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Results for “satisfiability problems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Unitarity of quantum tunneling decay for an analytical exact non-Hermitian resonant-state approach

Highlights: • Foundations of quantum mechanics • Quantum decay • Non-Hermitian Hamiltonian • Unitarity • Resonant state By using an analytical exact non-Hermitian formalism for quantum tunneling decay that involves the expansion of the decaying wave function as a linear combination of resonant states and transient functions associated with the complex poles of the outgoing Green’s function to the problem, it is shown that the integrated decaying probability density in the whole space satisfies unitarity at each value of time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Enhanced deep neural networks with transfer learning for distribution LMP considering load and PV uncertainties

As the flexibility of generation and demand increases in distribution systems, the residential loads are emerging as a promising means to participate in demand response and the transactive energy market. Market pricing is an instrumental mechanism for the distribution system operator to exploit the full potential of the flexible resources. The distribution locational marginal price (DLMP) can be used to guide the residential load consumption. This type of market signal helps the distribution system operator to optimize the scheduling of all resources while satisfying related network constraints through a day-ahead market. However, solving the optimization problem for large-scale systems can be computationally expensive. To address the scalability and practicability limitations of the DLMP framework, a learning-based approach is proposed in this paper to complement the day-ahead distribution market framework. Here, the proposed approach combines long short-term memory and transfer learning to develop deep neural network that can capture the spatial–temporal correlation of the input data. The model can determine the optimal DLMP for each node in a distribution system without the system parameters required to formulate the optimization problem. Testing results on IEEE 33-bus and 123-bus systems show that the proposed approach can generate a comparable DLMP against the optimization solutions.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1984

Advances in high speed jet aeroacoustics

This paper provides an assessment from an experimental point of view of the present understanding of high speed jet noise primarily as it pertains to shock containing supersonic jet plumes. The nature of this assessment involves an examination of the complex flow and related acoustic field associated with this problem. A certain emphasis is placed on prediction of the near acoustic field to satisfy a motivation driven by a new set of guiding principles, namely the high performance tactical fighter and second generation space transportation vehicles. The review concludes that after weighing all the experimental evidence, only after consideration of the role of large scale coherent structure is adopted can a consistent unifying theme be achieved to physically interpret and properly predict noise generation by the fundamental mechanisms.

Seiner, J. M.↗
NASA NTRS1989

Sonic-point capturing

A prototype scheme that produces perfectly smooth transonic solutions to nozzle-flow problems is derived and tested. The basic upwind scheme is described as well as satisfying the entropy condition, treatment of the source term, and numerical verification. The analysis yielded a numerical flux function for use near a sonic point, which is based on a full model of a transonic expansion wave, and a matched treatment for the source term.

Van Leer, Bram↗
NASA NTRS1991

Traction free finite elements with the assumed stress hybrid model

An effective approach in the finite element analysis of the stress field at the traction free boundary of a solid continuum was studied. Conventional displacement and assumed stress finite elements were used in the determination of stress concentrations around circular and elliptical holes. Specialized hybrid elements were then developed to improve the satisfaction of prescribed traction boundary conditions. Results of the stress analysis indicated that finite elements which exactly satisfy the free stress boundary conditions are the most accurate and efficient in such problems. A general approach for hybrid finite elements which incorporate traction free boundaries of arbitrary geometry was formulated.

Kafie, Kurosh↗
NASA NTRS1993

Some cautionary remarks about smoothed particle hydrodynamics

Potential difficulties with smoothed particle hydrodynamics are discussed. In particular, empirical tests are used to demonstrate that the errors resulting from the use of variable smoothing can be much larger than commonly believed. Fortunately, however, these errors, which are normally small, do not appear to promote instability on small scales, such as fragmentation in self-gravitating fluids. Still, while SPH remains a useful tool for many problems of astrophysical interest, a rigorous formulation of it, which is adaptive but still satisfies conservation properties, is clearly wanting.

Hernquist, Lars↗
NASA NTRS1947

Voltera's Solution of the Wave Equation as Applied to Three-Dimensional Supersonic Airfoil Problems

A surface integral is developed which yields solutions of the linearized partial differential equation for supersonic flow. These solutions satisfy boundary conditions arising in wing theory. Particular applications of this general method are made, using acceleration potentials, to flat surfaces and to uniformly loaded lifting surfaces. Rectangular and trapezoidal plan forms are considered along with triangular forms adaptable to swept-forward and swept-back wings. The case of the triangular plan form in sideslip is also included. Emphasis is placed on the systematic application of the method to the lifting surfaces considered and on the possibility of further application.

Heslet, Max A↗
NASA NTRS1993

Component modes damping assignment methodology for articulated, multiflexible body structures

To simulate the dynamical motion of articulated, multiflexible body structures, one can use multibody simulation packages such as DISCOS. To this end, one must supply appropriate reduced-order models for all of the flexible components involved. The component modes projection and assembly model reduction (COMPARE) methodology is one way to construct these reduced-order component models, which when reassembled capture important system input-to-output mapping of the full-order model at multiple system configurations of interest. In conjunction, we must also supply component damping matrices which when reassembled generate a system damping matrix that has certain desirable properties. The problem of determining the damping factors of components' modes to achieve a given system damping matrix is addressed here. To this end, we must establish from first principles a matrix-algebraic relation between the system's modal damping matrix and the components' modal damping matrices. An unconstrained/constrained optimization problem can then be formulated to determine the component modes' damping factors that best satisfy that matrix-algebraic relation. The effectiveness of the developed methodology, called ModeDamp, has been successfully demonstrated on a high-order, finite element model of the Galileo spacecraft.

Lee, Allan Y.↗
NASA NTRS2004

Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes

High order methods are frequently used in computational simulation for their high accuracy. An efficient way to avoid unnecessary computation in smooth regions of the solution is to use adaptive meshes which employ fine grids only in areas where they are needed. Nonconforming spectral elements allow the grid to be flexibly adjusted to satisfy the computational accuracy requirements. The method is suitable for computational simulations of unsteady problems with very disparate length scales or unsteady moving features, such as heat transfer, fluid dynamics or flame combustion. In this work, we select the Mark Element Method (MEM) to handle the non-conforming interfaces between elements. A new technique is introduced to efficiently implement MEM in 3-D nonconforming meshes. By introducing an "intermediate mortar", the proposed method decomposes the projection between 3-D elements and mortars into two steps. In each step, projection matrices derived in 2-D are used. The two-step method avoids explicitly forming/deriving large projection matrices for 3-D meshes, and also helps to simplify the implementation. This new technique can be used for both h- and p-type adaptation. This method is applied to an unsteady 3-D moving heat source problem. With our new MEM implementation, mesh adaptation is able to efficiently refine the grid near the heat source and coarsen the grid once the heat source passes. The savings in computational work resulting from the dynamic mesh adaptation is demonstrated by the reduction of the the number of elements used and CPU time spent. MEM and mesh adaptation, respectively, bring irregularity and dynamics to the computer memory access pattern. Hence, they provide a good way to gauge the performance of computer systems when running scientific applications whose memory access patterns are irregular and unpredictable. We select a 3-D moving heat source problem as the Unstructured Adaptive (UA) grid benchmark, a new component of the NAS Parallel Benchmarks (NPB). In this paper, we present some interesting performance results of ow OpenMP parallel implementation on different architectures such as the SGI Origin2000, SGI Altix, and Cray MTA-2.

Feng, Huiyu↗
DOE OSTI2021

Quantum Extremal Surfaces and the Holographic Entropy Cone

Quantum states with geometric duals are known to satisfy a stricter set of entropy inequalities than those obeyed by general quantum systems. The set of allowed entropies derived using the Ryu-Takayanagi (RT) formula defines the Holographic Entropy Cone (HEC). These inequalities are no longer satisfied once general quantum corrections are included by employing the Quantum Extremal Surface (QES) prescription. Nevertheless, the structure of the QES formula allows for a controlled study of how quantum contributions from bulk entropies interplay with HEC inequalities. In this paper, we initiate an exploration of this problem by relating bulk entropy constraints to boundary entropy inequalities. In particular, we show that requiring the bulk entropies to satisfy the HEC implies that the boundary entropies also satisfy the HEC. Further, we also show that requiring the bulk entropies to obey monogamy of mutual information (MMI) implies the boundary entropies also obey MMI.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1984

Optimization applications in aircraft engine design and test

Starting with the NASA-sponsored STAEBL program, optimization methods based primarily upon the versatile program COPES/CONMIN were introduced over the past few years to a broad spectrum of engineering problems in structural optimization, engine design, engine test, and more recently, manufacturing processes. By automating design and testing processes, many repetitive and costly trade-off studies have been replaced by optimization procedures. Rather than taking engineers and designers out of the loop, optimization has, in fact, put them more in control by providing sophisticated search techniques. The ultimate decision whether to accept or reject an optimal feasible design still rests with the analyst. Feedback obtained from this decision process has been invaluable since it can be incorporated into the optimization procedure to make it more intelligent. On several occasions, optimization procedures have produced novel designs, such as the nonsymmetric placement of rotor case stiffener rings, not anticipated by engineering designers. In another case, a particularly difficult resonance contraint could not be satisfied using hand iterations for a compressor blade, when the STAEBL program was applied to the problem, a feasible solution was obtained in just two iterations.

Pratt, T. K.↗
DOE OSTI2025

An Adaptive Newton-Based Free-Boundary Grad–Shafranov Solver

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for the poloidal magnetic flux, commonly known as the Grad–Shafranov equation. It is challenging to develop a scalable and accurate free-boundary Grad–Shafranov solver, since it is a fully nonlinear optimization problem that simultaneously solves for the magnetic field coil current outside the plasma to control the plasma shape. In this work, we develop a Newton-based free-boundary Grad–Shafranov solver using adaptive finite elements and preconditioning strategies. The free-boundary interaction leads to the evaluation of a domain-dependent nonlinear form of which its contribution to the Jacobian matrix is achieved through shape calculus. The optimization problem aims to minimize the distance between the plasma boundary and specified control points while satisfying two nontrivial constraints, which correspond to the nonlinear finite element discretization of the Grad–Shafranov equation and a constraint on the total plasma current involving a nonlocal coupling term. The linear system is solved by a block factorization, and AMG is called for subblock elliptic operators. The unique contributions of this work include the treatment of a global constraint, preconditioning strategies, nonlocal reformulation, and the implementation of adaptive finite elements. Furthermore, it is found that the resulting Newton solver is robust, successfully reducing the nonlinear residual to 1e-6 and lower in a small handful of iterations while addressing the challenging case to find a Taylor state equilibrium where conventional Picard-based solvers fail to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRSDate not supplied

Testing and Application of Commercial Thermodynamics Software for Solid-Gas Equilibria in Planetary Science Applications

The ability to calculate chemical equilibria from thermochemical constants (e.g., H, S, Cp) or other experimental data is a tool widely employed by scientists. However, phase equilibria for planetary science problems is limited by easy access to libraries of thermochemical data, as well as the software to invert that data. Many academic software packages are focused on specific types of problems (e.g., aqueous solutions or melting and crystallization of magmas). This focus makes them excellent tools for specific uses, but poorer tools for other scenarios, especially those involving elements or chemical species that are less well-studied in that specific scientific field (e.g. NaCl vapor). Amongst the more general thermodynamic software tools, there are closed academic software packages, open-source options, as well as commercial software. We have explored the extent to which commercial chemistry/chemical engineering software may be able to satisfy the need for thermochemical modeling packages that can accommodate the diverse species and conditions of planetary science problems. Here we compare the output of software package HSC Chemistry™ (Metso Outotec) to published vapor-solid phase diagrams for a variety of major and minor elements. HSC Chemistry™ has been used in several recent geochemical studies of terrestrial volcanic systems [2- 4]. However, it has not to our knowledge been benchmarked against peer-reviewed model results for the conditions and compositions relevant to planetary science. We present one such comparison here, the low- pressure environment of the solar nebula, using literature data. In short, we find excellent agreement between HSC Chemistry™ and the well-regarded academic software package CONDOR. These preliminary results suggest that at least some commercial software packages are capable of robust thermochemical calculations for planetary science.

planetary science↗
NASA NTRS2004

Employing Sensitivity Derivatives for Robust Optimization under Uncertainty in CFD

A robust optimization is demonstrated on a two-dimensional inviscid airfoil problem in subsonic flow. Given uncertainties in statistically independent, random, normally distributed flow parameters (input variables), an approximate first-order statistical moment method is employed to represent the Computational Fluid Dynamics (CFD) code outputs as expected values with variances. These output quantities are used to form the objective function and constraints. The constraints are cast in probabilistic terms; that is, the probability that a constraint is satisfied is greater than or equal to some desired target probability. Gradient-based robust optimization of this stochastic problem is accomplished through use of both first and second-order sensitivity derivatives. For each robust optimization, the effect of increasing both input standard deviations and target probability of constraint satisfaction are demonstrated. This method provides a means for incorporating uncertainty when considering small deviations from input mean values.

Newman, Perry A.↗
NASA NTRS1985

Analysis of a finite composite plate with smooth rigid pin

An elastic continuum method of analysis developed for a smooth rigid pin in a finite composite plate by using complex potentials that satisfy the governing orthotropic differential equation is presented. The plate is subjected to uniaxial loading and the nonlinear problems of partial contact in the pin-plate are studied. Three types of pin fits are examined: interference, push, and clearance. The problems of stresses due to pure interference, load contact behavior, and stresses variations are addressed. The effects of the rectangular geometry and the orthotropic property of the plate are demonstrated through numerical results. It is found that the use of large hole diameter/plate width ratios have deleterious effects and the use of interference has beneficial effects. The solutions obtained will help in the development of special finite elements for fastener joints. Finally, the boundary conditions on the finite outer boundaries are found to be satisfied by a successive integration technique.

Naidu, A. C. B.↗
NASA NTRS1990

Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming

The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Shi, Yun. Y.↗
DOE OSTI2023

Diagonally implicit Runge–Kutta schemes: Discrete energy-balance laws and compactness properties

Abstract We study diagonally implicit Runge–Kutta (DIRK) schemes when applied to abstract evolution problems that fit into the Gelfand-triple framework. We introduce novel stability notions that are well-suited to this setting and provide simple, necessary and sufficient, conditions to verify that a DIRK scheme is stable in our sense and in Bochner-type norms. We use several popular DIRK schemes in order to illustrate cases that satisfy the required structural stability properties and cases that do not. In addition, under some mild structural conditions on the problem we can guarantee compactness of families of discrete solutions with respect to time discretization.

Mathematics↗