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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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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Finite-temperature perturbation theory for the random directed polymer problem

We study the random directed polymer problem-the short-scale behavior of an elastic string (or polymer) in one transverse dimension subject to a disorder potential and finite temperature fluctuations. We are interested in the polymer short-scale wandering expressed through the displacement correlator Left-Pointing-Angle-Bracket [{delta}u(X)]{sup 2} Right-Pointing-Angle-Bracket , with {delta}u(X) being the difference in the displacements at two points separated by a distance X. While this object can be calculated at short scales using the perturbation theory in higher dimensions d > 2, this approach becomes ill-defined and the problem turns out to be nonperturbative in the lower dimensions and for an infinite-length polymer. In order to make progress, we redefine the task and analyze the wandering of a string of a finite length L. At zero temperature, we find that the displacement fluctuations Left-Pointing-Angle-Bracket [{delta}u(X)]{sup 2} Right-Pointing-Angle-Bracket {proportional_to} LX{sup 2} depend on L and scale with the square of the segment length X, which differs from a straightforward Larkin-type scaling. The result is best understood in terms of a typical squared angle Left-Pointing-Angle-Bracket {alpha}{sup 2} Right-Pointing-Angle-Bracket {proportional_to} L, where {alpha} = {partial_derivative}{sub x}u, from which the displacement scaling for the segment X follows naturally, Left-Pointing-Angle-Bracket [{delta}u(X)]{sup 2} Right-Pointing-Angle-Bracket {proportional_to} Left-Pointing-Angle-Bracket {alpha}{sup 2} Right-Pointing-Angle-Bracket X{sup 2}. At high temperatures, thermal fluctuations smear the disorder potential and the lowest-order results for disorder-induced fluctuations in both the displacement field and the angle vanish in the thermodynamic limit L {yields} {infinity}. The calculation up to the second order allows us to identify the regime of validity of the perturbative approach and provides a finite expression for the displacement correlator, albeit depending on the boundary conditions and the location relative to the boundaries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Finite groups and quantum physics

Concepts of quantum theory are considered from the constructive 'finite' point of view. The introduction of a continuum or other actual infinities in physics destroys constructiveness without any need for them in describing empirical observations. It is shown that quantum behavior is a natural consequence of symmetries of dynamical systems. The underlying reason is that it is impossible in principle to trace the identity of indistinguishable objects in their evolution-only information about invariant statements and values concerning such objects is available. General mathematical arguments indicate that any quantum dynamics is reducible to a sequence of permutations. Quantum phenomena, such as interference, arise in invariant subspaces of permutation representations of the symmetry group of a dynamical system. Observable quantities can be expressed in terms of permutation invariants. It is shown that nonconstructive number systems, such as complex numbers, are not needed for describing quantum phenomena. It is sufficient to employ cyclotomic numbers-a minimal extension of natural numbers that is appropriate for quantum mechanics. The use of finite groups in physics, which underlies the present approach, has an additional motivation. Numerous experiments and observations in the particle physics suggest the importance of finite groups of relatively small orders in some fundamental processes. The origin of these groups is unclear within the currently accepted theories-in particular, within the Standard Model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Three-body unitarity in the finite volume

We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativistic $3\to 3$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

End-to-end GPU acceleration of low-order-refined preconditioning for high-order finite element discretizations

In this article, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of effective preconditioners for high-order problems with optimal memory usage and computational complexity. The preconditioners are based on the construction of a spectrally equivalent low-order discretization on a refined mesh, which is then amenable to, for example, algebraic multigrid preconditioning. The constants of equivalence are independent of mesh size and polynomial degree. For vector finite element problems in H(curl) and H(div) (e.g., for electromagnetic or radiation diffusion problems), a specially constructed interpolation–histopolation basis is used to ensure fast convergence. Detailed performance studies are carried out to analyze the efficiency of the GPU algorithms. The kernel throughput of each of the main algorithmic components is measured, and the strong and weak parallel scalability of the methods is demonstrated. The different relative weighting and significance of the algorithmic components on GPUs and CPUs is discussed. Results on problems involving adaptively refined nonconforming meshes are shown, and the use of the preconditioners on a large-scale magnetic diffusion problem using all spaces of the finite element de Rham complex is illustrated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Generalization of mixed multiscale finite element methods with applications

Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixed multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Optimized Finite-Difference Coefficients for Acoustic Modeling.

Although using standard Taylor series coefficients for finite-difference operators is optimal in the sense that in the limit of infinitesimal space and time discretization, the solution approaches the correct analytic solution to the acousto-dynamic system of differential equations, other finite-difference operators may provide optimal computational run time given certain error bounds or source bandwidth constraints. This report describes the results of investigation of alternative optimal finite-difference coefficients based on several optimization/accuracy scenarios and provides recommendations for minimizing run time while retaining error within given error bounds.

58 GEOSCIENCES↗
DOE OSTI2018

Truly horizontal finite difference scheme in the WRF model FY18 Q1 Update

A main goal of the Wind Forecasting Improvement Project 2 (WFIP2) is to improve performance of the Weather Research and Forecasting (WRF) model over complex terrain. Two methods for improving model performance were outlined in the LLNL WFIP 2 annual operating plan. The first is modification to WRF’s horizontal finite difference scheme to utilize an improved numerical stencil. A second proposed model improvement is use of the immersed boundary method within the WRF model to facilitate improved simulations over complex terrain. In Q1, work focused on implementing an alternative finite difference scheme, with a deliverable of a project update. The alternative finite difference method was implemented for the temperature variable and shown to improve our selected test case, and recommendations are made to continue the work in Q2. In Q2 the focus should be on extending the method to additional model variables, mainly pressure, as well as to real test cases, such as the WFIP 2 cold pool test case. Additionally, use of the immersed boundary method will be pursed in Q2 and Q3, with a second project update due at the end of Q3.

17 WIND ENERGY↗
DOE OSTI2018

Generalized and High-Order Multiscale Finite-Element Methods for Seismic Wave Propagation [Slides]

We have developed a series of multiscale finite-element methods for simulating seismic wave propagation in complex media. The most important feature of multiscale finite-element methods is using medium- and mesh-dependent multiscale basis functions. For different wave equations, or for wave equation modeling in different domains, we design different local spectral/linear problems to compute multiscale basis functions. Multiscale basis functions can accurately capture the fine-scale medium information for coarse-scale modeling problems. Numerical examples have demonstrated the efficiency and accuracy of our multiscale finite-element method framework for wave equation modeling. Future works aim at further improving the efficiency using more levels of information encapsulation, and address more realistic physics problems.

58 GEOSCIENCES↗
DOE OSTI2020

Smoothers for Matrix-Free Algebraic Multigrid Preconditioning of High-Order Finite Elements

We investigate smoothers for use in matrix-free algebraic multigrid (AMG) preconditioning of high-order finite element problems. These AMG preconditioners are matrix-free in the sense that they are built from a related low-order refined finite element problem whose system matrix can be much more rapidly assembled than the high-order problem. Our proposed smoother, which we call distributive relaxation, is more robust to the anisotropy present in many low-order refined meshes which feature a clustering of nodes near the boundaries between high-order finite elements. For solving the low-order refined problem, we show that this new distributive relaxation smoother possesses significantly improved performance compared to more traditional smoothers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Effects of finite element discretization and model simplification on calculations of ductile failure initiation

The finite element method is a scheme to discretize the infinite number of degrees of freedom in continuum-level problems down to a finite number of degrees of freedom. This discretization is done in conjunction with methods that also reduce the field differential equations to sets of algebraic ones that can be solved by arithmetical operations. Therefore, solutions attained by finite element models are approximations to the exact solutions of the field equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

An Immersed Finite Element Lagrangian-Eulerian Code-Coupling Framework

This report presents an assessment of immersed Eulerian-Lagrangian code-coupling techniques suitable for use in a broad range of mechanics applications. The coupling algorithm is based on an immersed finite element method that considers the Lagrangian and Eulerian overlap regions in the overall variational formulation. In this report the basic formulation details are presented followed by various aspects of the code-coupling algorithm using OpenIFEM as the Lagrangian/coupling framework. A series of representative test cases that illustrate the code-coupling algorithm are discussed. The current work provides an in-depth investigation into the immersed finite element method for the purposes of providing a rigorous coupling technique that is minimally invasive in the respective Eulerian and Lagrangian codes. A number of extensions to the base immersed finite element method have been examined. These extension include nodal and quadrature-based indicator functions, a Lagrangian volume-fraction calculation in regions of overlap, and the use of penalty constraints between the Lagrangian and Eulerian domains. A unique MPI-based coupling strategy that retains the independent MPI structure of each code has been demonstrated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Finite-Size Scaling on a Digital Quantum Simulator Using Quantum Restricted Boltzmann Machine

The critical point and the critical exponents for a phase transition can be determined using the Finite-Size Scaling (FSS) analysis. This method assumes that the phase transition occurs only in the infinite size limit. However, there has been a lot of interest recently in quantum phase transitions occurring in finite size systems such as a single two-level system interacting with a single bosonic mode e.g., in the Quantum Rabi Model (QRM). Since these phase transitions occur at a finite system size, the traditional FSS method is rendered inapplicable for these cases. For cases like this, we propose an alternative FSS method in which the truncation of the system is done in the Hilbert space instead of the physical space. This approach has previously been used to calculate the critical parameters for stability and symmetry breaking of electronic structure configurations of atomic and molecular systems. We calculate the critical point for the quantum phase transition of the QRM using this approach. We also provide a protocol to implement this method on a digital quantum simulator using the Quantum Restricted Boltzmann Machine algorithm. Our work opens up a new direction in the study of quantum phase transitions on quantum devices.

Khalid, Bilal↗
DOE OSTI2016

EFFECT OF FINITE LARMOR RADIUS CORRECTIONS ON THE THERMAL INSTABILITY OF THERMALLY CONDUCTING VISCOUS PLASMA WITH HALL CURRENT AND ELECTRON INERTIA

The thermal instability of an infinite homogeneous, thermally conducting, and rotating plasma, incorporating finite electrical resistivity, finite electron inertia, and an arbitrary radiative heat-loss function in the presence of finite Larmor radius corrections and Hall current, has been studied. Analysis has been made with the help of linearized magnetohydrodynamics (MHD) equations. A general dispersion relation is obtained using the normal mode analysis method, and the dispersion relation is discussed for longitudinal propagation and transverse propagation separately. The dispersion relation has been solved numerically to obtain the dependence of the growth rate on the various parameters involved. The conditions of modified thermal instability and stability are discussed in the different cases of interest.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Development of Finite Element Field Solver in Gyrokinetic Toroidal Code

A new finite element (FE) field solver has been implemented in the gyrokinetic toroidal code (GTC) in attempt to extend the simulation domain to magnetic axis and beyond the last closed flux surface, which will enhance the capability the GTC code since the original finite difference (FD) solver will lose its capability in such circumstances. A method of manufactured solution is employed in the unit fidelity test for the new FE field solver, which is then further verified through integrated tests with three typical physical cases for the comparison between the new FE field solver and the original finite difference field solver. The results by the newly implemented FE field solver are in great accord with the original solver.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1971

Analysis of transient, linear wave propagation in shells by the finite difference method

The applicability of the finite difference method to propagation problems in shells, and the response of a cylindrical shell with cutouts to both longitudinal and radial transient excitations are investigated. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. The short wave length limitations of thin shell theory create significant convergence difficulties may often be overcome through proper selection of finite difference mesh dimensions and temporal or spatial smoothing of the excitation. Cutouts produce moderate changes in early and intermediate time response of a cylindrical shell to axisymmetric pulse loads applied at one end. The cutouts may facilitate the undesirable late-time transfer of load-injected extensional energy into nonaxisymmetric flexural response.

Geers, T. L.↗
NASA NTRS1971

Generation of Finite Life Distributional Goodman Diagrams for Reliability Prediction

The methodology of developing finite life distributional Goodman diagrams and surfaces is described for presenting allowable combinations of alternating stress and mean stress to the design engineer. The combined stress condition is that of an alternating bending stress and a constant shear stress. The finite life Goodman diagrams and surfaces are created from strength distributions developed at various ratios of alternating to mean stress at particular cycle life values. The conclusions indicate that the Von Mises-Hencky ellipse, for cycle life values above 1000 cycles, is an adequate model of the finite life Goodman diagram. In addition, suggestions are made which reduce the number of experimental data points required in a fatigue data acquisition program.

Kececioglu, D.↗
NASA NTRS1971

Finite-state machines as elements in control systems.

Demonstration that approximate solutions to certain classes of differential and difference equations can be expressed in form of finite state machines. Based on this result, a finite-state machine model of an adaptive gain changer in an aircraft stability augmentation system is developed. Results of simulated flights using the finite-state machine gain changer are presented.

Burgin, G. H.↗
NASA NTRS1971

Similarity and generalized finite-difference solutions of parabolic partial differential equations.

Techniques are presented for obtaining generalized finite-difference solutions to partial differential equations of the parabolic type. It is shown that the advantages of similarity in the solution of similar problems are generally not lost if the solution to the original partial differential equations is effected in the physical plane by finite-difference methods. The analysis results in a considerable saving in computational effort in the solution of both similar and nonsimilar problems. Several examples, including both the heat-conduction equation and the boundary-layer equations, are given. The analysis also provides a practical means of estimating the accuracy of finite-difference solutions to parabolic equations.

Clausing, A. M.↗