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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

SU-E-T-525: Dose Volume Histograms (DVH) Analysis and Comparison with ICRU Point Doses in MRI Guided HDR Brachytherapy for Cervical Cancer

Purpose: Brachytherapy plays a crucial role in management of cervix cancer. MRI compatible applicators have made it possible to accurately delineate gross-target-volume(GTV) and organs-at-risk(OAR) volumes, as well as directly plan, optimize and adapt dose-distribution for each insertion. We sought to compare DVH of tumor-coverage and OARs to traditional Point-A, ICRU-38 bladder and rectum point-doses for four different planning-techniques. Methods: MRI based 3D-planning was performed on Nucletron-Oncentra-TPS for 3 selected patients with varying tumor-sizes and anatomy. GTV,high-risk-clinical-target-volume(HR-CTV), intermediate-risk-clinical-target-volume(IR-CTV) and OARs: rectum, bladder, sigmoid-colon, vaginal-mucosa were delineated. Three conventionally used techniques: mg-Radium-equivalent(RaEq),equal-dwell-weights(EDW), Medical-College-of-Wisconsin proposed points-optimization (MCWO) and a manual-graphical-optimization(MGO) volume-coverage based technique were applied for each patient. Prescription was 6Gy delivered to point-A in Conventional techniques (RaEq, EDW, MCWO). For MGO, goal was to achieve 90%-coverage (D90) to HR-CTV with prescription-dose. ICRU point doses for rectum and bladder, point-A doses, DVH-doses for HR-CTV-D90,0.1cc-volume(D0.1),1ccvolume( D1),2cc-volume(D2) were collected for all plans and analyzed . Results: Mean D90 for HR-CTV normalized to MGO were 0.89,0.84,0.9,1.0 for EDW, RaEq, MCWO, MGO respectively. Mean point-A doses were 21.7% higher for MGO. Conventional techniques with Point-A prescriptions under covered HR-CTV-D90 by average of 12% as compared to MGO. Rectum, bladder and sigmoid doses were highest in MGO-plans for ICRU points as well as D0.1,D1 and D2 doses. Among conventional-techniques, rectum and bladder ICRU and DVH doses(0.1,1,2cc) were not significantly different (within 7%).Rectum D0.1 provided good estimation of ICRU-rectum-point doses (within 3.9%),rectum D0.1 were higher from 0.8 to 3.9% while bladder D0.1 overestimated the bladder ICRU point dose up to 43% for conventional-techniques.Bladder-D2 provided a good estimation of ICRU bladder point-doses(within 3.6%) for conventional-techniques. This correlation is not observed for MGO plans perhaps due to steering of isodose line, leading to unpredictable dwell-weighting. Conclusion: MRI based HDR-planning provides accurate delineation of tumor volumes and normal structures, and optimized tumor-coverage can be achieved with acceptable normal-tissue doses. This study showed that for conventional techniques D0.1 rectum dose and D2 bladder dose are good representation of ICRU-reference-point doses.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

A robust real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system

Purpose: To develop a robust and real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system. Methods: The authors have developed a robust and fast surface reconstruction method on point clouds acquired by the photogrammetry system, without explicitly solving the partial differential equation required by a typical variational approach. Taking advantage of the overcomplete nature of the acquired point clouds, their method solves and propagates a sparse linear relationship from the point cloud manifold to the surface manifold, assuming both manifolds share similar local geometry. With relatively consistent point cloud acquisitions, the authors propose a sparse regression (SR) model to directly approximate the target point cloud as a sparse linear combination from the training set, assuming that the point correspondences built by the iterative closest point (ICP) is reasonably accurate and have residual errors following a Gaussian distribution. To accommodate changing noise levels and/or presence of inconsistent occlusions during the acquisition, the authors further propose a modified sparse regression (MSR) model to model the potentially large and sparse error built by ICP with a Laplacian prior. The authors evaluated the proposed method on both clinical point clouds acquired under consistent acquisition conditions and on point clouds with inconsistent occlusions. The authors quantitatively evaluated the reconstruction performance with respect to root-mean-squared-error, by comparing its reconstruction results against that from the variational method. Results: On clinical point clouds, both the SR and MSR models have achieved sub-millimeter reconstruction accuracy and reduced the reconstruction time by two orders of magnitude to a subsecond reconstruction time. On point clouds with inconsistent occlusions, the MSR model has demonstrated its advantage in achieving consistent and robust performance despite the introduced occlusions. Conclusions: The authors have developed a fast and robust surface reconstruction method on point clouds captured from a 3D surface photogrammetry system, with demonstrated sub-millimeter reconstruction accuracy and subsecond reconstruction time. It is suitable for real-time motion tracking in radiotherapy, with clear surface structures for better quantifications.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2012

Apparatus and method for creating a photonic densely-accumulated ray-point

An optical apparatus includes an optical diffraction device configured for diffracting a predetermined wavelength of incident light onto adjacent optical focal points, and a photon detector for detecting a spectral characteristic of the predetermined wavelength. One of the optical focal points is a constructive interference point and the other optical focal point is a destructive interference point. The diffraction device, which may be a micro-zone plate (MZP) of micro-ring gratings or an optical lens, generates a constructive ray point using phase-contrasting of the destructive interference point. The ray point is located between adjacent optical focal points. A method of generating a densely-accumulated ray point includes directing incident light onto the optical diffraction device, diffracting the selected wavelength onto the constructive interference focal point and the destructive interference focal point, and generating the densely-accumulated ray point in a narrow region.

Park, Yeonjoon↗
NASA NTRS2021

Pointing Error Budget Development and Methodology on the Psyche Project

The Psyche mission was selected by NASA as the 14th mission in the Discovery Program in 2017. The Psyche spacecraft utilizes solar electric propulsion, and will journey to the asteroid (16) Psyche during a 3.5 year trajectory after its planned 2022 launch. The spacecraft instrument suite includes a magnetometer, a multispectral imager, a gamma ray neutron spectrometer, and an X-band radio telecommunications system. It also includes the Deep Space Optical Communication technical demonstration. These instruments along with other spacecraft components require pointing accuracy to meet their scientific and engineering performance requirements. Early on in the project development, the team established a methodology by which pointing accuracy (knowledge and control) is analyzed against the system requirements by means of pointing error budgets and requirement allocations. A margin policy was implemented to ensure the instrument and engineering component pointing accuracy requirements will be met during verification and in flight. Psyche’s pointing management framework defines detailed rationales for the system and subsystem error allocations of the top level pointing accuracy requirements, with sufficient project level pointing margin, and supports end-to-end pointing requirement verification. This paper will present an overview of the Psyche project’s pointing error budget development process, and discuss the rationale behind the methodology. Psyche’s pointing budget methodology integrates best practices and lessons learned from heritage missions, while focusing on the specific needs of the Psyche spacecraft and its science instruments. Key challenges in the pointing error budget development will be reviewed, and a deep dive into two key Psyche pointing budgets are presented. The systems engineering of Psyche’s pointing budget methodology outlined in this paper will serve as a resource for future deep space missions.

Lai, Peter↗
DOE OSTI2026

Statistical Correlation of Heliostat Pointing Deviation With Wind

This work was carried out as part of the Heliostat Consortium (HelioCon) Field Deployment subtask with the aim to develop a reduced order model framework for correlating wind speed and pointing deviation of a heliostat facet. There are only sparse field measurements of heliostat pointing deviations and accompanying wind conditions published in the literature. Heliostat test standards, such as IEC 62862-4-3, propose a suite of tests including laser pointing repeatability at wind speeds below 4 m/s, and provide technical requirements for heliostat slope and tracking deviations in coarse average wind speed bins of 4 m/s, 6 m/s, and 8 m/s. In addressing the gap of the variation of heliostat pointing deviation with wind speed, field measurements of laser pointing on a grid target and wind conditions were analyzed in this study at the Third-Party Metrology Platform at the National Laboratory of the Rockies (NLR) Flatirons Campus. Horizontal pointing deviations were found to follow a logarithmic relationship with peak wind speed, whereas vertical pointing deviations follow an exponential relationship with peak wind speed. Both horizontal and vertical pointing deviations also follow a second order polynomial relationship, as expected from the proportionality of elastic loads and deformations with the square of wind speed. The results indicate that heliostat facet pointing deviations in the vertical direction increase at a faster rate than in the horizontal direction with increasing wind speed over the tested range, however these are dependent on the heliostat structural design. Next steps are recommended for additional field measurements to confirm a linear relationship of pointing deviation with applied moment on a heliostat facet, and to distinguish between gravity-induced and wind-induced pointing deviations at different elevation angles. The derived correlations in the preliminary analysis in this report serve as a case study for heliostat developers and plant operators to estimate the wind-induced pointing deviations and their variation with peak gust wind speed. Next steps in future work would recommend higher resolution and longer duration datasets for different elevation angles and wind directions to reduce uncertainties and variance of collected laser beam spot data and their correlations with bin-averaged wind speed.

17 WIND ENERGY↗
DOE OSTI2014

Control Point Analysis comparison for 3 different treatment planning and delivery complexity levels using a commercial 3-dimensional diode array

To investigate the use of “Control Point Analysis” (Sun Nuclear Corporation, Melbourne, FL) to analyze and compare delivered volumetric-modulated arc therapy (VMAT) plans for 3 different treatment planning complexity levels. A total of 30 patients were chosen and fully anonymized for the purpose of this study. Overall, 10 lung stereotactic body radiotherapy (SBRT), 10 head-and-neck (H and N), and 10 prostate VMAT plans were generated on Pinnacle{sup 3} and delivered on a Varian linear accelerator (LINAC). The delivered dose was measured using ArcCHECK (Sun Nuclear Corporation, Melbourne, FL). Each plan was analyzed using “Sun Nuclear Corporation (SNC) Patient 6” and “Control Point Analysis.” Gamma passing percentage was used to assess the differences between the measured and planned dose distributions and to assess the role of various control point binning combinations. Of the different sites considered, the prostate cases reported the highest gamma passing percentages calculated with “SNC Patient 6” (97.5% to 99.2% for the 3%, 3 mm) and “Control Point Analysis” (95.4% to 98.3% for the 3%, 3 mm). The mean percentage of passing control point sectors for the prostate cases increased from 51.8 ± 7.8% for individual control points to 70.6 ± 10.5% for 5 control points binned together to 87.8 ± 11.0% for 10 control points binned together (2%, 2-mm passing criteria). Overall, there was an increasing trend in the percentage of sectors passing gamma analysis with an increase in the number of control points binned together in a sector for both the gamma passing criteria (2%, 2 mm and 3%, 3 mm). Although many plans passed the clinical quality assurance criteria, plans involving the delivery of high Monitor Unit (MU)/control point (SBRT) and plans involving high degree of modulation (H and N) showed less delivery accuracy per control point compared with plans with low MU/control point and low degree of modulation (prostate)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2018

Comparison between DVH-based doses and ICRU point-based doses to the rectum and the bladder using CT-based high-dose rate brachytherapy to the cervix

Traditionally, doses to the bladder and the rectum were quantified using the bladder and rectal reference points defined by the International Commission on Radiation Units and Measurements (ICRU) in Report No. 38. In this study, we compared the 0.1-, 1.0-, 2.0-cc doses to the bladder and the rectum with the corresponding ICRU point doses using computed tomography (CT)-based planning in the intracavitary brachytherapy of carcinoma of the cervix. CT datasets of 136 consecutive intracavitary brachytherapy insertions between January and May 2015 were analyzed. The bladder and the rectum were contoured on consecutive CT slices as per Groupe Europeen de Curietherapie and the European Socie Ty for Radiotherapy and Oncology recommendations. Dose volume histograms were generated and doses of 0.1, 1.0, and 2.0 cc to the bladder and the rectum were recorded. ICRU bladder and rectal points were identified in the treatment plan. Mean doses of 0.1, 1.0, and 2.0 cc to the bladder was found to be 2.02, 1.57, and 1.35 times the ICRU point dose, respectively. The maximum dose received by the bladder was found to be 5.83 times the average ICRU point dose. Mean doses of 0.1, 1.0, and 2.0 cc to the rectum were found to be 1.12, 0.90, and 0.78 times the ICRU rectal point dose, respectively. The maximum dose received by the rectum was 4.79 times the average ICRU point dose. The Pearson correlation coefficient value (r) was found to be 0.639 for D2cc and ICRU bladder point values. The Pearson correlation coefficient value was found to be 0.752 for D2cc and ICRU rectal point values. Our results show that the ICRU bladder points underestimated the dose to the bladder, which is in agreement with other studies. ICRU rectal point doses were higher than the corresponding D2cc doses. However, there was a good correlation between D2cc and ICRU point doses for both the bladder and the rectum.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Direct optical transitions at K- and H-point of Brillouin zone in bulk MoS{sub 2}, MoSe{sub 2}, WS{sub 2}, and WSe{sub 2}

Modulated reflectance (contactless electroreflectance (CER), photoreflectance (PR), and piezoreflectance (PzR)) has been applied to study direct optical transitions in bulk MoS{sub 2}, MoSe{sub 2}, WS{sub 2}, and WSe{sub 2}. In order to interpret optical transitions observed in CER, PR, and PzR spectra, the electronic band structure for the four crystals has been calculated from the first principles within the density functional theory for various points of Brillouin zone including K and H points. It is clearly shown that the electronic band structure at H point of Brillouin zone is very symmetric and similar to the electronic band structure at K point, and therefore, direct optical transitions at H point should be expected in modulated reflectance spectra besides the direct optical transitions at the K point of Brillouin zone. This prediction is confirmed by experimental studies of the electronic band structure of MoS{sub 2}, MoSe{sub 2}, WS{sub 2}, and WSe{sub 2} crystals by CER, PR, and PzR spectroscopy, i.e., techniques which are very sensitive to critical points of Brillouin zone. For the four crystals besides the A transition at K point, an A{sub H} transition at H point has been observed in CER, PR, and PzR spectra a few tens of meV above the A transition. The spectral difference between A and A{sub H} transition has been found to be in a very good agreement with theoretical predictions. The second transition at the H point of Brillouin zone (B{sub H} transition) overlaps spectrally with the B transition at K point because of small energy differences in the valence (conduction) band positions at H and K points. Therefore, an extra resonance which could be related to the B{sub H} transition is not resolved in modulated reflectance spectra at room temperature for the four crystals.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

How does Fitts' Law fit pointing and dragging?

Two experiments examined selecting text using a movement sequence of pointing and dragging. Experiment 1 showed that, in the Point-Drag sequence, the pointing time was related to the pointing distance but not to the width of the text to be selected; in contrast, pointing time was related to both the pointing distance and the width of the text in the Point-Click sequence. Experiment 2 demonstrated that both the pointing and dragging times for the Point-Drag sequence were sensitive to the height of the text that was selected. The discussion of the results centers around the application of Fitts' Law to pointing and dragging in a point-drag sequence, proposing that the target for pointing is the leftmost edge of the text to be selected, and the target for dragging is the rightmost edge of the text.

Gillan, Douglas J.↗
NASA NTRS1997

Micro Coronal Bright Points Observed in the Quiet Magnetic Network by SOHO/EIT

When one looks at SOHO/EIT Fe XII images of quiet regions, one can see the conventional coronal bright points (> 10 arcsec in diameter), but one will also notice many smaller faint enhancements in brightness (Figure 1). Do these micro coronal bright points belong to the same family as the conventional bright points? To investigate this question we compared SOHO/EIT Fe XII images with Kitt Peak magnetograms to determine whether the micro bright points are in the magnetic network and mark magnetic bipoles within the network. To identify the coronal bright points, we applied a picture frame filter to the Fe XII images; this brings out the Fe XII network and bright points (Figure 2) and allows us to study the bright points down to the resolution limit of the SOHO/EIT instrument. This picture frame filter is a square smoothing function (hlargelyalf a network cell wide) with a central square (quarter of a network cell wide) removed so that a bright point's intensity does not effect its own background. This smoothing function is applied to the full disk image. Then we divide the original image by the smoothed image to obtain our filtered image. A bright point is defined as any contiguous set of pixels (including diagonally) which have enhancements of 30% or more above the background; a micro bright point is any bright point 16 pixels or smaller in size. We then analyzed the bright points that were fully within quiet regions (0.6 x 0.6 solar radius) centered on disk center on six different days.

Falconer, D. A.↗
NASA NTRS2003

Multibody Parachute Flight Simulations for Planetary Entry Trajectories Using "Equilibrium Points"

A method has been developed to reduce numerical stiffness and computer CPU requirements of high fidelity multibody flight simulations involving parachutes for planetary entry trajectories. Typical parachute entry configurations consist of entry bodies suspended from a parachute, connected by flexible lines. To accurately calculate line forces and moments, the simulations need to keep track of the point where the flexible lines meet (confluence point). In previous multibody parachute flight simulations, the confluence point has been modeled as a point mass. Using a point mass for the confluence point tends to make the simulation numerically stiff, because its mass is typically much less that than the main rigid body masses. One solution for stiff differential equations is to use a very small integration time step. However, this results in large computer CPU requirements. In the method described in the paper, the need for using a mass as the confluence point has been eliminated. Instead, the confluence point is modeled using an "equilibrium point". This point is calculated at every integration step as the point at which sum of all line forces is zero (static equilibrium). The use of this "equilibrium point" has the advantage of both reducing the numerical stiffness of the simulations, and eliminating the dynamical equations associated with vibration of a lumped mass on a high-tension string.

Raiszadeh, Ben↗
DOE OSTI2014

Critical point analysis of phase envelope diagram

Phase diagram or phase envelope is a relation between temperature and pressure that shows the condition of equilibria between the different phases of chemical compounds, mixture of compounds, and solutions. Phase diagram is an important issue in chemical thermodynamics and hydrocarbon reservoir. It is very useful for process simulation, hydrocarbon reactor design, and petroleum engineering studies. It is constructed from the bubble line, dew line, and critical point. Bubble line and dew line are composed of bubble points and dew points, respectively. Bubble point is the first point at which the gas is formed when a liquid is heated. Meanwhile, dew point is the first point where the liquid is formed when the gas is cooled. Critical point is the point where all of the properties of gases and liquids are equal, such as temperature, pressure, amount of substance, and others. Critical point is very useful in fuel processing and dissolution of certain chemicals. Here in this paper, we will show the critical point analytically. Then, it will be compared with numerical calculations of Peng-Robinson equation by using Newton-Raphson method. As case studies, several hydrocarbon mixtures are simulated using by Matlab.

36 MATERIALS SCIENCE↗
DOE OSTI2014

SU-E-T-263: Point Dose Variation Using a Single Ir-192 HDR Brachytherapy Plan for Two Treatments with a Single Tandem-Ovoid Insertion for Cervical Cancer

Purpose: To evaluate the point dose variations between Ir-192 HDR treatments on two consecutive days using a single tandem-ovoid insertion without replanning in cervical cancer patients. Methods: This study includes eleven cervical cancer patients undergoing HDR brachytherapy with a prescribed dose of 28 Gy in 4 fractions. Each patient had two tandemovoid insertions one week apart. Each insertion was treated on consecutive days with rescanning and replanning prior to each treatment. To study the effect of no replanning for day 2 treatments, the day 1 plan dwell position and dwell time with decay were applied to the day 2 CT dataset. The point dose variations on the prescription point H (defined according to American Brachytherapy Society), and normal tissue doses at point B, bladder, rectum and vaginal mucosa (based on ICRU Report 38) were obtained. Results: Without replanning, the mean point H dose variation was 4.6 ± 10.7% on the left; 2.3 ± 2.9% on the right. The mean B point variation was 3.8 ± 4.9% on the left; 3.6 ± 4.7% on the right. The variation in the left vaginal mucosal point was 12.2 ± 10.7%; 9.5 ± 12.5% on the right; the bladder point 5.5 ± 7.4%; and the rectal point 7.9 ± 9.1%. Conclusion: Without replanning, there are variations both in the prescription point and the normal tissue point doses. The latter can vary as much as 10% or more. This is likely due to the steep dose gradient from brachytherapy compounded by shifts in the positions of the applicator in relationship to the patients anatomy. Imaging prior to each treatment and replanning ensure effective and safe brachytherapy are recommended.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

TH-AB-202-08: A Robust Real-Time Surface Reconstruction Method On Point Clouds Captured From a 3D Surface Photogrammetry System

Purpose: Surface photogrammetry (e.g. VisionRT, C-Rad) provides a noninvasive way to obtain high-frequency measurement for patient motion monitoring in radiotherapy. This work aims to develop a real-time surface reconstruction method on the acquired point clouds, whose acquisitions are subject to noise and missing measurements. In contrast to existing surface reconstruction methods that are usually computationally expensive, the proposed method reconstructs continuous surfaces with comparable accuracy in real-time. Methods: The key idea in our method is to solve and propagate a sparse linear relationship from the point cloud (measurement) manifold to the surface (reconstruction) manifold, taking advantage of the similarity in local geometric topology in both manifolds. With consistent point cloud acquisition, we propose a sparse regression (SR) model to directly approximate the target point cloud as a sparse linear combination from the training set, building the point correspondences by the iterative closest point (ICP) method. To accommodate changing noise levels and/or presence of inconsistent occlusions, we further propose a modified sparse regression (MSR) model to account for the large and sparse error built by ICP, with a Laplacian prior. We evaluated our method on both clinical acquired point clouds under consistent conditions and simulated point clouds with inconsistent occlusions. The reconstruction accuracy was evaluated w.r.t. root-mean-squared-error, by comparing the reconstructed surfaces against those from the variational reconstruction method. Results: On clinical point clouds, both the SR and MSR models achieved sub-millimeter accuracy, with mean reconstruction time reduced from 82.23 seconds to 0.52 seconds and 0.94 seconds, respectively. On simulated point cloud with inconsistent occlusions, the MSR model has demonstrated its advantage in achieving consistent performance despite the introduced occlusions. Conclusion: We have developed a real-time and robust surface reconstruction method on point clouds acquired by photogrammetry systems. It serves an important enabling step for real-time motion tracking in radiotherapy. This work is supported in part by NIH grant R01 CA169102-02.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2011

Automatic Tie Pointer for In-Situ Pointing Correction

The MARSAUTOTIE program generates tie points for use with the Mars pointing correction software "In-Situ Pointing Correction and Rover Microlocalization," (NPO-46696) Soft ware Tech Briefs, Vol. 34, No. 9 (September 2010), page 18, in a completely automated manner, with no operator intervention. It takes the place of MARSTIE, although MARSTIE can be used to interactively edit the tie points afterwards. These tie points are used to create a mosaic whose seams (boundaries of input images) have been geometrically corrected to reduce or eliminate errors and mis-registrations. The methods used to find appropriate tie points for use in creating a mosaic are unique, having been designed to work in concert with the "MARSNAV" program to be most effective in reducing or eliminating geometric seams in a mosaic. The program takes the input images and finds overlaps according to the nominal pointing. It then finds the most interesting areas using a scene activity metric. Points with higher scene activity are more likely to correlate successfully in the next step. It then uses correlation techniques to find matching points in the overlapped image. Finally, it performs a series of steps to reduce the number of tie points to a manageable level. These steps incorporate a number of heuristics that have been devised using experience gathered by tie pointing mosaics manually during MER operations. The software makes use of the PIG library as described in "Planetary Image Geometry Library" (NPO-46658), NASA Tech Briefs, Vol. 34, No. 12 (December 2010), page 30, so it is multi-mission, applicable without change to any in-situ mission supported by PIG. The MARSAUTOTIE algorithm is automated, so it requires no user intervention. Although at the time of this reporting it has not been done, this program should be suitable for integration into a fully automated mosaic production pipeline.

Deen, Robert G/↗
DOE OSTI2014

An optimum approximation of n-point correlation functions of random heterogeneous material systems

An approximate solution for n-point correlation functions is developed in this study. In the approximate solution, weight functions are used to connect subsets of (n-1)-point correlation functions to estimate the full set of n-point correlation functions. In previous related studies, simple weight functions were introduced for the approximation of three and four-point correlation functions. In this work, the general framework of the weight functions is extended and derived to achieve optimum accuracy for approximate n-point correlation functions. Such approximation can be utilized to construct global n-point correlation functions for a system when there exist limited information about these functions in a subset of space. To verify its accuracy, the new formulation is used to approximate numerically three-point correlation functions from the set of two-point functions directly evaluated from a virtually generated isotropic heterogeneous microstructure representing a particulate composite system. Similarly, three-point functions are approximated for an anisotropic glass fiber/epoxy composite system and compared to their corresponding reference values calculated from an experimental dataset acquired by computational tomography. Results from both virtual and experimental studies confirm the accuracy of the new approximation. The new formulation can be utilized to attain a more accurate approximation to global n-point correlation functions for heterogeneous material systems with a hierarchy of length scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow

Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points also play an important role. These points represent a bifurcation in local stability and Lagrangian topology. In this study, we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversal in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of both chaos and confinement, with the extent of each depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle–centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

SU-E-T-614: Derivation of Equations to Define Inflection Points and Its Analysis in Flattening Filter Free Photon Beams Based On the Principle of Polynomial function

Purpose: The objective of this work is to present a mechanism for calculating inflection points on profiles at various depths and field sizes and also a significant study on the percentage of doses at the inflection points for various field sizes and depths for 6XFFF and 10XFFF energy profiles. Methods: Graphical representation was done on Percentage of dose versus Inflection points. Also using the polynomial function, the authors formulated equations for calculating spot-on inflection point on the profiles for 6X FFF and 10X FFF energies for all field sizes and at various depths. Results: In a flattening filter free radiation beam which is not like in Flattened beams, the dose at inflection point of the profile decreases as field size increases for 10XFFF. Whereas in 6XFFF, the dose at the inflection point initially increases up to 10x10cm2 and then decreases. The polynomial function was fitted for both FFF beams for all field sizes and depths. For small fields less than 5x5 cm2 the inflection point and FWHM are almost same and hence analysis can be done just like in FF beams. A change in 10% of dose can change the field width by 1mm. Conclusion: The present study, Derivative of equations based on the polynomial equation to define inflection point concept is precise and accurate way to derive the inflection point dose on any FFF beam profile at any depth with less than 1% accuracy. Corrections can be done in future studies based on the multiple number of machine data. Also a brief study was done to evaluate the inflection point positions with respect to dose in FFF energies for various field sizes and depths for 6XFFF and 10XFFF energy profiles.

60 APPLIED LIFE SCIENCES↗