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Results for “variational method”

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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers

The transport of conserved quantities like spin and charge is fundamental to characterizing the behavior of quantum many-body systems. Numerically simulating such dynamics is generically challenging, which motivates the consideration of quantum computing strategies. However, the relatively high gate errors and limited coherence times of today's quantum computers pose their own challenge, highlighting the need to be frugal with quantum resources. In this work we report simulations on quantum hardware of infinite-temperature energy transport in the mixed-field Ising chain, a paradigmatic many-body system that can exhibit a range of transport behaviors at intermediate times. We consider a chain with L = 12 sites and find results broadly consistent with those from ideal circuit simulators over 90 Trotter steps, containing up to 990 entangling gates. To obtain these results, we use two key problem-tailored insights. First, we identify a convenient basis – the Pauli Y basis – in which to sample the infinite-temperature trace and provide theoretical and numerical justifications for its efficiency relative to, e.g., the computational basis. Second, in addition to a variety of problem-agnostic error mitigation strategies, we employ a renormalization strategy that compensates for global nonconservation of energy due to device noise. We discuss the applicability of the proposed sampling approach beyond the mixed-field Ising chain and formulate a variational method to search for a sampling basis with small sample-to-sample fluctuations for an arbitrary Hamiltonian. This opens the door to applying these techniques in more general models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach

Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting real-time measurements and post-processing them using the machinery of dynamic mode decomposition (DMD). From the perspective of quantum dynamics, we establish that our approach can be formally understood as a stable variational method on the function space of observables available from a quantum many-body system. We also provide strong theoretical and numerical evidence that our method converges rapidly even in the presence of a large degree of perturbative noise, and show that the method bears an isomorphism to robust matrix factorization methods developed independently across various scientific communities. Our numerical benchmarks on spin and molecular systems demonstrate an accelerated convergence and a favorable resource reduction over state-of-the-art algorithms. The DMD-centric strategy can systematically mitigate noise and stands out as a leading hybrid quantum-classical eigensolver.

Shen, Yizhi↗
DOE OSTI2019

Comparing Treatments of Weak Reactions with Nuclei in Simulations of Core-collapse Supernovae

We perform an extensive study of the influence of nuclear weak interactions on core-collapse supernovae, paying particular attention to consistency between nuclear abundances in the equation of state (EOS) and nuclear weak interactions. We compute properties of uniform matter based on the variational method. For inhomogeneous nuclear matter, we take a full ensemble of nuclei into account with various finite-density and thermal effects and directly use the nuclear abundances to compute nuclear weak interaction rates. To quantify the impact of a consistent treatment of nuclear abundances on CCSN dynamics, we carry out spherically symmetric CCSN simulations with full Boltzmann neutrino transport, systematically changing the treatment of weak interactions, EOSs, and progenitor models. We find that the inconsistent treatment of nuclear abundances between the EOS and weak interaction rates weakens the EOS dependence of both the dynamics and neutrino signals. We also test the validity of two artificial prescriptions for weak interactions of light nuclei and find that both prescriptions affect the dynamics. Furthermore, there are differences in neutrino luminosities by ~10% and in average neutrino energies by 0.25–1 MeV from those of the fiducial model. We also find that the neutronization burst neutrino signal depends on the progenitor more strongly than on the EOS, preventing a detection of this signal from constraining the EOS.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1968

Guidance and control analysis and integration

Automation of variational methods for solution of optimum control problems, optical data sources for Mars-encounter earth-based orbit determination, and operational support equipment

Source record↗
NASA NTRS1971

Stress concentration in a cylindrical shell containing a circular hole.

The state of stress in a cylindrical shell containing a circular cutout was determined for axial tension, torsion, and internal pressure loading. The solution was obtained for the shallow shell equations by a variational method. The results were expressed in terms of a nondimensional curvature parameter which was a function of shell radius, shell thickness, and hole radius. The function chosen for the solution was such that when the radius of the cylindrical shell approaches infinity, the flat-plate solution was obtained. The results are compared with solutions obtained by more rigorous analytical methods, and with some experimental results. For small values of the curvature parameter, the agreement is good. For higher values of the curvature parameter, the present solutions indicate a limiting value of stress concentration, which is in contrast to previous results.

Adams, N. J. I.↗
NASA NTRS1972

Variational solutions by the use of stepwise constant functions. I - Linear case.

Demonstration that accurate solutions to the integral equation or to the extremal function can be easily obtained by the variational method in many cases when a stepwise constant function is used for the trial function. The evaluation procedure is simple and straightforward; integrals of the kernel function can be evaluated analytically; the method provides, when the solution involves singularities, the best mean value across the singularity; the results are accurate in both the detailed physical quantities and their averages; the resultant solution can be further integrated analytically over the parameters associated with the problem; and the method can be readily applied to nonlinear integral equations.

Yoshikawa, K. K.↗
NASA NTRS1972

Design and development of polyphenylene oxide foam as a reusable internal insulation for LH2 tanks, phase 2

PPO form was tested for mechanical strength, for the effects of 100 thermal cycles from 450 K (359 F) to 21 K (-423 F) and for gas flow resistance characteristics. PPO foam panels were investigated for density variations, methods for joining panels were studied and panel joint thermal test specimens were fabricated. The range of foam panel thickness under investigation was extended to include 7 mm (0.3 in) and 70 mm (2.8 in) panels which also were tested for thermal performance.

Source record↗
NASA NTRS1973

Nonlinear problems of the theory of heterogeneous slightly curved shells

An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.

Kantor, B. Y.↗