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Results for “computable general equilibrium”

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At least 271 records · Page 15

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NASA NTRS1991

A method for the geometrically nonlinear analysis of compressively loaded prismatic composite structures

A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite material.

Stoll, Frederick↗

DOE OSTI2025

Peeling-ballooning modes in spherical tokamaks: Multi-branch instabilities and effects beyond ideal MHD

A number of important physics effects on the stability of relatively high-n (n is the toroidal mode number) peeling-ballooning modes (PBMs) are investigated based on an equilibrium reconstructed from a NSTX discharge, utilizing extended magnetohydrodynamic (MHD) eigenvalue solvers. For a given toroidal mode number n, multiple branches of instabilities are computed, with the total number of unstable branches roughly linearly scaling with n. Most of the unstable branches are located in the plasma core region, but edge-localized branches, i.e., PBMs, are also identified at higher n-numbers. For the single-fluid-wise most unstable PBM with n = 19⁠, stabilizing/destabilizing effects due to various physics beyond ideal MHD are systematically investigated. Plasma toroidal flow is found to be weakly stabilizing. Local flow shear is generally stabilizing as well, with the degree of stabilization depending on the initial growth rate (without flow shear) of the mode. The plasma resistivity can strongly destabilize the PBM within the single-fluid framework. Anisotropic thermal transport, strong parallel sound wave damping, as well as two-fluid effects are all stabilizing to the mode. In particular, diamagnetic stabilization (within the two-fluid model) is found to be very strong for this mode.

Linear stability analysis↗

NASA NTRS1980

Nonlinear transient analysis by energy minimization: A theoretical basis for the ACTION computer code

The formulation basis for establishing the static or dynamic equilibrium configurations of finite element models of structures which may behave in the nonlinear range are provided. With both geometric and time independent material nonlinearities included, the development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. Representations of a rigid link and an impenetrable contact plane are added to the deformation model so that any number of nodes of the finite element model may be connected by a rigid link or may contact the plane. Equilibrium configurations are derived as the stationary conditions of a potential function of the generalized nodal variables of the model. Minimization of the nonlinear potential function is achieved by using the best current variable metric update formula for use in unconstrained minimization. Powell's conjugate gradient algorithm, which offers very low storage requirements at some slight increase in the total number of calculations, is the other alternative algorithm to be used for extremely large scale problems.

Kamat, M. P.↗

DOE OSTI2025

Network analysis of memristive device circuits: dynamics, stability and correlations

Abstract Networks with memristive devices are a potential basis for the next generation of computing devices. They are also an important model system for basic science, from modeling nanoscale conductivity to providing insight into the information-processing of neurons. The resistance in a memristive device depends on the history of the applied bias and thus displays a type of memory. The interplay of this memory with the dynamic properties of the network can give rise to new behavior, offering many fascinating theoretical challenges. But methods to analyze general memristive circuits are not well described in the literature. In this paper we develop a general circuit analysis for networks that combine memristive devices alongside resistors, capacitors and inductors and under various types of control. We derive equations of motion for the memory parameters of these circuits and describe the conditions for which a network should display properties characteristic of a resonator system. For the case of a purely memresistive network, we derive Lyapunov functions, which can be used to study the stability of the network dynamics. Surprisingly, analysis of the Lyapunov functions show that these circuits do not always have a stable equilibrium in the case of nonlinear resistance and window functions. The Lyapunov function allows us to study circuit invariances, wherein different circuits give rise to similar equations of motion, which manifest through a gauge freedom and node permutations. Finally, we identify the relation between the graph Laplacian and the operators governing the dynamics of memristor networks operators, and we use these tools to study the correlations between distant memristive devices through the effective resistance.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Universality of Collective Density Fluctuations in Liquids at and away from Equilibrium – An Integrated Neutron Scattering, Theoretical, and Computational Study (Final Technical Report)

Liquids, ubiquitous on earth, are prototypical disordered condensed matter. As the mediate phase between non-structured gases and ordered solids, liquids p ossess intriguing complexities that are absent on either extreme counter phase, especially when they are driven away from equilibrium. Despite decades of studies, the physics of liquids still keeps surprising us and challenges our understanding of condensed matter, emergent phenomena, and complex systems. Among the many interesting properties, the nature of collective dynamics in liquids remains elusive because of both the presence of strong interactions and the absence of translational invariance. This project studied the universal features of collective density fluctuations (or collective modes), which include both phonon-like excitations and collective relaxations, in the Q-dependent generalized hydrodynamic regime in liquids and liquid-like matter both at and away from equilibrium. We performed systematic studies of the fast collective dynamics (including both phonon-like excitations and collective relaxations) of four classes of liquids characterized by different fragilities and interactions using synergistically integrated coherent neutron scattering experiments (Inelastic Neutron Scattering (INS), Quasi-Elastic Neutron Scattering (QENS), and Neutron Spin Echo (NSE)), a ViscoElastic Hydrodynamics theory we have been developing, andMolecular Dynamics (MD) simulations and our analysis package LiquidLib. The transformative knowledge of the collective dynamics in liquids is important to understand and ultimately control the transport of mass, energy, and charge in liquids, both at and away from thermal equilibrium, which may will likely impact a wide range of disciplines.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Ground State Properties of the Wide Band Gap Semiconductor Beryllium Sulfide (BeS)

We report the results from self-consistent calculations of electronic, transport, and bulk properties of beryllium sulfide (BeS) in the zinc-blende phase, and employed an ab-initio local density approximation (LDA) potential and the linear combination of atomic orbitals (LCAO). We obtained the ground state properties of zb-BeS with the Bagayoko, Zhao, and Williams (BZW) computational method, as enhanced by Ekuma and Franklin (BZW-EF). Our findings include the electronic energy bands, the total (DOS) and partial (pDOS) densities of states, electron and hole effective masses, the equilibrium lattice constant, and the bulk modulus. The calculated band structure clearly shows that zb-BeS has an indirect energy band gap of 5.436 eV, from Γ to a point between Γ and X, for an experimental lattice constant of 4.863 Å. This is in excellent agreement with the experiment, unlike the findings of more than 15 previous density functional theory (DFT) calculations that did not perform the generalized minimization of the energy functional, required by the second DFT theorem, which is inherent to the implementation of our BZW-EF method.

36 MATERIALS SCIENCE↗

DOE OSTI2020

EBS Task Force: Task 9/FEBEX Modeling Final Report: Thermo-Hydrological Modeling with PFLOTRAN

This report outlines Sandia National Laboratories modeling studies applied to Stage 1 and Stage 2 of the Full-scale Engineered Barriers Experiment in Crystalline Host Rock (FEBEX) in situ test for the SKB EBS Task Force Task 9. The FEBEX test was a full-scale test conducted over ~18 years at the Grimsel, Switzerland Underground Research Laboratory (URL) managed by NAGRA. It involved emplacing simulated waste packages, in the form of welded cylindrical heaters, inside a tunnel in crystalline granitic rock and surrounded by a bentonite barrier and cement plug. Sensors emplaced within the bentonite monitored the wetting-up, heating, and drying out of the bentonite barrier, and the large resulting data set provides an excellent opportunity for validation of multiphysics Thermal-Hydrological (TH), Thermal-Hydrologic-Chemical (THC), and Thermal-Hydrological-Mechanical (THM) modeling approaches for underground nuclear waste storage and the performance of engineered bentonite barriers. The present status of the EBS Task Force is finalizing Task 9, which follows years of modeling studies of the FEBEX test, by many notable modeling teams (Gens et al., 2009; Sanchez et al. 2010; 2012; Samper et al., 2018). These modeling studies generally use two-dimensional axisymmetric meshes, ignoring threedimensional effects, gravity and asymmetric wetting and dry out of the bentonite engineered barrier. This study investigates these effects with use of the PFLOTRAN THC code with massively parallel computational methods in modeling FEBEX Stage 1 and Stage 2 results. The PFLOTRAN numerical code is an open source, state-of-the-art, massively parallel subsurface flow and reactive transport code operating in a high-performance computing environment (Hammond et al., 2014). Section 2 describes the applied partial differential equations describing mass, momentum and energy balance used in this study, considerations derived by assuming phase equilibrium between gas and liquid phases, constitutive equations for granite, cement plug, and bentonite domains, and specific approaches for use inthe PFLOTRAN code. Section 3 describes the geometry, meshing, and model set-up. Section 4 describes modeling results, Section 5 compares modeling results to field testing data, and Section 6 gives conclusions. The Appendix provides detailed information required by the EBSTask Force for final reporting.

42 ENGINEERING↗

NASA NTRS1998

Elemental Fractionation During Rapid Accretion of the Moon Triggered by a Giant Impact

Recently, Ida et al. made an N-body simulation of lunar accretion from a protolunar disk formed by a giant impact. One of their important conclusions is that the accretion time of the Moon is as short as one month. Such rapid accretion is a necessary consequence of the high surface density of a lunar mass disk accreting just beyond the Roche limit (about 3Re); the Safronov accretion time (a few days) is even shorter. The energy of accretion always exceeds the gravitational binding energy of newly arriving matter. Hence, without an energy sink, the accreting body is thermally unstable. For the Earth and other planets, radiation acts as the sink. However, in such a short accretion time, the Moon cannot radiate the accretional energy. Even radiating at a silicate cloudtop temperature of roughly 2000 K, it would take more than 100 yr to radiatively cool the Moon. The plausible alternative heat sinks are heat capacity, latent heat of vaporization, and thermal escape of the gas to space (i.e., hydrodynamic blowoff). The latter becomes plausible for the Moon because the scale height at 2000 K (about 300 km) is a significant fraction of the lunar radius. The early stages of lunar (or "lunatesimal") growth release relatively little energy and can occur simply by heating the material, especially if the accreting material is originally cold. However, the material is unlikely to be cold, because the disk itself is hot and cooling time is long, while the lunar accretion time iss very short. Therefore, the moon is likely to accrete condensed material just after it condenses. Accordingly, the newly accreted material will be on the verge of vaporization and will have very little heat capacity to spare. The immediate heat sink is the latent heat of vaporization. Most of the vapor will escape from the moon, because the thermal energy in the gas can be used to drive escape. However, vaporization is generally incomplete. the latent heat of vaporization exceeds the energy of accretion. Viewed globally, the accretional energy is about half the energy required to vaporize the entire Moon. Thus to first approximation, half of the Moon-forming material can be vaporized and lost during accretion. During this process, we would expect preferential loss of relatively volatile elements. Escape will retard the rate of accretion. To test these ideas, we computed detailed models of the thermal state of the Moon during accretion. We pay special attention to the structure of the silicate atmosphere and its loss rate by calculating the chemical species at equilibrium. We used the PHEQ program which includes 12 elements (H,O,C,Mg,Si,Fe,Ca, Al, Na,Ti, and N.) and 272 compounds (including ionic compounds). Because of the large heats of vaporization and ionization, the adiabatic atmosphere is nearly isothermal and massive escape is expected. The pressure of the atmosphere is determined by the balance between vaporization of a accreting material and escape. If the accretion time is one month, a 0.3 bar atmosphere is expected. Elemental fractionation depends strongly on the temperature of the accreting material. The initial temperature of the material can be estimated from the condition of gravitational instability in the protolunar disk. As shown by Ida et al, accretion starts when gravitational instability occurs when more than 99% of the material condenses. At this point, all of Ca, Al, Si, Mg, and Fe, and 95% of Na (probably K also), are in condensed phases. If the moon is formed from the accretion of such material, volatile elements such as Na, and K are retained by the moon only early in accretion. At later times, K and Na are lost and a fraction of the MG, Si and Fe is lost. However, refractory elements such as Ca and Al are retained and so achieve a mild degree (factor 2) of superabundance.

Abe, Y.↗

NASA NTRS2003

A Generalized Multi-Phase Framework for Modeling Cavitation in Cryogenic Fluids

A generalized multi-phase formulation for cavitation in fluids operating at temperatures elevated relative to their critical temperatures is presented. The thermal effects and the accompanying property variations due to phase change are modeled rigorously. Thermal equilibrium is assumed and fluid thermodynamic properties are specified along the saturation line using the NIST-12 databank. Fundamental changes in the physical characteristics of the cavity when thermal effects become pronounced are identified; the cavity becomes more porous, the interface less distinct, and has increased entrainment when temperature variations are present. Quantitative estimates of temperature and pressure depressions in both liquid nitrogen and liquid hydrogen were computed and compared with experimental data of Hord for hydrofoils. Excellent estimates of the leading edge temperature and pressure depression were obtained while the comparisons in the cavity closure region were reasonable. Liquid nitrogen cavities were consistently found to be in thermal equilibrium while liquid hydrogen cavities exhibited small, but distinct, non-equilibrium effects.

Dorney, Dan↗

DOE OSTI2023

Evolution of Two-Phase High Explosive Reactive Flow [Slides]

Reactive hydrodynamics involve rapid conversion of reactants to products along a detonation wave and needs a closure rule: P-T equilibrium. To calculate P-T equilibrium, we use a root finding method, which can be a computational bottleneck. We evolve the guess for the root finder rather than using the previous value to reduce iterations. Evolving products volume fraction Φ p for an initial root finding guess does reduce root finding iterations and seems to give the best results immediately following a detonation wave (reducing root finding iterations from 5 to 2).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Multireference Equation-of-Motion Driven Similarity Renormalization Group: Theoretical Foundations and Applications to Ionized States

We present a formulation and implementation of an equation-of-motion (EOM) extension of the multireference driven similarity renormalization group (MR-DSRG) formalism for ionization potentials (IP-EOM-DSRG). The IP-EOM-DSRG formalism results in a Hermitian generalized eigenvalue problem, delivering accurate ionization potentials for strongly correlated systems. The EOM step scales as O(N 5 ) with the basis set size N, allowing for efficient calculation of spectroscopic properties, such as transition energies and intensities. The IP-EOM-DSRG formalism is combined with three truncation schemes of the parent MR-DSRG theory: an iterative nonperturbative method with up to two-body excitations [MR-LDSRG(2)] and second- and third-order perturbative approximations [DSRG-MRPT2/3]. We benchmark these variants by computing (1) the vertical valence ionization potentials of a series of small molecules at both equilibrium and stretched geometries; (2) the spectroscopic constants of several low-lying electronic states of the OH, CN, N 2 + , and CO + radicals; and (3) the binding curves of low-lying electronic states of the CN radical. A comparison with experimental data and theoretical results shows that all three IP-EOM-DSRG methods accurately reproduce the vertical ionization potentials and spectroscopic constants of these systems. Notably, the DSRG-MRPT3 and MR-LDSRG(2) versions outperform several state-of-the-art multireference methods of comparable or higher cost.

Hamiltonians↗

DOE OSTI2023

A new approach for simulating inhomogeneous chemical kinetics

Abstract In this paper, inhomogeneous chemical kinetics are simulated by describing the concentrations of interacting chemical species by a linear expansion of basis functions in such a manner that the coupled reaction and diffusion processes are propagated through time efficiently by tailor-made numerical methods. The approach is illustrated through modelling $$\alpha$$ α - and $$\gamma$$ γ -radiolysis in thin layers of water and at their solid interfaces from the start of the chemical phase until equilibrium was established. The method’s efficiency is such that hundreds of such systems can be modelled in a few hours using a single core of a typical laptop, allowing the investigation of the effects of the underlying parameter space. Illustrative calculations showing the effects of changing dose-rate and water-layer thickness are presented. Other simulations are presented which show the approach’s capability to solve problems with spherical symmetry (an approximation to an isolated radiolytic spur), where the hollowing out of an initial Gaussian distribution is observed, in line with previous calculations. These illustrative simulations show the generality and the computational efficiency of this approach to solving reaction-diffusion problems. Furthermore, these example simulations illustrate the method’s suitability for simulating solid-fluid interfaces, which have received a lot of experimental attention in contrast to the lack of computational studies.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1973

Linear convective modes and the energy transport in stellar convection zones.

Model stars whose convection zones had been prepared in accordance with the standard mixing-length theory were used as a basis for the computation of unstable convective modes. It was found that no superposition of statistically independent, nonviscous, adiabatic, convective modes can reproduce the radial dependence of the convective flux of the model. This implies that the representation of a stellar convection zone as a superposition of unstable adiabatic linear modes is inconsistent with the mixing-length theory, and that conclusions based upon such a representation should be regarded with caution. It is also shown that if the linear scale of convective motions is greater than (or of the same order as) the pressure scale height, then the fractional deviation of the pressure from equilibrium will generally not be negligible, as assumed in the mixing-length theory, but will be at least of the same order as the fractional deviation of the density from equilibrium.

Hart, M. H.↗

NASA NTRS1993

A comparison of the predictive capabilities of several turbulence models using upwind and central-difference computer codes

Four turbulence models are described and evaluated for transonic flows using the upwind code CFL3D and the central-difference code TLNS3D. In particular, the effects of recent modifications to the half-equation model of Johnson-King are explored in detail, and different versions of the model are compared. This model can obtain good results for both two-dimensional (2D) and three-dimensional (3D) separated flows. The one-equation models of Baldwin-Barth and Spalart-Allmaras perform well for separated airfoil flows, but can predict the shock too far forward at the outboard stations of a separated wing. The equilibrium model of Baldwin-Lomax predicts the shock location too far aft for both 2D and 3D separated flows, as expected. In general, all models perform well for attached or mildly separated flows.

Rumsey, Christopher L.↗

NASA NTRS1993

A Comparison of the Predictive Capabilities of Several Turbulence Models using Upwind and Central-Difference Computer Codes

Rumsey, Christopher L.↗

NASA NTRS2013

radEq Add-On Module for CFD Solver Loci-CHEM

Loci-CHEM to be applied to flow velocities where surface radiation due to heating from compression and friction becomes significant. The module adds a radiation equilibrium boundary condition to the computational fluid dynamics (CFD) code to produce accurate results. The module expanded the upper limit for accurate CFD solutions of Loci-CHEM from Mach 4 to Mach 10 based on Space Shuttle Orbiter Re-Entry trajectories. Loci-CHEM already has a very promising architecture and performance, but absence of radiation equilibrium boundary condition limited the application of Loci-CHEM to below Mach 4. The immediate advantage of the add-on module is that it allows Loci-CHEM to work with supersonic flows up to Mach 10. This transformed Loci-CHEM from a rocket engine- heritage CFD code with general subsonic and low-supersonic applications, to an aeroheating code with hypersonic applications. The follow-on advantage of the module is that it is a building block for additional add-on modules that will solve for the heating generated at Mach numbers higher than 10.

McCloud, Peter↗

DOE OSTI2024

Influence of fourth-order vibrational corrections on semi-experimental (reSE) structures of linear molecules

Semi-experimental structures (reSE) are derived from experimental ground state rotational constants combined with theoretical vibrational corrections. They permit a meaningful comparison with equilibrium structures based on high-level ab initio calculations. Typically, the vibrational corrections are evaluated with second-order vibrational perturbation theory (VPT2). The amount of error introduced by this approximation is generally thought to be small; however, it has not been thoroughly quantified. Herein, we assess the accuracy of theoretical vibrational corrections by extending the treatment to fourth order (VPT4) for a series of small linear molecules. Typical corrections to bond distances are on the order of 10−5 Å. Larger corrections, nearly 0.0002 Å, are obtained to the bond lengths of NCCN and CNCN. A borderline case is CCCO, which will likely require variational computations for a satisfactory answer. Treatment of vibrational effects beyond VPT2 will thus be important when one wishes to know bond distances confidently to four decimal places (10−4 Å). Certain molecules with shallow bending potentials, e.g., HOC+, are not amenable to a VPT2 description and are not improved by VPT4.

Chemistry↗

DOE OSTI2026

Simulating plasma wave propagation on a superconducting quantum chip

Quantum computers may one day enable the efficient simulation of strongly coupled plasmas that lie beyond the reach of classical computation in regimes where quantum effects are important and the scale separation is large. Here, in this article, we take a first step toward efficient simulation of quantum plasmas by demonstrating linear plasma wave propagation on a superconducting quantum chip. Using high-fidelity and highly expressive device-native gates, combined with an error-mitigation technique, we simulate the scattering of laser pulses from inhomogeneous plasmas. Our approach is made feasible by the identification of a suitable local spin model whose excitations mimic plasma waves, and whose circuit implementation requires a lower gate count than other proposed approaches that would require a future fault-tolerant quantum computer. This work opens avenues to study more complicated phenomena that cannot be simulated efficiently on classical computers, such as nonlinear quantum dynamics when strongly coupled plasmas are driven out of equilibrium.

general physics↗