Results for “Implicit functions” — Page 16

NASA NTRS1987

Adaptation, plant evolution, and the fossil record

The importance of adaptation in determining patterns of evolution has become an important focus of debate in evolutionary biology. As it pertains to paleobotany, the issue is whether or not adaptive evolution mediated by natural selection is sufficient to explain the stratigraphic distributions of taxa and character states observed in the plant fossil record. One means of addressing this question is the functional evaluation of stratigraphic series of plant organs set in the context of paleoenvironmental change and temporal patterns of floral composition within environments. For certain organ systems, quantitative estimates of biophysical performance can be made on the basis of structures preserved in the fossil record. Performance estimates for plants separated in time or space can be compared directly. Implicit in different hypotheses of the forces that shape the evolutionary record (e.g. adaptation, mass extinction, rapid environmental change, chance) are predictions about stratigraphic and paleoenvironmental trends in the efficacy of functional performance. Existing data suggest that following the evolution of a significant structural innovation, adaptation for improved functional performance can be a major determinant of evolutionary changes in plants; however, there are structural and development limits to functional improvement, and once these are reached, the structure in question may no longer figure strongly in selection until and unless a new innovation evolves. The Silurian-Devonian paleobotanical record is consistent with the hypothesis that the succession of lowland floodplain dominants preserved in the fossil record of this interval was determined principally by the repeated evolution of new taxa that rose to ecological importance because of competitive advantages conferred by improved biophysical performance. This does not seem to be equally true for Carboniferous-Jurassic dominants of swamp and lowland floodplain environments. In these cases, environmental disruption appears to have been a major factor in shaping the fossil record. This does not mean that continuing adaptation was not important during this interval, but it may indicate that adaptive evolution was strongest in environments other than those best represented in the paleobotanical record.

NASA Discipline Exobiology↗

NASA NTRS2010

Trajectory Optimization: OTIS 4

The latest release of the Optimal Trajectories by Implicit Simulation (OTIS4) allows users to simulate and optimize aerospace vehicle trajectories. With OTIS4, one can seamlessly generate optimal trajectories and parametric vehicle designs simultaneously. New features also allow OTIS4 to solve non-aerospace continuous time optimal control problems. The inputs and outputs of OTIS4 have been updated extensively from previous versions. Inputs now make use of objectoriented constructs, including one called a metastring. Metastrings use a greatly improved calculator and common nomenclature to reduce the user s workload. They allow for more flexibility in specifying vehicle physical models, boundary conditions, and path constraints. The OTIS4 calculator supports common mathematical functions, Boolean operations, and conditional statements. This allows users to define their own variables for use as outputs, constraints, or objective functions. The user-defined outputs can directly interface with other programs, such as spreadsheets, plotting packages, and visualization programs. Internally, OTIS4 has more explicit and implicit integration procedures, including high-order collocation methods, the pseudo-spectral method, and several variations of multiple shooting. Users may switch easily between the various methods. Several unique numerical techniques such as automated variable scaling and implicit integration grid refinement, support the integration methods. OTIS4 is also significantly more user friendly than previous versions. The installation process is nearly identical on various platforms, including Microsoft Windows, Apple OS X, and Linux operating systems. Cross-platform scripts also help make the execution of OTIS and post-processing of data easier. OTIS4 is supplied free by NASA and is subject to ITAR (International Traffic in Arms Regulations) restrictions. Users must have a Fortran compiler, and a Python interpreter is highly recommended.

Riehl, John P.↗

DOE OSTI2024

Prediction of Redox Potentials for Ac, Th, and Pa in Aqueous Solution

Density functional theory in conjunction with small core pseudopotentials and the associated basis sets was used to calculate potentials for multiple redox couples, covering a range of oxidation states for Ac (0 to III), Th (0 to IV), and Pa (0 to V) in aqueous solution. Solvation effects were incorporated using a supermolecule-continuum approach, with 30 water molecules representing two solvation shells, and the COSMO and SMD implicit solvation models. The calculated geometries for Ac(III), Th(IV), and Pa(V) were in reasonable agreement with the available experimental data. Using the COSMO model with the B3LYP functional, the calculated redox potentials were within ± 0.2 V from experiment for most redox couples. Several pathways were explored for the Pa(V/IV) redox couple for different forms of Pa(V) and Pa(IV). Most Pa(V/IV) redox couples have very similar potentials, ranging from 0 to -0.4 V up to a pH of 1.4. At pH = 1.4, the potentials shift to values that are more negative than -0.7 V, reflecting the growing unfavorable nature of the redox process at higher pH levels. The calculated values for An(III/II) potentials were consistent with prior estimates and the available experimental data. The predicted redox potentials for An(II/I) were highly negative, as expected. For An(I/0) potentials, Th and Pa exhibited positive values, contrasting with the negative values calculated for Ac. Furthermore, the An +m /An(0) potentials agreed better with the experimental data when using the COSMO solvation model as compared to the SMD model.

Chemical calculations↗

DOE OSTI2013

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach can be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Adaptive Sparse Grid Discretization (ASGarD)

This code solves the Vlasov-Poisson equations in 6-dimensions without approximation. It uses sparse grid discretization to solve the high-dimensional PDEs. The code functions as a discontinuous Galerkin finite element solver. Advantages/benefits include no approximations, supports high-dimensionality, leadership-scale capability, and implicit time advance.

Hahn, Steven [Oak Ridge National Laboratory (ORNL)↗

NASA NTRS1987

Ultra-high-energy cosmic rays in a galactic wind and its termination shock

Results are reported from numerical modeling of the acceleration and transport of ultra-high-energy cosmic rays in a galactic wind and its termination shock. A two-dimensional (azimuthally symmetric) wind and spiral magnetic field, with a spherical termination shock, where the velocity drops suddenly, is assumed. The time-dependent cosmic-ray transport equation, including all major transport effects is solved using an implicit finite-difference scheme. Particles are injected as the shock of low energy, and the subsequent evolution of the distribution function is followed. Iron nuclei are readily accelerated at the shock to energies up to 100 billion GeV, and protons to 10 billion GeV. A major effect aiding the acceleration of these particles is the spiral of the magnetic field carried out by the wind, caused by the rotation of the Galaxy, with the result that the shock is nearly normal over most of its area. Increasing the magnetic field or rotation rate increases the maximum energy attainable. Anisotropies and energy densities of the particles are also discussed. It is concluded that the process is consistent with observations of ultra-high-energy cosmic rays.

Jokipii, J. R.↗

NASA NTRS1989

The effect of an unsteady three-dimensional wake on elastic blade-flapping eigenvalues in hover

This paper describes the formulation of a finite-state inflow model based on an acceleration potential and a helical wake geometry. The states of the model are coefficients of an inflow expansion in terms of a Fourier series (azimuthally) and of special polynomials (radially). The integrals over the wake are done in closed-form to obtain a set of ordinary differential equations for the inflow coefficients. The forcing functions for these equations are generalized forces which are integrals of the blade loading exactly as in structural dynamics. This model implicitly includes (for the hover case) Prandtl-Goldstein tip losses, dynamic inflow, and Theodorsen/Loewy lift deficiency. Thus, it is a fully three-dimensional unsteady wake model. Here, this model is coupled with elastic-blade equations in hover and eigenvalues are found. The results show that the three-dimensional wake has a large effect on the flap damping of all modes.

Peters, David A.↗

DOE OSTI2014

TRIPOLI-4{sup R} version 9 Shielding for the Shielding Community: Overview, Relevant Benchmarking for Shielding and Licensing Policy - Paper 49

This is a review paper of the Shielding only version of TRIPOLI-4. TRIPOLI-4 and TRIPOLI-4 S: TRIPOLI{sup R} represents a family of radiation transport codes using the Monte Carlo method (1,2). It has been continuously developed at CEA since the mid 60's. TRIPOLI-4{sup R}, being the fourth generation, has been developed starting from the mid 90's in C++. It tracks neutrons from 20 MeV down to 10{sup -5} eV, photons, electrons and positrons from 100 MeV to 1 keV, in 3D arbitrary geometries either in TRIPOLI{sup R} proprietary format or ROOT(4) format. It reads its continuous energy nuclear data from any evaluation in ENDF format, including but not limited to JEFF-3.1.1 and ENDF/BVII.0. It has various simulation modes, fixed-source (with or without fission), criticality, or both of them chained. A variety of tallies are available: averaged flux in a volume (track length and collision estimators), surface flux and current, point flux, reaction rates, deposited energy, dpa, pka, gamma spectroscopy, mesh tallies, tallies for criticality (k{sub eff}, beta eff, kinetic parameters). It provides the user with embedded response functions from IRDF and EAF as well. Several variance reduction techniques (3), including automated ones, make it particularly suitable to deep penetration problems (implicit capture, Russian roulette, exponential biasing with automatic estimation of the importance map). It may run in parallel, on single multi-core machines as well as heterogeneous networks of stations or massively parallel machines. It comes with productivity tools designed to speed-up the elaboration and verification of the input deck as well as the output analysis: 2D interactive display of geometry; 2D display of mesh tallies and collision sites; 3D input deck modeler; compatibility with ROOT tools to post-process TRIPOLI{sup R} outputs. Its V and V test base is made of more than 1000 internationally accepted benchmarks from ICSBEP and SINBAD (REPLICA, ASPIS, NESDIP) and covers all its application domains, including several shielding cases which will be detailed in the talk. TRIPOLI-4{sup R} is the reference Monte Carlo code for CEA, EDF, and also for AREVA for a number of applications. A 'Shielding-only' version has been designed to specifically answer the needs of the shielding community. It is distributed through the NEA Databank with a license for R and D, covering the fusion applications, whose terms are detailed in the paper.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2019

Unified Approach to Implicit and Explicit Solvent Simulations of Electrochemical Reaction Energetics

One of the major open challenges in ab initio simulations of the electrochemical interface is the determination of electrochemical barriers under a constant driving force. Existing methods to do so include extrapolation techniques based on fully explicit treatments of the electrolyte, as well as implicit solvent models which allow for a continuous variation in electrolyte charge. Emerging hybrid continuum models have the potential to revolutionize the field, since they account for the electrolyte with little computational cost while retaining some explicit electrolyte, representing a “best of both worlds” method. In this work, we present a unified approach to determine reaction energetics from fully explicit, implicit, and hybrid treatments of the electrolyte based on a new multicapacitor model of the electrochemical interface. A given electrode potential can be achieved by a variety of interfacial structures; a crucial insight from this work is that the effective surface charge gives a good proxy of the local potential, the true driving force of electrochemical processes. In contrast, we show that the traditionally considered work function gives rise to multivalued functions depending on the simulation cell size. Furthermore, we show that the reaction energetics are largely insensitive to the countercharge distribution chosen in hybrid implicit/explicit models, which means that any of the myriad implicit electrolyte models can be equivalently applied. Furthermore, this work thus paves the way for the accurate treatment of ab initio reaction energetics of general surface electrochemical processes using both implicit and explicit electrolytes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Impact of solvation on the GW quasiparticle spectra of molecules

First-principles calculations for electrochemistry require accurate treatment of both electronic structure and solvation. The perturbative GW approximation starting from density functional theory (DFT) calculations accurately models materials systems with varying dimensionality. Continuum solvation models enable efficient treatment of solvation effects in DFT calculations, but their applications with beyond-DFT electronic structure methods such as GW have been limited. Here, we introduce the frequency-dependent liquid polarizability from a nonlocal continuum solvation model in the screened Coulomb interaction of full-frequency GW calculations with a solvated DFT starting point. In this study, we show that the liquid screening contributions substantially reduce the HOMO–LUMO gap of molecules by 3–5 eV, while solvent effects on the DFT starting point negligibly impact the GW gap. The resulting framework facilitates the simultaneous electronic and solvation accuracy needed for first-principles electrochemistry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1983

Wall-function boundary conditions in the solution of the Navier-Stokes equations for complex compressible flows

To make computer codes for two-dimensional compressible flows more robust and economical, wall functions for these flows, under adiabatic conditions, have been developed and tested. These wall functions have been applied to three two-equation models of turbulence. The tests consist of comparisons of calculated and experimental results for transonic and supersonic flow over a flat plate and for two-dimensional and axisymmetrical transonic shock-wave/boundary-layer interaction flows with and without separation. The calculations are performed with an implicit algorithm that solves the Reynolds-averaged Navier-Stokes equations. It is shown that results obtained agree very well with the data for the complex compressible flows tested, provided criteria for use of the wall functions are followed. The expected savings in cost of the computations and improved robustness of the code were achieved.

Viegas, J. R.↗

DOE OSTI2016

A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

In this study, we present the design and implementation of an L 2 -stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations is iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L 2 -stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Sierra/Solid Mechanics 4.48 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Sierra/SolidMechanics 4.46 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Sierra/SolidMechanics 4.56 User's Guide

Siera/SolidMechanics (Sierra / SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra / SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra / SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes . This document describes the functionality and input syntax for Sierra/SM.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Sierra/SolidMechanics 4.58 User's Guide

Sierra / SolidMechanics (Sierra / SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra / SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra / SM has a versatile library of continuum and structural elements, an d a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes . This document describes the functionality and input syntax for Sierra / SM.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Sierra/SolidMechanics 4.50 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

42 ENGINEERING↗

DOE OSTI2019

Sierra/SolidMechanics 4.52 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

97 MATHEMATICS AND COMPUTING↗