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DOE OSTI2014

SU(2s+1) symmetry and nonlinear dynamics of high spin magnets

The article is devoted to the description of dynamics of magnets with arbitrary spin on the basis of the Hamiltonian formalism. The relationship of quantum states and magnetic degrees of freedom has been considered. Subalgebras of Poisson bracket of magnetic values for spin s=1/2; 1; 3/2 have been established. We have obtained non-linear dynamic equations for the normal and degenerate non-equilibrium states of high-spin magnets with the SO(3), SU(4), SU(2)×SU(2), SU(3), SO(4), SO(5) symmetries of exchange interaction. The connection between models of magnetic exchange energy and the Casimir invariants has been discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

MechElastic: A Python library for analysis of mechanical and elastic properties of bulk and 2D materials

We report the MechElastic Python package evaluates the mechanical and elastic properties of bulk and 2D materials using the elastic coefficient matrix ( C ij ) obtained from any ab-initio density-functional theory (DFT) code. The current version of this package reads the output of VASP, ABINIT, and Quantum Espresso codes (but it can be easily generalized to any other DFT code) and performs the appropriate post-processing of elastic constants as per the requirement of the user. This program can also detect the input structure's crystal symmetry and test the mechanical stability of all crystal classes using the Born-Huang criteria. Various useful material-specific properties such as elastic moduli, longitudinal and transverse elastic wave velocities, Debye temperature, elastic anisotropy, 2D layer modulus, hardness, Pugh's ratio, Cauchy's pressure, Kleinman's parameter, and Lame's coefficients, can be estimated using this program. Another existing feature of this program is to employ the ELATE package (2016) [29] and plot the spatial variation of several elastic properties such as Poisson's ratio, linear compressibility, shear modulus, and Young's modulus in three dimensions. Further, the MechElastic package can plot the equation of state (EOS) curves for energy and pressure for a variety of EOS models such as Murnaghan, Birch, Birch-Murnaghan, and Vinet, by reading the inputted energy/pressure versus volume data obtained via numerical calculations or experiments. This package is particularly useful for the high-throughput analysis of elastic and mechanical properties of materials.

2D materials↗

DOE OSTI2024

Assessing Critical Conditions for Scour Near Obstructions using Bed Shear, Particle Onset of Motion Balances, and CFD-DEM Modeling of Granular Beds

Computational Fluid Dynamics combined with a Discrete Element Method is one of the computational methods that can be used to model multiphase flows. In this method various phases, gas and liquid or solid, are present in the same computational domain. The local averaged Navier–Stokes equations determine the flow of the continuous phase fluid and are solved using the traditional CFD finite volume approach. DEM is based on a Lagrangian formulation, which solves the equations of motion, expressed in ordinary differential equations, for representative particles as they move in space and time. The interactions between the continuous fluid phase and discrete solid phase are modeled with the use of Newton’s laws of motion via drag force. The particles interact with each other and with the boundaries of the fluid continuum, and the resulting contact forces are included in the equations of motion. The properties of solid particles and boundaries are treated as elastic bodies, with specified density, elastic modulus, and Poisson’s ratio. Particle shapes may vary from single spherical particles to more complex-shaped composite particles. The particles may be introduced into the domain by random or structured injection at a point, surface, or volume, depending on the application. More details on the formulation can be found in the Simcenter STAR-CCM+ User’s Manual and OpenFOAM website.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1974

Fast direct numerical solution of the nonhomogeneous Cauchy-Riemann equations

A fast direct (noniterative) 'Cauchy-Riemann Solver' is developed for solving the finite-difference equations representing systems of first-order elliptic partial differential equations in the form of the nonhomogeneous Cauchy-Riemann equations. The method is second-order accurate and requires approximately the same computer time as a fast cyclic-reduction Poisson solver. The accuracy and efficiency of the direct solver are demonstrated in an application to solving an example problem in aerodynamics: subsonic inviscid flow over a biconvex airfoil. The analytical small-perturbation solution contains singularities, which are captured well by the computational technique. The algorithm is expected to be useful in nonlinear subsonic and transonic aerodynamics.

Lomax, H.↗

NASA NTRS1993

The spatial distribution of coronae and related features on Venus

Coronae are large quasi-circular geologica features that are common on Venus. They appear to be the surface tectonic and volcanic expressions of mantle diapirs that have impinged on the underside of the venusian lithosphere. We have investigated the spatial distribution of 335 coronae and related features identified in Magellan radar data. It is more clustered than a Poisson distribution, with a statistical certainty of more than 99%. It is dominated by a single large cluster centered near the equator at about 245 deg longitude. The features are preferentially found at elevation and geoid values close to the planetary mean, with a paucity at both the highest and lowest levels of topgraphy and geoid. Some coronae appear aligned in quasi-linear chains. We attribute the clustering of coronae and related features to preferential formation of these features above regions of broad-scale mantle upwelling, and suggest that a major mantle upwelling underlies the one large cluster. We suggest that coronae are rare at the lowest elevations because these may be regions of mantle downwelling. The shortage of coronae at the highest elevations may result both from obscuration by other intense tectonism there and from suppression there of their formation by an unusually thick crust. Corona chains may be produced by enhanced passive mantle uplift below failed or incipient rifts.

Squyres, Steven W.↗

DOE OSTI2012

Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations

This is the second part of a work dealing with key issues that have not been addressed in the modeling and numerical optimization of nonlinear stochastic delay systems. We consider new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. Part I was concerned with issues concerning the class of admissible controls and their approximations, since the classical definitions are inadequate for our models. This part is concerned with transportation equation representations and their approximations. Such representations of nonlinear stochastic delay models have been crucial in the development of numerical algorithms with much reduced memory and computational requirements. The representations for the new models are not obvious and are developed. They also provide a template for the adaptation of the Markov chain approximation numerical methods.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1977

Sampling errors in the measurement of rain and hail parameters

Attention is given to a general derivation of the fractional standard deviation (FSD) of any integrated property X such that X(D) = cD to the n. This work extends that of Joss and Waldvogel (1969). The equation is applicable to measuring integrated properties of cloud, rain or hail populations (such as water content, precipitation rate, kinetic energy, or radar reflectivity) which are subject to statistical sampling errors due to the Poisson distributed fluctuations of particles sampled in each particle size interval and the weighted sum of the associated variances in proportion to their contribution to the integral parameter to be measured. Universal curves are presented which are applicable to the exponential size distribution permitting FSD estimation of any parameters from n = 0 to n = 6. The equations and curves also permit corrections for finite upper limits in the size spectrum and a realistic fall speed law.

Gertzman, H. S.↗

DOE OSTI2021

On the prescription of boundary conditions for nonlocal Poisson's and peridynamics models

We introduce a technique to automatically convert local boundary conditions into nonlocal volume constraints for nonlocal Poisson’s and peridynamic models. The proposed strategy is based on the approximation of nonlocal Dirichlet or Neumann data with a local solution obtained by using available boundary, local data. The corresponding nonlocal solution converges quadratically to the local solution as the nonlocal horizon vanishes, making the proposed technique asymptotically compatible. The proposed conversion method does not have any geometry or dimensionality constraints and its computational cost is negligible, compared to the numerical solution of the nonlocal equation. The consistency of the method and its quadratic convergence with respect to the horizon is illustrated by several two-dimensional numerical experiments conducted by meshfree discretization for both the Poisson’s problem and the linear peridynamic solid model.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1982

The crack problem for a nonhomogeneous plane

The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.

Delale, F.↗

NASA NTRS1983

The crack problem for a nonhomogeneous plane

Delale, F.↗

DOE OSTI2017

Turbulent Spot Pressure Fluctuation Wave Packet Model

Wave packet analysis provides a connection between linear small disturbance theory and subsequent nonlinear turbulent spot flow behavior. The traditional association between linear stability analysis and nonlinear wave form is developed via the method of stationary phase whereby asymptotic (simplified) mean flow solutions are used to estimate dispersion behavior and stationary phase approximation are used to invert the associated Fourier transform. The resulting process typically requires nonlinear algebraic equations inversions that can be best performed numerically, which partially mitigates the value of the approximation as compared to a more complete, e.g. DNS or linear/nonlinear adjoint methods. To obtain a simpler, closed-form analytical result, the complete packet solution is modeled via approximate amplitude (linear convected kinematic wave initial value problem) and local sinusoidal (wave equation) expressions. Significantly, the initial value for the kinematic wave transport expression follows from a separable variable coefficient approximation to the linearized pressure fluctuation Poisson expression. The resulting amplitude solution, while approximate in nature, nonetheless, appears to mimic many of the global features, e.g. transitional flow intermittency and pressure fluctuation magnitude behavior. A low wave number wave packet models also recover meaningful auto-correlation and low frequency spectral behaviors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1993

The effect of dissipative inhomogeneous medium on the statistics of the wave intensity

One of the main theoretical points in the theory of wave propagation in random medium is the derivation of closed form equations to describe the statistics of the propagating waves. In particular, in one dimensional problems, the closed form representation of the multiple scattering effects is important since it contributes in understanding such problems like wave localization, backscattering enhancement, and intensity fluctuations. In this the propagation of plane waves in a layer of one-dimensional dissipative random medium is considered. The medium is modeled by a complex permittivity whose real part is a constant representing the absorption. The one dimensional problem is mathematically equivalent to the analysis of a transmission line with randomly perturbed distributed parameters and a single mode lossy waveguide and the results can be used to study the propagation of radio waves through atmosphere and the remote sensing of geophysical media. It is assumed the scattering medium consists of an ensemble of one-dimensional point scatterers randomly positioned in a layer of thickness L with diffuse boundaries. A Poisson impulse process with density lambda is used to model the position of scatterers in the medium. By employing the Markov properties of this process an exact closed form equation of Kolmogorov-Feller type was obtained for the probability density of the reflection coefficient. This equation was solved by combining two limiting cases: (1) when the density of scatterers is small; and (2) when the medium is weakly dissipative. A two variable perturbation method for small lambda was used to obtain solutions valid for thick layers. These solutions are then asymptotically evaluated for small dissipation. To show the effect of dissipation, the mean and fluctuations of the reflected power are obtained. The results were compared with a lossy homogeneous medium and with a lossless inhomogeneous medium and the regions where the effect of absorption is not essential were discussed.

Saatchi, Sasan S.↗

DOE OSTI2015

Self-consistent description of electrokinetic phenomena in particle-based simulations

A new computational method is presented for study suspensions of charged particles undergoing fluctuating hydrodynamic and electrostatic interactions. The proposed model is appropriate for polymers, proteins, and porous particles embedded in a continuum electrolyte. A self-consistent Langevin description of the particles is adopted in which hydrodynamic and electrostatic interactions are included through a Green's function formalism. An Ewald-like split is adopted in order to satisfy arbitrary boundary conditions for the Stokeslet and Poisson Green functions, thereby providing a formalism that is applicable to any geometry and that can be extended to deformable objects. The convection-diffusion equation for the continuum ions is solved simultaneously considering Nernst-Planck diffusion. In conclusion, the method can be applied to systems at equilibrium and far from equilibrium. Its applicability is demonstrated in the context of electrokinetic motion, where it is shown that the ionic clouds associated with individual particles can be severely altered by the flow and concentration, leading to intriguing cooperative effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Thermal transport in a noncommutative hydrodynamics

We find the hydrodynamic equations of a system of particles constrained to be in the lowest Landau level. We interpret the hydrodynamic theory as a Hamiltonian system with the Poisson brackets between the hydrodynamic variables determined from the noncommutativity of space. We argue that the most general hydrodynamic theory can be obtained from this Hamiltonian system by allowing the Righi-Leduc coefficient to be an arbitrary function of thermodynamic variables. We compute the Righi-Leduc coefficient at high temperatures and show that it satisfies the requirements of particle-hole symmetry, which we outline.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1973

Direct numerical solution of three-dimensional equations containing elliptic operators.

A direct three-dimensional elliptic solver is presented for application in a wide class of numerical methods for solving partial differential equations in physics and engineering. The derived algorithm and FORTRAN code implement Buzbee, Golub and Nielson's proposed extension of Buneman's Cyclic-Reduction Poisson solver to three dimensions. Both a 'most direct' cyclic reduction and a revised method (to eliminate roundoff error difficulties) are derived. Tests on an IBM 360/67 computer, using various optional combinations of subroutines, showed significant differences in accuracy and computing time, with the optimum subroutine combination depending on mesh size.

Martin, E. D.↗

NASA NTRS1982

Tensile stress-strain behavior of graphite/epoxy laminates

The tensile stress-strain behavior of a variety of graphite/epoxy laminates was examined. Longitudinal and transverse specimens from eleven different layups were monotonically loaded in tension to failure. Ultimate strength, ultimate strain, and strss-strain curves wee obtained from four replicate tests in each case. Polynominal equations were fitted by the method of least squares to the stress-strain data to determine average curves. Values of Young's modulus and Poisson's ratio, derived from polynomial coefficients, were compared with laminate analysis results. While the polynomials appeared to accurately fit the stress-strain data in most cases, the use of polynomial coefficients to calculate elastic moduli appeared to be of questionable value in cases involving sharp changes in the slope of the stress-strain data or extensive scatter.

Garber, D. P.↗

DOE OSTI2014

Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems

Understanding electromagnetic phenomena is the key in many scientific investigation and engineering designs such as solar cell designs, studying biological ion channels for diseases, and creating clean fusion energies, among other things. The objectives of the project are to develop high order numerical methods to simulate evanescent electromagnetic waves occurring in plasmon solar cells and biological ion-channels, where local field enhancement within random media in the former and long range electrostatic interactions in the latter are of major challenges for accurate and efficient numerical computations. We have accomplished these objectives by developing high order numerical methods for solving Maxwell equations such as high order finite element basis for discontinuous Galerkin methods, well-conditioned Nedelec edge element method, divergence free finite element basis for MHD, and fast integral equation methods for layered media. These methods can be used to model the complex local field enhancement in plasmon solar cells. On the other hand, to treat long range electrostatic interaction in ion channels, we have developed image charge based method for a hybrid model in combining atomistic electrostatics and continuum Poisson-Boltzmann electrostatics. Such a hybrid model will speed up the molecular dynamics simulation of transport in biological ion-channels.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Stability and Conservation properties of Hermite-based approximations of the Vlasov-Poisson System

Spectral approximation based on Hermite-Fourier expansion of the Vlasov-Poisson model for a collisionless plasma in the electro-static limit is provided by adding high-order artificial collision operators of Lenard-Bernstein type. These differential operators are suitably designed in order to preserve the physically-meaningful invariants (number of particles, momentum, energy). In view of time-discretization, stability results in appropriate norms are presented. In this study, necessary conditions link the magnitude of the artificial collision term, the number of spectral modes of the discretization, as well as the time-step. The analysis, carried out in full for the Hermite discretization of a simple linear problem in one-dimension, is then partly extended to cover the complete nonlinear Vlasov-Poisson model.

97 MATHEMATICS AND COMPUTING↗