have limited domains of validity; the proposed solution is to use theoretical models, which is validated by experiments, to establish the region in which the radar response is most sensitive to the parameters of interest; theoretically simulated data will be used to generate simple invertible models over the region. For applications to the remote sensing of sea ice, the developed theoretical models need to be tested with experimental measurements. With measured ground truth such as ice thickness, temperature, salinity, and structure, input parameters to the theoretical models can be obtained to calculate the polarimetric scattering coefficients for radars or brightness temperature for radiometers and then compare theoretical results with experimental data. Validated models will play an important role in the interpretation and classification of ice in monitoring global ice cover from space borne remote sensors in the future. We present an inversion algorithm based on a recently developed inversion method referred to as the Renormalized Source-Type Integral Equation approach. The objective of this method is to overcome some of the limitations and difficulties of the iterative Born technique. It recasts the inversion, which is nonlinear in nature, in terms of the solution of a set of linear equations; however, the final inversion equation is still nonlinear. The derived inversion equation is an exact equation which sums up the iterative Neuman (or Born) series in a closed form and, thus, is a valid representation even in the case when the Born series diverges; hence, the name Renormalized Source-Type Integral Equation Approach.
Yueh, Herng-Aung↗
Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems
In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.
Sidi, Avram↗
Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems
In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.
Sidi, Avram↗
Analysis of Photothermal Characterization of Layered Materials: Design of Optimal Experiments
In this paper numerical calculations are presented for the steady-periodic temperature in layered materials and functionally-graded materials to simulate photothermal methods for the measurement of thermal properties. No laboratory experiments were performed. The temperature is found from a new Green s function formulation which is particularly well-suited to machine calculation. The simulation method is verified by comparison with literature data for a layered material. The method is applied to a class of two-component functionally-graded materials and results for temperature and sensitivity coefficients are presented. An optimality criterion, based on the sensitivity coefficients, is used for choosing what experimental conditions will be needed for photothermal measurements to determine the spatial distribution of thermal properties. This method for optimal experiment design is completely general and may be applied to any photothermal technique and to any functionally-graded material.
Cole, Kevin D.↗
Electronic structure of chromium trihalides beyond density functional theory
In this work, we explore the electronic band structure of freestanding monolayers of chromium trihalides Cr X 3 , X = Cl, Br, I, within an advanced ab initio theoretical approach based on the use of Green's function functionals. We compare the local density approximation with the quasiparticle self-consistent GW (QS GW ) approximation and its self-consistent extension ( QS G W ^ ) by solving the particle-hole ladder Bethe-Salpeter equations to improve the effective interaction W . We show that, at all levels of theory, the valence band consistently changes shape in the sequence Cl → Br → I , and the valence band maximum shifts from the M point to the Γ point. By analyzing the dynamic and momentum-dependent self-energy, we show that QS G W ^ adds to the localization of the systems in comparison with QS GW , thereby leading to a narrower band and reduced amount of halogens in the valence band manifold. Further analysis shows that X = Cl is most strongly correlated, and X = I is least correlated (most bandlike) as the hybridization between Cr d and X p enhances in the direction Cl → Br → I . For CrBr 3 and CrI 3 , we observe remarkable differences between the QS GW and QS G W ^ valence band structures, while their eigenfunctions are very similar. We show that weak perturbations, like moderate strain, weak changes to the d - p hybridization, and adding small U , can flip the valence band structures between these two solutions in these materials.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Global crustal response model
A computer program was developed for calculating the radial displacement due to the body tide as a function of spatial position and time. The positions of the moon and sun were evaluated by means of the Hill-Brown and Newcomb theories, respectively. Green's functions were utilized to simulate the elastic Earth responses due to point loads, a convolution program has been developed to evaluate the elastic Earth responses due to ocean loading by a given ocean tide constituent. These responses include radial and horizontal displacement, tilt and gravity acceleration, and strain tensor components.
Source record↗
Effect of Flight on the Noise from Turbulent Jets in the Generalized Acoustic Analogy
This paper presents an extension of a noise prediction method for static jets based on the Generalized Acoustic Analogy to include a non-zero ambient stream to simulate the effects of flight. Extended formulae for the propagator functions, source terms and the far-field acoustic spectrum are derived. The formulations of the equation and the boundary conditions for numerical solution of the scalar adjoint Green’s function in the presence of a non-zero ambient stream are also given. Wherever possible, the corresponding equations in the original papers for the static case and their extensions to include a flight stream are identified. The extended formulation is implemented into an existing code and used to make predictions of the effect of the flight stream on the observed far-field noise for a series of subsonic, unheated, axisymmetric jets over a range of jet-exit and free-stream velocities using Reynolds-averaged Navier-Stokes flow solutions as input. The predictions are compared with data from experiments conducted at NASA Glenn Research Center which extend a fundamental jet noise database to include a flight stream of various speeds. Descriptions of the experimental setup, data acquisition, post-processing and corrections applied to account for the external shear-layer are given. It is shown that the acoustic analogy-based method can provide reasonably good predictions of the impact of an external flight stream on the spectral characteristics of noise from unheated round jets.
Jet noise↗
Effect of Flight on the Noise from Turbulent Jets in the Generalized Acoustic Analogy
This paper presents an extension of a noise prediction method for static jets based on the Generalized Acoustic Analogy to include a non-zero ambient stream to simulate the effects of flight. Extended formulae for the propagator functions, source terms and the far-field acoustic spectrum are derived. The formulations of the equation and the boundary conditions for numerical solution of the scalar adjoint Green’s function in the presence of a non-zero ambient stream are also given. Wherever possible, the corresponding equations in the original papers for the static case and their extensions to include a flight stream are identified. The extended formulation is implemented into an existing code and used to make predictions of the effect of the flight stream on the observed far-field noise for a series of subsonic, unheated, axisymmetric jets over a range of jet-exit and free-stream velocities using Reynolds-averaged Navier-Stokes flow solutions as input. The predictions are compared with data from experiments conducted at NASA Glenn Research Center which extend a fundamental jet noise database to include a flight stream of various speeds. Descriptions of the experimental setup, data acquisition, post-processing and corrections applied to account for the external shear-layer are given. It is shown that the acoustic analogy-based method can provide reasonably good predictions of the impact of an external flight stream on the spectral characteristics of noise from unheated round jets.
Jet noise↗