Variational problems involving functional differential equations.
Variational or optimal control for delayed systems, involving integrated maximum principle for problems with nonlinear functional differential systems
Banks, H. T.↗
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Path optimization by a variational reaction coordinate method. I. Development of formalism and algorithms
The development of algorithms to optimize reaction pathways between reactants and products is an active area of study. Existing algorithms typically describe the path as a discrete series of images (chain of states) which are moved downhill toward the path, using various reparameterization schemes, constraints, or fictitious forces to maintain a uniform description of the reaction path. The Variational Reaction Coordinate (VRC) method is a novel approach that finds the reaction path by minimizing the variational reaction energy (VRE) of Quapp and Bofill. The VRE is the line integral of the gradient norm along a path between reactants and products and minimization of VRE has been shown to yield the steepest descent reaction path. In the VRC method, we represent the reaction path by a linear expansion in a set of continuous basis functions and find the optimized path by minimizing the VRE with respect to the linear expansion coefficients. Improved convergence is obtained by applying constraints to the spacing of the basis functions and coupling the minimization of the VRE to the minimization of one or more points along the path that correspond to intermediates and transition states. The VRC method is demonstrated by optimizing the reaction path for the Müller-Brown surface and by finding a reaction path passing through 5 transition states and 4 intermediates for a 10 atom Lennard-Jones cluster.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Direct S{sub N} Treatment of the Scattering Source with Phase Functions
In deterministic transport, the angular dependency of the scattering source is described using a so-called phase function. The scattering operator is commonly expressed using a spherical harmonics (P{sub N}) expansion of this phase function. Not only does this require minimal modifications if the problem dimensionality is changed, but it also contains little to no approximation whenever the scattering anisotropy degree is small. An alternative method relying on a discrete ordinates (S{sub N}) approach - essentially computing the angular integral of the phase function with a finite number of weighted directions - is theoretically possible and has shown some advantages. In particular, this method was introduced for neutron elastic scattering and was shown to be more accurate for highly anisotropic group-to-group transfer cross-sections. Benefits were further shown in the case of a collimated beam in highly forward peaked scattering media, particularly reducing the memory usage by storing an angle-to-angle collision matrix rather than a large number of angular moments. In addition, the scattering source was expressed using that same method, the phase function having been previously expanded using Legendre polynomials, in the context of achieving extreme precision while solving the 1D radiative transfer equation. Based on these previous works, we aim at exploring two questions. First, we wish to derive an expression of the phase function in reduced geometries that does not require any more angular quadrature points than for a standard S N calculation. This is particularly relevant because the reduced phase function does not solely depend on the product of the incoming and outgoing directions. Second, we wish to better understand the relationship between the S{sub N} and P{sub N} treatments. We in particular show equivalence if the phase function in the former case is expanded Legendre polynomials. This equivalence is verified numerically and the computational costs of the methods are compared on a test problem involving a Dirac delta phase function.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Shuttle payload interface verification equipment study. Volume 1: Executive summary
A preliminary design analysis of a stand alone payload integration device (IVE) is provided that is capable of verifying payload compatibility in form, fit and function with the shuttle orbiter prior to on-line payload/orbiter operations. The IVE is a high fidelity replica of the orbiter payload accommodations capable of supporting payload functional checkout and mission simulation. A top level payload integration analysis developed detailed functional flow block diagrams of the payload integration process for the broad spectrum of P/L's and identified degree of orbiter data required by the payload user and potential applications of the IVE.
Source record↗
Development of MLPG and LBIE Methods for Nonlinear Problems of Fracture
The truly meshless local Petrov-Galerkin (MLPG) method holds a great promise in solving boundary value problems, using a local symmetric weak form as a natural approach. In the present paper, in the context of MLPG and the meshless interpolation of a moving least squares (MLS) type, a method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The sub-domains for the shape functions in the MLS approximation are defined only from the primary nodes, and the secondary nodes use the same sub-domains. The shape functions based on the MLS approximation, in an integration domain, have a single type of a rational function, which reduces the difficulty of numerical integration to evaluate the weak form. The present method is very useful in an adaptive calculation, because the secondary nodes can be easily added and/or moved without an additional mesh. The essential boundary conditions can be imposed exactly, and non-convex boundaries can be treated without special techniques. Several numerical examples are presented to illustrate the performance of the present method.
Atluri, Satya N.↗
Near equilibrium distributions for beams with space charge in linear and nonlinear periodic focusing systems
Not Available
Sonnad, Kiran G.↗
Integration of first-principles methods and crystallographic database searches for new ferroelectrics: Strategies and explorations
In this concept paper, the development of strategies for the integration of first-principles methods with crystallographic database mining for the discovery and design of novel ferroelectric materials is discussed, drawing on the results and experience derived from exploratory investigations on three different systems: (1) the double perovskite Sr(Sb{sub 1/2}Mn{sub 1/2})O{sub 3} as a candidate semiconducting ferroelectric; (2) polar derivatives of schafarzikite MSb{sub 2}O{sub 4}; and (3) ferroelectric semiconductors with formula M{sub 2}P{sub 2}(S,Se){sub 6}. A variety of avenues for further research and investigation are suggested, including automated structure type classification, low-symmetry improper ferroelectrics, and high-throughput first-principles searches for additional representatives of structural families with desirable functional properties. - Graphical abstract: Integration of first-principles methods with crystallographic database mining, for the discovery and design of novel ferroelectric materials, could potentially lead to new classes of multifunctional materials. Highlights: Black-Right-Pointing-Pointer Integration of first-principles methods and database mining. Black-Right-Pointing-Pointer Minor structural families with desirable functional properties. Black-Right-Pointing-Pointer Survey of polar entries in the Inorganic Crystal Structural Database.
36 MATERIALS SCIENCE↗
Adsorbate-Induced Changes in Magnetic Interactions in Fe 2 (dobdc) with Adsorbed Hydrocarbon Molecules
Metal–organic frameworks, which are a special case of coordination polymers, form a class of materials with numerous applications due to their high porosities and large internal surface areas and in some cases also due to paramagnetic metal ions. A family of such materials of general formula M 2 (dobdc) (where M is a divalent metal ion, and dobdc 4 – is 2,5-dioxido-1,4-benzenedicarboxylate) has attracted considerable attention for gas separation, catalysis, and magnetism. Here, in this work, we explore the magnetic properties of a member of this class, Fe 2 (dobdc), both in the activated form (bare MOF after solvent removal) and when hydrocarbons are bound to the open coordination sites of the metal. We report quantum mechanical electronic structure calculations using both cluster models and a periodic model, and we compare our results to previously reported theoretical studies. We find that hydrocarbon adsorption only mildly affects the isotropic couplings, but that the isotropic magnetic couplings obtained with hybrid exchange–correlation functionals for the cluster models were found to be in good agreement with the experimental values, and the ones obtained using local exchange–correlation functionals with empirical Coulomb and exchange integrals for the periodic models were also found to agree well with experiments. Furthermore, hybrid density functionals for cluster models and local density functionals with empirical Coulomb and exchange integrals for periodic models are both found to give good agreement with the experimental result that the adsorption of ethylene changes the magnetic ordering. We also used second-order n-electron valence state perturbation theory and contracted spin-orbit configuration interaction to study the role of adsorption on the crystal-field splitting of the quintet manifold and on the single-ion anisotropy of the iron center.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Regression models using shapes of functions as predictors
Functional variables are often used as predictors in regression problems. A commonly used parametric approach, called scalar-on-function regression, uses the $\mathbb L^2$ inner product to map functional predictors into scalar responses. This method can perform poorly when predictor functions contain undesired phase variability, causing phases to have disproportionately large influence on the response variable. One past solution has been to perform phase–amplitude separation (as a pre-processing step) and then use only the amplitudes in the regression model. In this paper, we propose a more integrated approach, termed elastic functional regression model (EFRM), where phase-separation is performed inside the regression model, rather than as a pre-processing step. This approach generalizes the notion of phase in functional data, and is based on the norm-preserving time warping of predictors. Due to its invariance properties, this representation provides robustness to predictor phase variability and results in improved predictions of the response variable over traditional models. We demonstrate this framework using a number of datasets involving gait signals, NMR data, and stock market prices.
97 MATHEMATICS AND COMPUTING↗
Development of a transfer function method for dynamic stability measurement
Flutter testing method based on transfer function measurements is developed. The error statistics of several dynamic stability measurement methods are reviewed. It is shown that the transfer function measurement controls the error level by averaging the data and correlating the input and output. The method also gives a direct estimate of the error in the response measurement. An algorithm is developed for obtaining the natural frequency and damping ratio of low damped modes of the system, using integrals of the transfer function in the vicinity of a resonant peak. Guidelines are given for selecting the parameters in the transfer function measurement. Finally, the dynamic stability measurement technique is applied to data from a wind tunnel test of a proprotor and wing model.
Johnson, W.↗
Summary of Consolidated Interim Storage Advantages and Disadvantages from an Integrated Systems Perspective from Prior Reports and Studies
The question of whether centralized storage of civilian spent nuclear fuel (SNF) should be part of the federal waste management system as an intermediate step before permanent disposal has been debated for more than four decades. Centralized storage facilities were included as a potential component of the U.S. spent fuel management system in the Nuclear Waste Policy Act of 1982 (NWPA), but these facilities were not identified as being essential. When the NWPA was passed, it was expected that a permanent repository would be available around the turn of the century to meet the commitments that were made to start accepting waste by that time. For a number of reasons, a permanent repository was not available at that stage. This report summarizes the advantages and disadvantages of including an ISF as part of an integrated waste management system that have been identified in numerous analyses of the impacts of a consolidated interim storage facility (ISF), previously discussed as monitored retrievable storage, the form of ISF authorized in the NWPA) by the U.S. Department of Energy (DOE) and independent groups. Storing SNF before disposal is a functional requirement for an integrated waste management system. As described below, the studies reviewed in this report have identified a range of benefits that could be obtained by adding a consolidated ISF to the waste management system, including (1) earlier acceptance of fuel by the federal government, (2) reduction in the number of unintended long-term storage sites, (3) added system flexibility and opportunity for better integration, and (4) near-term development and demonstration of institutional and technical infrastructures for large-scale management of SNF. At the same time, these studies have identified potential drawbacks to deployment of an ISF, including (1) potential adverse impacts on development of a repository, (2) additional transportation of SNF, and (3) a large upfront economic investment to establish the consolidated storage capability. In general, the studies that have considered the positive and negative impacts of consolidated storage most comprehensively have concluded that in light of these considerations, the benefits of including an ISF as part of an integrated waste management system can outweigh any real or perceived disadvantages.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
The analysis and interpretation of solar X-ray photographs
The paper examines methods of analyzing and interpreting solar X-ray photographs obtained by soft X-ray telescopes such as those used during the Skylab mission, to obtain information on the physical conditions that give rise to coronal X-ray emitting features revealed by inspection or microdensitometry of the X-ray photographs. First, the differential emission measure function is defined. By choosing models for this function and calculating the integral for the irradiance at the film for each filter, one calculates the effective temperature and emission measure. This method gives correct results only when applied to isothermal regions. For heterothermal regions, a modeling approach which predicts the run of temperature and density, and thus the form of the differential measure function, is used.
Underwood, J. H.↗
Adjoint methods for aerodynamic wing design
A model inverse design problem is used to investigate the effect of flow discontinuities on the optimization process. The optimization involves finding the cross-sectional area distribution of a duct that produces velocities that closely match a targeted velocity distribution. Quasi-one-dimensional flow theory is used, and the target is chosen to have a shock wave in its distribution. The objective function which quantifies the difference between the targeted and calculated velocity distributions may become non-smooth due to the interaction between the shock and the discretization of the flowfield. This paper offers two techniques to resolve the resulting problems for the optimization algorithms. The first, shock-fitting, involves careful integration of the objective function through the shock wave. The second, coordinate straining with shock penalty, uses a coordinate transformation to align the calculated shock with the target and then adds a penalty proportional to the square of the distance between the shocks. The techniques are tested using several popular sensitivity and optimization methods, including finite-differences, and direct and adjoint discrete sensitivity methods. Two optimization strategies, Gauss-Newton and sequential quadratic programming (SQP), are used to drive the objective function to a minimum.
Grossman, Bernard↗
Implementation of Adaptive Digital Controllers on Programmable Logic Devices
Much has been made of the capabilities of FPGA's (Field Programmable Gate Arrays) in the hardware implementation of fast digital signal processing (DSP) functions. Such capability also makes and FPGA a suitable platform for the digital implementation of closed loop controllers. There are myriad advantages to utilizing an FPGA for discrete-time control functions which include the capability for reconfiguration when SRAM- based FPGA's are employed, fast parallel implementation of multiple control loops and implementations that can meet space level radiation tolerance in a compact form-factor. Other researchers have presented the notion that a second order digital filter with proportional-integral-derivative (PID) control functionality can be implemented in an FPGA. At Marshall Space Flight Center, the Control Electronics Group has been studying adaptive discrete-time control of motor driven actuator systems using digital signal processor (DSF) devices. Our goal is to create a fully digital, flight ready controller design that utilizes an FPGA for implementation of signal conditioning for control feedback signals, generation of commands to the controlled system, and hardware insertion of adaptive control algorithm approaches. While small form factor, commercial DSP devices are now available with event capture, data conversion, pulse width modulated outputs and communication peripherals, these devices are not currently available in designs and packages which meet space level radiation requirements. Meeting our goals requires alternative compact implementation of such functionality to withstand the harsh environment encountered on spacecraft. Radiation tolerant FPGA's are a feasible option for reaching these goals.
Gwaltney, David A.↗
Dissipation of Energy of an AC Electric Field in a Semi-Infinite Electron Plasma with Mirror Boundary Conditions
Absorption of the electromagnetic energy in a semi-infinite electron plasma is calculated for an arbitrary degree of the electron gas degeneracy. Absorption is determined by solving the boundary-value problem on the oscillations of electron plasma in a half-space with mirror boundary conditions for electrons. The Vlasov−Boltzmann kinetic equation with the Bhatnagar–Gross–Krook collision integral for the electron distribution function and Maxwell’s equation for the electric field are employed. The electron distribution function and the electric field inside plasma are searched for in the form of expansions in the eigenfunctions of the initial set of equations. The expansion coefficients are found for the case of mirror boundary conditions. The contribution of the plasma surface to absorption is analyzed. Cases with different degrees of electron gas degeneracy are considered. It is shown that absorption of the electromagnetic energy near the surface depends substantially on the ratio between the electric field frequency and the volumetric electron collision frequency.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Integrated Operations for Nuclear: Work Reduction Opportunity Demonstration
Integrated Operations for Nuclear: Work Reduction Opportunity Demonstration The DI BCA document also identifies specific, digitally enabled WRO categories for further study. These were selected as most relevant by Reference Plant personnel from a larger list of WRO areas identified across the nuclear industry as captured INL/RPT-21-64134, “Process for Significant Nuclear Work Function Innovation Based on Integrated Operations Concepts.” This ION WRO demonstration report was developed to provide illustrative, specific, and actionable direction for intertwined PTPG changes associated with digital modernization efforts. The coordinated changes in these areas are intended to maximize safe plant operational and economic performance. This includes enabling WROs associated with detailed configuration, implementation, and use of digital systems and how they are supported over their lifecycle. Illustrating this direction through a minimum set of advanced technology examples establishes a model PTPG framework that can be leveraged across the spectrum of nuclear plant digital modernization efforts going forward. This document addresses many related concepts. To promote an integrated understanding of the topics that make up this work, this document contains an extensive set of internal hyperlinks. This set includes hyperlinks to page numbers in the table of contents, section numbers, items in lists, figures, tables, and references to other documents within the report. When hovering the cursor above hyperlinked text in Adobe, the cursor will change from “ ” to “ .” When the “ ” appears, a left mouse click will take the reader to the referenced location in the document. To return to the original location in the document, the reader need only press and hold the “alt” button on the keyboard and then simultaneously press the “<” directional key on the keyboard.
42 ENGINEERING↗
Quantum Monte Carlo estimation of complex-time correlations for the study of the ground-state dynamic structure function
We present a method based on the path integral Monte Carlo formalism for the calculation of ground-state time correlation functions in quantum systems. The key point of the method is the consideration of time as a complex variable whose phase δ acts as an adjustable parameter. By using high-order approximations for the quantum propagator, it is possible to obtain Monte Carlo data all the way from purely imaginary time to δ values near the limit of real time. As a consequence, it is possible to infer accurately the spectral functions using simple inversion algorithms. We test this approach in the calculation of the dynamic structure function S(q, ω) of two one-dimensional model systems, harmonic and quartic oscillators, for which S(q, ω) can be exactly calculated. We notice a clear improvement in the calculation of the dynamic response with respect to the common approach based on the inverse Laplace transform of the imaginary-time correlation function.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Investigating the eco‐evolutionary response of microbiomes to environmental change
Abstract Microorganisms are the primary engines of biogeochemical processes and foundational to the provisioning of ecosystem services to human society. Free‐living microbial communities (microbiomes) and their functioning are now known to be highly sensitive to environmental change. Given microorganisms' capacity for rapid evolution, evolutionary processes could play a role in this response. Currently, however, few models of biogeochemical processes explicitly consider how microbial evolution will affect biogeochemical responses to environmental change. Here, we propose a conceptual framework for explicitly integrating evolution into microbiome–functioning relationships. We consider how microbiomes respond simultaneously to environmental change via four interrelated processes that affect overall microbiome functioning (physiological acclimation, demography, dispersal and evolution). Recent evidence in both the laboratory and the field suggests that ecological and evolutionary dynamics occur simultaneously within microbiomes; however, the implications for biogeochemistry under environmental change will depend on the timescales over which these processes contribute to a microbiome's response. Over the long term, evolution may play an increasingly important role for microbially driven biogeochemical responses to environmental change, particularly to conditions without recent historical precedent.
54 ENVIRONMENTAL SCIENCES↗