Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “HISTOGRAM”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Exploratory Study of 4D versus 3D Robust Optimization in Intensity Modulated Proton Therapy for Lung Cancer

Purpose: The purpose of this study was to compare the impact of uncertainties and interplay on 3-dimensional (3D) and 4D robustly optimized intensity modulated proton therapy (IMPT) plans for lung cancer in an exploratory methodology study. Methods and Materials: IMPT plans were created for 11 nonrandomly selected non-small cell lung cancer (NSCLC) cases: 3D robustly optimized plans on average CTs with internal gross tumor volume density overridden to irradiate internal target volume, and 4D robustly optimized plans on 4D computed tomography (CT) to irradiate clinical target volume (CTV). Regular fractionation (66 Gy [relative biological effectiveness; RBE] in 33 fractions) was considered. In 4D optimization, the CTV of individual phases received nonuniform doses to achieve a uniform cumulative dose. The root-mean-square dose-volume histograms (RVH) measured the sensitivity of the dose to uncertainties, and the areas under the RVH curve (AUCs) were used to evaluate plan robustness. Dose evaluation software modeled time-dependent spot delivery to incorporate interplay effect with randomized starting phases of each field per fraction. Dose-volume histogram (DVH) indices comparing CTV coverage, homogeneity, and normal tissue sparing were evaluated using Wilcoxon signed rank test. Results: 4D robust optimization plans led to smaller AUC for CTV (14.26 vs 18.61, respectively; P=.001), better CTV coverage (Gy [RBE]) (D{sub 95%} CTV: 60.6 vs 55.2, respectively; P=.001), and better CTV homogeneity (D{sub 5%}-D{sub 95%} CTV: 10.3 vs 17.7, resspectively; P=.002) in the face of uncertainties. With interplay effect considered, 4D robust optimization produced plans with better target coverage (D{sub 95%} CTV: 64.5 vs 63.8, respectively; P=.0068), comparable target homogeneity, and comparable normal tissue protection. The benefits from 4D robust optimization were most obvious for the 2 typical stage III lung cancer patients. Conclusions: Our exploratory methodology study showed that, compared to 3D robust optimization, 4D robust optimization produced significantly more robust and interplay-effect-resistant plans for targets with comparable dose distributions for normal tissues. A further study with a larger and more realistic patient population is warranted to generalize the conclusions.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Clinical Significance of Accounting for Tissue Heterogeneity in Permanent Breast Seed Implant Brachytherapy Planning

Purpose: The inhomogeneity correction factor (ICF) method provides heterogeneity correction for the fast calculation TG43 formalism in seed brachytherapy. This study compared ICF-corrected plans to their standard TG43 counterparts, looking at their capacity to assess inadequate coverage and/or risk of any skin toxicities for patients who received permanent breast seed implant (PBSI). Methods and Materials: Two-month postimplant computed tomography scans and plans of 140 PBSI patients were used to calculate dose distributions by using the TG43 and the ICF methods. Multiple dose-volume histogram (DVH) parameters of clinical target volume (CTV) and skin were extracted and compared for both ICF and TG43 dose distributions. Short-term (desquamation and erythema) and long-term (telangiectasia) skin toxicity data were available on 125 and 110 of the patients, respectively, at the time of the study. The predictive value of each DVH parameter of skin was evaluated using the area under the receiver operating characteristic (ROC) curve for each toxicity endpoint. Results: Dose-volume histogram parameters of CTV, calculated using the ICF method, showed an overall decrease compared to TG43, whereas those of skin showed an increase, confirming previously reported findings of the impact of heterogeneity with low-energy sources. The ICF methodology enabled us to distinguish patients for whom the CTV V{sub 100} and V{sub 90} are up to 19% lower compared to TG43, which could present a risk of recurrence not detected when heterogeneity are not accounted for. The ICF method also led to an increase in the prediction of desquamation, erythema, and telangiectasia for 91% of skin DVH parameters studied. Conclusions: The ICF methodology has the advantage of distinguishing any inadequate dose coverage of CTV due to breast heterogeneity, which can be missed by TG43. Use of ICF correction also led to an increase in prediction accuracy of skin toxicities in most cases.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Assessment of Intrafraction Breathing Motion on Left Anterior Descending Artery Dose During Left-Sided Breast Radiation Therapy

Purpose: To use 4-dimensional computed tomography (4D-CT) imaging to predict the level of uncertainty in cardiac dose estimates of the left anterior descending artery that arises due to breathing motion during radiation therapy for left-sided breast cancer. Methods and Materials: The fast helical CT (FH-CT) and 4D-CT of 30 left-sided breast cancer patients were retrospectively analyzed. Treatment plans were created on the FH-CT. The original treatment plan was then superimposed onto all 10 phases of the 4D-CT to quantify the dosimetric impact of respiratory motion through 4D dose accumulation (4D-dose). Dose-volume histograms for the heart, left ventricle (LV), and left anterior descending (LAD) artery obtained from the FH-CT were compared with those obtained from the 4D-dose. Results: The 95% confidence interval of 4D-dose and FH-CT differences in mean dose estimates for the heart, LV, and LAD were ±0.5 Gy, ±1.0 Gy, and ±8.7 Gy, respectively. Conclusion: Fast helical CT is a good approximation for doses to the heart and LV; however, dose estimates for the LAD are susceptible to uncertainties that arise due to intrafraction breathing motion that cannot be ascertained without the additional information obtained from 4D-CT and dose accumulation. For future clinical studies, we suggest the use of 4D-CT–derived dose-volume histograms for estimating the dose to the LAD.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Verification of Dose Distribution in Carbon Ion Radiation Therapy for Stage I Lung Cancer

Purpose: To evaluate robustness of dose distribution of carbon-ion radiation therapy (C-ion RT) in non-small cell lung cancer (NSCLC) and to identify factors affecting the dose distribution by simulated dose distribution. Methods and Materials: Eighty irradiation fields for delivery of C-ion RT were analyzed in 20 patients with stage I NSCLC. Computed tomography images were obtained twice before treatment initiation. Simulated dose distribution was reconstructed on computed tomography for confirmation under the same settings as actual treatment with respiratory gating and bony structure matching. Dose-volume histogram parameters, such as %D95 (percentage of D95 relative to the prescribed dose), were calculated. Patients with any field for which the %D95 of gross tumor volume (GTV) was below 90% were classified as unacceptable for treatment, and the optimal target margin for such cases was examined. Results: Five patients with a total of 8 fields (10% of total number of fields analyzed) were classified as unacceptable according to %D95 of GTV, although most patients showed no remarkable change in the dose-volume histogram parameters. Receiver operating characteristic curve analysis showed that tumor displacement and change in water-equivalent pathlength were significant predictive factors of unacceptable cases (P<.001 and P=.002, respectively). The main cause of degradation of the dose distribution was tumor displacement in 7 of the 8 unacceptable fields. A 6-mm planning target volume margin ensured a GTV %D95 of >90%, except in 1 extremely unacceptable field. Conclusions: According to this simulation analysis of C-ion RT for stage I NSCLC, a few fields were reported as unacceptable and required resetting of body position and reconfirmation. In addition, tumor displacement and change in water-equivalent pathlength (bone shift and/or chest wall thickness) were identified as factors influencing the robustness of dose distribution. Such uncertainties should be regarded in planning.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2013

Notes on representing grain size distributions obtained by electron backscatter diffraction

Grain size distributions measured by electron backscatter diffraction are commonly represented by histograms using either number or area fraction definitions. It is shown here that they should be presented in forms of density distribution functions for direct quantitative comparisons between different measurements. Here we make an interpretation of the frequently seen parabolic tales of the area distributions of bimodal grain structures and a transformation formula between the two distributions are given in this paper. - Highlights: • Grain size distributions are represented by density functions. • The parabolic tales corresponds to equal number of grains in a bin of the histogram. • A simple transformation formula is given to number and area weighed distributions. • The particularities of uniform and lognormal distributions are examined.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Fission gas bubble identification using MATLAB's image processing toolbox

Automated image processing routines have the potential to aid in the fuel performance evaluation process by eliminating bias in human judgment that may vary from person-to-person or sample-to-sample. This study presents several MATLAB based image analysis routines designed for fission gas void identification in post-irradiation examination of uranium molybdenum (U–Mo) monolithic-type plate fuels. Frequency domain filtration, enlisted as a pre-processing technique, can eliminate artifacts from the image without compromising the critical features of interest. This process is coupled with a bilateral filter, an edge-preserving noise removal technique aimed at preparing the image for optimal segmentation. Adaptive thresholding proved to be the most consistent gray-level feature segmentation technique for U–Mo fuel microstructures. The Sauvola adaptive threshold technique segments the image based on histogram weighting factors in stable contrast regions and local statistics in variable contrast regions. Once all processing is complete, the algorithm outputs the total fission gas void count, the mean void size, and the average porosity. The final results demonstrate an ability to extract fission gas void morphological data faster, more consistently, and at least as accurately as manual segmentation methods. - Highlights: •Automated image processing can aid in the fuel qualification process. •Routines are developed to characterize fission gas bubbles in irradiated U–Mo fuel. •Frequency domain filtration effectively eliminates FIB curtaining artifacts. •Adaptive thresholding proved to be the most accurate segmentation method. •The techniques established are ready to be applied to large scale data extraction testing.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Quantitative assessment of the accuracy of dose calculation using pencil beam and Monte Carlo algorithms and requirements for clinical quality assurance

To compare the doses calculated using the BrainLAB pencil beam (PB) and Monte Carlo (MC) algorithms for tumors located in various sites including the lung and evaluate quality assurance procedures required for the verification of the accuracy of dose calculation. The dose-calculation accuracy of PB and MC was also assessed quantitatively with measurement using ionization chamber and Gafchromic films placed in solid water and heterogeneous phantoms. The dose was calculated using PB convolution and MC algorithms in the iPlan treatment planning system from BrainLAB. The dose calculation was performed on the patient's computed tomography images with lesions in various treatment sites including 5 lungs, 5 prostates, 4 brains, 2 head and necks, and 2 paraspinal tissues. A combination of conventional, conformal, and intensity-modulated radiation therapy plans was used in dose calculation. The leaf sequence from intensity-modulated radiation therapy plans or beam shapes from conformal plans and monitor units and other planning parameters calculated by the PB were identical for calculating dose with MC. Heterogeneity correction was considered in both PB and MC dose calculations. Dose-volume parameters such as V95 (volume covered by 95% of prescription dose), dose distributions, and gamma analysis were used to evaluate the calculated dose by PB and MC. The measured doses by ionization chamber and EBT GAFCHROMIC film in solid water and heterogeneous phantoms were used to quantitatively asses the accuracy of dose calculated by PB and MC. The dose-volume histograms and dose distributions calculated by PB and MC in the brain, prostate, paraspinal, and head and neck were in good agreement with one another (within 5%) and provided acceptable planning target volume coverage. However, dose distributions of the patients with lung cancer had large discrepancies. For a plan optimized with PB, the dose coverage was shown as clinically acceptable, whereas in reality, the MC showed a systematic lack of dose coverage. The dose calculated by PB for lung tumors was overestimated by up to 40%. An interesting feature that was observed is that despite large discrepancies in dose-volume histogram coverage of the planning target volume between PB and MC, the point doses at the isocenter (center of the lesions) calculated by both algorithms were within 7% even for lung cases. The dose distributions measured with EBT GAFCHROMIC films in heterogeneous phantoms showed large discrepancies of nearly 15% lower than PB at interfaces between heterogeneous media, where these lower doses measured by the film were in agreement with those by MC. The doses (V95) calculated by MC and PB agreed within 5% for treatment sites with small tissue heterogeneities such as the prostate, brain, head and neck, and paraspinal tumors. Considerable discrepancies, up to 40%, were observed in the dose-volume coverage between MC and PB in lung tumors, which may affect clinical outcomes. The discrepancies between MC and PB increased for 15 MV compared with 6 MV indicating the importance of implementation of accurate clinical treatment planning such as MC. The comparison of point doses is not representative of the discrepancies in dose coverage and might be misleading in evaluating the accuracy of dose calculation between PB and MC. Thus, the clinical quality assurance procedures required to verify the accuracy of dose calculation using PB and MC need to consider measurements of 2- and 3-dimensional dose distributions rather than a single point measurement using heterogeneous phantoms instead of homogenous water-equivalent phantoms.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2014

On the equivalence of the RTI and SVM approaches to time correlated analysis

Recently two papers on how to perform passive neutron auto-correlation analysis on time gated histograms formed from pulse train data, generically called time correlation analysis (TCA), have appeared in this journal [1,2]. For those of us working in international nuclear safeguards these treatments are of particular interest because passive neutron multiplicity counting is a widely deployed technique for the quantification of plutonium. The purpose of this letter is to show that the skewness-variance-mean (SVM) approach developed in [1] is equivalent in terms of assay capability to the random trigger interval (RTI) analysis laid out in [2]. Mathematically we could also use other numerical ways to extract the time correlated information from the histogram data including for example what we might call the mean, mean square, and mean cube approach. The important feature however, from the perspective of real world applications, is that the correlated information extracted is the same, and subsequently gets interpreted in the same way based on the same underlying physics model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Validation of the two-region Rossi-alpha model for reflected assemblies

Nuclear criticality safety, nonproliferation and safeguards, emergency response, and stockpile stewardship utilize estimates of the k eff multiplication factor. The value of k eff cannot be directly measured, but it can be inferred from the prompt neutron period. One modality of measuring the prompt neutron period is the Rossi-alpha method, which is predicated on fitting a histogram of detection time differences due to the nonrandom temporal distribution of same-fission-chain neutrons. Recent works have developed the motivation and theory to expand traditional one-region point kinetic models resulting in one-exponential histogram fits to two-region models that result in two-exponential fits. This paper validates the new two-region model using organic scintillator measurements of copper-reflected weapons-grade plutonium (0:83 ≤ k eff ≤ 0:94) and high-density- polyethylene-reflected highly enriched uranium (0:73 ≤ k eff ≤ 0:95). Furthermore, the results show that more thermal systems have shorter prompt neutron periods in the core region due to increased induced-fission probabilities for moderated neutrons. Here, a new parameter introduced by the two- region model is also shown to be correlated to the amount of reflection, and may be used to infer assembly properties such as type and amount of reflector.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

A STUDY OF CHANGES IN DEFORMATION AND METABOLISM IN LEFT VENTRICLE AS A FUNCTION OF HYPERTROPHY IN SPONTANEOUS HYPERTENSIVE RATS USING MICROPET TECHNOLOGY

Problem: In the case of hypertrophy caused by pressure overload (hypertension) there is an increase in cardiac mass and modification cardiac metabolism. Aim: This study was designed to study the changes in glucose metabolism, ejection fraction, and deformation in the left ventricle with the progression of hypertrophy in spontaneous hypertensive rats (SHR). Methods: Dynamic PET data were acquired using the microPET II at UC Davis. Two rats were imaged at 10-week intervals for 18 months. Each time a dose of approximately 1- 1.5 mCi of F-18-FDG was injected into a normotensive Wistar Kyoto (WKY) rat and the same dose was injected into a SHR rat. Each rat was imaged using a gated dynamic acquisition for 80 minutes acquiring list mode data with cardiac gating of approximately 600-900 million total counts. For the analysis of glucose of metabolism, the list mode data were histogrammed into a dynamic sequence (42 frames over 80 mins). For each time frame, projection data of 1203 140x210 sinograms of 0.582 mm bins were formed by summing the last three gates before and one after the R-wave trigger to correspond to the diastolic phase of the cardiac cycle. Dynamic sequences of 128x128x83 matrices of 0.4x0.4x0.582 mm3 voxels in x, y, and z were reconstructed using an iterative MAP reconstruction which used a prior that penalized the high frequency components of the reconstruction using appropriate weighting between 26 nearest neighboring voxels. Time activity curves were generated from the dynamic reconstructed sequence for the blood and left ventricular tissue regions of interest which were fit to a 2-compartment model to obtain a least squares fit for the kinetic parameters. For the analysis of deformation, the list mode data were histogrammed into 8 gates of the cardiac cycle, each gate was the total sum of the later 60 mins of the 80 min acquisition. Images of 128x128x83 matrices for each gate were reconstructed using the same iterative MAP reconstruction used to reconstruct the dynamic sequence. The in-plane image dimensions were doubled to 256x256x83 in order to increase the resolution for the Warping analyses. These image data sets were then cropped to 128x128x83. The end-systolic image data sets were designated as the template images and the end-diastole image data sets were designated as the target images, thus providing an analysis of the diastolic relaxation and filling phases of the cardiac cycle. The template images were manually segmented to create surface definitions representing the epi- and endocardial surfaces. Finite element models of the left ventricles were created using the segmented surfaces and defining a transversely isotropic material with fiber angles varying from the epicardial surface to the endocardial surface. A Warping analyses was performed to obtain the LV strain tensor and fiber stretch distributions. Results: In one study, the average first principal Green-Lagrange strain, fiber stretch, ejection fraction, and metabolic rate of F-18-FDG was 0.22, 1.08, 80%, 0.1 for the WKY rat and 0.16, 1.06, 50%, 0.25 for the SHR rat, respectively. These same rats studied a year later presented with a metabolic rate of F-18-FDG of 0.11 and 0.25 for the WKY and SHR, respectively. A follow-up study the average strain (n=10) and ejection fraction (n=18) was 0.21, 72.7% for WKY and 0.17, 69.8% for the SHR, respectively. Conclusion: In the case of pressure overload there is an increased reliance on carbohydrate oxidation in an attempt to maintain contractile function.

Sitek, Arkadiusz↗
DOE OSTI2024

On the instrument-dependent appearance of ion dissociation events in atom probe tomography mass spectra

The successful application of atom probe tomography (APT) relies on the accurate interpretation of the mass spectrum (i.e. m/z histogram) from a sample. Some materials yield mass spectra that are amenable to a straightforward peak assignment/ranging, however, there are many materials that produce mass spectra with features that defy simple interpretation. One such example is Ga 2 O 3 which yields mass spectra containing several broad and difficult to interpret features. Herein, we study the GaO 2+ → O 1+ + Ga 1+ dissociation and we explain how this dissociation process gives rise to broad and previously unassigned features in the mass spectrum. Trajectory simulations are performed for the dissociation reaction utilizing realistic electrostatic models and compared to experiments using commercially available straight flight and reflectron based local electrode (LE) APT instruments. It is shown that the appearance of these features is strongly dependent on the specific design of the time-of-flight (ToF) mass analyzer. Additionally, we explore how various experimental parameters can affect the appearance of the dissociation process in the one-dimensional (1D) mass spectrum and in the two-dimensional (2D) correlation histogram. While the focus of this work is on a particular dissociation process related to Ga 2 O 3 , the understanding gained in the course of these simulations and experiments should be applicable to the interpretation of dissociation processes in other materials.

47 OTHER INSTRUMENTATION↗
DOE OSTI2016

Planck intermediate results: XLIV. Structure of the Galactic magnetic field from dust polarization maps of the southern Galactic cap

Using data from the Planck satellite, we study in this paper the statistical properties of interstellar dust polarization at high Galactic latitudes around the south pole (b < -60°). Our aim is to advance the understanding of the magnetized interstellar medium (ISM), and to provide a modelling framework of the polarized dust foreground for use in cosmic microwave background (CMB) component-separation procedures. We examine the Stokes I, Q, and U maps at 353 GHz, and particularly the statistical distribution of the polarization fraction (p) and angle (ψ), in order to characterize the ordered and turbulent components of the Galactic magnetic field (GMF) in the solar neighbourhood. The Q and U maps show patterns at large angular scales, which we relate to the mean orientation of the GMF towards Galactic coordinates (l 0 ,b 0 ) = (70° ± 5°,24° ± 5°). The histogram of the observed p values shows a wide dispersion up to 25%. The histogram of ψ has a standard deviation of 12° about the regular pattern expected from the ordered GMF. We build a phenomenological model that connects the distributions of p and ψ to a statistical description of the turbulent component of the GMF, assuming a uniform effective polarization fraction (p 0 ) of dust emission. To compute the Stokes parameters, we approximate the integration along the line of sight (LOS) as a sum over a set of N independent polarization layers, in each of which the turbulent component of the GMF is obtained from Gaussian realizations of a power-law power spectrum. We are able to reproduce the observed p and ψ distributions using a p 0 value of 26%, a ratio of 0.9 between the strengths of the turbulent and mean components of the GMF, and a small value of N. The mean value of p (inferred from the fit of the large-scale patterns in the Stokes maps) is 12 ± 1%. We relate the polarization layers to the density structure and to the correlation length of the GMF along the LOS. We emphasize the simplicity of our model (involving only a few parameters), which can be easily computed on the celestial sphere to produce simulated maps of dust polarization. Finally, our work is an important step towards a model that can be used to assess the accuracy of component-separation methods in present and future CMB experiments designed to search the B mode CMB polarization from primordial gravity waves.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Fast correlation function calculator: A high-performance pair-counting toolkit

A novel high-performance exact pair-counting toolkit called fast correlation function calculator (FCFC) is presented. With the rapid growth of modern cosmological datasets, the evaluation of correlation functions with observational and simulation catalogues has become a challenge. High-efficiency pair-counting codes are thus in great demand. We introduce different data structures and algorithms that can be used for pair-counting problems, and perform comprehensive benchmarks to identify the most efficient algorithms for real-world cosmological applications. We then describe the three levels of parallelisms used by FCFC, SIMD, OpenMP, and MPI, and run extensive tests to investigate the scalabilities. Finally, we compare the efficiency of FCFC with alternative pair-counting codes. The data structures and histogram update algorithms implemented in FCFC are shown to outperform alternative methods. FCFC does not benefit greatly from SIMD because the bottleneck of our histogram update algorithm is mainly cache latency. Nevertheless, the efficiency of FCFC scales well with the numbers of OpenMP threads and MPI processes, even though speedups may be degraded with over a few thousand threads in total. FCFC is found to be faster than most (if not all) other public pair-counting codes for modern cosmological pair-counting applications.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Conductance fluctuation of edge-disordered graphene nanoribbons: Crossover from diffusive transport to Anderson localization

Conductance fluctuation of edge-disordered graphene nanoribbons (ED-GNRs) is examined using the non-equilibrium Green's function technique combined with the extended Hückel approximation. The mean free path λ and the localization length ξ of the ED-GNRs are determined to classify the quantum transport regimes. In the diffusive regime where the length L{sub c} of the ED-GNRs is much longer than λ and much shorter than ξ, the conductance histogram is given by a Gaussian distribution function with universal conductance fluctuation. In the localization regime where L{sub c}≫ξ, the histogram is no longer the universal Gaussian distribution but a lognormal distribution that characterizes Anderson localization.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Two-state theory of binned photon statistics for a large class of waiting time distributions and its application to quantum dot blinking

A theoretical method is proposed for the calculation of the photon counting probability distribution during a bin time. Two-state fluorescence and steady excitation are assumed. A key feature is a kinetic scheme that allows for an extensive class of stochastic waiting time distribution functions, including power laws, expanded as a sum of weighted decaying exponentials. The solution is analytic in certain conditions, and an exact and simple expression is found for the integral contribution of “bright” and “dark” states. As an application for power law kinetics, theoretical results are compared with experimental intensity histograms from a number of blinking CdSe/ZnS quantum dots. The histograms are consistent with distributions of intensity states around a “bright” and a “dark” maximum. A gap of states is also revealed in the more-or-less flat inter-peak region. The slope and to some extent the flatness of the inter-peak feature are found to be sensitive to the power-law exponents. Possible models consistent with these findings are discussed, such as the combination of multiple charging and fluctuating non-radiative channels or the multiple recombination center model. A fitting of the latter to experiment provides constraints on the interaction parameter between the recombination centers. Further extensions and applications of the photon counting theory are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism

Some dynamical properties for an oval billiard with a scatterer in its interior are studied. The dynamics consists of a classical particle colliding between an inner circle and an external boundary given by an oval, elliptical, or circle shapes, exploring for the first time some natural generalizations. The billiard is indeed a generalization of the annular billiard, which is of strong interest for understanding marginally unstable periodic orbits and their role in the boundary between regular and chaotic regions in both classical and quantum (including experimental) systems. For the oval billiard, which has a mixed phase space, the presence of an obstacle is an interesting addition. We demonstrate, with details, how to obtain the equations of the mapping, and the changes in the phase space are discussed. We study the linear stability of some fixed points and show both analytically and numerically the occurrence of direct and inverse parabolic bifurcations. Lyapunov exponents and generalized bifurcation diagrams are obtained. Moreover, histograms of the number of successive iterations for orbits that stay in a cusp are studied. These histograms are shown to be scaling invariant when changing the radius of the scatterer, and they have a power law slope around −3. The results here can be generalized to other kinds of external boundaries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence

One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ{sub 1} : λ{sub 2} : λ{sub 3} is shown to be about 4:1:−5, compared to about 8:3:−11 when using only the strain-rate tensor for calculating fluid volume deformations. The results serve to characterize the fundamental statistical and geometric structure of turbulence at small scales including cumulative, time integrated effects. These are important for deformable particles such as droplets and polymers advected by turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗