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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

A geometric representation scheme suitable for shape optimization

A geometric representation scheme is outlined which utilizes the natural design variable concept. A base configuration with distinct topological features is created. This configuration is then deformed to define components with similar topology but different geometry. The values of the deforming loads are the geometric entities used in the shape representation. The representation can be used for all geometric design studies; it is demonstrated here for structural optimization. This technique can be used in parametric design studies, where the system response is defined as functions of geometric entities. It can also be used in shape optimization, where the geometric entities of an original design are modified to maximize performance and satisfy constraints. Two example problems are provided. A cantilever beam is elongated to meet new design specifications and then optimized to reduce volume and satisfy stress constraints. A similar optimization problem is presented for an automobile crankshaft section. The finite element method is used to perform the analyses.

Tortorelli, Daniel A.↗
NASA NTRS2011

Symbolically Modeling Concurrent MCAPI Executions

Improper use of Inter-Process Communication (IPC) within concurrent systems often creates data races which can lead to bugs that are challenging to discover. Techniques that use Satisfiability Modulo Theories (SMT) problems to symbolically model possible executions of concurrent software have recently been proposed for use in the formal verification of software. In this work we describe a new technique for modeling executions of concurrent software that use a message passing API called MCAPI. Our technique uses an execution trace to create an SMT problem that symbolically models all possible concurrent executions and follows the same sequence of conditional branch outcomes as the provided execution trace. We check if there exists a satisfying assignment to the SMT problem with respect to specific safety properties. If such an assignment exists, it provides the conditions that lead to the violation of the property. We show how our method models behaviors of MCAPI applications that are ignored in previously published techniques.

Fischer, Topher↗
DOE OSTI2024

Compiling Quantum Circuits for Dynamically Field-Programmable Neutral Atoms Array Processors

Dynamically field-programmable qubit arrays (DPQA) have recently emerged as a promising platform for quantum information processing. In DPQA, atomic qubits are selectively loaded into arrays of optical traps that can be reconfigured during the computation itself. Leveraging qubit transport and parallel, entangling quantum operations, different pairs of qubits, even those initially far away, can be entangled at different stages of the quantum program execution. Such reconfigurability and non-local connectivity present new challenges for compilation, especially in the layout synthesis step which places and routes the qubits and schedules the gates. In this paper, we consider a DPQA architecture that contains multiple arrays and supports 2D array movements, representing cutting-edge experimental platforms. Within this architecture, we discretize the state space and formulate layout synthesis as a satisfiability modulo theories problem, which can be solved by existing solvers optimally in terms of circuit depth. For a set of benchmark circuits generated by random graphs with complex connectivities, our compiler OLSQ-DPQA reduces the number of two-qubit entangling gates on small problem instances by 1.7x compared to optimal compilation results on a fixed planar architecture. To further improve scalability and practicality of the method, we introduce a greedy heuristic inspired by the iterative peeling approach in classical integrated circuit routing. Using a hybrid approach that combined the greedy and optimal methods, we demonstrate that our DPQA-based compiled circuits feature reduced scaling overhead compared to a grid fixed architecture, resulting in 5.1X less two-qubit gates for 90 qubit quantum circuits. These methods enable programmable, complex quantum circuits with neutral atom quantum computers, as well as informing both future compilers and future hardware choices.

Physics↗
NASA NTRS1989

A time accurate finite volume high resolution scheme for three dimensional Navier-Stokes equations

A time accurate, three-dimensional, finite volume, high resolution scheme for solving the compressible full Navier-Stokes equations is presented. The present derivation is based on the upwind split formulas, specifically with the application of Roe's (1981) flux difference splitting. A high-order accurate (up to the third order) upwind interpolation formula for the inviscid terms is derived to account for nonuniform meshes. For the viscous terms, discretizations consistent with the finite volume concept are described. A variant of second-order time accurate method is proposed that utilizes identical procedures in both the predictor and corrector steps. Avoiding the definition of midpoint gives a consistent and easy procedure, in the framework of finite volume discretization, for treating viscous transport terms in the curvilinear coordinates. For the boundary cells, a new treatment is introduced that not only avoids the use of 'ghost cells' and the associated problems, but also satisfies the tangency conditions exactly and allows easy definition of viscous transport terms at the first interface next to the boundary cells. Numerical tests of steady and unsteady high speed flows show that the present scheme gives accurate solutions.

Liou, Meng-Sing↗
NASA NTRS1998

Self-Similar Compressible Free Vortices

Lie group methods are used to find both exact and numerical similarity solutions for compressible perturbations to all incompressible, two-dimensional, axisymmetric vortex reference flow. The reference flow vorticity satisfies an eigenvalue problem for which the solutions are a set of two-dimensional, self-similar, incompressible vortices. These solutions are augmented by deriving a conserved quantity for each eigenvalue, and identifying a Lie group which leaves the reference flow equations invariant. The partial differential equations governing the compressible perturbations to these reference flows are also invariant under the action of the same group. The similarity variables found with this group are used to determine the decay rates of the velocities and thermodynamic variables in the self-similar flows, and to reduce the governing partial differential equations to a set of ordinary differential equations. The ODE's are solved analytically and numerically for a Taylor vortex reference flow, and numerically for an Oseen vortex reference flow. The solutions are used to examine the dependencies of the temperature, density, entropy, dissipation and radial velocity on the Prandtl number. Also, experimental data on compressible free vortex flow are compared to the analytical results, the evolution of vortices from initial states which are not self-similar is discussed, and the energy transfer in a slightly-compressible vortex is considered.

vonEllenrieder, Karl↗
NASA NTRS2011

Development Roadmap for an Adjustable X-Ray Optics Observatory

We are developing adjustable X-ray optics to use on a mission such as SMART-X (see posters 38.02, 38.03 and Presentation 30.03). To satisfy the science problems expected to be posed by the next decadal survey, we anticipate requiring effective area greater than 1 square meter and Chandra-like angular resolution: approximately equal to 0.5 inches. To achieve such precise resolution we are developing adjustable mirror technology for X-ray astronomy application. This uses a thin film of piezoelectric material deposited on the back surface of the mirror to correct for figure distortions, including manufacturing errors and deflections due to gravity and thermal effects. We present here a plan to raise this technology from its current Level 2, to Level 6, by 2018.

Schwartz, Dan↗
NASA NTRS1990

A tool for modeling concurrent real-time computation

Real-time computation is a significant area of research in general, and in AI in particular. The complexity of practical real-time problems demands use of knowledge-based problem solving techniques while satisfying real-time performance constraints. Since the demands of a complex real-time problem cannot be predicted (owing to the dynamic nature of the environment) powerful dynamic resource control techniques are needed to monitor and control the performance. A real-time computation model for a real-time tool, an implementation of the QP-Net simulator on a Symbolics machine, and an implementation on a Butterfly multiprocessor machine are briefly described.

Sharma, D. D.↗
NASA NTRS1983

Accommodation of practical constraints by a linear programming jet select

An experimental spacecraft control system will be incorporated into the Space Shuttle flight software and exercised during a forthcoming mission to evaluate its performance and handling qualities. The control system incorporates a 'phase space' control law to generate rate change requests and a linear programming jet select to compute jet firings. Posed as a linear programming problem, jet selection must represent the rate change request as a linear combination of jet acceleration vectors where the coefficients are the jet firing times, while minimizing the fuel expended in satisfying that request. This problem is solved in real time using a revised Simplex algorithm. In order to implement the jet selection algorithm in the Shuttle flight control computer, it was modified to accommodate certain practical features of the Shuttle such as limited computer throughput, lengthy firing times, and a large number of control jets. To the authors' knowledge, this is the first such application of linear programming. It was made possible by careful consideration of the jet selection problem in terms of the properties of linear programming and the Simplex algorithm. These modifications to the jet select algorithm may by useful for the design of reaction controlled spacecraft.

Bergmann, E.↗
NASA NTRS1984

Structural optimization using optimality criteria methods

Optimality criteria methods take advantage of some concepts as those of statically determinate or indeterminate structures, and certain variational principles of structural dynamics, to develop efficient algorithms for the sizing of structures that are subjected to stiffness-related constraints. Some of the methods and iterative strategies developed over the last decade for calculations of the Lagrange multipliers in stressand displacement-limited problems, as well as for satisfying the appropriate optimality criterion, are discussed. The application of these methods are illustrated by solving problems with stress and displacement constraints.

Khot, N. S.↗
NASA NTRS2004

Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

observers↗
NASA NTRS1974

An Analytical Investigation of Wing-Jet Interaction

The aerodynamic interaction between the wing and an inviscid jet with Mach number nonuniformity is formulated by using a two-vortex-sheet model for the jet. One of the vortex sheets accounts for the induced jet flow and the other the induced outer flow. No additional source distribution is needed for the jet at an angle of attack. The above problem is solved by satisfying the jet and wing tangency and the jet pressure-continuity conditions and using a quasi vortex lattice method for computing the induced flow field. The latter method is derived through theoretical consideration by properly accounting for singularities present in the equations and possesses the same simplicity and generality as the conventional vortex lattice method but has a better rate of numerical convergence. The resulting system of algebraic equations is solved by Purcell's vector method. The numerical formulation is first applied to the wing-slipstream interaction problem. Results for one centered-jet configuration are compared with those predicted by some existing theories.

Lan, E. C.↗
NASA NTRS1989

Constructing space difference schemes which satisfy a cell entropy inequality

A numerical methodology for solving convection problems is presented, using finite difference schemes which satisfy the second law of thermodynamics on a cell-by-cell basis in addition to the usual conservation laws. It is shown that satisfaction of a cell entropy inequality is sufficient, in some cases, to guarantee nonlinear stability. Some details are given for several one-dimensional problems, including the quasi-one-dimensional Euler equations applied to flow in a nozzle.

Merriam, Marshal L.↗
NASA NTRS1973

On the decentralized control of large-scale systems

The decentralized control of stochastic large scale systems was considered. Particular emphasis was given to control strategies which utilize decentralized information and can be computed in a decentralized manner. The deterministic constrained optimization problem is generalized to the stochastic case when each decision variable depends on different information and the constraint is only required to be satisfied on the average. For problems with a particular structure, a hierarchical decomposition is obtained. For the stochastic control of dynamic systems with different information sets, a new kind of optimality is proposed which exploits the coupled nature of the dynamic system. The subsystems are assumed to be uncoupled and then certain constraints are required to be satisfied, either in a off-line or on-line fashion. For off-line coordination, a hierarchical approach of solving the problem is obtained. The lower level problems are all uncoupled. For on-line coordination, distinction is made between open loop feedback optimal coordination and closed loop optimal coordination.

Chong, C.↗
DOE OSTI2025

Extended FFT-based micromechanical formulation to consider general non-periodic boundary conditions

Here, this paper presents a new approach for applying non-periodic boundary conditions in the context of FFT-based methods to solve micromechanical problems in heterogeneous solids. The domain of the original problem is extended to satisfy the periodicity requirements at the boundary of the extended domain. The velocity constraint on the boundary of the original domain is replaced by a corresponding constraint on the velocity gradient in the extended volume, and a two-level augmented Lagrangian method is used to enforce the constraint. The proposed method is implemented as an extension of the large-strain elasto-viscoplastic FFT-based (LS-EVPFFT) model of Zecevic et al. (2022). The proposed method is verified in the cases of fully imposed velocity boundary conditions and mixed velocity/traction-free boundary conditions. The accuracy and convergence of the method are studied next, followed by applications to bending and indentation of polycrystals that illustrate the extended capabilities of the proposed formulation.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Short-depth circuits for efficient expectation-value estimation

The evaluation of expectation values Tr[$\rho \mathcal{O}$] for some pure state $\rho$ and Hermitian operator $\mathcal{O}$ is of central importance in a variety of quantum algorithms. Near-optimal techniques have been developed in the past and require a number of measurements N approaching the Heisenberg limit N = O(1/ ε) as a function of target accuracy ε. The use of quantum phase estimation (QPE) requires, however, long circuit depths C = O(1/ ε) making its implementation difficult on near-term noisy devices. The more direct strategy of operator averaging is usually preferred as it can be performed using N = O(1/ε 2 ) measurements and no additional gates aside from those needed for the state preparation. In this work we use a simple but realistic model to describe the bound state of a neutron and a proton (the deuteron) to show that the latter strategy can require an overly large number of measurements in order to achieve a prefixed relative target accuracy ε r . Further, we propose to overcome this problem using a single step of QPE and classical postprocessing. This approach leads to a circuit depth C = O (ε μ ) (with μ ≥ 0) and to a number of measurements N = O (1/ε 2 + ν ) for 0 < ν ≤ 1 and a much smaller prefactor. We provide detailed descriptions of two implementations of our strategy for ν = 1 and ν ≈ 0.5 and derive appropriate conditions that a particular problem instance has to satisfy in order for our method to provide an advantage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1994

Dynamic Load Balancing for Computational Plasticity on Parallel Computers

The simulation of the computational plasticity on a complex structure remains a formidable computational task, especially when a highly nonlinear, complex material model was used. It appears that the computational requirements for a such problem can only be satisfied by massively parallel architectures. In order to effectively harness the tremendous computational power provided by such architectures, it is imperative to investigate and to study the algorithmic and implementation issues pertaining to dynamic load balancing for computational plasticity on a highly parallel, distributed-memory, multiple-instruction, multiple-data computers. This paper will measure the effectiveness of the algorithms developed in handling the dynamic load balancing.

Pramono, Eddy↗
DOE OSTI2020

Cooperative Routing for an Air–Ground Vehicle Team—Exact Algorithm, Transformation Method, and Heuristics

This paper considers a cooperative vehicle routing problem for an intelligence, surveillance, and reconnaissance mission in the presence of communication constraints between the vehicles. The proposed framework uses a ground vehicle and an unmanned aerial vehicle (UAV) that travel cooperatively and visit a set of targets while satisfying the communication constraints. The problem is formulated as a mixed-integer linear program, and a branch-and-cut algorithm is developed to solve the problem to optimality. Furthermore, a transformation method and a heuristic are also developed for the problem. The effectiveness of all the algorithms is corroborated through extensive computational experiments on several randomly generated instances. Furthermore, this paper is motivated by an intelligence, surveillance, and reconnaissance mission involving a single unmanned aerial vehicle (UAV) and a ground vehicle, where the vehicles must coordinate their activity in the presence of communication constraints. The combination of a small UAV and a ground vehicle is an ideal platform for such missions, since small UAVs can fly at low altitudes and can avoid obstacles or threats that would be problematic for the ground vehicle alone. This paper addresses the coordinated routing problem involving these two vehicles and presents an algorithm to obtain an optimal solution for this problem, fast heuristics to obtain good feasible solutions, and also a transformation method to transform any instance of this cooperative vehicle routing problem to an instance of the one-in-a-set traveling salesman problem.

33 ADVANCED PROPULSION SYSTEMS↗