Engineering Papers⌕ Search

SEARCH · Engineering Papers

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Quantum discord for general two-qubit states: Analytical progress

We present a reliable algorithm to evaluate quantum discord for general two-qubit states, amending and extending an approach recently put forward for the subclass of X states. A closed expression for the discord of arbitrary states of two qubits cannot be obtained, as the optimization problem for the conditional entropy requires the solution to a pair of transcendental equations in the state parameters. We apply our algorithm to run a numerical comparison between quantum discord and an alternative, computable measure of nonclassical correlations, namely, the geometric discord. We identify the extremally nonclassically correlated two-qubit states according to the (normalized) geometric discord, at a fixed value of the conventional quantum discord. The latter cannot exceed the square root of the former for systems of two qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Reply to ''Comment on 'Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators'''

In a Comment [Deych, Phys. Rev. A 84, 017801 (2011)] on our recent article [Chembo and Yu, Phys. Rev. A 82, 033801 (2010)] on Kerr comb generation in monolithic whispering-gallery-mode (WGM) resonators, the author claims that even though our main results ''remain intact'', the framework of our analysis contains some mathematical errors. In this Reply, we demonstrate that the author's criticisms and his alternative theory are incorrect, and that all the disagreeing claims come from the author's misunderstanding of the physical system under investigation. In particular, the main conceptual error in the Comment is the confusion between evanescent and radiative coupling mechanisms for WGM resonators (in terms of Q factor, this is in our case a confusion between {approx}10{sup 9} and {approx}10{sup 2000}, respectively). This essential misconception leads for example the author to introduce a nonphysical {approx}10{sup 2000} multiplicative correction factor for the laser pump power. We show in this Reply that our WGM resonators are radiatively closed (because of the quasi-infinite radiative Q factor), so that the Mie scattering formalism proposed by Deych, which relies on radiative coupling, can only lead to erroneous results. We also show that the modal expansion approach in our original paper is appropriate, and all our approximations are physically well justified. We therefore stand by our modeling results, which are moreover in excellent agreement with the experiments reported in [Chembo, Strekalov, and Yu, Phys. Rev. Lett. 104, 103902 (2010)].

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Quantization of general linear electrodynamics

General linear electrodynamics allow for an arbitrary linear constitutive relation between the field strength 2-form and induction 2-form density if crucial hyperbolicity and energy conditions are satisfied, which render the theory predictive and physically interpretable. Taking into account the higher-order polynomial dispersion relation and associated causal structure of general linear electrodynamics, we carefully develop its Hamiltonian formulation from first principles. Canonical quantization of the resulting constrained system then results in a quantum vacuum which is sensitive to the constitutive tensor of the classical theory. As an application we calculate the Casimir effect in a birefringent linear optical medium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Science &Technology Review (September 2022)

Computer modeling is essential to scientific research. Models simulate natural phenomena to aid scientists in understanding their underlying principles. While the most complex models running on supercomputers may contain millions of lines of code and generate billions of data points, models never simulate reality perfectly. Experiments—in contrast—have been fundamental to the study of natural phenomena from science’s earliest days. However, some of today’s complex experiments generate too much data for the human mind to interpret.

42 ENGINEERING↗
NASA NTRS1990

What can formal methods offer to digital flight control systems design

Formal methods research begins to produce methods which will enable mathematic modeling of the physical behavior of digital hardware and software systems. The development of these methods directly supports the NASA mission of increasing the scope and effectiveness of flight system modeling capabilities. The conventional, continuous mathematics that is used extensively in modeling flight systems is not adequate for accurate modeling of digital systems. Therefore, the current practice of digital flight control system design has not had the benefits of extensive mathematical modeling which are common in other parts of flight system engineering. Formal methods research shows that by using discrete mathematics, very accurate modeling of digital systems is possible. These discrete modeling methods will bring the traditional benefits of modeling to digital hardware and hardware design. Sound reasoning about accurate mathematical models of flight control systems can be an important part of reducing risk of unsafe flight control.

Good, Donald I.↗
DOE OSTI2014

Overview of the 2014 Edition of the International Handbook of Evaluated Reactor Physics Benchmark Experiments (IRPhEP Handbook)

The International Reactor Physics Experiment Evaluation Project (IRPhEP) is a widely recognized world class program. The work of the IRPhEP is documented in the International Handbook of Evaluated Reactor Physics Benchmark Experiments (IRPhEP Handbook). Integral data from the IRPhEP Handbook is used by reactor safety and design, nuclear data, criticality safety, and analytical methods development specialists, worldwide, to perform necessary validations of their calculational techniques. The IRPhEP Handbook is among the most frequently quoted reference in the nuclear industry and is expected to be a valuable resource for future decades.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2014

Evaluation of Low Power ARM Processors for Monte Carlo Particle Transport: MCNP6 on the ARM Cortex-A8 - Paper 83

In the push towards exascale computing, the limiting factors are power requirements and heat dissipation. Using current technology, the power required to drive an exascale supercomputer would near 400-MW. Clearly, future computing hardware will have to be more energy efficient in order to achieve exascale performance. Most of the current research in advanced computing architectures is in the use of standard CPUs with accelerators. However, these accelerators are not generally supported by the traditional scientific programming languages (C, C++, and Fortran) and the scientific software must be tailored specifically to take advantage of the accelerators. Large scale scientific software (hundreds-of-thousand to millions of lines of code) can not be easily ported to the computing platform du jour. The widespread use of low power ARM based processors in the mobile computing market offer a low power alternative to accelerators that are also supported by the traditional scientific programming languages and programming paradigms such as MPI and OpenMP. Computing architectures for scientific computing are often assessed using standard benchmarks such as LINPACK benchmark or using suites of mini-applications that are greatly simplified stand-ins for scientific software. Often the real applications that will deployed on the scientific supercomputers are not ported or tested until delivery of the machines. In order to evaluate the use of ARM processors for scientific computing the Monte Carlo particle transport code, MCNP version 6 was compiled on the ARM Cortex-A8 and a set of benchmark problems were used to assess performance in comparison to an Intel Xeon E5-2670 and the low power Intel Atom N270. MCNP is a continuous energy Monte Carlo particle transport code in development at Los Alamos National Laboratory since 1977. MCNP is used to transport neutrons, photon, electrons, and charged particles using continuous energy interaction data. It is commonly used in fields of nuclear power, nuclear medicine, radiation protection, and high-energy physics through-out the world. MCNP version 6 is approximately 450 thousand lines of code, written primary in Fortran90, with some C and C++. MCNP supports distributed multiprocessing using MPI and threading with OpenMP. The ARM Cortex-A8 executes MCNP6 using about twice as much power as the Intel Xeon E5-2670 and about the same amount of power as the Intel Atom N270. However, these results are encouraging for the use of low-power ARM chips in future supercomputers. The ARM Cortex-A8 is a 32-bit CPU and it's NEON general-purpose SIMD (single-instruction multiple data) engine does not support double-precision floating-point arithmetic. More recent ARM processors (ARM Cortex-A53 and Cortex-A57) support 64-bit addressing and have NEON co-processors that support double-precision floating-point arithmetic. ARM claims that the A50 series delivers a performance increase of 15 times the Cortex-A8 performance for similar power usage. (authors)

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 OSTI2012

KIVA Development - 2012

Los Alamos National Laboratory and its collaborators are facilitating engine modeling by improving accuracy of the modeling, and improving the robustness of software. We also continue to improve the physical modeling methods. We are developing and implementing new mathematical algorithms, those which represent the physics within an engine. We provide software that others may use directly or that they may alter with various models e.g., sophisticated chemical kinetics, different turbulent closure methods or other fuel injection systems.

02 PETROLEUM↗
DOE OSTI2011

Comment on 'Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators'

Authors of a recent paper [Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010)] claimed to have developed a general framework for description of nonlinear effects in whispering-gallery-mode resonators with particular focus on optical-frequency-comb generation. In this Comment we demonstrate that the author's approach contains mathematical errors affecting some of the results of the paper. Fortunately, analysis of this phenomenon using a mathematically more rigorous approach shows that the main conclusions of that paper remain intact.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Machine learning and algebraic approaches towards complete matter spectra in 4d F-theory

Motivated by engineering vector-like (Higgs) pairs in the spectrum of 4d F-theory compactifications, we combine machine learning and algebraic geometry techniques to analyze line bundle cohomologies on families of holomorphic curves. To quantify jumps of these cohomologies, we first generate 1.8 million pairs of line bundles and curves embedded in dP 3 , for which we compute the cohomologies. A white-box machine learning approach trained on this data provides intuition for jumps due to curve splittings, which we use to construct additional vector-like Higgs-pairs in an F-Theory toy model. We also find that, in order to explain quantitatively the full dataset, further tools from algebraic geometry, in particular Brill-Noether theory, are required. Using these ingredients, we introduce a diagrammatic way to express cohomology jumps across the parameter space of each family of matter curves, which reflects a stratification of the F-theory complex structure moduli space in terms of the vector-like spectrum. Furthermore, these insights provide an algorithmically efficient way to estimate the possible cohomology dimensions across the entire parameter space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers

Graphical abstract: - Abstract: Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Interface- and discontinuity-aware numerical schemes for plasma 3-T radiation diffusion in two and three dimensions

A set of numerical schemes is developed for two- and three-dimensional time-dependent 3-T radiation diffusion equations in systems involving multi-materials. To resolve sub-cell structure, interface reconstruction is implemented within any cell that has more than one material. Therefore, the system of 3-T radiation diffusion equations is solved on two- and three-dimensional polyhedral meshes. The focus of the development is on the fully coupling between radiation and material, the treatment of nonlinearity in the equations, i.e., in the diffusion terms and source terms, treatment of the discontinuity across cell interfaces in material properties, the formulations for both transient and steady states, the property for large time steps, and second order accuracy in both space and time. The discontinuity of material properties between different materials is correctly treated based on the governing physics principle for general polyhedral meshes and full nonlinearity. The treatment is exact for arbitrarily strong discontinuity. The scheme is fully nonlinear for the full nonlinearity in the 3-T diffusion equations. Three temperatures are fully coupled and are updated simultaneously. The scheme is general in two and three dimensions on general polyhedral meshes. The features of the scheme are demonstrated through numerical examples for transient problems and steady states. The effects of some simplifications of numerical schemes are also shown through numerical examples, such as linearization, simple average of diffusion coefficient, and approximate treatment for the coupling between radiation and material.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

An analysis of the spatio-temporal resolution of the immersed boundary method with direct forcing

The immersed boundary method (IBM) with direct forcing is very popular in the simulation of rigid particulate flows. In the IBM, an interaction force is introduced at the interface between fluid and particle in order to approximate the no-slip boundary condition. The interaction force is calculated through dividing the velocity difference (or error) between fluid and particle at the interface by the time step. Here, a dynamic equation for the velocity difference is derived. Additionally, analyses on the dynamic equation provide a few new findings: (i) The interaction force is the solution of a least-squares error problem, with the direct implication that the Lagrangian marker distribution has no effect on the large scale flow structure once the distribution of Lagrangian markers become saturated along the interface (i.e., each marker remains properly correlated with all its neighbors); (ii) The Lagrangian volume-weight is a relaxation factor to control how fast the velocity error decays to the ideal value of zero; (iii) The optimal choice of the Lagrangian volume-weight is the largest value permissible by a stability condition. A comprehensive convergence analysis with regard to the spatial and temporal resolution is presented for the velocity error and also for the shear-stress and surface pressure. In three simple canonical problems, it is analytically and numerically shown that the IBM results converge to the theoretical solutions obtained with precise imposition of no-slip and no-penetration boundary conditions. It is observed that it is not necessary to match the Lagrangian marker volume-weight to that of the local Eulerian cell volume and in fact this matching leads to lower than optimal computational efficiency. However, it is found that extremely high Eulerian grid resolution and small time step have to be used to obtain high precision simulation results. Especially, the time step should be inversely proportional to the particle Reynolds number for low Reynolds number flows. For high frequency oscillation problems, the grid size needs to be reduced by a factor of the square root of the frequency, and the time step to be reduced by a factor of the frequency. The theoretical findings here can be used to alleviate the technical difficulties in simulating non-spherical particles by not requiring the Lagrangian marker distribution to match the Eulerian grids and also in the implementation of IBM on non-uniform Eulerian grids. The present work also provides simple practical guidance on the choice of temporal and spatial resolution so as to control the simulation error a priori.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Learning functional priors and posteriors from data and physics

In this work, we develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems. Specifically, the proposed approach has two stages: (1) prior learning and (2) posterior estimation. At the first stage, we employ the physics-informed Generative Adversarial Networks (PI-GAN) to learn a functional prior either from a prescribed function distribution, e.g., Gaussian process, or from historical data and physics. At the second stage, we employ the Hamiltonian Monte Carlo (HMC) method to estimate the posterior in the latent space of PI-GANs. In addition, we use two different approaches to encode the physics: (1) automatic differentiation, used in the physicsinformed neural networks (PINNs) for scenarios with explicitly known partial differential equations (PDEs), and (2) operator regression using the deep operator network (DeepONet) for PDE-agnostic scenarios. We then test the proposed method for (1) meta-learning for one-dimensional regression, and forward/inverse PDE problems (combined with PINNs); (2) PDE-agnostic physical problems (combined with DeepONet), e.g., fractional diffusion as well as saturated stochastic (100-dimensional) flows in heterogeneous porous media; and (3) spatial-temporal regression problems, i.e., inference of a marine riser displacement field using experimental data from the Norwegian Deepwater Programme (NDP). The results demonstrate that the proposed approach can provide accurate predictions as well as uncertainty quantification given very limited scattered and noisy data, since historical data could be available to provide informative priors. In summary, the proposed method is capable of learning flexible functional priors, e.g., both Gaussian and non-Gaussian process, and can be readily extended to big data problems by enabling mini-batch training using stochastic HMC or normalizing flows since the latent space is generally characterized as low dimensional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Two-dimensional Imaging Velocity Interferometry: Technique and Data Analysis

We describe the data analysis procedures for an emerging interferometric technique for measuring motion across a two-dimensional image at a moment in time, i.e. a snapshot 2d-VISAR. Velocity interferometers (VISAR) measuring target motion to high precision have been an important diagnostic in shockwave physics for many years Until recently, this diagnostic has been limited to measuring motion at points or lines across a target. We introduce an emerging interferometric technique for measuring motion across a two-dimensional image, which could be called a snapshot 2d-VISAR. If a sufficiently fast movie camera technology existed, it could be placed behind a traditional VISAR optical system and record a 2d image vs time. But since that technology is not yet available, we use a CCD detector to record a single 2d image, with the pulsed nature of the illumination providing the time resolution. Consequently, since we are using pulsed illumination having a coherence length shorter than the VISAR interferometer delay ({approx}0.1 ns), we must use the white light velocimetry configuration to produce fringes with significant visibility. In this scheme, two interferometers (illuminating, detecting) having nearly identical delays are used in series, with one before the target and one after. This produces fringes with at most 50% visibility, but otherwise has the same fringe shift per target motion of a traditional VISAR. The 2d-VISAR observes a new world of information about shock behavior not readily accessible by traditional point or 1d-VISARS, simultaneously providing both a velocity map and an 'ordinary' snapshot photograph of the target. The 2d-VISAR has been used to observe nonuniformities in NIF related targets (polycrystalline diamond, Be), and in Si and Al.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Impact response of US Army and National Football League helmet pad systems

Lawrence Livermore National Laboratory [LLNL] was tasked to compare the impact response of NFL helmet pad systems and U.S. Army pad systems compatible with an Advanced Combat Helmet [ACH] at impact velocities up to 20 ft/s. This was a one-year study funded by the U.S. Army and JIEDDO. The Army/JIEDDO point of contact is COL R. Todd Dombroski, DO, JIEDDO Surgeon. LLNL was chosen by committee to perform the research based on prior published computational studies of the mechanical response of helmets and skulls to blast. Our collaborators include the U.S. Army Aeromedical Research Laboratory [USAARL] (a DoD laboratory responsible for impact testing helmets), Team Wendy and Oregon Aero (current and former ACH pad manufacturers), Riddell and Xenith (NFL pad manufacturers), and d3o (general purpose sports pad manufacturer). The manufacturer-supplied pad systems that were studied are shown in the figure below. The first two are the Army systems, which are bilayer foam pads with both hard and soft foam and a water-resistant airtight wrapper (Team Wendy) or a water-resistant airtight coating (Oregon Aero). The next two are NFL pad systems. The Xenith system consists of a thin foam pad and a hollow air-filled cylinder that elastically buckles under load. The Riddell system is a bilayer foam pad that is encased in an inflatable airbag with relief channels to neighboring pads in the helmet. The inflatable airbag is for comfort and provides no enhancement to impact mitigation. The d3o system consists of a rate-sensitive homogeneous dense foam. LLNL performed experiments to characterize the material properties of the individual foam materials and the response of the complete pad systems, to obtain parameters needed for the simulations. LLNL also performed X-ray CT scans of an ACH helmet shell that were used to construct a geometrically accurate computational model of the helmet. Two complementary sets of simulations were performed. The first set of simulations reproduced the experimental helmet impact certification tests performed by USAARL, who provided data for comparison. The goal of this set of simulations was to demonstrate the overall validity of LLNL's computational analyses and methods and understand the general physics of helmet impacts. In these tests and the corresponding simulations, an inverted ACH containing pads and a head-form are dropped onto a hemispherical anvil, at 10 and 14.14 ft/s impact velocities. The simulations predicted peak accelerations (the metric used by USAARL for comparing the performance of pad systems), rebound velocities, and impact durations consistent with the experimental data, thus demonstrating the validity and relevance of the simulation methods. Because the NFL pad systems are approximately double the thickness of the U.S. Army pads, they do not fit into the ACH. As a result, the NFL pads could not be simply placed into an ACH shell in either a simulation or an experiment without modifying their size and shape. Since impact mitigation depends critically on the available stopping distance and the area over which the stopping force is applied, it is important to consider identically shaped pads in order to compare their performance in a fair and meaningful manner. Consequently, the second set of simulations utilized a simplified simulation geometry consisting of a 5 kg cylindrical impactor (equal in mass to a head) striking equally sized pads from each manufacturer. The simulated bilayer foam pads had the same proportions of hard and soft foam as the actual pad systems, while the Xenith pads were simulated as a bilayer foam pad with material properties adjusted to give the same response as the actual Xenith pads. The effects of trapped air were included in the simulations of the Team Wendy and Oregon Aero pads. All simulations used material properties derived from the experiments conducted at LLNL. The acceleration history of the center of mass of the impactor was used to calculate the Head Injury Criterion (HIC) for each simulation, to assess the pad performance. The HIC is a well-established metric that combines both acceleration and duration of impact to assess the danger of injury, and is a more robust measure than peak acceleration. Our key findings are: (1) The performance of a pad depends on the range of impact velocities. At lower impact velocity, softer pads perform better. At higher impact velocity, harder pads perform better; (2) Thicker pads perform better at all velocities, but especially at high velocities; and (3) For comparable thicknesses, neither the NFL systems nor the Oregon Aero pads outperform the Team Wendy pads currently used in the ACH system in militarily-relevant impact scenarios (impact speeds less than 20 ft/s). The second finding suggests a commercial off-the-shelf solution for mitigating impact-related traumatic brain injury to soldiers.

42 ENGINEERING↗