LIbration Point Trajectory Design
Orbits about the Sun-Earth L1 and L2 libration points hve become very popular for space physics and astrophysics missions.
trajectory design mathematical methods libration l↗
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Results for “mathematical 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.
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Learning physics-based reduced-order models from data using nonlinear manifolds
Here we present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation.
97 MATHEMATICS AND COMPUTING↗
Characterizing the acceleration time of laser-driven ion acceleration with data-informed neural networks
Peak ion energy is an important figure-of-merit in short-pulse, laser-driven ion acceleration and is dependent on an associated acceleration time. Standard metrics for these quantities depend on analytical results such as the self-similar fluid model or empirical models based on relatively small experimental and simulation datasets. In this work we attempt to use a data-informed neural network (NN) as a surrogate model for a large ensemble of PIC simulations to investigate an effective acceleration time. We explore the application of a stacked convolutional and recurrent NN architecture for improved regression by incorporating the time dependencies of the data into the training process. Of particular note is how pretraining a network on lower fidelity data, e.g. 1D analytical results, greatly improves the network's ability to learn more complex, higher fidelity data. Finally, the dependency of the acceleration time on various laser and plasma parameters is explored.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Application of quantum machine learning using the quantum variational classifier method to high energy physics analysis at the LHC on IBM quantum computer simulator and hardware with 10 qubits
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Final Report for The Creation of a Physics-based Ground-effect Model, Phase 2 - Inclusion of the Effects of Wind, Stratification, and Shear into the New Ground Effect Model
The reduction of the separation of the leading and following aircrafts is desirable to enhance the airport capacity provided that there is a physics-based operational model applicable to all regions of the flight domain (out of ground effect, OGE; near ground effect, NGE; and in ground effect, IGE) and that the quality of the quantitative input from the measurements of the prevailing atmospheric conditions and the quality of the total airport operations regarding the safety and the sound interpretation of the prevailing conditions match the quality of the analysis and numerical simulations. In the absence of an analytical solution, the physics of the flow is best expressed by a mathematical model based on numerical simulations, field and laboratory experiments, and heuristic reasoning. This report deals with the creation of a sound physics-based real-time IGE model of the aircraft wake vortices subjected to crosswind, stratification and shear.
Sarpkaya, Turgut↗
A generalized procedure for constructing an upwind based TVD scheme
A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some linear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to scalar nonlinear equations and a constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance in numerical experiments. The formulation is extended to the nonlinear system. It is demonstrated that the present procedure can easily convert existing central or upwind, and second- or higher-order differencing schemes to preserve monotonicity and yield physically admissible solutions. The formulation is simple mathematically as well as numerically; both matrix-vector multiplication and Riemann solver are avoided. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made.
Liou, Meng-Sing↗
Synchronization effects on rest frame energy and momentum densities in the proton
We obtain two-dimensional relativistic densities and currents of energy and momentum in a proton at rest. These densities are obtained at surfaces of fixed light front time, which physically corresponds to using an alternative synchronization convention. Mathematically, this is done using tilted light front coordinates, which consist of light front time and ordinary spatial coordinates. In this coordinate system, all 16 components of the energy-momentum tensor (EMT) obtain clear physical interpretations, and the nine Galilean components reproduce results from standard light front coordinates. We find angular modulations in several densities that are absent in the corresponding instant form results, which are explained as optical effects arising from using fixed light front time when motion is present within the target. Additionally, transversely polarized spin-half targets exhibit an energy dipole moment—which evaluates to −1/4 for all targets if the Belinfante EMT is used, but which is target dependent and vanishes for pointlike fermions if the asymmetric EMT is instead used.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
A generalized procedure for constructing an upwind-based TVD scheme
A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some nonlinear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to a scalar nonlinear equation and constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance to numerical experiments. Then the formulation is formally extended to the nonlinear system of equations. It is demonstrated that use of the present procedure allows easy conversion of existing central or upwind, and second- or higher-order differencing schemes so as to preserve monotonicity and to yield physically admissible solutions. The formulation is simple mathematically as well as numerically; neither matrix-vector multiplication nor Riemann solver is required. Roughly twice as much computational effort is needed as compared to conventional scheme. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made. Numerical examples including various ranges of problems show both time- and spatial-accuracy in comparison with exact solutions.
Liou, Meng-Sing↗
Review: knots and other new topological effects in liquid crystals and colloids
Abstract Humankind has been obsessed with knots in religion, culture and daily life for millennia, while physicists like Gauss, Kelvin and Maxwell already involved them in models centuries ago. Nowadays, colloidal particles can be fabricated to have shapes of knots and links with arbitrary complexity. In liquid crystals, closed loops of singular vortex lines can be knotted by using colloidal particles and laser tweezers, as well as by confining nematic fluids into micrometer-sized droplets with complex topology. Knotted and linked colloidal particles induce knots and links of singular defects, which can be interlinked (or not) with colloidal particle knots, revealing the diversity of interactions between topologies of knotted fields and topologically nontrivial surfaces of colloidal objects. Even more diverse knotted structures emerge in nonsingular molecular alignment and magnetization fields in liquid crystals and colloidal ferromagnets. The topological solitons include hopfions, skyrmions, heliknotons, torons and other spatially localized continuous structures, which are classified based on homotopy theory, characterized by integer-valued topological invariants and often contain knotted or linked preimages, nonsingular regions of space corresponding to single points of the order parameter space. A zoo of topological solitons in liquid crystals, colloids and ferromagnets promises new breeds of information displays and a plethora of data storage, electro-optic and photonic applications. Their particle-like collective dynamics echoes coherent motions in active matter, ranging from crowds of people to schools of fish. This review discusses the state of the art in the field, as well as highlights recent developments and open questions in physics of knotted soft matter. We systematically overview knotted field configurations, the allowed transformations between them, their physical stability and how one can use one form of knotted fields to model, create and imprint other forms. The large variety of symmetries accessible to liquid crystals and colloids offer insights into stability, transformation and emergent dynamics of fully nonsingular and singular knotted fields of fundamental and applied importance. The common thread of this review is the ability to experimentally visualize these knots in real space. The review concludes with a discussion of how the studies of knots in liquid crystals and colloids can offer insights into topologically related structures in other branches of physics, with answers to many open questions, as well as how these experimentally observable knots hold a strong potential for providing new inspirations to the mathematical knot theory.
Physics↗
Comparison of analytical and physical modeling of planetesimal accumulation
Three cases for which the analytic solutions to the planetary embryo coagulation equation are known, namely those of constant coagulation rate, of rate proportional to the sum of the masses of the two colliding bodies, and of rate proportional to the product of their masses, are presently used to test the mathematical validity of the Wetherill and Stewart (1989) physical model for the evolution of planetary embryos' mass distribution. In all cases, excellent agreement is found between numerical physical modeling results and those of the analytic solutions. The treatment of the runaway case can proceed via extension of the efforts of Trubnikov (1971).
Wetherill, George W.↗
Nonstandard Analysis and Shock Wave Jump Conditions in a One-Dimensional Compressible Gas
Nonstandard analysis is a relatively new area of mathematics in which infinitesimal numbers can be defined and manipulated rigorously like real numbers. This report presents a fairly comprehensive tutorial on nonstandard analysis for physicists and engineers with many examples applicable to generalized functions. To demonstrate the power of the subject, the problem of shock wave jump conditions is studied for a one-dimensional compressible gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. To use conservations laws, smooth pre-distributions of the Dirac delta measure are applied whose supports are contained within the shock thickness. Furthermore, smooth pre-distributions of the Heaviside function are applied which vary from zero to one across the shock wave. It is shown that if the equations of motion are expressed in nonconservative form then the relationships between the jump functions for the flow parameters may be found unambiguously. The analysis yields the classical Rankine-Hugoniot jump conditions for an inviscid shock wave. Moreover, non-monotonic entropy jump conditions are obtained for both inviscid and viscous flows. The report shows that products of generalized functions may be defined consistently using nonstandard analysis; however, physically meaningful products of generalized functions must be determined from the physics of the problem and not the mathematical form of the governing equations.
Baty, Roy S.↗
Modeling "Soft" Errors in Bipolar Integrated Circuits
Mathematical models represent single-event upset in bipolar memory chips. Physics of single-event upset in integrated circuits discussed in theoretical paper. Pair of companion reports present mathematical models to predict critical charges for producing single-event upset in bipolar randomaccess memory (RAM) chips.
Zoutendyk, J.↗
Exploring physics of ferroelectric domain walls via Bayesian analysis of atomically resolved STEM data
The physics of ferroelectric domain walls is explored using the Bayesian inference analysis of atomically resolved STEM data. We demonstrate that domain wall profile shapes are ultimately sensitive to the nature of the order parameter in the material, including the functional form of Ginzburg-Landau-Devonshire expansion, and numerical value of the corresponding parameters. The preexisting materials knowledge naturally folds in the Bayesian framework in the form of prior distributions, with the different order parameters forming competing (or hierarchical) models. Here, we explore the physics of the ferroelectric domain walls in BiFeO 3 using this method, and derive the posterior estimates of relevant parameters. More generally, this inference approach both allows learning materials physics from experimental data with associated uncertainty quantification, and establishing guidelines for instrumental development answering questions on what resolution and information limits are necessary for reliable observation of specific physical mechanisms of interest.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Incorporation of physics phenomenology into an adaptive algorithm framework, RSLA-002-20, Year 2 of 2
Presentation to be presented during the Site-Directed Research and Development (SDRD) program FY 2021 review meeting (Webex), September 22–23, 2021.
97 MATHEMATICS AND COMPUTING↗
Rapid Inverse Parameter Inference Using Physics-Informed Neural Network
As Li-ion batteries become more essential in today's economy, tools need to be developed to accurately and rapidly diagnose a battery's internal state-of-health. Using a Li-ion battery's (high-rate) voltage response, it is proposed to determine a battery's internal state through Bayesian calibration. However, Bayesian calibration is notoriously slow and requires thousands of model runs. To accelerate parameter inference using Bayesian calibration, a surrogate model is developed to replace the underlying physics-based Li-ion model. Developing a surrogate model for rapid Bayesian calibration analysis is discussed for both the single particle model (SPM) and the pseudo two-dimensional (P2D) model. Surrogate models are constructed using physics-informed neural networks (PINNs) that encode the influence of internal properties on observed voltage responses. In practice, a neural network can be trained by: 1) using simulation results of the physics-based model (i.e., a data-loss approach); 2) using the residuals of the governing equations themselves (i.e., a physics-loss approach); or 3) using a combination of simulation results and governing equation residuals. In the present work, PINNs are developed using a variety of training losses and neural network architectures. In this analysis, it is shown that a PINN surrogate model can be reliably trained with only physics-informed loss. However, using a coupled data-informed and physics-loss approach produced the most accurate PINNs.
Bayesian calibration↗
Identifying quenched jets in heavy ion collisions with machine learning
Measurements of jet substructure in ultra-relativistic heavy ion collisions suggest that the jet showering process is modified by the interaction with the quark-gluon plasma. Modifications of the hard substructure of jets can be explored with modern data-driven techniques. In this study, a machine learning approach to the identification of quenched jets is designed. Jet showering processes are simulated with a jet quenching model JEWEL and a non-quenching model PYTHIA 8. Sequential substructure variables are extracted from the jet clustering history following an angular-ordered sequence and are used in the training of a neural network built on top of a long short-term memory network. We show that this approach successfully identifies the quenching effect in the presence of the large uncorrelated background of soft particles created in heavy-ion collisions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Thermodynamic Profiling Through ASSIST Observations and TROPoe Retrievals
This report reviews the most relevant theoretical aspects of thermodynamic profiling techniques based on spectral observations from ASSIST-II infrared radiometers and TROPoe retrievals. The ASSIST+TROPoe system is a cutting-edge remote sensing technology deployed during the AWAKEN and WFIP3 field campaigns to estimate high-frequency profiles of temperature and humidity in the atmosphere. These profiles are highly valuable for characterizing atmospheric stratification, improving wind models, and understanding the impacts of wind plants on the climate. In this document, we discuss the operating principles of ASSIST, the physics of atmospheric infrared radiation, and the mathematical framework and capabilities of TROPoe. Sources of uncertainties in both the instrument and the retrieval method are also thoroughly addressed. This guide is designed to help users of ASSIST, TROPoe, and thermodynamic data in collecting, estimating, and applying thermodynamic profiles rigorously and scientifically.
17 WIND ENERGY↗
Cosmic rays in a random magnetic field: Breakdown of the quasilinear derivation of the kinetic equation
The problem of deriving a kinetic equation for the cosmic ray distribution function in a random magnetic field is considered. A model is adopted which is mathematically simple but which contains the essential physics. The perturbation expansion upon which the quasi-linear treatment is based is investigated. The existence of resonant particles causes the breakdown of the adiabatic approximation frequently used in this theory. Resonant particles cause a general secular growth of higher order terms in the expansion which invalidates the entire perturbative approach.
Kaiser, T. B.↗