A more exact theory of backscattering from statistically rough surfaces
Physical optics and other approximations examined for improving and extending theory of electromagnetic backscattering from rough surfaces
APPROXIMATION METHOD↗
SEARCH · Engineering Papers
Results for “Statistical physics”
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.
An overview of the mathematical and statistical analysis component of RICIS
Mathematical and statistical analysis components of RICIS (Research Institute for Computing and Information Systems) can be used in the following problem areas: (1) quantification and measurement of software reliability; (2) assessment of changes in software reliability over time (reliability growth); (3) analysis of software-failure data; and (4) decision logic for whether to continue or stop testing software. Other areas of interest to NASA/JSC where mathematical and statistical analysis can be successfully employed include: math modeling of physical systems, simulation, statistical data reduction, evaluation methods, optimization, algorithm development, and mathematical methods in signal processing.
Hallum, Cecil R.↗
Dualities in One-Dimensional Quantum Lattice Models: Symmetric Hamiltonians and Matrix Product Operator Intertwiners
Not Available
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Algebraic Bethe Circuits
The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA into unitary form, for its direct implementation on a quantum computer. This is achieved by distilling the non-unitary R matrices that make up the ABA into unitaries using the QR decomposition. Our algorithm is deterministic and works for both real and complex roots of the Bethe equations. We illustrate our method on the spin-$\frac{1}{2}$ XX and XXZ models. We show that using this approach one can efficiently prepare eigenstates of the XX model on a quantum computer with quantum resources that match previous state-of-the-art approaches. We run small-scale error mitigated implementations on the IBM quantum computers, including the preparation of the ground state for the XX and XXZ models on 4 sites. Finally, we derive a new form of the Yang-Baxter equation using unitary matrices, and also verify it on a quantum computer.
97 MATHEMATICS AND COMPUTING↗
Validating Nuclear Data Uncertainties Obtained from a Statistical Analysis of Experimental Data with the “Physical Uncertainty Bounds” Method
Concerns within the nuclear data community led to substantial increases of Neutron Data Standards (NDS) uncertainties from its previous to the current version. For example, those associated with the NDS reference cross section 239 Pu(n,f) increased from 0.6–1.6% to 1.3–1.7% from 0.1–20 MeV. These cross sections, among others, were adopted, e.g., by ENDF/B-VII.1 (previous NDS) and ENDF/B-VIII.0 (current NDS). There has been a strong desire to be able to validate these increases based on objective criteria given their impact on our understanding of various application uncertainties. Here, the “Physical Uncertainty Bounds” method (PUBs) by Vaughan et al. is applied to validate evaluated uncertainties obtained by a statistical analysis of experimental data. We investigate with PUBs whether ENDF/B-VII.1 or ENDF/B-VIII.0 239 Pu(n,f) cross-section uncertainties are more realistic given the information content used for the actual evaluation. It is shown that the associated conservative (1.5–1.8%) and minimal realistic (1.1–1.3%) uncertainty bounds obtained by PUBs enclose ENDF/B-VIII.0 uncertainties and indicate that ENDF/B-VII.1 uncertainties are underestimated.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
The effects of estimation of censoring, truncation, transformation and partial data vectors
The purpose of this research was to attack statistical problems concerning the estimation of distributions for purposes of predicting and measuring assembly performance as it appears in biological and physical situations. Various statistical procedures were proposed to attack problems of this sort, that is, to produce the statistical distributions of the outcomes of biological and physical situations which, employ characteristics measured on constituent parts. The techniques are described.
Hartley, H. O.↗
Propagation of statistical uncertainties in covariant density functional theory: Ground state observables and single-particle properties
Statistical errors in ground state observables and single-particle properties of spherical even-even nuclei and their propagation to the limits of nuclear landscape have been investigated in covariant density functional theory (CDFT) for the first time. Here, we consider only covariant energy density functionals with non-linear density dependency. Statistical errors for binding energies and neutron skins significantly increase on approaching two-neutron drip line. On the contrary, such a trend does not exist for statistical errors in charge radii and two-neutron separation energies. The absolute and relative energies of the single-particle states in the vicinity of the Fermi level are characterized by low statistical errors ($\sigma(e_i)\sim 0.1$ MeV). Statistical errors in the predictions of spin-orbit splittings are rather small. Statistical errors in physical observables are substantially smaller than related systematic uncertainties. As a result, at the present level of the development of theory, theoretical uncertainties at nuclear limits are dominated by systematic ones. Statistical errors in the description of physical observables related to the ground state and single-particle degrees of freedom are typically substantially lower in CDFT as compared with Skyrme density functional theory. The correlations between the model parameters are studied in detail. The parametric correlations are especially pronounced for the $g_2$ and $g_3$ parameters which are responsible for the density dependence of the model. The accounting of this fact potentially allows to reduce the number of free parameters of non-linear meson coupling model from six to five.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
SU-G-JeP1-12: Head-To-Head Performance Characterization of Two Multileaf Collimator Tracking Algorithms for Radiotherapy
Purpose: Multi-leaf collimator (MLC) tracking is being clinically pioneered to continuously compensate for thoracic and abdominal motion during radiotherapy. The purpose of this work is to characterize the performance of two MLC tracking algorithms for cancer radiotherapy, based on a direct optimization and a piecewise leaf fitting approach respectively. Methods: To test the algorithms, both physical and in silico experiments were performed. Previously published high and low modulation VMAT plans for lung and prostate cancer cases were used along with eight patient-measured organ-specific trajectories. For both MLC tracking algorithm, the plans were run with their corresponding patient trajectories. The physical experiments were performed on a Trilogy Varian linac and a programmable phantom (HexaMotion platform). For each MLC tracking algorithm, plan and patient trajectory, the tracking accuracy was quantified as the difference in aperture area between ideal and fitted MLC. To compare algorithms, the average cumulative tracking error area for each experiment was calculated. The two-sample Kolmogorov-Smirnov (KS) test was used to evaluate the cumulative tracking errors between algorithms. Results: Comparison of tracking errors for the physical and in silico experiments showed minor differences between the two algorithms. The KS D-statistics for the physical experiments were below 0.05 denoting no significant differences between the two distributions pattern and the average error area (direct optimization/piecewise leaf-fitting) were comparable (66.64 cm2/65.65 cm2). For the in silico experiments, the KS D-statistics were below 0.05 and the average errors area were also equivalent (49.38 cm2/48.98 cm2). Conclusion: The comparison between the two leaf fittings algorithms demonstrated no significant differences in tracking errors, neither in a clinically realistic environment nor in silico. The similarities in the two independent algorithms give confidence in the use of either algorithm for clinical implementation.
60 APPLIED LIFE SCIENCES↗
Simulating dielectric spectra: A demonstration of the direct electric field method and a new model for the nonlinear dielectric response
Here we demonstrate a method to compute the dielectric spectra of fluids in molecular dynamics (MD) by directly applying electric fields to the simulation. We obtain spectra from MD simulations with low magnitude electric fields (≈0.01 V/Å) in agreement with spectra from the fluctuation–dissipation method for water and acetonitrile. We examine this method’s trade-off between noise at low field magnitudes and the nonlinearity of the response at higher field magnitudes. We then apply the Booth equation to describe the nonlinear response of both fluids at low frequency (0.1 GHz) and high field magnitude (up to 0.5 V/Å). We develop a model of the frequency-dependent nonlinear response by combining the Booth description of the static nonlinear dielectric response of fluids with the frequency-dependent linear dielectric response of the Debye model. We find good agreement between our model and the MD simulations of the nonlinear dielectric response for both acetonitrile and water.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Lectures on statistical mechanics
Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.
plasma dynamics↗
WE-A-201-00: Anne and Donald Herbert Distinguished Lectureship On Modern Statistical Modeling
Chris Marshall: Memorial Introduction Donald Edmonds Herbert Jr., or Don to his colleagues and friends, exemplified the “big tent” vision of medical physics, specializing in Applied Statistics and Dynamical Systems theory. He saw, more clearly than most, that “Making models is the difference between doing science and just fooling around [ref Woodworth, 2004]”. Don developed an interest in chemistry at school by “reading a book” - a recurring theme in his story. He was awarded a Westinghouse Science scholarship and attended the Carnegie Institute of Technology (later Carnegie Mellon University) where his interest turned to physics and led to a BS in Physics after transfer to Northwestern University. After (voluntary) service in the Navy he earned his MS in Physics from the University of Oklahoma, which led him to Johns Hopkins University in Baltimore to pursue a PhD. The early death of his wife led him to take a salaried position in the Physics Department of Colorado College in Colorado Springs so as to better care for their young daughter. There, a chance invitation from Dr. Juan del Regato to teach physics to residents at the Penrose Cancer Hospital introduced him to Medical Physics, and he decided to enter the field. He received his PhD from the University of London (UK) under Prof. Joseph Rotblat, where I first met him, and where he taught himself statistics. He returned to Penrose as a clinical medical physicist, also largely self-taught. In 1975 he formalized an evolving interest in statistical analysis as Professor of Radiology and Head of the Division of Physics and Statistics at the College of Medicine of the University of South Alabama in Mobile, AL where he remained for the rest of his career. He also served as the first Director of their Bio-Statistics and Epidemiology Core Unit working in part on a sickle-cell disease. After retirement he remained active as Professor Emeritus. Don served for several years as a consultant to the Nuclear Regulatory Commission and may be remembered for his critique of the National Academy of Sciences BEIR III report (stating that their methodology “imposes a Delphic quality to the .. risk estimates”.) This led to his appointment as a member of the BEIR V committee. Don presented refresher courses at the AAPM, ASTRO and RSNA meetings and was active in the AAPM as a member or chair of several committees. He was the principal author of AAPM Report 43, which is essentially a critique of established clinical studies prior to 1992. He was co-editor of the Proceedings of many symposia on Time, Dose and Fractionation held in Madison, Wisconsin. He received the AAPM lifetime Achievement award in 2004. Don’s second wife of 46 years, Ann, predeceased him and he is survived by daughters Hillary and Emily, son John and two grandsons. Don was a true gentleman with a unique and erudite writing style illuminated by pithy quotations. If he had a fault it was, perhaps, that he did not realize how much smarter he was than the rest of us. This presentation draws heavily on a biography and video interview in the History and Heritage section of the AAPM website. The quote is his own. Andrzej Niemierko: Statistical modeling plays an essential role in modern medicine for quantitative evaluation of the effect of treatment. This session will feature an overview of statistical modeling techniques used for analyzing the many types of research data and an exploration of recent advances in new statistical modeling methodologies. Learning Objectives: To learn basics of statistical modeling methodology. To discuss statistical models that are frequently used in radiation oncology To discuss advanced modern statistical modeling methods and applications.
60 APPLIED LIFE SCIENCES↗
WE-A-201-02: Modern Statistical Modeling
Chris Marshall: Memorial Introduction Donald Edmonds Herbert Jr., or Don to his colleagues and friends, exemplified the “big tent” vision of medical physics, specializing in Applied Statistics and Dynamical Systems theory. He saw, more clearly than most, that “Making models is the difference between doing science and just fooling around [ref Woodworth, 2004]”. Don developed an interest in chemistry at school by “reading a book” - a recurring theme in his story. He was awarded a Westinghouse Science scholarship and attended the Carnegie Institute of Technology (later Carnegie Mellon University) where his interest turned to physics and led to a BS in Physics after transfer to Northwestern University. After (voluntary) service in the Navy he earned his MS in Physics from the University of Oklahoma, which led him to Johns Hopkins University in Baltimore to pursue a PhD. The early death of his wife led him to take a salaried position in the Physics Department of Colorado College in Colorado Springs so as to better care for their young daughter. There, a chance invitation from Dr. Juan del Regato to teach physics to residents at the Penrose Cancer Hospital introduced him to Medical Physics, and he decided to enter the field. He received his PhD from the University of London (UK) under Prof. Joseph Rotblat, where I first met him, and where he taught himself statistics. He returned to Penrose as a clinical medical physicist, also largely self-taught. In 1975 he formalized an evolving interest in statistical analysis as Professor of Radiology and Head of the Division of Physics and Statistics at the College of Medicine of the University of South Alabama in Mobile, AL where he remained for the rest of his career. He also served as the first Director of their Bio-Statistics and Epidemiology Core Unit working in part on a sickle-cell disease. After retirement he remained active as Professor Emeritus. Don served for several years as a consultant to the Nuclear Regulatory Commission and may be remembered for his critique of the National Academy of Sciences BEIR III report (stating that their methodology “imposes a Delphic quality to the .. risk estimates”.) This led to his appointment as a member of the BEIR V committee. Don presented refresher courses at the AAPM, ASTRO and RSNA meetings and was active in the AAPM as a member or chair of several committees. He was the principal author of AAPM Report 43, which is essentially a critique of established clinical studies prior to 1992. He was co-editor of the Proceedings of many symposia on Time, Dose and Fractionation held in Madison, Wisconsin. He received the AAPM lifetime Achievement award in 2004. Don’s second wife of 46 years, Ann, predeceased him and he is survived by daughters Hillary and Emily, son John and two grandsons. Don was a true gentleman with a unique and erudite writing style illuminated by pithy quotations. If he had a fault it was, perhaps, that he did not realize how much smarter he was than the rest of us. This presentation draws heavily on a biography and video interview in the History and Heritage section of the AAPM website. The quote is his own. Andrzej Niemierko: Statistical modeling plays an essential role in modern medicine for quantitative evaluation of the effect of treatment. This session will feature an overview of statistical modeling techniques used for analyzing the many types of research data and an exploration of recent advances in new statistical modeling methodologies. Learning Objectives: To learn basics of statistical modeling methodology. To discuss statistical models that are frequently used in radiation oncology To discuss advanced modern statistical modeling methods and applications.
60 APPLIED LIFE SCIENCES↗
Determination of the critical manifold tangent space and curvature with Monte Carlo renormalization group
We show that the critical manifold of a statistical mechanical system in the vicinity of a critical point is locally accessible through correlation functions at that point. A practical numerical method is presented to determine the tangent space and the curvature to the critical manifold with variational Monte Carlo renormalization group. Because of the use of a variational bias potential of the coarse-grained variables, critical slowing down is greatly alleviated in the Monte Carlo simulation. In addition, this method is free of truncation error. Furthermore, we study the isotropic Ising model on square and cubic lattices, the anisotropic Ising model, and the tricritical Ising model on square lattices to illustrate the method.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Microscopic Theory of Fluctuating Hydrodynamics in Nonlinear Lattices
The theory of fluctuating hydrodynamics has been an important tool for analyzing macroscopic behavior in nonlinear lattices. However, despite its practical success, its microscopic derivation is still incomplete. In this work, we provide the microscopic derivation of fluctuating hydrodynamics, using the coarse-graining and projection technique; the equivalence of ensembles turns out to be critical. The Green-Kubo (GK)-like formula for the bare transport coefficients are presented in a numerically computable form. Our numerical simulations show that the bare transport coefficients exist for a sufficiently large but finite coarse-graining length in the infinite lattice within the framework of the GK-like formula. Finally, this demonstrates that the bare transport coefficients uniquely exist for each physical system.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Tutorial: Automated Implementation of Statistical Signal Detectors against Proliferation Signatures (Application to Multi-Physics Waveforms)
Explore the source record for details and available documents.
Signal processing, statistics, applied math↗
Entanglement transitions from restricted Boltzmann machines
The search for novel entangled phases of matter has lead to the recent discovery of a new class of “en- tanglement transitions,” exemplified by random tensor networks and monitored quantum circuits. Most known examples can be understood as some classical ordering transitions in an underlying statistical mechanics model, where entanglement maps onto the free-energy cost of inserting a domain wall. In this paper we study the possibility of entanglement transitions driven by physics beyond such statistical mechanics mappings. Motivated by recent applications of neural-network-inspired variational Ansätze, we investigate under what conditions on the variational parameters these Ansätze can capture an entanglement transition. We study the entanglement scaling of short-range restricted Boltzmann machine (RBM) quantum states with random phases. For uncorrelated random phases, we analytically demonstrate the absence of an entanglement transition and reveal subtle finite-size effects in finite-size numerical simulations. Introducing phases with correlations decaying as 1/r α in real space, we observe three regions with a different scaling of entanglement entropy depending on the exponent α. We study the nature of the transition between these regions, finding numerical evidence for critical behavior. Furthermore, our work establishes the presence of long-range correlated phases in RBM-based wave functions as a required ingredient for entanglement transitions.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
mystic : software for autonomous discovery and design under uncertainty
Throughout the diverse range of science and engineering applications, there is a growing desire to develop computational methods that can reliably predict the behavior of complex systems. Specifically, there is a strategic need for tools that can robustly forecast the behavior of complex physical systems, where data may be high-dimensional, noisy, or sparse, and models of the system may be time-dependent or include uncertainty. We use mystic to build tools that leverage statistical learning, physics-informed learning, and active learning in the efficient generation of reliably predictive surrogates for complex physical systems. mystic is a robust, proven, open-source optimization and uncertainty quantification toolkit with over a decade of use in the design and optimization of neutron instrumentation, solar-powered drones, and gasguns, and in iterative tuning of models for Raman spectroscopy and elastoplastic materials strength. Recent developments have focused on automated learning of statistically robust surrogates under uncertainty, with applications in materials in extreme environments, nanostructures, materials simulations and strength models, and the failure of shielding under particle radiation. In 2020, McKerns demonstrated active learning of optimally robust surrogates with respect to new simulated data for molecular dynamics simulations of materials mixing in warm dense matter, and is currently applying active learning to the automated steering of particle accelerator beams and the optimal design and control of quantum optical sensor instrumentation.
42 ENGINEERING↗
Importance of Engineered and Learned Molecular Representations in Predicting Organic Reactivity, Selectivity, and Chemical Properties
Machine-readable chemical structure representations are foundational in all attempts to harness machine learning for the prediction of reactivities, selectivities, and chemical properties directly from molecular structure. The featurization of discrete chemical structures into a continuous vector space is a critical phase undertaken before model selection, and the development of new ways to quantitatively encode molecules is an active area of research. Here, we highlight the application and suitability of different representations, from expert-guided “engineered” descriptors to automatically “learned” features, in different prediction tasks relevant to organic and organometallic chemistry, where differing amounts of training data are available. These tasks include statistical models of stereo- and enantioselectivity, thermochemistry, and kinetics developed using experimental and quantum chemical data. The use of expert-guided molecular descriptors provides an opportunity to incorporate chemical knowledge, domain expertise, and physical constraints into statistical modeling. In applications to stereoselective organic and organometallic catalysis, where data sets may be relatively small and 3D-geometries and conformations play an important role, mechanistically informed features can be used successfully to obtain predictive statistical models that are also chemically interpretable. We provide an overview of several recent applications of this approach to obtain quantitative models for reactivity and selectivity, where topological descriptors, quantum mechanical calculations of electronic and steric properties, along with conformational ensembles, all feature as essential ingredients of the molecular representations used. Alternatively, more flexible, general-purpose molecular representations such as attributed molecular graphs can be used with machine learning approaches to learn the complex relationship between a structure and prediction target. This approach has the potential to out-perform more traditional representation methods such as “hand-crafted” molecular descriptors, particularly as data set sizes grow. One area where this is particularly relevant is in the use of large sets of quantum mechanical data to train quantitative structure–property relationships. A general approach toward curating useful data sets and training highly accurate graph neural network models is discussed in the context of organic bond dissociation enthalpies, where this strategy outperforms regression using precomputed descriptors. Finally, we describe how graph neural network predictions can be incorporated into mechanistically informed statistical models of chemical reactivity and selectivity. Once trained, this approach avoids the expensive computational overhead associated with quantum mechanical calculations, while maintaining chemical interpretability. We illustrate examples for which fast predictions of bond dissociation enthalpy and of the identities of radicals formed through cleavage of a molecule’s weakest bond are used in simple physical models of site-selectivity and reactivity.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗