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DOE OSTI2025

Enhanced quasiparticle relaxation in a superconductor via the proximity effect

Quasiparticle dynamics have been identified as an important factor in the operational performance of superconductors in quantum computing and sensing applications. In order to study such dynamics, we performed measurements of quasiparticle transport in a superconductor engineered to enhance quasiparticle relaxation. We found that a thin, highly disordered normal metal layer can be used to greatly reduce the relaxation time of quasiparticles in a superconductor, as seen by a large reduction in the quasiparticle charge imbalance in a fully proximitized Cu/Al bilayer wire, without significantly affecting the properties of the superconductor. The enhanced relaxation is likely due to an increased electron–electron scattering rate in the disordered normal metal. Our results provide a positive indication that quasiparticle relaxation can be substantially enhanced via a simple and technologically viable method, and demonstrate that direct measurement of quasiparticle imbalance can be a useful tool for the assessment and engineering of superconductors in various applications at mK temperatures.

Ryan, Kevin M. [Northwestern U.] (ORCID:0000000293↗

DOE OSTI2025

Extended molecular eigenmodes treatment of dipole–dipole NMR relaxation in real fluids

Traditional models of NMR relaxation fail to account for the complex, multi-exponential behavior of the autocorrelation function in realistic systems characterized by soft-interactions and molecules that are chemically and physically complex. Here, in this study, we describe the relative diffusion of the spin dipoles by means of a Fokker–Planck equation that includes an interaction potential of mean force to account for the response of the physical/chemical environment around the dipoles. By numerically solving the Fokker–Planck equation for the diffusion propagator, we estimate dipole–dipole NMR relaxation for like- and unlike-spin systems via its eigenmode solution. We test the model against molecular simulations of diffusing dipoles with harmonic potentials and also validate using experimental longitudinal relaxation data from real systems, including Gd(III)–aqua and Gd(III)–DO3A–butrol complexes, the latter being an important MRI contrast agent. Using this novel approach, we predict both the inner- and outer-shell contributions to the relaxivity rates with excellent accuracy at frequencies relevant to MRI. We also show that, under the appropriate assumptions, our framework naturally recovers the Bloembergen–Purcell–Pound, the Solomon–Bloembergen–Morgan, and the Hwang–Freed models. Our implementation is general and publicly available for application to a broad range of systems.

Pinheiro dos Santos, Thiago J. [Rice Univ., Housto↗

DOE OSTI2026

Query Relaxation for LLM-Generated SPARQL Queries over Building Knowledge Graphs

When Knowledge Graph (KG) queries fail to match a pattern in a KG, they return no results. Identifying the statements causing these failures is tedious, especially for LLM-generated queries, which tend to be longer and more complex than queries written by hand. Query relaxation addresses this by systematically loosening query constraints until results are recovered. To evaluate the effectiveness of query relaxation against LLM generated queries, we propose a two-stage relaxation method combining triple deletion and path relaxation and test it against 1,823 failed queries for building KGs.

Paul, Lazlo↗

NASA NTRS1965

Theory of Intramolecular Relaxation Processes

A master equation is derived to describe internal relaxation processes in molecular systems with a relatively small number of degrees of freedom. It is an inhomogeneous equation, taking into account nondiagonal elements of the coarse‐grained density matrix which prove to be the most relevant ones for the problem under consideration. Various relaxational time scales, inherent in a molecular system, can thus be shown to exist. Relaxation mechanisms and equilibrium states on these time scales can be determined. The general character and different types of solutions of the master equation are investigated. The theory is applied to internal vibrational relaxation and intramolecular rearrangement (isomerization) reactions.

Hofacker, G. Ludwig↗

NASA NTRS1973

Relaxation factors for supercritical flows.

Relaxation procedures for solution of steady supercritical transonic flows are investigated. Von Neumann (Fourier-mode) stability analysis is used to find bounds of relaxation factors. The bounds depend on local Mach number and local mesh aspect ratio. Long wave instability of Murman-Cole implicit method is indicated. Two new relaxation procedures are introduced. Both employ central differencing exclusively. Group velocities of Fourier modes are used to study signal propagation. It was found necessary to avoid or to damp out signals propagating upstream in supersonic zones in order to obtain physically meaningful transonic solutions. It appears that requirements of high rate of convergence, of stability and accuracy, are in conflict, and that a combination of relaxation methods must be used in order not to compromise the requirements.

Kentzer, C. P.↗

NASA NTRS1974

Low-temperature relaxations in amorphous polyolefins

The dynamic mechanical relaxation behavior of two series of amorphous polyolefins, was investigated from 4.2 K to the glass transition. Most of the polymers show a damping maximum or plateau in the 40 to 50 K region. Various mechanisms which have been suggested for cryogenic relaxations in amorphous polymers are considered as they might relate to the polyolefins. Two secondary relaxation processes above 80 K are distinguished. A relaxation at about 160 K (beta) in the second and third member of each series is associated with restricted blackbone motion. This process requires a certain degree of chain flexibility since it is not observed in the first member of each series. A lower temperature process (gamma) is observed in each member of the second series and is attributed to motion of the ethyl side group.

Hiltner, A.↗

NASA NTRS1975

Relaxation methods in fluid mechanics

The present work considers the iterative solution of a coupled set of difference equations and examines methods that carry successive approximates to a state that is invariant with further iteration and independent of the initial guess. Methods are studied with regard to their efficiency and economy of computer resources. The basic principles of classical relaxation are set forth, with attention confined to linear elliptic equations. This discussion involves the evaluation of the spectral radius that is the magnitude of the eigenvalue with largest modulus. The subject of relaxation is then related to the study of ordinary differential equations and hyperbolic partial differential equations. Problems that occur when linearly dependent eigenvectors appear in the relaxation matrix are discussed, leading to multiply connected eigenvalues in the Jordan canonical form. Finally, a brief survey of relaxation methods used in aerodynamics is given.

Lomax, H.↗

NASA NTRS1976

Numerical simulation of supersonic and hypersonic turbulent compression corner flows using relaxation models

Relaxation turbulence eddy viscosity models are incorporated to solve the complete Navier-Stokes equations for supersonic and hypersonic flows over a two-dimensional compression corner. The system of equations is solved by a time-split, second-order accurate numerical scheme. Details of relaxation process are studied, and several relaxation models are tested and compared. Good improvement in the prediction of upstream pressure propagation is obtained for a Mach number of 2.96, and Reynolds number of 10,000,000, with wedge angle of 25 deg. However, the application of the relaxation models to hypersonic flow at Mach number 8.66 and Reynolds number of 22,000,000, with highly cooled wall, shows unfavorable effects on heat transfer and skin friction in the reattachment and recompression regions.

Hung, C. M.↗

NASA NTRS1979

A simultaneous coordinate relaxation algorithm for large, sparse matrix eigenvalue problems

An algorithm is proposed for a scheme of simultaneous coordinate relaxation. A variant of root-shifting coordinate relaxation, this procedure consists of iterating several vectors at the same time, instead of one at a time. Results of application of the algorithm to test matrices are discussed. For many matrix eigenvalue problems for which coordinate relaxation is a viable approach, the present algorithm is more effective than previous implementations of coordinate relaxation. Total central processor operations should be decreased due to significantly improved convergence.

Raffenetti, R. C.↗

NASA NTRS1983

Bolt clampup relaxation in a graphite/epoxy laminate

A simple bolted joint was analyzed to calculate bolt clampup relaxation for a graphite/epoxy (T300/5208) laminate. A viscoelastic finite element analysis of a double-lap joint with a steel bolt was conducted. Clampup forces were calculated for various steady-state temperature-moisture conditions using a 20-year exposure duration. The finite element analysis predicted that clampup forces relax even for the room-temperature-dry condition. The relaxations were 8, 13, 20, and 30 percent for exposure durations of 1 day, 1 month, 1 year, and 20 years, respectively. As expected, higher temperatures and moisture levels each increased the relaxation rate. The combined viscoelastic effects of steady-state temperature and moisture appeared to be additive. From the finite-element analysis, a simple equation was used to calculate clampup forces for the same temperature-moisture conditions as used in the finite-element analysis. The two sets of calculated results agreed well. Previously announced in STAR as N82-19320

Shivakumar, K. N.↗

NASA NTRS1988

Power law rheology of ice and the relaxation style and retention of craters on Ganymede

A numerical finite element model of viscous relaxation of craters in ice is presented which incorporates rheological data for ice at temperatures and pressures appropriated to the near-surface regions of Ganymede. For temperature gradients in reasonable agreement with those obtained from thermal and structural models of Ganymede, relaxation times greater than 10 to the 7th years were obtained for craters with diameters less than 100 km. For all craters with diameters greater than 10 km, the dependence of viscosity on stress was found to significantly shorten the relaxation time. The rheological laws which dominate crater relaxation are discussed for craters of various sizes. The results are compared with imagery from Voyager.

Thomas, Paul J.↗

NASA NTRS1989

Variable thermal properties and thermal relaxation time in hyperbolic heat conduction

Numerical solutions were obtained for a finite slab with an applied surface heat flux at one boundary using both the hyperbolic (MacCormack's method) and parabolic (Crank-Nicolson method) heat conduction equations. The effects on the temperature distributions of varying density, specific heat, and thermal relaxation time were calculated. Each of these properties had an effect on the thermal front velocity (in the hyperbolic solution) as well as the temperatures in the medium. In the hyperbolic solutions, as the density or specific heat decreased with temperature, both the temperatures within the medium and the thermal front velocity increased. The value taken for the thermal relaxation time was found to determine the 'hyperbolicity' of the heat conduction model. The use of a time dependent relaxation time allowed for solutions where the thermal energy propagated as a high temperature wave initially, but approached a diffusion process more rapidly than was possible with a constant large relaxation time.

Glass, David E.↗

NASA NTRS1990

Relaxation processes in a turbulent compressible magnetofluid

The compressible extensions of time asymptotic relaxation states of incompressible two-dimensional magnetohydrodynamic turbulence are studied. A polytropic equation of state is used with viscous and resistive dissipation. The incompressible case is known to allow three distinct time asymptotic types of behavior: magnetic energy dominated relaxation, kinetic energy dominated relaxation, and cross helicity dominated relaxation. At low Mach numbers the incompressible scenario is reproducible from the compressible simulations, and compressibility plays only a secondary role. At moderate, but still subsonic, Mach numbers the distinct incompressible processes are still recognizable, but strong compressibility features dominate the high-wave-number regime of several simulations. In particular, the magnetic and kinetic energy dominated simulations display regions of strong acoustic turbulence near the dissipation scale.

Ghosh, S.↗

NASA NTRS1991

Asynchronous, macrotasked relaxation strategies for the solution of viscous, hypersonic flows

A point-implicit, asynchronous macrotasked relaxation of the steady, thin-layer, Navier-Stokes equations is presented. The method employs multidirectional, single-level storage Gauss-Seidel relaxation sweeps, which effectively communicate perturbations across the entire domain in 2n sweeps, where n is the dimension of the domain. In order to enhance convergence the application of relaxation factors to specific components of the Jacobian is examined using a stability analysis of the advection and diffusion equations. Attention is also given to the complications associated with asynchronous multitasking. Solutions are generated for hypersonic flows over blunt bodies in two and three dimensions with chemical reactions, utilizing single-tasked and multitasked relaxation strategies.

Gnoffo, Peter A.↗

NASA NTRS1992

Point-implicit relaxation strategies for viscous, hypersonic flows

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for 3D, viscous, hypersonic flows in chemical and thermal nonequilibrium is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with a modified Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's symmetric total variation diminishing scheme. Newton relaxation of the fully coupled equation set is employed on a cell-to-cell basis. Under-relaxation of the inviscid and over-relaxation of the viscous contributions to the residual are implemented. Computational work is easily partitioned among many processors in an asynchronous, dynamic mode for convergence acceleration. An overview of the physical models employed herein for thermochemical nonequilibrium is included. Several test cases and comparisons with experimental data are presented involving hypersonic flow over blunt bodies which illustrate the qualitative and quantitative capabilities of this approach.

Gnoffo, P. A.↗

NASA NTRS1989

Upwind-biased, point-implicit relaxation strategies for hypersonic flowfield simulations on supercomputers

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for three-dimensional, viscous, hypersonic flows in chemical and thermal nonequilibrium is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. The relaxation strategy is well suited for computers employing either vector or parallel architectures, and the relation between computer architecture and algorithm is emphasized. It is also well suited to the numerical solution of the governing equations on unstructured grids. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large. block tri-diagonal systems. A single relaxation step depends only on information from nearest neighbors. Predictions for pressure distributions, surface heating, and aerodynamic coefficients compare well with experimental data for Mach 10 flow over a blunt body. Predictions for the hypersonic flow of air in chemical and thermal nonequilibrium (velocity = 8917 m/s, altitude = 78 km.) over the Aeroassist Flight Experiment (AFE) configuration obtained on a multi-domain grid are discussed.

Gnoffo, Peter A.↗

NASA NTRS1990

Mathematical theory of a relaxed design problem in structural optimization

Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.

Kikuchi, Noboru↗

NASA NTRS1993

Relaxation schemes for Chebyshev spectral multigrid methods

Two relaxation schemes for Chebyshev spectral multigrid methods are presented for elliptic equations with Dirichlet boundary conditions. The first scheme is a pointwise-preconditioned Richardson relaxation scheme and the second is a line relaxation scheme. The line relaxation scheme provides an efficient and relatively simple approach for solving two-dimensional spectral equations. Numerical examples and comparisons with other methods are given.

Kang, Yimin↗