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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Analytical Study and Experimental Verification of Shear-Thinning Ink Flow in Direct Ink Writing Process

Abstract Direct ink writing (DIW) process is a facile additive manufacturing technology to fabricate three-dimensional (3D) objects with various materials. Its versatility has attracted considerable interest in academia and industry in recent years. As such, upsurging endeavors are invested in advancing the ink flow behaviors in order to optimize the process resolution and the printing quality. However, so far, the physical phenomena during the DIW process are not revealed in detail, leaving a research gap between the physical experiments and its underlying theories. Here, we present a comprehensive analytical study of non-Newtonian ink flow behavior during the DIW process. Different syringe-nozzle geometries are modeled for the comparative case studies. By using the computational fluid dynamics (CFD) simulation method, we reveal the shear-thinning property during the ink extrusion process. Besides, we study the viscosity, shear stress, and velocity fields, and analyze the advantages and drawbacks of each syringe-nozzle model. On the basis of these investigations and analyses, we propose an improved syringe-nozzle geometry for stable extrusion and high printing quality. A set of DIW printing experiments and rheological characterizations are carried out to verify the simulation studies. The results developed in this work offer an in-depth understanding of the ink flow behavior in the DIW process, providing valuable guidelines for optimizing the physical DIW configuration toward high-resolution printing and, consequently, improving the performance of DIW-printed objects.

Engineering↗
DOE OSTI2020

Data Analytics Applied to Coal Fired Boilers for Detecting Leaks

Data analytics were used to detect boiler leaks from five different coal-fired boilers including both subcritical and supercritical systems. Discriminant functions were developed that detected leaks up to two weeks prior to forced plant shutdowns for repairs. The leaks were identified to occur at different sections of the boiler for each plant, including waterwalls, economizer and superheater using conventional process measurement data. Leaking conditions were detected with a high degree of confidence (≪ 1% misclassified observations) and were able to distinguish normal operations from those time periods with steam leaks even while operating the power plants in power cycling mode.Multivariable statistical analyses, including Principal Component (PCA), cluster, and Fischer Discriminant Analysis (FDA) were used to characterize the leak occurrence. Normal and operational states with steam leaks were provided in the original process datasets. These datasets were split into two different groups for training and validation purposes. The data were sorted chronologically, and every third observation was assigned to training the Discriminant Function Model (DFM) while the rest were reserved for validation. PCA was used to reduce dimensionality of the original datasets. Canonical and FDA analyses were used to investigate the relationship between process variables. The outcome of the analyses revealed that nearly 35,000 observations were classified correctly; less than 0.05% of total observations were misclassified to be leaking, i.e. both false positives and false negatives.

Indrawan, Natarianto↗
DOE OSTI2013

Evaluation of an analytic linear Boltzmann transport equation solver for high-density inhomogeneities

Purpose: Acuros external beam (Acuros XB) is a novel dose calculation algorithm implemented through the ECLIPSE treatment planning system. The algorithm finds a deterministic solution to the linear Boltzmann transport equation, the same equation commonly solved stochastically by Monte Carlo methods. This work is an evaluation of Acuros XB, by comparison with Monte Carlo, for dose calculation applications involving high-density materials. Existing non-Monte Carlo clinical dose calculation algorithms, such as the analytic anisotropic algorithm (AAA), do not accurately model dose perturbations due to increased electron scatter within high-density volumes. Methods: Acuros XB, AAA, and EGSnrc based Monte Carlo are used to calculate dose distributions from 18 MV and 6 MV photon beams delivered to a cubic water phantom containing a rectangular high density (4.0-8.0 g/cm{sup 3}) volume at its center. The algorithms are also used to recalculate a clinical prostate treatment plan involving a unilateral hip prosthesis, originally evaluated using AAA. These results are compared graphically and numerically using gamma-index analysis. Radio-chromic film measurements are presented to augment Monte Carlo and Acuros XB dose perturbation data. Results: Using a 2% and 1 mm gamma-analysis, between 91.3% and 96.8% of Acuros XB dose voxels containing greater than 50% the normalized dose were in agreement with Monte Carlo data for virtual phantoms involving 18 MV and 6 MV photons, stainless steel and titanium alloy implants and for on-axis and oblique field delivery. A similar gamma-analysis of AAA against Monte Carlo data showed between 80.8% and 87.3% agreement. Comparing Acuros XB and AAA evaluations of a clinical prostate patient plan involving a unilateral hip prosthesis, Acuros XB showed good overall agreement with Monte Carlo while AAA underestimated dose on the upstream medial surface of the prosthesis due to electron scatter from the high-density material. Film measurements support the dose perturbations demonstrated by Monte Carlo and Acuros XB data. Conclusions: Acuros XB is shown to perform as well as Monte Carlo methods and better than existing clinical algorithms for dose calculations involving high-density volumes.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2014

Analytical, experimental, and Monte Carlo system response matrix for pinhole SPECT reconstruction

Purpose: To assess the performance of two approaches to the system response matrix (SRM) calculation in pinhole single photon emission computed tomography (SPECT) reconstruction. Methods: Evaluation was performed using experimental data from a low magnification pinhole SPECT system that consisted of a rotating flat detector with a monolithic scintillator crystal. The SRM was computed following two approaches, which were based on Monte Carlo simulations (MC-SRM) and analytical techniques in combination with an experimental characterization (AE-SRM). The spatial response of the system, obtained by using the two approaches, was compared with experimental data. The effect of the MC-SRM and AE-SRM approaches on the reconstructed image was assessed in terms of image contrast, signal-to-noise ratio, image quality, and spatial resolution. To this end, acquisitions were carried out using a hot cylinder phantom (consisting of five fillable rods with diameters of 5, 4, 3, 2, and 1 mm and a uniform cylindrical chamber) and a custom-made Derenzo phantom, with center-to-center distances between adjacent rods of 1.5, 2.0, and 3.0 mm. Results: Good agreement was found for the spatial response of the system between measured data and results derived from MC-SRM and AE-SRM. Only minor differences for point sources at distances smaller than the radius of rotation and large incidence angles were found. Assessment of the effect on the reconstructed image showed a similar contrast for both approaches, with values higher than 0.9 for rod diameters greater than 1 mm and higher than 0.8 for rod diameter of 1 mm. The comparison in terms of image quality showed that all rods in the different sections of a custom-made Derenzo phantom could be distinguished. The spatial resolution (FWHM) was 0.7 mm at iteration 100 using both approaches. The SNR was lower for reconstructed images using MC-SRM than for those reconstructed using AE-SRM, indicating that AE-SRM deals better with the projection noise than MC-SRM. Conclusions: The authors' findings show that both approaches provide good solutions to the problem of calculating the SRM in pinhole SPECT reconstruction. The AE-SRM was faster to create and handle the projection noise better than MC-SRM. Nevertheless, the AE-SRM required a tedious experimental characterization of the intrinsic detector response. Creation of the MC-SRM required longer computation time and handled the projection noise worse than the AE-SRM. Nevertheless, the MC-SRM inherently incorporates extensive modeling of the system and therefore experimental characterization was not required.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

SU-E-T-171: Evaluation of the Analytical Anisotropic Algorithm in a Small Finger Joint Phantom Using Monte Carlo Simulation

Purpose: This study investigated the performance of the anisotropic analytical algorithm (AAA) in dose calculation in radiotherapy concerning a small finger joint. Monte Carlo simulation (EGSnrc code) was used in this dosimetric evaluation. Methods: Heterogeneous finger joint phantom containing a vertical water layer (bone joint or cartilage) sandwiched by two bones with dimension 2 × 2 × 2 cm{sup 3} was irradiated by the 6 MV photon beams (field size = 4 × 4 cm{sup 2}). The central beam axis was along the length of the bone joint and the isocenter was set to the center of the joint. The joint width and beam angle were varied from 0.5–2 mm and 0°–15°, respectively. Depth doses were calculated using the AAA and DOSXYZnrc. For dosimetric comparison and normalization, dose calculations were repeated in water phantom using the same beam geometry. Results: Our AAA and Monte Carlo results showed that the AAA underestimated the joint doses by 10%–20%, and could not predict joint dose variation with changes of joint width and beam angle. The calculated bone dose enhancement for the AAA was lower than Monte Carlo and the depth of maximum dose for the phantom was smaller than that for the water phantom. From Monte Carlo results, there was a decrease of joint dose as its width increased. This reflected the smaller the joint width, the more the bone scatter contributed to the depth dose. Moreover, the joint dose was found slightly decreased with an increase of beam angle. Conclusion: The AAA could not handle variations of joint dose well with changes of joint width and beam angle based on our finger joint phantom. Monte Carlo results showed that the joint dose decreased with increase of joint width and beam angle. This dosimetry comparison should be useful to radiation staff in radiotherapy related to small bone joint.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

SU-E-T-481: Dosimetric Comparison of Acuros XB and Anisotropic Analytic Algorithm with Commercial Monte Carlo Based Dose Calculation Algorithm for Stereotactic Body Radiation Therapy of Lung Cancer

Purpose: To evaluate performance of three commercially available treatment planning systems for stereotactic body radiation therapy (SBRT) of lung cancer using the following algorithms: Boltzmann transport equation based algorithm (AcurosXB AXB), convolution based algorithm Anisotropic Analytic Algorithm (AAA); and Monte Carlo based algorithm (XVMC). Methods: A total of 10 patients with early stage non-small cell peripheral lung cancer were included. The initial clinical plans were generated using the XVMC based treatment planning system with a prescription of 54Gy in 3 fractions following RTOG0613 protocol. The plans were recalculated with the same beam parameters and monitor units using AAA and AXB algorithms. A calculation grid size of 2mm was used for all algorithms. The dose distribution, conformity, and dosimetric parameters for the targets and organs at risk (OAR) are compared between the algorithms. Results: The average PTV volume was 19.6mL (range 4.2–47.2mL). The volume of PTV covered by the prescribed dose (PTV-V100) were 93.97±2.00%, 95.07±2.07% and 95.10±2.97% for XVMC, AXB and AAA algorithms, respectively. There was no significant difference in high dose conformity index; however, XVMC predicted slightly higher values (p=0.04) for the ratio of 50% prescription isodose volume to PTV (R50%). The percentage volume of total lungs receiving dose >20Gy (LungV20Gy) were 4.03±2.26%, 3.86±2.22% and 3.85±2.21% for XVMC, AXB and AAA algorithms. Examination of dose volume histograms (DVH) revealed small differences in targets and OARs for most patients. However, the AAA algorithm was found to predict considerable higher PTV coverage compared with AXB and XVMC algorithms in two cases. The dose difference was found to be primarily located at the periphery region of the target. Conclusion: For clinical SBRT lung treatment planning, the dosimetric differences between three commercially available algorithms are generally small except at target periphery. XVMC and AXB algorithms are recommended for accurate dose estimation at tissue boundaries.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

SU-E-T-135: Assessing the Clinical Impact of Approximations in Analytical Dose Calculations for Proton Therapy

Purpose: To estimate the clinical relevance of approximations made in analytical dose calculation methods (ADCs) used for treatment planning on tumor coverage and tumor control probability (TCP) in proton therapy. Methods: We compared dose distributions planned with ADC to delivered dose distributions (as determined by TOPAS Monte Carlo (MC) simulations). We investigated 10 patients per site for 5 treatment sites (head-and-neck, lung, breast, prostate, liver). We evaluated differences between the two dose distributions analyzing dosimetric indices based on the dose-volume-histograms, the γ-index and the TCP. The normal tissue complication probability (NTCP) was estimated for the bladder and anterior rectum for the prostate patients. Results: We find that the target doses are overestimated by the ADC by 1–2% on average for all patients considered. All dosimetric indices (the mean dose, D95, D50 and D02, the dose values covering 95%, 50% and 2% of the target volume, respectively) are predicted within 5% of the delivered dose. A γ-index with a 3%/3mm criteria had a passing rate for target volumes above 96% for all patients. The TCP predicted by the two algorithms was up to 2%, 2.5%, 6%, 6.5%, and 11% for liver and breast, prostate, head-and-neck and lung patients, respectively. Differences in NTCP for anterior-rectum and bladder for prostate patients were less than 3%. Conclusion: We show that ADC provide adequate dose distributions for most patients, however, they can Result in underdosage of the target by as much as 5%. The TCP was found to be up to 11% lower than predicted. Advanced dose-calculation methods like MC simulations may be necessary in proton therapy to ensure target coverage for heterogeneous patient geometries, in clinical trials comparing proton therapy to conventional radiotherapy to avoid biases due to systematic discrepancies in calculated dose distributions, and, if tighter range margins are considered. Fully funded by NIH grants.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

SU-E-T-290: Dosimetric Accuracy of Acuros XB and Analytical Anisotropic Algorithm in Stereotactic Ablative Radiotherapy of Small Lung Lesions

Purpose: The accuracy of dose calculation for lung stereotactic ablative radiotherapy (SABR) of small lesions critically depends on the proper modeling of the lateral scatter in heterogeneous media. In recent years, grid-based Boltzman solvers such as Acuros XB (AXB) have been introduced for enhanced modeling of radiation transport in heterogeneous media. The purpose of this study is to evaluate the dosimetric impact of dose calculation between AXB and convolution-superposition algorithms such as analytical anisotropic algorithm (AAA) for small lesion sizes and different beam energies. Methods: Five lung SABR VMAT cases with GTV ranged from 0.8cm to 2.5cm in diameter were studied. For each case, doses were calculated by AAA, AXB (V11031) and Monte Carlo simulation (MC) with the same plan parameters for 10MV and 6MV. The dose calculation accuracy were evaluated by comparing DVHs and dose distributions with MC as the benchmark. The accuracy of calculated dose was also validated by EBT3 film measurement with a field size of 3cmx3cm in a thorax phantom. Results: For 10MV and GTV less than 1cm, dose calculated by AXB agrees well with MC compared to AAA. Dose difference calculated with AXB and AAA could be up to 30%. For GTV greater than 2cm, calculation results of AXB and AAA agree within 5% in GTV. For 6MV, the difference between calculated doses by AXB and AAA is less 10% for GTV less than 1cm. Based on film measurements, lung dose was overestimated 10% and 20% by AAA for 6MV and 10MV. Conclusion: Lateral scatter and transport is modeled more accurately by AXB than AAA in heterogeneous media, especially for small field size and high energy beams. The accuracy depends on the assigned material in calculation. If grid-based Boltzman solvers or MC are not available for calculation, lower energy beams should be used for treatment.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Analytic image reconstruction from partial data for a single-scan cone-beam CT with scatter correction

Purpose: A beam-blocker composed of multiple strips is a useful gadget for scatter correction and/or for dose reduction in cone-beam CT (CBCT). However, the use of such a beam-blocker would yield cone-beam data that can be challenging for accurate image reconstruction from a single scan in the filtered-backprojection framework. The focus of the work was to develop an analytic image reconstruction method for CBCT that can be directly applied to partially blocked cone-beam data in conjunction with the scatter correction. Methods: The authors developed a rebinned backprojection-filteration (BPF) algorithm for reconstructing images from the partially blocked cone-beam data in a circular scan. The authors also proposed a beam-blocking geometry considering data redundancy such that an efficient scatter estimate can be acquired and sufficient data for BPF image reconstruction can be secured at the same time from a single scan without using any blocker motion. Additionally, scatter correction method and noise reduction scheme have been developed. The authors have performed both simulation and experimental studies to validate the rebinned BPF algorithm for image reconstruction from partially blocked cone-beam data. Quantitative evaluations of the reconstructed image quality were performed in the experimental studies. Results: The simulation study revealed that the developed reconstruction algorithm successfully reconstructs the images from the partial cone-beam data. In the experimental study, the proposed method effectively corrected for the scatter in each projection and reconstructed scatter-corrected images from a single scan. Reduction of cupping artifacts and an enhancement of the image contrast have been demonstrated. The image contrast has increased by a factor of about 2, and the image accuracy in terms of root-mean-square-error with respect to the fan-beam CT image has increased by more than 30%. Conclusions: The authors have successfully demonstrated that the proposed scanning method and image reconstruction algorithm can effectively estimate the scatter in cone-beam projections and produce tomographic images of nearly scatter-free quality. The authors believe that the proposed method would provide a fast and efficient CBCT scanning option to various applications particularly including head-and-neck scan.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-T-148: Are the Approximations in Analytic Semi-Empirical Dose Calculation Algorithms for Intensity Modulated Proton Therapy for Complex Heterogeneities of Head and Neck Clinically Significant?

Purpose: Evaluate the differences in dose distributions between the proton analytic semi-empirical dose calculation algorithm used in the clinic and Monte Carlo calculations for a sample of 50 head-and-neck (H&N) patients and estimate the potential clinical significance of the differences. Methods: A cohort of 50 H&N patients, treated at the University of Texas Cancer Center with Intensity Modulated Proton Therapy (IMPT), were selected for evaluation of clinical significance of approximations in computed dose distributions. H&N site was selected because of the highly inhomogeneous nature of the anatomy. The Fast Dose Calculator (FDC), a fast track-repeating accelerated Monte Carlo algorithm for proton therapy, was utilized for the calculation of dose distributions delivered during treatment plans. Because of its short processing time, FDC allows for the processing of large cohorts of patients. FDC has been validated versus GEANT4, a full Monte Carlo system and measurements in water and for inhomogeneous phantoms. A gamma-index analysis, DVHs, EUDs, and TCP and NTCPs computed using published models were utilized to evaluate the differences between the Treatment Plan System (TPS) and FDC. Results: The Monte Carlo results systematically predict lower dose delivered in the target. The observed differences can be as large as 8 Gy, and should have a clinical impact. Gamma analysis also showed significant differences between both approaches, especially for the target volumes. Conclusion: Monte Carlo calculations with fast algorithms is practical and should be considered for the clinic, at least as a treatment plan verification tool.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-T-157: Physics Considerations Regarding Dosimetric Accuracy of Analytical Dose Calculations for Small Field Proton Therapy: A Monte Carlo Study

Purpose: To evaluate the accuracy of dose calculations by analytical dose calculation methods (ADC) for small field proton therapy in a gantry based passive scattering facility. Methods: 50 patients with intra-cranial disease were evaluated in the study. Treatment plans followed standard prescription and optimization procedures of proton stereotactic radiosurgery. Dose distributions calculated with the Monte Carlo (MC) toolkit TOPAS were used to represent delivered treatments. The MC dose was first adjusted using the output factor (OF) applied clinically. This factor is determined from the field size and the prescribed range. We then introduced a normalization factor to measure the difference in mean dose between the delivered dose (MC dose with OF) and the dose calculated by ADC for each beam. The normalization was determined by the mean dose of the center voxels of the target area. We compared delivered dose distributions and those calculated by ADC in terms of dose volume histogram parameters and beam range distributions. Results: The mean target dose for a whole treatment is generally within 5% comparing delivered dose (MC dose with OF) and ADC dose. However, the differences can be as great as 11% for shallow and small target treated with a thick range compensator. Applying the normalization factor to the MC dose with OF can reduce the mean dose difference to less than 3%. Considering range uncertainties, the generally applied margins (3.5% of the prescribed range + 1mm) to cover uncertainties in range might not be sufficient to guarantee tumor coverage. The range difference for R90 (90% distal dose falloff) is affected by multiple factors, such as the heterogeneity index. Conclusion: This study indicates insufficient accuracy calculating proton doses using ADC. Our results suggest that uncertainties of target doses are reduced using MC techniques, improving the dosimetric accuracy for proton stereotactic radiosurgery. The work was supported by NIH/NCI under CA U19 021239. CG was partially supported by the Chinese Scholarship Council (CSC) and the National Natural Science Foundation of China (Grant No. 11475087).

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-T-622: Comparative Analysis of Pencil Beam and Anisotropic Analytical Algorithm (AAA) for Stereotactic Body Radiation Therapy (SBRT) of Thoracic Spine

Purpose: To compare the impact of Pencil Beam(PB) and Anisotropic Analytic Algorithm(AAA) dose calculation algorithms on OARs and planning target volume (PTV) in thoracic spine stereotactic body radiation therapy (SBRT). Methods: Ten Spine SBRT patients were planned on Brainlab iPlan system using hybrid plan consisting of 1–2 non-coplanar conformal-dynamic arcs and few IMRT beams treated on NovalisTx with 6MV photon. Dose prescription varied from 20Gy to 30Gy in 5 fractions depending on the situation of the patient. PB plans were retrospectively recalculated using the Varian Eclipse with AAA algorithm using same MUs, MLC pattern and grid size(3mm).Differences in dose volume parameters for PTV, spinal cord, lung, and esophagus were analyzed and compared for PB and AAA algorithms. OAR constrains were followed per RTOG-0631. Results: Since patients were treated using PB calculation, we compared all the AAA DVH values with respect to PB plan values as standard, although AAA predicts the dose more accurately than PB. PTV(min), PTV(Max), PTV(mean), PTV(D99%), PTV(D90%) were overestimated with AAA calculation on average by 3.5%, 1.84%, 0.95%, 3.98% and 1.55% respectively as compared to PB. All lung DVH parameters were underestimated with AAA algorithm mean deviation of lung V20, V10, V5, and 1000cc were 42.81%,19.83%, 18.79%, and 18.35% respectively. AAA overestimated Cord(0.35cc) by mean of 17.3%; cord (0.03cc) by 12.19% and cord(max) by 10.5% as compared to PB. Esophagus max dose were overestimated by 4.4% and 5cc by 3.26% for AAA algorithm as compared to PB. Conclusion: AAA overestimated the PTV dose values by up to 4%.The lung DVH had the greatest underestimation of dose by AAA versus PB. Spinal cord dose was overestimated by AAA versus PB. Given the critical importance of accuracy of OAR and PTV dose calculation for SBRT spine, more accurate algorithms and validation of calculated doses in phantom models are indicated.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

MO-DE-207A-07: Filtered Iterative Reconstruction (FIR) Via Proximal Forward-Backward Splitting: A Synergy of Analytical and Iterative Reconstruction Method for CT

Purpose: This work is to develop a general framework, namely filtered iterative reconstruction (FIR) method, to incorporate analytical reconstruction (AR) method into iterative reconstruction (IR) method, for enhanced CT image quality. Methods: FIR is formulated as a combination of filtered data fidelity and sparsity regularization, and then solved by proximal forward-backward splitting (PFBS) algorithm. As a result, the image reconstruction decouples data fidelity and image regularization with a two-step iterative scheme, during which an AR-projection step updates the filtered data fidelity term, while a denoising solver updates the sparsity regularization term. During the AR-projection step, the image is projected to the data domain to form the data residual, and then reconstructed by certain AR to a residual image which is in turn weighted together with previous image iterate to form next image iterate. Since the eigenvalues of AR-projection operator are close to the unity, PFBS based FIR has a fast convergence. Results: The proposed FIR method is validated in the setting of circular cone-beam CT with AR being FDK and total-variation sparsity regularization, and has improved image quality from both AR and IR. For example, AIR has improved visual assessment and quantitative measurement in terms of both contrast and resolution, and reduced axial and half-fan artifacts. Conclusion: FIR is proposed to incorporate AR into IR, with an efficient image reconstruction algorithm based on PFBS. The CBCT results suggest that FIR synergizes AR and IR with improved image quality and reduced axial and half-fan artifacts. The authors was partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000), and the Shanghai Pujiang Talent Program (#14PJ1404500).

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Benchmark analytical solutions for steady state high frequency broadband sound fields in three rectangular enclosures

Analytical solutions are presented for broadband sound fields in three rectangular enclosures with absorption applied on the floor and ceiling, rigid sidewalls, and a vertically oriented dipole source. The solutions are intended to serve as benchmarks that can be used to assess the performance of broadband techniques, particularly energy-based methods, in a relatively straightforward configuration with precisely specified boundary conditions. A broadband Helmholtz solution is developed using a frequency-by-frequency modal approach to determine the exact band averaged mean-square pressures along spatial trajectories within each enclosure. Due to the specific choice of enclosure configuration and absorption distribution, an approximate specular solution can be obtained through a summation of uncorrelated image sources. Comparisons between the band averaged Helmholtz solution and the uncorrelated image solution reveal excellent agreement for a wide range of absorption levels and improve the understanding of correlation effects in broadband sound fields. In conclusion, a boundary element solution with diffuse boundaries is also presented, which produces consistently higher mean-square pressures in comparison with the specular solution, emphasizing the careful attention that must be placed on correctly modeling reflecting boundary conditions and demonstrating the errors that can result from assuming a Lambertian surface.

42 ENGINEERING↗
DOE OSTI2013

Ellipsoidal concentrators for laboratory X-ray sources: Analytical approach for optimization

Extremely low intensity of most existing laboratory X-ray sources ({lambda} {approx} 0.01-10 nm) calls for the development of collimating and concentrating optics, which allow to increase significantly the radiation power on the sample surface. The problem of optimizing concentrator parameters is analytically solved in this study. This solution allows one to determine (without any auxiliary calculations) the maximum possible efficiency of a concentrator at any wavelength and analyze the dependence of its efficiency on the source size, wavelength, the source-sample distance, etc.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Analytical study of bound states in graphene nanoribbons and carbon nanotubes: The variable phase method and the relativistic Levinson theorem

The problem of localized states in 1D systems with a relativistic spectrum, namely, graphene stripes and carbon nanotubes, is studied analytically. The bound state as a superposition of two chiral states is completely described by their relative phase, which is the foundation of the variable phase method (VPM) developed herein. Based on our VPM, we formulate and prove the relativistic Levinson theorem. The problem of bound states can be reduced to the analysis of closed trajectories of some vector field. Remarkably, the Levinson theorem appears as the Poincaré index theorem for these closed trajectories. The VPM equation is also reduced to the nonrelativistic and semiclassical limits. The limit of a small momentum p{sub y} of transverse quantization is applicable to an arbitrary integrable potential. In this case, a single confined mode is predicted.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

On the analytical properties of the magneto-conductivity in the case of presence of stable open electron trajectories on a complex Fermi surface

We consider the electric conductivity in normal metals in presence of a strong magnetic field. It is assumed here that the Fermi surface of a metal has rather complicated form such that different types of quasiclassical electron trajectories can appear on the Fermi level for different directions of B. The effects we consider are connected with the existence of regular (stable) open electron trajectories which arise in general on complicated Fermi surfaces. The trajectories of this type have a nice geometric description and represent quasiperiodic lines with a fixed mean direction in the p-space. Being stable geometric objects, the trajectories of this kind exist for some open regions in the space of directions of B, which can be represented by “Stability Zones” on the unit sphere S{sup 2}. The main goal of the paper is to give a description of the analytical behavior of conductivity in the Stability Zones, which demonstrates in general rather nontrivial properties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Analytical and numerical calculations of spectral and optical characteristics of spheroidal quantum dots

In the effective mass approximation for electronic (hole) states of a spheroidal quantum dot with and without external fields the perturbation theory schemes are constructed in the framework of the Kantorovich and adiabatic methods. The eigenvalues and eigenfunctions of the problem, obtained in both analytical and numerical forms, were applied for the analysis of spectral and optical characteristics of spheroidal quantum dots in homogeneous electric fields.

74 ATOMIC AND MOLECULAR PHYSICS↗