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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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203 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Replica symmetry breaking for the integrable two-site Sachdev–Ye–Kitaev model

We analyze a two-body non-Hermitian two-site Sachdev–Ye–Kitaev (SYK) model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of second-order phase transitions, which is a consequence of the factorization of the partition function into a product over Matsubara frequencies. We calculate the quenched free energy in two different ways: first in terms of the single-particle energies and second by solving the Schwinger–Dyson equations of the two-site model. The first calculation can be done entirely in terms of a one-site model. The conjugate replica enters due to non-analyticities when Matsubara frequencies enter the spectral support of the coupling matrix. The second calculation is based on the replica trick of the two-site partition function. Both methods give the same result. The free-fermion partition function can also be rephrased as a matrix model for the coupling matrix. Up to minor details, this model is the random matrix model that describes the chiral phase transition of QCD, and the order parameter of the two-body model corresponds to the chiral condensate of QCD. Comparing to the corresponding four-body model, we are able to determine which features of the free energy are due to the chaotic nature of the four-body model. The high-temperature phase of both models is entropy dominated, and in both cases, the free energy is determined by the spectral density. The chaotic four-body SYK model has a low-temperature phase whose free energy is almost temperature-independent, signaling an effective gap of the theory even though the actual spectrum does not exhibit a gap. On the other hand, the low-temperature free energy of the two-body SYK model is not flat; in fact, it oscillates to arbitrarily low temperature. This indicates a less desirable feature that the entropy of the two-body model is not always positive in the low-temperature phase, which most likely is a consequence of the non-hermiticity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Next-Cycle Optimal Dilute Combustion Control via Online Learning of Cycle-to-Cycle Variability Using Kernel Density Estimators

Dilute combustion using exhaust gas recirculation (EGR) presents a cost-effective method for increasing the efficiency of spark-ignition (SI) engines. However, the maximum amount of EGR that can be used at a given condition is limited by a rapid increment of cycle-to-cycle variability (CCV). This study describes a methodology to design a model-based stochastic optimal controller to adjust the cycle-to-cycle fuel injection quantity in order to reduce CCV and further extend the dilute limit. Given the complexity and chaotic nature of combustion events, the controller was enhanced with online learning in order to identify the statistical properties of combustion efficiency, which are needed to generate predictions for next-cycle events. This study showed that a kernel density estimator (KDE) can be used to learn the combustion properties in real time and can be incorporated into the feedback policy in order to calculate the optimal control command. Experimental results suggested that the dilute limit can be extended from 18.5% to 21% EGR fraction at an operating condition relevant for highway cruising. Additionally, the proposed controller can achieve a large CCV reduction with less fuel enrichment compared to previous methods, overall contributing to an increase in 0.2% indicated fuel conversion efficiency.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Visualization of Multi-Fidelity Approximations of Stochastic Economic Dispatch

As renewable energy generation deployment increases, the operation of electrical grids becomes more complex. Economic dispatch is part of a grid operator's regular decision process where the amount of energy to generate is determined based on the number of available generators and the actual level of energy demand. Renewable generators are inherently stochastic due to the chaotic nature of weather patterns, and thus, real-time decisions of economic dispatch become increasingly complex. Modeling efforts to assist in these decisions in the highest fidelity typically take hours to days to solve on leadership-class computers; too long for the 5-minute operational time-frame demanded of operators. Alternatively, multi-fidelity approximations can be used to predict generation levels quickly and with sufficient accuracy to be used for real-time operations. We have developed a visualization tool to demonstrate the utility of multi-fidelity approximations by displaying contextual results of economic dispatch approximations, comparisons across fidelity levels of generation levels and possible failures to meet demand, and meta-data on the modeling setup.

interactive visualization↗
DOE OSTI2021

Insights on the continuous representations of piecewise-smooth nonlinear systems: limits of applicability and effectiveness

Dynamical systems subject to intermittent contact are often modeled with piecewise-smooth contact forces. However, the discontinuous nature of the contact can cause inaccuracies in numerical results or failure in numerical solvers. Representing the piecewise contact force with a continuous and smooth function can mitigate these problems, but not all continuous representations may be appropriate for this use. Here, five representations used by previous researchers (polynomial, rational polynomial, hyperbolic tangent, arctangent, and logarithm-arctangent functions) are studied to determine which ones most accurately capture nonlinear behaviors including super- and subharmonic resonances, multiple solutions, and chaos. The test case is a single-DOF forced Duffing oscillator with freeplay nonlinearity, solved using direct time integration. This work intends to expand on past studies by determining the limits of applicability for each representation and what numerical problems may occur.

42 ENGINEERING↗
DOE OSTI2020

Fluctuation dynamo in a weakly collisional plasma

The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle–particle collisions allows departures from local thermodynamic equilibrium. These departures – pressure anisotropies – exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present an extensive numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart, particularly when the magnetic field is dynamically weak. If instead the parallel viscous stress is left unabated – a situation relevant to recent kinetic simulations of the fluctuation dynamo and, we argue, to the early stages of the dynamo in a magnetized ICM – the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics reminiscent of the saturated state of the large-Prandtl-number ( ${Pm}\gtrsim {1}$ ) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches simulated dynamo growth rates and magnetic-energy spectra. A prediction of this model, confirmed by our numerical simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. Finally, in all cases that do exhibit a viable dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗