Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “TENSOR FORCES”

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 127 records · Page 7

Some properties of transient phenomena in the extra-tropical region and their importance in the seasonal mean flow

When studying data for one season, it is convenient to divide transient eddies into those of the synoptic time scale and those of lower frequency. Where the dividing line is placed is not crucial, but a 10-day period is used in a study of the 1979-1980 Northern Hemisphere winter. The synoptic time scale eddies exhibit maximum kinetic energy in stormtracks slightly downstream from and poleward of the Atlantic and Pacific jet maximum. An alternative approach is via the anisotropic part of the horizontal velocity correlation tensor, the axis of which gives the local orientation of the eddies and the magnitude a measure of the extension of the eddies. When the man velocity field is almost that of the plane waves, the horizontal group velocity relative to the mean field is also related to this tensor. The synoptic time scale eddies force the mean flow in the sense of reducing the baroclinic component in the upstream of the region of the stormtrack. The lower frequency eddies have a very different signature.

Hoskins, B. J.↗

Large-Eddy Simulations with Explicit Equations for Subgrid-Scale Quantities

Various alternative formulations of the LES equations have been explored in which additional evolution equations for variables such as the acceleration, the subgrid-scale stress tensor, or the subgrid-scale force are explicitly carried. Statistics of the velocity field obtained from the equation for the acceleration are shown to depend strongly on the initial conditions. This feature, which is independent of LES modeling issues, seems to prove that the velocity-acceleration formulation of the Navier-Stokes is not useful for numerical simulation. Equations for the subgrid-scale quantities appear to be much more stable. However, models required by this formulation of the LES problem still require additional study.

Carati, Daniele↗

Extended Lagrangian Born–Oppenheimer molecular dynamics for orbital-free density-functional theory and polarizable charge equilibration models

We report extended Lagrangian Born–Oppenheimer molecular dynamics (XL-BOMD) is formulated for orbital-free Hohenberg–Kohn density-functional theory and for charge equilibration and polarizable force-field models that can be derived from the same orbital-free framework. The purpose is to introduce the most recent features of orbital-based XL-BOMD to molecular dynamics simulations based on charge equilibration and polarizable force-field models. These features include a metric tensor generalization of the extended harmonic potential, preconditioners, and the ability to use only a single Coulomb summation to determine the fully equilibrated charges and the interatomic forces in each time step for the shadow Born–Oppenheimer potential energy surface. The orbital-free formulation has a charge-dependent, short-range energy term that is separate from long-range Coulomb interactions. This enables local parameterizations of the short-range energy term, while the long-range electrostatic interactions can be treated separately. The theory is illustrated for molecular dynamics simulations of an atomistic system described by a charge equilibration model with periodic boundary conditions. The system of linear equations that determines the equilibrated charges and the forces is diagonal, and only a single Ewald summation is needed in each time step. The simulations exhibit the same features in accuracy, convergence, and stability as are expected from orbital-based XL-BOMD.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables

Here, we introduce a mesh-adaption framework that employs a multi-physical configurational force and Lie algebra to capture multiphysical responses of fluid-infiltrating geological materials while maintaining the efficiency of the computational models. To resolve sharp gradients of both displacement and pore pressure, we introduce an energy-estimate-free re-meshing criterion by extending the configurational force theory to consider the energy dissipation due to the fluid diffusion and the gradient-dependent plastic flow. To establish new equilibria after remeshing, the local tensorial history-dependent variables at the integration points are first decomposed into spectral forms. Then, the principal values and directions are projected onto smooth fields interpolated by the basis function of the finite element space via the Lie-algebra mapping. Our numerical results indicate that this Lie algebra operator in general leads to a new trial state closer to the equilibrium than the ones obtained from the tensor component mapping approach. A new configurational force for dissipative fluid-infiltrating porous materials that exhibit gradient-dependent plastic flow is introduced such that the remeshing may accommodate the need to resolve the sharp pressure gradient as well as the strain localization. The predicted responses are found to be not influenced by the mesh size due to the micromorphic regularization, while the adaptive meshing enables us to capture the width of deformation bands without the necessity of employing fine mesh everywhere in the domain.

42 ENGINEERING↗

No fifth force in a scale invariant universe

We revisit the possibility that the Planck mass is spontaneously generated in scale-invariant scalar-tensor theories of gravity, typically leading to a “dilaton.” The fifth force, arising from the dilaton, is severely constrained by astrophysical measurements. We explore the possibility that nature is fundamentally scale invariant and argue that, as a consequence, the fifth-force effects are dramatically suppressed and such models are viable. Finally, we discuss possible obstructions to maintaining scale invariance and how these might be resolved.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Computing bulk and shear viscosities from simulations of fluids with dissipative and stochastic interactions

Exact values for bulk and shear viscosity are important to characterize a fluid, and they are a necessary input for a continuum description. Here we present two novel methods to compute bulk viscosities by non-equilibrium molecular dynamics simulations of steady-state systems with periodic boundary conditions — one based on frequent particle displacements and one based on the application of external bulk forces with an inhomogeneous force profile. In equilibrium simulations, viscosities can be determined from the stress tensor fluctuations via Green-Kubo relations; however, the correct incorporation of random and dissipative forces is not obvious. We discuss different expressions proposed in the literature and test them at the example of a dissipative particle dynamics fluid.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Introduction to Vector Field Visualization

Vector field visualization techniques are essential to help us understand the complex dynamics of flow fields. These can be found in a wide range of applications such as study of flows around an aircraft, the blood flow in our heart chambers, ocean circulation models, and severe weather predictions. The vector fields from these various applications can be visually depicted using a number of techniques such as particle traces and advecting textures. In this tutorial, we present several fundamental algorithms in flow visualization including particle integration, particle tracking in time-dependent flows, and seeding strategies. For flows near surfaces, a wide variety of synthetic texture-based algorithms have been developed to depict near-body flow features. The most common approach is based on the Line Integral Convolution (LIC) algorithm. There also exist extensions of LIC to support more flexible texture generations for 3D flow data. This tutorial reviews these algorithms. Tensor fields are found in several real-world applications and also require the aid of visualization to help users understand their data sets. Examples where one can find tensor fields include mechanics to see how material respond to external forces, civil engineering and geomechanics of roads and bridges, and the study of neural pathway via diffusion tensor imaging. This tutorial will provide an overview of the different tensor field visualization techniques, discuss basic tensor decompositions, and go into detail on glyph based methods, deformation based methods, and streamline based methods. Practical examples will be used when presenting the methods; and applications from some case studies will be used as part of the motivation.

Kao, David↗

Probing the Repulsive Core of the Nucleon-Nucleon Interaction via the 4 He(e,e`pN) Triple-Coincidence Reaction

We studied simultaneously the 4 He(e,e'p), 4 He(e,e'pp), and 4 He(e,e'pn) reactions at Q 2 =2 [GeV/c] 2 and x B >1, for a (e,e'p) missing-momentum range of 400 to 830 MeV/c. The knocked-out proton was detected in coincidence with a proton or neutron recoiling almost back to back to the missing momentum, leaving the residual A=2 system at low excitation energy. These data were used to identify two-nucleon short-range correlated pairs and to deduce their isospin structure as a function of missing momentum in a region where the nucleon-nucleon force is expected to change from predominantly tensor to repulsive. Neutron-proton pairs dominate the high-momentum tail of the nucleon momentum distributions, but their abundance is reduced as the nucleon momentum increases beyond ~500 MeV/c. The extracted fraction of proton-proton pairs is small and almost independent of the missing momentum in the range we studied. Our data are compared with ab-initio calculations of two-nucleon momentum distributions in 4 He.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Visualization of 2-D and 3-D Tensor Fields

In previous work we have developed a novel approach to visualizing second order symmetric 2-D tensor fields based on degenerate point analysis. At degenerate points the eigenvalues are either zero or equal to each other, and the hyperstreamlines about these points give rise to trisector or wedge points. These singularities and their connecting hyperstreamlines determine the topology of the tensor field. In this study we are developing new methods for analyzing and displaying 3-D tensor fields. This problem is considerably more difficult than the 2-D one, as the richness of the data set is much larger. Here we report on our progress and a novel method to find, analyze and display 3-D degenerate points. First we discuss the theory, then an application involving a 3-D tensor field, the Boussinesq problem with two forces.

Hesselink, Lambertus↗

Visualization of 2-D and 3-D Tensor Fields

In previous work we have developed a novel approach to visualizing second order symmetric 2-D tensor fields based on degenerate point analysis. At degenerate points the eigenvalues are either zero or equal to each other, and the hyper-streamlines about these points give rise to tri-sector or wedge points. These singularities and their connecting hyper-streamlines determine the topology of the tensor field. In this study we are developing new methods for analyzing and displaying 3-D tensor fields. This problem is considerably more difficult than the 2-D one, as the richness of the data set is much larger. Here we report on our progress and a novel method to find , analyze and display 3-D degenerate points. First we discuss the theory, then an application involving a 3-D tensor field, the Boussinesq problem with two forces.

Hesselink, Lambertus↗

GravitoMagnetic force in modified Newtonian dynamics

We introduce the Gauge Vector-Tensor (GVT) theory by extending the AQUAL's approach to the GravitoElectroMagnetism (GEM) approximation of gravity. GVT is a generally covariant theory of gravity composed of a pseudo Riemannian metric and two U(1) gauge connections that reproduces MOND in the limit of very weak gravitational fields while remains consistent with the Einstein-Hilbert gravity in the limit of strong and Newtonian gravitational fields. GVT also provides a simple framework to study the GEM approximation to gravity. We illustrate that the gravitomagnetic force at the edge of a galaxy can be in accord with either GVT or ΛCDM but not both. We also study the physics of the GVT theory around the gravitational saddle point of the Sun and Jupiter system. We notice that the conclusive refusal of the GVT theory demands measuring either both of the gravitoelectric and gravitomagnetic fields inside the Sun-Jupiter MOND window, or the gravitoelectric field inside two different solar GVT MOND windows. The GVT theory, however, will be favored by observing an anomaly in the gravitoelectric field inside a single MOND window.

79 ASTRONOMY AND ASTROPHYSICS↗

Transport coefficients for the shear dynamo problem at small Reynolds numbers

We build on the formulation developed in S. Sridhar and N. K. Singh [J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients {alpha}{sub il} and {eta}{sub iml} are derived. We prove that when the velocity field is nonhelical, the transport coefficient {alpha}{sub il} vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X{sub 3} and time {tau}; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Raedler, M. Rheinhardt, and P. J. Kaepylae [Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensor {eta}{sub ij}({tau}). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Vaidya spacetime in the diagonal coordinates

We have analyzed the transformation from initial coordinates (v, r) of the Vaidya metric with light coordinate v to the most physical diagonal coordinates (t, r). An exact solution has been obtained for the corresponding metric tensor in the case of a linear dependence of the mass function of the Vaidya metric on light coordinate v. In the diagonal coordinates, a narrow region (with a width proportional to the mass growth rate of a black hole) has been detected near the visibility horizon of the Vaidya accreting black hole, in which the metric differs qualitatively from the Schwarzschild metric and cannot be represented as a small perturbation. It has been shown that, in this case, a single set of diagonal coordinates (t, r) is insufficient to cover the entire range of initial coordinates (v, r) outside the visibility horizon; at least three sets of diagonal coordinates are required, the domains of which are separated by singular surfaces on which the metric components have singularities (either g{sub 00} = 0 or g{sub 00} = ∞). The energy–momentum tensor diverges on these surfaces; however, the tidal forces turn out to be finite, which follows from an analysis of the deviation equations for geodesics. Therefore, these singular surfaces are exclusively coordinate singularities that can be referred to as false fire-walls because there are no physical singularities on them. We have also considered the transformation from the initial coordinates to other diagonal coordinates (η, y), in which the solution is obtained in explicit form, and there is no energy–momentum tensor divergence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Electrostatic interaction of two charged macroparticles in an equilibrium plasma

This article is a critical review of publications devoted to studying the electrostatic interaction of two charged macroparticles in an equilibrium plasma. It is shown from an analysis of the force of interaction based on the Maxwell stress tensor that two macroparticles with identical charges in the Poisson–Boltzmann model always repel each other both in isothermal and nonisothermal plasmas. At distances between macroparticles for which the Boltzmann exponents can be linearized, the interaction between macroparticles is completely described by the Debye–Hückel model. The correction to free energy due to the electrostatic interaction in the system of two macroparticles is determined by integrating the correction to the internal energy and by direct calculation of the correction for entropy. It is shown that the free energy coincides with the Yukawa potential. The coincidence of the interaction energy obtained by integrating the force of interaction with the free energy leads to the conclusion about the potential nature of the force of interaction between two macroparticles in an equilibrium plasma. The effect of the outer boundary on the electrostatic interaction force is analyzed; it is shown that the type of interaction depends on the choice of the boundary conditions at the outer boundary. It is also shown that the accumulation of space charge near the outer boundary can lead to the attraction of similarly charged particles at distances comparable with the radius of the outer boundary.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Understanding Large-Scale Dynamos in Unstratified Rotating Shear Flows

For this work, we combine simulations with new analyses that overcome previous pitfalls to explicate how nonhelical mean-field dynamos grow and saturate in unstratified, magnetorotationally driven turbulence. Shear of the mean radial magnetic field amplifies the azimuthal component. Radial fields are regenerated by velocity fluctuations that induce shear of radial magnetic fluctuations, followed by Lorentz and Coriolis forces that source a negative off-diagonal component in the turbulent diffusivity tensor. We present a simple schematic to illustrate this dynamo growth. A different part of the Lorentz force forms a third-order correlator in the mean electromotive force that saturates the dynamo.

accretion disk & black-hole plasma↗

MONTE CARLO RADIATION-HYDRODYNAMICS WITH IMPLICIT METHODS

We explore the application of Monte Carlo transport methods to solving coupled radiation-hydrodynamics (RHD) problems. We use a time-dependent, frequency-dependent, three-dimensional radiation transport code that is special relativistic and includes some detailed microphysical interactions such as resonant line scattering. We couple the transport code to two different one-dimensional (non-relativistic) hydrodynamics solvers: a spherical Lagrangian scheme and a Eulerian Godunov solver. The gas–radiation energy coupling is treated implicitly, allowing us to take hydrodynamical time-steps that are much longer than the radiative cooling time. We validate the code and assess its performance using a suite of radiation hydrodynamical test problems, including ones in the radiation energy dominated regime. We also develop techniques that reduce the noise of the Monte Carlo estimated radiation force by using the spatial divergence of the radiation pressure tensor. The results suggest that Monte Carlo techniques hold promise for simulating the multi-dimensional RHD of astrophysical systems.

79 ASTRONOMY AND ASTROPHYSICS↗

Calculation of the detonation state of HN 3 with quantum accuracy

HN 3 is a unique liquid energetic material that exhibits ultrafast detonation chemistry and a transition to metallic states during detonation. We combine the Chebyshev interaction model for efficient simulation (ChIMES) many-body reactive force field and the extended-Lagrangian multiscale shock technique molecular dynamics method to calculate the detonation properties of HN 3 with the accuracy of Kohn–Sham density-functional theory. ChIMES is based on a Chebyshev polynomial expansion and can accurately reproduce density-functional theory molecular dynamics (DFT-MD) simulations for a wide range of unreactive and decomposition conditions of liquid HN 3 . We show that addition of random displacement configurations and the energies of gas-phase equilibrium products in the training set allows ChIMES to efficiently explore the complex potential energy surface. Schemes for selecting force field parameters and the inclusion of stress tensor and energy data in the training set are examined. Structural and dynamical properties and chemistry predictions for the resulting models are benchmarked against DFT-MD. We demonstrate that the inclusion of explicit four-body energy terms is necessary to capture the potential energy surface across a wide range of conditions. Our results generally retain the accuracy of DFT-MD while yielding a high degree of computational efficiency, allowing simulations to approach orders of magnitude larger time and spatial scales. The techniques and recipes for MD model creation we present allow for direct simulation of nanosecond shock compression experiments and calculation of the detonation properties of materials with the accuracy of Kohn–Sham density-functional theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On the Stability of Stochastically Forced Parametric Oscillators

We present a method for determining the moment stability of stochastically forced ordinary differential equations. We provide many details omitted. We consider the case where the forcing arises from passing white noise through an nth order filter. We carry out a perturbation analysis for marginal moment tensors, based on a small parameter ε that gives the amplitude of the forcing. Our perturbation analysis is based on ladder operator approach to the vector Ornstein-Uhlenbeck process developed by the authors.

Blass, Timothy↗