Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “DIRICHLET PROBLEM”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies

Consider the one dimensional nonlinear beam equation u{sub tt} + u{sub xxxx} + mu + u{sup 3} = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form. .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

An efficient reconstruction algorithm for differential phase-contrast tomographic images from a limited number of views

The main focus of this paper is reconstruction of tomographic phase-contrast image from a set of projections. We propose an efficient reconstruction algorithm for differential phase-contrast computed tomography that can considerably reduce the number of projections required for reconstruction. The key result underlying this research is a projection theorem that states that the second derivative of the projection set is linearly related to the Laplacian of the tomographic image. The proposed algorithm first reconstructs the Laplacian image of the phase-shift distribution from the second-derivative of the projections using total variation regularization. The second step is to obtain the phase-shift distribution by solving a Poisson equation whose source is the Laplacian image previously reconstructed under the Dirichlet condition. We demonstrate the efficacy of this algorithm using both synthetically generated simulation data and projection data acquired experimentally at a synchrotron. The experimental phase data were acquired from a human coronary artery specimen using dark-field-imaging optics pioneered by our group. Our results demonstrate that the proposed algorithm can reduce the number of projections to approximately 33% as compared with the conventional filtered backprojection method, without any detrimental effect on the image quality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized Dirichlet condition

We consider an elliptic operator in a multidimensional domain with frequently changing boundary conditions in the case when the homogenized operator contains the Dirichlet boundary condition. We prove the uniform resolvent convergence of the perturbed operator to the homogenized operator and obtain estimates for the rate of convergence. A complete asymptotic expansion is constructed for the resolvent when it acts on sufficiently smooth functions. Bibliography: 41 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Galactic cosmic-ray modulation near the heliopause

We investigate the modulation of galactic cosmic rays in the inner and outer heliosheaths using three-dimensional numerical simulations. The model is based on the Parker transport equation integrated using a stochastic phase-space trajectory method. Integration is performed on a plasma background obtained from a global three-dimensional magnetohydrodynamic simulations. Our results predict a negligible amount of modulation in the outer heliosheath because of weak scattering of cosmic ray ions owing to very low levels of magnetic fluctuation power at wavenumbers relevant to the transport of cosmic rays with MeV to GeV energies. This means that the heliopause may be treated as a Dirichlet-type boundary for the purpose of energetic particle modeling. We present models with and without drift velocity to facilitate comparison with papers published earlier. We also attempt to reproduce the sudden step-like increases of cosmic-ray intensity observed by Voyager 1 before its encounter with the heliopause. Our results indicate that very slow cross-field diffusion in the outer heliosheath could produce a large gradient of cosmic rays inside the heliospheric boundary. The resulting large gradient in cosmic-ray intensity near the heliopause qualitatively agrees with recent Voyager 1 observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

A Dirichlet process mixture model for automatic {sup 18}F-FDG PET image segmentation: Validation study on phantoms and on lung and esophageal lesions

Purpose: The aim of this study was to implement a Dirichlet process mixture (DPM) model for automatic tumor edge identification on {sup 18}F-fluorodeoxyglucose positron emission tomography ({sup 18}F-FDG PET) images by optimizing the parameters on which the algorithm depends, to validate it experimentally, and to test its robustness. Methods: The DPM model belongs to the class of the Bayesian nonparametric models and uses the Dirichlet process prior for flexible nonparametric mixture modeling, without any preliminary choice of the number of mixture components. The DPM algorithm implemented in the statistical software package R was used in this work. The contouring accuracy was evaluated on several image data sets: on an IEC phantom (spherical inserts with diameter in the range 10–37 mm) acquired by a Philips Gemini Big Bore PET-CT scanner, using 9 different target-to-background ratios (TBRs) from 2.5 to 70; on a digital phantom simulating spherical/uniform lesions and tumors, irregular in shape and activity; and on 20 clinical cases (10 lung and 10 esophageal cancer patients). The influence of the DPM parameters on contour generation was studied in two steps. In the first one, only the IEC spheres having diameters of 22 and 37 mm and a sphere of the digital phantom (41.6 mm diameter) were studied by varying the main parameters until the diameter of the spheres was obtained within 0.2% of the true value. In the second step, the results obtained for this training set were applied to the entire data set to determine DPM based volumes of all available lesions. These volumes were compared to those obtained by applying already known algorithms (Gaussian mixture model and gradient-based) and to true values, when available. Results: Only one parameter was found able to significantly influence segmentation accuracy (ANOVA test). This parameter was linearly connected to the uptake variance of the tested region of interest (ROI). In the first step of the study, a calibration curve was determined to automatically generate the optimal parameter from the variance of the ROI. This “calibration curve” was then applied to contour the whole data set. The accuracy (mean discrepancy between DPM model-based contours and reference contours) of volume estimation was below (1 ± 7)% on the whole data set (1 SD). The overlap between true and automatically segmented contours, measured by the Dice similarity coefficient, was 0.93 with a SD of 0.03. Conclusions: The proposed DPM model was able to accurately reproduce known volumes of FDG concentration, with high overlap between segmented and true volumes. For all the analyzed inserts of the IEC phantom, the algorithm proved to be robust to variations in radius and in TBR. The main advantage of this algorithm was that no setting of DPM parameters was required in advance, since the proper setting of the only parameter that could significantly influence the segmentation results was automatically related to the uptake variance of the chosen ROI. Furthermore, the algorithm did not need any preliminary choice of the optimum number of classes to describe the ROIs within PET images and no assumption about the shape of the lesion and the uptake heterogeneity of the tracer was required.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

WE-H-BRC-06: A Unified Machine-Learning Based Probabilistic Model for Automated Anomaly Detection in the Treatment Plan Data

Purpose: The purpose of this work was to investigate the ability of a machine-learning based probabilistic approach to detect radiotherapy treatment plan anomalies given initial disease classes information. Methods In total we obtained 1112 unique treatment plans with five plan parameters and disease information from a Mosaiq treatment management system database for use in the study. The plan parameters include prescription dose, fractions, fields, modality and techniques. The disease information includes disease site, and T, M and N disease stages. A Bayesian network method was employed to model the probabilistic relationships between tumor disease information, plan parameters and an anomaly flag. A Bayesian learning method with Dirichlet prior was useed to learn the joint probabilities between dependent variables in error-free plan data and data with artificially induced anomalies. In the study, we randomly sampled data with anomaly in a specified anomaly space.We tested the approach with three groups of plan anomalies – improper concurrence of values of all five plan parameters and values of any two out of five parameters, and all single plan parameter value anomalies. Totally, 16 types of plan anomalies were covered by the study. For each type, we trained an individual Bayesian network. Results: We found that the true positive rate (recall) and positive predictive value (precision) to detect concurrence anomalies of five plan parameters in new patient cases were 94.45±0.26% and 93.76±0.39% respectively. To detect other 15 types of plan anomalies, the average recall and precision were 93.61±2.57% and 93.78±3.54% respectively. The computation time to detect the plan anomaly of each type in a new plan is ∼0.08 seconds. Conclusion: The proposed method for treatment plan anomaly detection was found effective in the initial tests. The results suggest that this type of models could be applied to develop plan anomaly detection tools to assist manual and automated plan checks. The senior author received research grants from ViewRay Inc. and Varian Medical System.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Structure of complexes of uranyl succinate with carbamide and dimethylurea

Three new succinate-containing complexes of uranyl with carbamide (Urea) and N,N'-dimethylurea (s-Dmur) are synthesized and studied by IR spectroscopy and X-ray diffraction. Structures of the same type, [UO{sub 2}(Urea){sub 4}(H{sub 2}O)][(UO{sub 2}){sub 2}(C{sub 4}H{sub 4}O{sub 4})3] · 3H{sub 2}О and [UO{sub 2}(Urea){sub 4}(H{sub 2}O)][(UO{sub 2}){sub 2}(C{sub 4}H{sub 4}O{sub 4})3] · 2Urea contain two sorts of uranium-containing complex groups, namely, mononuclear [UO{sub 2}(Urea){sub 4}(H{sub 2}O)]{sup 2+} cations and two-dimensional [(UO{sub 2}){sub 2}(C{sub 4}H{sub 4}O{sub 4}){sub 3}]{sup 2–} anions described by crystal-chemical formulas AМ{sub 5}{sup 1} and A{sub 2}Q{sub 3}{sup 02}, respectively (A = UO{sub 2}{sup 2+}, M{sup 1} = Urea or H{sub 2}O, Q{sup 02} = C{sub 4}H{sub 4}O{sub 4}{sup 2-}), and differ only in the nature of noncoordinated molecules—water and carbamide. The main structural groups of the [(UO{sub 2}){sub 2}(C{sub 4}H{sub 4}O{sub 4}){sub 2}(s-Dmur){sub 3}] crystals are [(UO{sub 2}){sub 2}(C{sub 4}H{sub 4}O{sub 4}){sub 2}(s-Dmur){sub 3}] chains belonging to the А{sub 2}Q{sub 2}{sup 02}M{sub 3}{sup 1} (A = UO{sub 2}{sup 2+}, Q{sup 02} = C{sub 4}H{sub 4}O{sub 4}{sup 2-}, M{sup 1} = s-Dmur) crystal-chemical group. Specific features of intermolecular interactions in the crystal structures are revealed using the Voronoi–Dirichlet method of molecular polyhedra.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1982

Improved definition of crustal magnetic anomalies for MAGSAT data

The routine correction of MAGSAT vector magnetometer data for external field effects such as the ring current and the daily variation by filtering long wavelength harmonics from the data is described. Separation of fields due to low altitude sources from those caused by high altitude sources is affected by means of dual harmonic expansions in the solution of Dirichlet's problem. This regression/harmonic filter procedure is applied on an orbit by orbit basis, and initial tests on MAGSAT data from orbit 1176 show reduction in external field residuals by 24.33 nT RMS in the horizontal component, and 10.95 nT RMS in the radial component.

Brown, R. D.↗
DOE OSTI2013

A high-order integral solver for scalar problems of diffraction by screens and apertures in three-dimensional space

We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three-dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules. The new integral formulations involve weighted versions of the classical integral operators related to the thin-screen Dirichlet and Neumann problems as well as a generalization to the open-surface problem of the classical Calderón formulae. The high-order quadrature rules we introduce for these operators, in turn, resolve the multiple Green function and edge singularities (which occur at arbitrarily close distances from each other, and which include weakly singular as well as hypersingular kernels) and thus give rise to super-algebraically fast convergence as the discretization sizes are increased. When used in conjunction with Krylov-subspace linear algebra solvers such as GMRES, the resulting solvers produce results of high accuracy in small numbers of iterations for low and high frequencies alike. We demonstrate our methodology with a variety of numerical results for screen and aperture problems at high frequencies—including simulation of classical experiments such as the diffraction by a circular disc (featuring in particular the famous Poisson spot), evaluation of interference fringes resulting from diffraction across two nearby circular apertures, as well as solution of problems of scattering by more complex geometries consisting of multiple scatterers and cavities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1986

Low frequency acoustic and electromagnetic scattering

This paper deals with two classes of problems arising from acoustics and electromagnetics scattering in the low frequency stations. The first class of problem is solving Helmholtz equation with Dirichlet boundary conditions on an arbitrary two dimensional body while the second one is an interior-exterior interface problem with Helmholtz equation in the exterior. Low frequency analysis show that there are two intermediate problems which solve the above problems accurate to 0(k/2/ log k) where k is the frequency. These solutions greatly differ from the zero frequency approximations. For the Dirichlet problem numerical examples are shown to verify the theoretical estimates.

Hariharan, S. I.↗
NASA NTRS1983

Low frequency acoustic and electromagnetic scattering

This paper deals with two classes of problems arising from acoustics and electromagnetics scattering in the low frequency stations. The first class of problem is solving Helmholtz equation with Dirichlet boundary conditions on an arbitrary two dimensional body while the second one is an interior-exterior interface problem with Helmholtz equation in the exterior. Low frequency analysis show that there are two intermediate problems which solve the above problems accurate to 0(k(2) log k) where k is the frequency. These solutions greatly differ from the zero frequency approximations. For the Dirichlet problem numerical examples are shown to verify the theoretical estimates.

Hariharan, S. I.↗
DOE OSTI2018

Finite-Dimensional Approximations of the Steklov–Poincaré Operator for the Helmholtz Equation in Periodic Waveguides

We consider the Dirichlet and Neumann problems for the Laplace operator in periodic waveguides. Integro-differential connections between the solution and its normal derivative, interpreted as a finite-dimensional version of the Steklov–Poincaré operator, are imposed on the artificial face of the truncated waveguide. These connections are obtained from the orthogonality and normalization conditions for the Floquet waves which are oscillating incoming/outgoing, as well as exponentially decaying/growing in the periodic waveguide. Under certain conditions, we establish the unique solvability of the problem and obtain error estimates for the solution itself, as well as for scattering coefficients in the solution. We give examples of trapped waves in periodic waveguides.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Fractional heat conduction with heat absorption in a sphere under Dirichlet boundary condition

The time-fractional heat conduction equation with the Caputo derivative and with heat absorption term proportional to temperature is considered in a sphere in the case of central symmetry. The fundamental solution to the Dirichlet boundary value problem is found, and the solution to the problem under constant boundary value of temperature is studied. The integral transform technique is used. The solutions are obtained in terms of series containing the Mittag-Leffler functions being the generalization of the exponential function. The numerical results are illustrated graphically.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Holography beyond conformal invariance and AdS isometry?

We suggest that the principle of holographic duality be extended beyond conformal invariance and AdS isometry. Such an extension is based on a special relation between functional determinants of the operators acting in the bulk and on its boundary, provided that the boundary operator represents the inverse propagators of the theory induced on the boundary by the Dirichlet boundary value problem in the bulk spacetime. This relation holds for operators of a general spin-tensor structure on generic manifolds with boundaries irrespective of their background geometry and conformal invariance, and it apparently underlies numerous O(N{sup 0}) tests of the AdS/CFT correspondence, based on direct calculation of the bulk and boundary partition functions, Casimir energies, and conformal anomalies. The generalized holographic duality is discussed within the concept of the “double-trace” deformation of the boundary theory, which is responsible in the case of large-N CFT coupled to the tower of higher-spin gauge fields for the renormalization group flow between infrared and ultraviolet fixed points. Potential extension of this method beyond the one-loop order is also briefly discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Comparison of Asymptotic and Numerical Approaches to the Study of the Resonant Tunneling in Two-Dimensional Symmetric Quantum Waveguides of Variable Cross-Sections

The waveguide considered coincides with a strip having two narrows of width ε. An electron wave function satisfies the Dirichlet boundary value problem for the Helmholtz equation. The part of the waveguide between the narrows serves as a resonator, and conditions for the electron resonant tunneling may occur. In the paper, asymptotic formulas as ε → 0 for characteristics of the resonant tunneling are used. The asymptotic results are compared with the numerical ones obtained by approximate calculation of the scattering matrix for energies in the interval between the second and third thresholds. The comparison allows us to state an interval of ε, where the asymptotic and numerical approaches agree. The suggested methods can be applied to more complicated models than that considered in the paper. In particular, the same approach can be used for asymptotic and numerical analysis of the tunneling in three-dimensional quantum waveguides of variable cross-sections. Bibliography: 3 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Nonlocal Boundary-Value Problem for a Differential-Operator Equation with Weak Nonlinearity in the Spaces of Dirichlet–Taylor Series with Fixed Spectrum

We study the nonlocal boundary-value problem for a differential-operator equation with nonlinear right-hand side and an operator B = (B{sub 1},…B{sub p}), where its components B{sub j} ≡ z{sub j}∂/∂z{sub j}, j = 1,…,p, are the operators of generalized differentiation with respect to the complex variable z{sub j}. By using the Nash–Moser iterative scheme, we establish the conditions of solvability of this problem in the scale of spaces of functions of several complex variables, which are Dirichlet–Taylor series with fixed spectrum.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Laplace's equation and the Dirichlet-Neumann map in multiply connected domains

A variety of problems in material science and fluid dynamics require the solution of Laplace's equation in multiply connected domains. Integral equation methods are natural candidates for such problems, since they discretize the boundary alone, require no special effort for free boundaries, and achieve superalgebraic convergence rates on sufficiently smooth domains in two space dimensions, regardless of shape. Current integral equation methods for the Dirichlet problem, however, require the solution of M independent problems of dimension N, where M is the number of boundary components and N is the total number of points in the discretization. In this paper, we present a new boundary integral equation approach, valid for both interior and exterior problems, which requires the solution of a single linear system of dimension N + M. We solve this system by making use of an iterative method (GMRES) combined with the last multipole method for the rapid calculation of the necessary matrix vector products. For a two-dimensional system with 200 components and 100 points on each boundary, we gain a speedup of a factor of 100 from the new analytic formulation and a factor of 50 from the fast multipole method. The resulting scheme brings large scale calculations in extremely complex domains within practical reach.

Greenbaum, A.↗
NASA NTRS1981

Inverse scattering for an exterior Dirichlet program

Scattering due to a metallic cylinder which is in the field of a wire carrying a periodic current is considered. The location and shape of the cylinder is obtained with a far field measurement in between the wire and the cylinder. The same analysis is applicable in acoustics in the situation that the cylinder is a soft wall body and the wire is a line source. The associated direct problem in this situation is an exterior Dirichlet problem for the Helmholtz equation in two dimensions. An improved low frequency estimate for the solution of this problem using integral equation methods is presented. The far field measurements are related to the solutions of boundary integral equations in the low frequency situation. These solutions are expressed in terms of mapping function which maps the exterior of the unknown curve onto the exterior of a unit disk. The coefficients of the Laurent expansion of the conformal transformations are related to the far field coefficients. The first far field coefficient leads to the calculation of the distance between the source and the cylinder.

Hariharan, S. I.↗