SEARCH · Engineering Papers
Results for “perturbation methods”
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.
Hamiltonian Truncation Effective Theory
Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states spanned by the eigenvectors of the free Hamiltonian H_0 H 0 with eigenvalues below some energy cutoff E_\text{max} E max . In this work, we show how to treat Hamiltonian truncation systematically using effective field theory methodology. We define the finite-dimensional effective Hamiltonian by integrating out the states above E_\text{max} E max . The effective Hamiltonian can be computed by matching a transition amplitude to the full theory, and gives corrections order by order as an expansion in powers of 1/E_\text{max} 1 / E max . The effective Hamiltonian is non-local, with the non-locality controlled in an expansion in powers of H_0/E_\text{max} H 0 / E max . The effective Hamiltonian is also non-Hermitian, and we discuss whether this is a necessary feature or an artifact of our definition. We apply our formalism to 2D \lambda\phi^4 λ ϕ 4 theory, and compute the the leading 1/E_\text{max}^2 1 / E max 2 corrections to the effective Hamiltonian. We show that these corrections nontrivially satisfy the crucial property of separation of scales. Numerical diagonalization of the effective Hamiltonian gives residual errors of order 1/E_\text{max}^3 1 / E max 3 , as expected by our power counting. We also present the power counting for 3D \lambda \phi^4 λ ϕ 4 theory and perform calculations that demonstrate the separation of scales in this theory.
Beryllium Dynamic Strength Measurements (Report on Task 1, Agreement #B590737)
Goal of the work under Agreement #B590737 is development of experimentally justified model of beryllium shear strength of American production ( Be S200F ) in the pressure range of ∼10÷60 GPa and strain rates up to $\dot{ε_i}$ ≈10 6 s -1 . The Be shear strength models, which are available in this range of parameters, have no sufficiently reliable experimental justification. Therefore it is planned to perform tests using the dynamic method of perturbations with shockless loading of the investigated Be S200F samples up to pressure P m ≈55 GPa. Growth of specified perturbations will be recorded by pulse X-ray radiography. The existing relaxation model of beryllium strength will be corrected basing on test results. Besides, the model should also describe the other published results of tests with investigation of dynamic properties of beryllium. Also it is planned to perform two tests with loading of beryllium samples up to pressure P∼50÷60 GPa with recovery followed by metallographic investigation. Goal of the metallographic investigation is determination of peculiarities of high-rate deformation of Be , determination of density of dislocations and twins in the loaded samples. These data will allow developing a more justified constitutive equation (the strength model). Objective of this Task of Agreement #B590737 consists of review of the published data on deformation and shear strength of Be , as well as numerical-theoretical justification of the tests, which will be performed under the frameworks of Task 3 of the Agreement. Besides, this report includes the earlier published data on measurements of velocities of vanadium liners accelerated by explosive two-stage device.
Acoustoelasticity Testing: Changing Boundary Conditions and Damping
A series of modal tests were performed on an acoustoelastic system to explore how changes to the air and structural components affect the acoustoelastic coupling. This work is a continuation of previous experimental and analytical efforts. Here, the test method and perturbations were much more controlled than in previous tests, resulting in more refined data. Outputs of interest here are the coupled system modes as well as the resulting frequency response for various perturbations of the coupled system. Perturbations explored in this work include mass loading the structure, changing the air damping, and changing the air boundary conditions. Results of these tests indicate that simply adding damping to the air component, using foam or other absorptive material, is not sufficient to fully decouple the system. Rather, it is preferred to employ a change to the air boundary conditions, in the form of volume inclusions or scatterers, to prevent formation of the acoustic coupled mode.
Theory and Simulation of Nanoscale Phenomena
The Center for Integrated Nanotechnologies (CINT) is a Department of Energy/Office of Science Nanoscale Science Research Center (NSRC), operating as a national user facility devoted to establishing the scientific principles that govern nanoscale integration. Nanoscale integration is defined as assembling diverse nanoscale materials across length scales to design and achieve new properties and functionality. The CINT Theory and Simulation of Nanoscale Phenomena thrust is the component of CINT dedicated to developing and applying theory to enable nanoscale integration. Our focus is on understanding and simulating the unique behavior of integrated materials and systems with nanoscale structure. This mission is achieved through collaborations with CINT Users, between thrust scientists, and with CINT scientists from other thrusts. Our research is focused on three science directions that together form the basis for integration at the nanoscale, namely (i) Hierarchical structure and dynamics in soft matter, (ii) Excitation and Transport in Nanostructured Systems, and (iii) Emergent phenomena at surfaces and interfaces. A broad spectrum of techniques is developed and applied including continuum fluid theory, atomistic and coarse-grained molecular dynamics simulations, static and dynamic electronic structure calculations, multiscale modeling, low-energy effective Hamiltonian methods, and perturbative and exact quantum many-body approaches. These tools are applied to physical systems of interest to CINT Users, the other CINT thrusts, and the general scientific community with the goals of understanding and controlling the interactions between nanoscale building blocks to assemble specific integrated structures, controlling energy transfer and other interactions over multiple length scales, and designing and exploiting the interactions within assembled structures to achieve new materials functionality.
CSPlib - A Software Toolkit for the Analysis of Dynamical Systems and Chemical Kinetic Models
CSPlib is an open source software library for analyzing general ordinary differential equation (ODE) systems and detailed chemical kinetic ODE systems. It relies on the computational singular perturbation (CSP) method for the analysis of these systems. The software provides support for: General ODE models (gODE model class) for computing source terms and Jacobians for a generic ODE system; TChem model (ChemElemODETChem model class) for computing source term, Jacobian, other necessary chemical reaction data, as well as the rates of progress for a homogenous batch reactor using an elementary step detailed chemical kinetic reaction mechanism. This class relies on the TChem [2] library; A set of functions to compute essential elements of CSP analysis (Kernel class). This includes computations of the eigensolution of the Jacobian matrix, CSP basis vectors and co-vectors, time scales (reciprocals of the magnitudes of the Jacobian eigenvalues), mode amplitudes, CSP pointers, and the number of exhausted modes. This class relies on the Tines library; A set of functions to compute the eigensolution of the Jacobian matrix using Tines library GPU eigensolver; A set of functions to compute CSP indices (Index Class). This includes participation indices and both slow and fast importance indices.
CSPlib - A Toolkit for the Analysis of ODE/DAE Dynamical Systems and Chemical Kinetic Models
CSPlib is an open source software library for analyzing general ordinary differential equation (ODE) systems and detailed chemical kinetic ODE/DAE systems. It relies on the computational singular perturbation (CSP) method for the analysis of these systems.
Life at the Landau Pole
If a quantum field theory has a Landau pole, the theory is usually called ‘sick’ and dismissed as a candidate for an interacting UV-complete theory. In a recent study on the interacting 4d O(N) model at large N, it was shown that at the Landau pole, observables remain well-defined and finite. In this work, I investigate both relevant and irrelevant deformations of the said model at the Landau pole, finding that physical observables remain unaffected. Apparently, the Landau pole in this theory is benign. As a phenomenological application, I compare the O(N) model to QCD by identifying $Λ_{\overline{MS}}$ with the Landau pole in the O(N) model.
K-shell Emission from O vi Near 19 Å
Abstract Laboratory measurements of O vi K-shell emission lines are presented that are situated near the O viii Ly α line at 19 Å. The data provide additional rest-frame references for velocity determinations based on absorption features in the spectra of warm absorbers in active galactic nuclei and other astrophysical objects. They also provide benchmarks for testing atomic structure calculations of energy levels with electrons in a high principal quantum number ( n = 3, 4). Excellent agreement is found with our calculations using the many-body perturbation theory method, and we provide a complete listing of the O vi energy levels calculated with this approach.
Relativistic MR–MP Energy Levels for L-shell Ions of Silicon
Level energies are reported for Si v, Si vi, Si vii, Si viii, Si ix, Si x, Si xi, and Si xii. The energies have been calculated with the relativistic Multi-Reference Møller–Plesset Perturbation Theory method and include valence and K-vacancy states with nl up to 5f. The accuracy of the calculated level energies is established by comparison with the recommended data listed in the National Institute of Standards and Technology (NIST) online database. The average deviation of valence level energies ranges from 0.20 eV in Si v to 0.04 eV in Si xii. For K-vacancy states, the available values recommended in the NIST database are limited to Si xii and Si xiii. The average energy deviation is below 0.3 eV for K-vacancy states. The extensive and accurate data set presented here greatly augments the amount of available reference level energies. Here, we expect our data to ease the line identification of L-shell ions of Si in celestial sources and laboratory-generated plasmas, and to serve as energy references in the absence of more accurate laboratory measurements.
Relativistic MR-MP Energy Levels for L-shell Ions of Sulfur and Argon
Calculated level energies for valence and K-vacancy states are given for the ion series S vii–S xiv and Ar ix–Ar xvi. The calculations were performed with the relativistic Multi-Reference Møller–Plesset Perturbation Theory method (MR-MP). The data set includes all the level energies with configurations $1{s}^{2}2{(s,p)}^{q}$, $1{s}^{2}2{(s,p)}^{q-1}{nl}$, $1{s}^{1}2{(s,p)}^{q+1}$, $1{s}^{1}2{(s,p)}^{q}{nl}$, $2{(s,p)}^{q+2}$, and $2{(s,p)}^{q+1}{nl}$, where 1 ≤ q ≤ 8, n ≤ 5, and l ≤ 3. We have compared our results with data from the National Institute of Standards and Technology (NIST) online database and with previous calculations. The average deviation of valence level energies ranges from 0.16 eV in Ne-like ions to 0.01 eV in Li-like ions, demonstrating that the present MR-MP valence level energies are highly accurate. In the case of K-vacancy states, the deviation is generally below 0.3 eV for Li-like S xiv and Ar xvi. The deviation for K-vacancy energies in other L-shell ions (Be-, B-, C-, N-, and O-like Ar ions) is higher but likely because the NIST-recommended values have a higher uncertainty. The data set includes many n = 4 and n = 5 valence and K-vacancy levels in L-shell ions of S and Ar that have not been previously reported. The data can be used for line identification and modeling of L-shell ions of S and Ar in astrophysical and laboratory-generated plasmas, and as energy references in the absence of more accurate laboratory calculations.
Identification of a linear system from sampled noisy data, part C Final project report
Step input linear system modeling from nonlinear system sampled noisy data based on method of perturbation or quasilinearization of automatic control system data
A study of numerical methods for computing reentry trajectories for shuttle-type space vehicles
The reuseable exterior insulation system (REI) is studied to determine the optimal reentry trajectory for a space shuttle, which minimizes the heat input to the fuselage. The REI is composed of titanium, covered by a surface insulation material. The method of perturbation functions was used to generate the trajectories, and proved to be an effective technique for generating families of solutions, once an initial trajectory has been obtained.
Hydrogen atom in intense magnetic field.
The structure of a hydrogen atom situated in an intense magnetic field is investigaged. Three approaches are employed. An elementary Bohr picture establishes a crucial magnetic field strength, H sub a approximately equal to 5 x 10 to the 9th G. Fields in excess of H sub a are intense in that they are able to modify the characteristic atomic scales of length and binding energy. A second approach solves the Schrodinger equation by a combination of variational methods and perturbation theory. It yields analytic expressions for the wave functions and energy eigenvalues. A third approach determines the energy eigenvalues by reducing the Schrodinger equation to a one-dimensional wave equation, which is then solved numerically. Energy eigenvalues are tabulated for field strengths of 2 x 10 to the 10th G and 2 x 10 to the 12th G. It is found that at 2 x 10 to the 12th G the lowest energy eigenvalue is changed from -13.6 to about -180 eV in agreement with previous variational computations.
Investigation into the propagation of Omega very low frequency signals and techniques for improvement of navigation accuracy including differential and composite omega
An analysis of Very Low Frequency propagation in the atmosphere in the 10-14 kHz range leads to a discussion of some of the more significant causes of phase perturbation. The method of generating sky-wave corrections to predict the Omega phase is discussed. Composite Omega is considered as a means of lane identification and of reducing Omega navigation error. A simple technique for generating trapezoidal model (T-model) phase prediction is presented and compared with the Navy predictions and actual phase measurements. The T-model prediction analysis illustrates the ability to account for the major phase shift created by the diurnal effects on the lower ionosphere. An analysis of the Navy sky-wave correction table is used to provide information about spatial and temporal correlation of phase correction relative to the differential mode of operation.
Computational study of nonlinear plasma waves. I - Simulation model and monochromatic wave propagation. II - Sideband instability and satellite growth
A hybrid plasma simulation model is described and applied to the study of electrostatic wave propagation in a one-dimensional Maxwellian plasma with periodic boundary conditions. The model employs a cloud-in-cell scheme which can drastically reduce the fluctuations in particle simulation models and greatly ease the computational difficulties of the Vlasov equation approach. A grid in velocity space is introduced and the particles are represented by points in the x-v phase space. The model is tested first in the absence of an applied signal and then in the presence of a small-amplitude perturbation. The method is also used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories.
A uniformly valid solution for motion about the interior libration point of the perturbed elliptic-restricted problem
Bounded motion about Lagrange collinear libration points is considered for a perturbed elliptic-restricted problem. A practical application is the motion of a satellite near a libration point collinear with the sun and the earth-moon barycenter. Such a system is treated here as an earth-sun-satellite elliptic restricted problem with lunar perturbations. The method of dual time scales is utilized to develop a uniformly valid three-dimensional analytical solution to the satellite's equations of motion. The analytical development applies somewhat generally to that class of four-body problems where the second primary mass is much greater than the first, and the third primary mass is much greater than the second.
Analytic theory of orbit contraction due to atmospheric drag
Theory of space vehicle flight in near vacuum and in a planetary atmosphere is unified for the case of a spherically symmetric atmosphere with exponential variation of density with height. Dimensionless equations of motion are established that bridge the gap between satellite theory and entry theory. Integration is done by Poincare's method of perturbations. Solutions for the dimensionless semimajor axis are numerically obtained.