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 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Test Problem: Tilted Rayleigh-Taylor for 2-D Mixing Studies

The 'tilted-rig' test problem originates from a series of experiments (Smeeton & Youngs, 1987, Youngs, 1989) performed at AWE in the late 1980's, that followed from the 'rocket-rig' experiments (Burrows et al., 1984; Read & Youngs, 1983), and exploratory experiments performed at Imperial College (Andrews, 1986; Andrews and Spalding, 1990). A schematic of the experiment is shown in Figure 1, and comprises a tank filled with light fluid above heavy, and then 'tilted' on one side of the apparatus, thus causing an 'angled interface' to the acceleration history due to rockets. Details of the configuration given in the next chapter include: fluids, dimensions, and other necessary details to simulate the experiment. Figure 2 shows results from two experiments, Case 110 (which is the source for this test problem) that has an Atwood number of 0.5, and Case 115 (a secondary source described in Appendix B), with Atwood of 0.9 Inspection of the photograph in Figure 2 (the main experimental diagnostic) for Case 110. reveals two main areas for mix development; 1) a large-scale overturning motion that produces a rising plume (spike) on the left, and falling plume (bubble) on the right, that are almost symmetric; and 2) a Rayleigh-Taylor driven mixing central mixing region that has a large-scale rotation associated with the rising and falling plumes, and also experiences lateral strain due to stretching of the interface by the plumes, and shear across the interface due to upper fluid moving downward and to the right, and lower fluid moving upward and to the left. Case 115 is similar but differs by a much larger Atwood of 0.9 that drives a strong asymmetry between a left side heavy spike penetration and a right side light bubble penetration. Case 110 is chosen as the source for the present test problem as the fluids have low surface tension (unlike Case 115) due the addition of a surfactant, the asymmetry small (no need to have fine grids for the spike), and there is extensive reasonable quality photographic data. The photographs in Figure 2 also reveal the appearance of a boundary layer at the left and right walls; this boundary layer has not been included in the test problem as preliminary calculations suggested it had a negligible effect on plume penetration and RT mixing. The significance of this test problem is that, unlike planar RT experiments such as the Rocket-Rig (Youngs, 1984), Linear Electric Motor - LEM (Dimonte, 1990), or the Water Tunnel (Andrews, 1992), the Tilted-Rig is a unique two-dimensional RT mixing experiment that has experimental data and now (in this TP) Direct Numerical Simulation data from Livescu and Wei. The availability of DNS data for the tilted-rig has made this TP viable as it provides detailed results for comparison purposes. The purpose of the test problem is to provide 3D simulation results, validated by comparison with experiment, which can be used for the development and validation of 2D RANS models. When such models are applied to 2D flows, various physics issues are raised such as double counting, combined buoyancy and shear, and 2-D strain, which have not yet been adequately addressed. The current objective of the test problem is to compare key results, which are needed for RANS model validation, obtained from high-Reynolds number DNS, high-resolution ILES or LES with explicit sub-grid-scale models. The experiment is incompressible and so is directly suitable for algorithms that are designed for incompressible flows (e.g. pressure correction algorithms with multi-grid); however, we have extended the TP so that compressible algorithms, run at low Mach number, may also be used if careful consideration is given to initial pressure fields. Thus, this TP serves as a useful tool for incompressible and compressible simulation codes, and mathematical models. In the remainder of this TP we provide a detailed specification; the next section provides the underlying assumptions for the TP, fluids, geometry details, boundary conditions (and alternative set-ups), initial conditions, and acceleration history (and ways to treat the acceleration ramp at the start of the experiment). This is followed by a section that defines data to be collected from the simulations, with results from the experiments and DNS from Livescu using the CFDNS code, and ILES simulations from Youngs using the compressible TURMOIL code and Andrews using the incompressible RTI3D code. We close the TP with concluding remarks, and Appendices that includes details of the sister Case 115, initial condition specifications for density and pressure fields. The Tilted-Rig Test Problem is intended to serve as a validation problem for RANS models, and as such we have provided ILES and DNS simulations in support of the test problem definition. The generally good agreement between experiment, ILES and DNS supports our assertion that the Tilted-Rig is useful, and the only 2-D TP that can be used to validate RANS models.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Accelerometer Modeling in the State-Space

Generically, accelerometers are sensors that measure the accelerating force applied to an object. Their operation is based on a simple mechanical system and D’Alembert’s force principle along with Newton’s laws of motion. This device is typically mounted to the body of the test object under investigation that is subjected to an accelerating force. The displacement of the seismic or “proof” mass due to the acceleration is sensed by an embedded component from which the acceleration is determined. Interestingly enough, the resulting the resulting mathematical relations governing the dynamical motion is based on the underlying physics, sensor materials, geometry and fabrication. Mathematically, the various designs satisfy the underlying Newtonian equations of motion, but their type and performance differ significantly.

42 ENGINEERING↗
DOE OSTI2016

A variational treatment of material configurations with application to interface motion and microstructural evolution

We present a unified variational treatment of evolving configurations in crystalline solids with microstructure. The crux of our treatment lies in the introduction of a vector configurational field. This field lies in the material, or configurational, manifold, in contrast with the traditional displacement field, which we regard as lying in the spatial manifold. We identify two distinct cases which describe (a) problems in which the configurational field's evolution is localized to a mathematically sharp interface, and (b) those in which the configurational field's evolution can extend throughout the volume. The first case is suitable for describing incoherent phase interfaces in polycrystalline solids, and the latter is useful for describing smooth changes in crystal structure and naturally incorporates coherent (diffuse) phase interfaces. These descriptions also lead to parameterizations of the free energies for the two cases, from which variational treatments can be developed and equilibrium conditions obtained. For sharp interfaces that are out-of-equilibrium, the second law of thermodynamics furnishes restrictions on the kinetic law for the interface velocity. The class of problems in which the material undergoes configurational changes between distinct, stable crystal structures are characterized by free energy density functions that are non-convex with respect to configurational strain. For physically meaningful solutions and mathematical well-posedness, it becomes necessary to incorporate interfacial energy. This we have done by introducing a configurational strain gradient dependence in the free energy density function following ideas laid out by Toupin (Arch. Rat. Mech. Anal., 11, 1962, 385-414). The variational treatment leads to a system of partial differential equations governing the configuration that is coupled with the traditional equations of nonlinear elasticity. The coupled system of equations governs the configurational change in crystal structure, and elastic deformation driven by elastic, Eshelbian, and configurational stresses. As a result, numerical examples are presented to demonstrate interface motion as well as evolving microstructures of crystal structures.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Umov-Mandelshtam radiation conditions in elastic periodic waveguides

We study settings of the problem of elasticity theory on wave propagation in an elastic periodic waveguide with radiation conditions at infinity. We present a mathematical theory for energy radiation conditions based on Mandelshtam's energy principle and the Umov-Poynting vector, as well as using the technique of weighted spaces with detached asymptotics and the energy transfer symplectic form. We establish that in a threshold situation, that is, when standing and polynomial elastic Floquet waves appear, the well-known limiting absorption principle, in contrast to the energy principle that is being applied, cannot identify the direction of the wave's motion. Bibliography: 37 titles. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Integrated Multiscale Modeling of Molecular Computing Devices

The main bottleneck in modeling transport in molecular devices is to develop the correct formulation of the problem and efficient algorithms for analyzing the electronic structure and dynamics using, for example, the time-dependent density functional theory. We have divided this task into several steps. The first step is to developing the right mathematical formulation and numerical algorithms for analyzing the electronic structure using density functional theory. The second step is to study time-dependent density functional theory, particularly the far-field boundary conditions. The third step is to study electronic transport in molecular devices. We are now at the end of the first step. Under DOE support, we have made subtantial progress in developing linear scaling and sub-linear scaling algorithms for electronic structure analysis. Although there has been a huge amount of effort in the past on developing linear scaling algorithms, most of the algorithms developed suffer from the lack of robustness and controllable accuracy. We have made the following progress: (1) We have analyzed thoroughly the localization properties of the wave-functions. We have developed a clear understanding of the physical as well as mathematical origin of the decay properties. One important conclusion is that even for metals, one can choose wavefunctions that decay faster than any algebraic power. (2) We have developed algorithms that make use of these localization properties. Our algorithms are based on non-orthogonal formulations of the density functional theory. Our key contribution is to add a localization step into the algorithm. The addition of this localization step makes the algorithm quite robust and much more accurate. Moreover, we can control the accuracy of these algorithms by changing the numerical parameters. (3) We have considerably improved the Fermi operator expansion (FOE) approach. Through pole expansion, we have developed the optimal scaling FOE algorithm.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2011

VECTOR MAGNETIC FIELDS OF A SOLAR POLAR REGION

We study the vector magnetic fields of a solar polar region (PR) based on Solar Optical Telescope/Spectro-Polarimeter measurements. To better understand the polar magnetic properties, we compare the observed polar field with that in two solar quiet regions at the limb (QRL) and the disk center (QRD), and with that in a region of a low-latitude coronal hole (CHR). The following results are discussed: (1) The average vertical flux density of PR is 16 G, while the average horizontal flux density is 91 G. If we assume that the observed polar field suffers the same amount of limb weakening in polarization measurements as the Sun's quiet region, the average unsigned flux density in the pole would be 54 G, 60% stronger than that in the CHR. (2) The kG field in the PR occupies 6.7% of the region. The magnetic filling factor in the PR is characterized by a two-peak distribution, which appears at a field strength close to 100 G and 1000 G, respectively. (3) For the network elements, a correlation holds between the vertical and horizontal flux densities, suggesting the same physical entity is manifested by the observed stronger vertical and horizontal components. (4) The ratio of the magnetic flux in the minority polarity to that in the dominant polarity is approximately 0.5, implying that only 1/3 of the magnetic flux in the PR opens to the interplanetary space. Exemplified with CHR by a quasi-linear force-free extrapolation of the observed magnetic field, we find that the photospheric open flux is not always associated with strong vertical magnetic elements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Complete parametrizations of diffusive quantum monitorings

The master equation for the state of an open quantum system can be unravelled into stochastic trajectories described by a stochastic master equation. Such stochastic differential equations can be interpreted as an update formula for the system state conditioned on results obtained from monitoring the bath. So far only one parametrization (mathematical representation) for arbitrary diffusive unravellings (quantum trajectories arising from monitorings with Gaussian white noise) of a system described by a master equation with L Lindblad terms has been found [H. M. Wiseman and A. C. Doherty, Phys. Rev. Lett. 94, 070405 (2005)]. This parametrization, which we call the U representation parameterizes diffusive unravellings by L{sup 2}+2L real numbers, arranged in a matrix U subject to three constraints. In this paper we investigate alternative parametrizations of diffusive measurements. We find, rather surprisingly, the description of diffusive unravellings can be unified by a single equation for a nonsquare complex matrix M if one is willing to allow for some redundancy by lifting the number of real parameters necessary from L{sup 2}+2L to 3L{sup 2}+L. We call this parametrization the M representation. Both the M representation and U representation lack a physical picture of what the measurement should look like. We thus propose another parametrization, the B representation that details how the measurement is implemented in terms of beam-splitters, phase shifters, and homodyne detectors. Relations between the different representations are derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

What do we mean by the word “Shock”?

From one vantage point, a shock is a continuous but drastic change in state variables that occurs over very small time and length scales. These scales and associated changes in state variables can be measured experimentally. From another vantage point, a shock is a mathematical singularity consisting of instantaneous changes in state variables. This more mathematical view gives rise to analytical solutions to idealized problems. And from a third vantage point, a shock is a structure in a hydrocode prediction. Its width depends on the simulation’s grid resolution and artificial viscosity. These three vantage points can be in conflict when ideas from the associated fields are combined, and yet combining them is an important goal of an integrated modeling program. This presentation explores an example of how models for real materials in the presence of real shocks react to a hydrocode’s numerical shocks of finite width. The presentation will include an introduction to plasticity for the novice, an historical view of plasticity algorithms, a demonstration of how pursuing the meaning of “shock” has resulted in hydrocode improvements, and will conclude by answering some of the questions that arise from that pursuit. After the technical part of the presentation, a few slides advertising LANL’s Computational Physics Student Summer Workshop will be shown.

36 MATERIALS SCIENCE↗
DOE OSTI2015

A global solution to the Schrödinger equation: From Henstock to Feynman

One of the key elements of Feynman’s formulation of non-relativistic quantum mechanics is a so-called Feynman path integral. It plays an important role in the theory, but it appears as a postulate based on intuition, rather than a well-defined object. All previous attempts to supply Feynman’s theory with rigorous mathematics underpinning, based on the physical requirements, have not been satisfactory. The difficulty comes from the need to define a measure on the infinite dimensional space of paths and to create an integral that would possess all of the properties requested by Feynman. In the present paper, we consider a new approach to defining the Feynman path integral, based on the theory developed by Muldowney [A Modern Theory of Random Variable: With Applications in Stochastic Calcolus, Financial Mathematics, and Feynman Integration (John Wiley & Sons, Inc., New Jersey, 2012)]. Muldowney uses the Henstock integration technique and deals with non-absolute integrability of the Fresnel integrals, in order to obtain a representation of the Feynman path integral as a functional. This approach offers a mathematically rigorous definition supporting Feynman’s intuitive derivations. But in his work, Muldowney gives only local in space-time solutions. A physical solution to the non-relativistic Schrödinger equation must be global, and it must be given in the form of a unitary one-parameter group in L{sup 2}(ℝ{sup n}). The purpose of this paper is to show that a system of one-dimensional local Muldowney’s solutions may be extended to yield a global solution. Moreover, the global extension can be represented by a unitary one-parameter group acting in L{sup 2}(ℝ{sup n})

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

An Introduction to Variational Calculus

Variational Calculus is an advanced topic in mathematics. This document exists to compile the basics of Variational Calculus in a readable and digestible manner for application by engineers. This document is a living document and will be updated as time moves forward. It is the hope that by reading this document, the basics of Variational Calculus can be readily applied to any system/function of interest. This does not serve as a replacement for textbooks or other learned sources but should act as a companion piece to better serve the reader in times of confusion and distress.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Phase Portraits of Dynamical Equations of Motion of a Rigid Body in a Resistive Medium

We consider a mathematical model of the influence of a medium on a rigid body with a specific shape of its surface. In this model, we take into account the additional dependence of the moment of the interaction force on the angular velocity of the body. We present a complete system of equations of motion under the quasi-stationarity conditions. The dynamical part of equations of motion forms an independent third-order system, which contains, in its turn, an independent secondorder subsystem. We ovtain a new family of phase portraits on the phase cylinder of quasi-velocities, which differs from families obtained earlier.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Incompact3d: A powerful tool to tackle turbulence problems with up to O(105) computational cores

Understanding the nature of complex turbulent flows remains one of the most challenging problems in classical physics. Significant progress has been made recently using high performance computing, and computational fluid dynamics is now a credible alternative to experiments and theories in order to understand the rich physics of turbulence. In this paper, we present an efficient numerical tool called Incompact3d that can be coupled with massive parallel platforms in order to simulate turbulence problems with as much complexity as possible, using up to O(105) computational cores by means of direct numerical simulation (DNS). DNS is the simplest approach conceptually to investigate turbulence, featuring the highest temporal and spatial accuracy and it requires extraordinary powerful resources. This paper is an extension of Laizet et al.(Comput. Fluids 2010; 39(3):471–484) where the authors proposed a strategy to run DNS with up to 1024 computational cores. Copyright © 2010 John Wiley & Sons, Ltd.

Computer Science↗
DOE OSTI2022

Bayesian Monte Carlo Evaluation Framework for Imperfect Data and Models [Abstract]

Nuclear data evaluation methods conventionally make the following assumptions: prior and posterior probability distribution functions (PDFs) of all model parameters and data are normal (Gaussian); the linear approximation is sufficiently accurate for minimization of a cost function (even for non-linear models); and that both the model (of, e.g., neutron cross section) and experimental data (including their covariance data) are perfect. These assumptions are inherent to the well-known generalized linear least squares (GLLS) minimization method commonly used for evaluations of resolved resonance region (RRR) neutron cross sections. However, these assumptions are often not justified due to the presence of non-normal PDFs, non-linear models (e.g. R -matrix formalism), and inherent imperfections in data and models (e.g. discrepant data sets, discrepancies between the previous evaluation and newly measured data, or imperfect covariance data). We remove the said assumptions in a mathematical framework of Bayes’ theorem, and implement it using the Metropolis-Hastings Monte Carlo method. Parameters of a new kind are introduced to parameterize inherent imperfections, e.g. , any discrepancies between the theoretical model and measured data. These new parameters enable evaluators to quantify their expert judgement about any discrepancies or imperfections in a reproducible manner. We demonstrate the framework with an ongoing evaluation of 233 U in the eV region using the ENDF-B/VIII library and transmission data measured by Guber, et al. , and compare the posterior parameters to those obtained by conventional evaluation methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2011

Optimal control of the electronic current density: Application to one- and two-dimensional one-electron systems

Quantum optimal control theory is a powerful tool for engineering quantum systems subject to external fields such as the ones created by intense lasers. The formulation relies on a suitable definition for a target functional, that translates the intended physical objective to a mathematical form. We propose the use of target functionals defined in terms of the one-particle density and its current. A strong motivation for this is the possibility of using time-dependent density-functional theory for the description of the system dynamics. We exemplify this idea by defining an objective functional that on one hand attempts a large overlap with a target density and on the other hand minimizes the current. The latter requirement leads to optimized states with increased stability, which we prove with a few examples of one- and two-dimensional one-electron systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Multistability in Chua's circuit with two stable node-foci

Only using one-stage op-amp based negative impedance converter realization, a simplified Chua's diode with positive outer segment slope is introduced, based on which an improved Chua's circuit realization with more simpler circuit structure is designed. The improved Chua's circuit has identical mathematical model but completely different nonlinearity to the classical Chua's circuit, from which multiple attractors including coexisting point attractors, limit cycle, double-scroll chaotic attractor, or coexisting chaotic spiral attractors are numerically simulated and experimentally captured. Furthermore, with dimensionless Chua's equations, the dynamical properties of the Chua's system are studied including equilibrium and stability, phase portrait, bifurcation diagram, Lyapunov exponent spectrum, and attraction basin. The results indicate that the system has two symmetric stable nonzero node-foci in global adjusting parameter regions and exhibits the unusual and striking dynamical behavior of multiple attractors with multistability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1986

Physics through the 1990s: Elementary-particle physics

The volume begins with a non-mathematical discussion of the motivation behind, and basic ideas of, elementary-particle physics theory and experiment. The progress over the past two decades with the quark model and unification of the electromagnetic and weak interactions is reviewed. Existing theoretical problems in the field, such as the origin of mass and the unification of the fundamental forces, are detailed, along with experimental programs to test the new theories. Accelerators, instrumentation, and detectors are described for both current and future facilities. Interactions with other areas of both theoretical and applied physics are presented. The sociology of the field is examined regarding the education of graduate students, the organization necessary in large-scale experiments, and the decision-making process involved in high-cost experiments. Finally, conclusions and recommendations for maintaining US excellence in theory and experiment are given. Appendices list both current and planned accelerators, and present statistical data on the US elementary-particle physics program. A glossary is included.

Source record↗
DOE OSTI2025

Diffusion Codes: Self-Correction from Small(er)-Set Expansion with Tunable Non-locality

Optimal constructions of classical LDPC codes can be obtained by choosing the Tanner graph uniformly at random among biregular graphs. We introduce a class of codes that we call ``diffusion codes'', defined by placing each edge connecting bits and checks on some graph, and acting on that graph with a random SWAP network. By tuning the depth of the SWAP network, we can tune a tradeoff between the amount of randomness -- and hence the optimality of code parameters -- and locality with respect to the underlying graph. For diffusion codes defined on the cycle graph, if the SWAP network has depth $\sim Tn$ with $T> n^{2β}$ for arbitrary $β>0$, then we prove that almost surely the Tanner graph is a lossless ``smaller set'' vertex expander for small sets up size $δ\sim \sqrt T \sim n^β$, with bounded bit and check degree. At the same time, the geometric size of the largest stabilizer is bounded by $\sqrt T$ in graph distance. We argue, based on physical intuition, that this result should hold more generally on arbitrary graphs. By taking hypergraph products of these classical codes we obtain quantum LDPC codes defined on the torus with smaller-set boundary and co-boundary expansion and the same expansion/locality tradeoffs as for the classical codes. These codes are self-correcting and admit single-shot decoding, while having the geometric size of the stabilizer growing as an arbitrarily small power law. Our proof technique establishes mixing of a random SWAP network on small subsystems at times scaling with only the subsystem size, which may be of independent interest.

Combinatorics (math.CO)↗