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DOE OSTI2021

Data-driven learning of Mori–Zwanzig operators for isotropic turbulence

Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori–Zwanzig (MZ) formalism provides a mathematically exact procedure for constructing reduced-order representations of high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. Turbulence models based on MZ formalism have been scarce due to the limited knowledge of the MZ operators, which originates from the difficulty in deriving MZ kernels for complex nonlinear dynamical systems. In this work, we apply a recently developed data-driven learning algorithm, which is based on Koopman's description of dynamical systems and Mori's linear projection operator, on a set of fully resolved isotropic turbulence datasets to extract the Mori–Zwanzig operators. With data augmentation using known turbulence symmetries, the extracted Markov term, memory kernel, and orthogonal dynamics are statistically converged and the generalized fluctuation–dissipation relation can be verified. The properties of the memory kernel and orthogonal dynamics, and their dependence on the choices of observables are investigated to address the modeling assumptions that are commonly used in MZ-based models. A series of numerical experiments are then constructed using the extracted kernels to evaluate the memory effects on prediction. The results show that the prediction errors are strongly affected by the choice of observables and can be further reduced by including the past history of the observables in the memory kernel.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Anisotropic time-domain electronic response in cuprates driven by midinfrared pulses

Superconductivity in the cuprates is characterized by an anisotropic electronic gap of d -wave symmetry. The aim of this study is to understand how this anisotropy affects the nonequilibrium electronic response of high-T c superconductors. Here we use a polarization selective time domain experiment to address the dynamics of electronic excitation of different symmetry in optimally doped Bi 2 Sr 2 Y 0.08 Ca 0.92 Cu 2 O 8+δ and measure the nodal and antinodal nonequilibrium response resulting from photoexcitations with ultrashort pulses with photon energy comparable to the superconducting gap. The response to long wavelength photoexcitation with pump polarization along the Cu-Cu axis of the sample is discussed with the support of an effective d-wave BCS model which suggests that such transient response could be ascribed to an increase of pair coherence in the antinodal region.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Minijet quenching in a concurrent jet + hydro evolution and the nonequilibrium quark-gluon plasma

Minijets, created by perturbative hard QCD collisions at moderate energies, can represent a significant portion of the total multiplicity of a heavy-ion collision event. Since their transverse momenta are initially larger than the typical saturation scale describing the bulk of the equilibrating quark-gluon plasma (QGP), they ought to be described through the physics of parton energy loss. Indeed, their typical stopping distances are larger than the usual hydrodynamization time, so they do not in general hydrodynamize at the same pace than the bulk of the collision. Therefore, in general minijets cannot be described solely by a unique preequilibrium stage that bridges the initial, overoccupied glasma state, with the hydrodynamical evolution. In this work we make use of a new concurrent minijet+hydrodynamic framework in which the properties of the hydrodynamically evolving QGP are modified due to the injection of energy and momentum from the minijets. We study the system for different choices of the minimum transverse momentum associated with minijet production. In order to achieve a realistic description of charged particle multiplicity, the amount of entropy associated to the low- x initial state needs to be reduced. Moreover, the fact that the injected momentum from the randomly oriented minijets is not correlated with the spatial gradients of the system reduces overall flow, and the value of the QGP transport coefficients needs to be reduced accordingly in order to describe the measured flow coefficients in experiments. They are, in effect, an important new source of fluctuations, resulting in a spikier, notably modified hydrodynamical evolution when compared to the scenario in which the presence of minijets is ignored. We avow that their abundance makes it necessary to include their physics in holistic descriptions of heavy-ion collisions. We discuss the impact of the minijets on a number of observables, such as p T spectra and p T -differential flow v n for a wide range of centrality classes. In contrast to elliptic, triangular or quadrangular flow, here we find that directed flow, v 1 , has the strongest potential to discriminate between different minijet production rates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Time reversal symmetry breaking and odd viscosity in active fluids: Green–Kubo and NEMD results

Active fluids, which are driven at the microscale by non-conservative forces, are known to exhibit novel transport phenomena due to the breaking of time reversal symmetry. Recently, Epstein and Mandadapu [arXiv:1907.10041 (2019)] obtained Green-Kubo relations for the full set of viscous coefficients governing isotropic chiral active fluids, including the so-called odd viscosity, invoking Onsager's regression hypothesis for the decay of fluctuations in active non-equilibrium steady states. In this Communication, we test these Green-Kubo relations using molecular dynamics simulations of a canonical model system consisting of actively torqued dumbbells. We find the resulting odd and shear viscosity values from the Green-Kubo relations to be in good agreement with values measured independently through non-equilibrium molecular dynamics flow simulations. This provides a test of the Green-Kubo relations and lends support to the application of the Onsager regression hypothesis in relation to viscous behaviors of active matter systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Monitored Fluctuating Hydrodynamics

We introduce a hydrodynamic framework for describing monitored classical stochastic processes. We study the conditional ensembles for these monitored processes—i.e., we compute spacetime correlation functions conditioned on a fixed, typical measurement record. In the presence of global symmetries we show that these conditional ensembles can undergo measurement-induced “sharpening” phase transitions as a function of the monitoring rate; moreover, even weak monitoring can give rise to novel critical phases, derived entirely from a classical perspective. We give a simple hydrodynamic derivation of the known “charge-fuzzy phase” for weakly monitored diffusive many-body quantum systems. We show that although the unmonitored symmetric and asymmetric exclusion processes are in different universality classes of transport, the fluctuations in their conditional ensembles flow to the same fixed point with emergent relativistic invariance under monitoring. On the other hand, weakly monitored systems with non-Abelian symmetries enter a novel strongly coupled fixed point with nontrivial dynamical exponent, which we characterize. Our formalism naturally accounts for monitoring general observables, such as currents or density gradients, and allows for a direct calculation of information-theoretic diagnostics of sharpening transitions, including the Shannon entropy of the measurement record.

classical statistical mechanics↗

DOE OSTI2024

Multidimensional coherent spectroscopy of light-driven states and their collective modes in multiband superconductors

We present a comprehensive theory of light-controlled multiband superconductivity, and apply it to predict distinctive signatures of light-driven superconducting (SC) states in terahertz multidimensional coherent spectroscopy (THz-MDCS) experiments. We first derive gauge-invariant Maxwell-Bloch equations for multiband BCS superconductors with spatial fluctuations. We consider driving electromagnetic fields determined self-consistently by Maxwell's equations. By calculating the THz-MDCS spectra measured experimentally in the clean SC limit, we identify unique signatures of finite-momentum Cooper-pairing states that live longer than the laser pulse. They are controlled by a pair of THz laser pulses with well-defined relative phase (pulse pair). The pseudospin oscillators that describe the properties of these SC states are parametrically driven by both finite-momentum Cooper pairing and by time oscillations of the order-parameter relative phase. We show that such strong parametric driving leads to drastic changes in the THz-MDCS spectral shape from the predictions of third-order nonlinear susceptibility calculations. These spectral changes strongly depend on the interband-to-intraband interaction ratio and on the collective modes of the light-driven state. For negligible interband interaction, the spectra show a transition with increasing field, from traditional pump-probe, four-wave-mixing, and third-harmonic generation peaks determined by the laser frequency to sidebands determined by the excitations of the driven system. These sidebands emerge from difference-frequency Raman processes in the nonequilibrium SC state. For interband couplings weaker than the intraband pairing, we show that the Leggett phase collective mode leads to harmonic sidebands around the traditional pump-probe peaks. Additional Higgs collective mode peaks result from light-induced inversion-symmetry breaking in a thin-film geometry. For strong interband coupling, we find a transition from a nonequilibrium finite Cooper-pair momentum state characterized by hybrid-Higgs amplitude mode peaks in THz-MDCS spectra to a driven state identified experimentally by the emergence of Floquet-type sidebands at bi-Higgs frequencies. Those dominant bi-Higgs-frequency satellites are manifestations of a new order parameter relative phase collective mode that characterizes the nonequilibrium SC state. The predicted interaction- and field-dependent transitions in the spectral profile allow us to propose THz-MDCS experiments for quantum tomography of light-driven superconductivity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles

The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble’s ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2014

Spectroscopic Measurement Techniques for Aerospace Flows

The conditions that characterize aerospace flows are so varied, that a single diagnostic technique is not sufficient for its measurement. Fluid dynamists use knowledge of similarity to help categorize and focus on different flow conditions. For example, the Reynolds number represents the ratio of inertial to viscous forces in a flow. When the velocity scales, length scales, and gas density are large and the magnitude of the molecular viscosity is low, the Reynolds number becomes large. This corresponds to large scale vehicles (e.g Airbus A380), fast moving objects (e.g. artillery projectiles), vehicles in dense fluids (e.g. submarine in water), or flows with low dynamic viscosity (e.g. skydiver in air). In each of these cases, the inertial forces dominate viscous forces, and unsteady turbulent fluctuations in the flow variables are observed. In contrast, flows with small length scales (e.g. dispersion of micro-particles in a solid rocket nozzle), slow moving objects (e.g. micro aerial vehicles), flows with low density gases (e.g. atmospheric re-entry), or fluids with a large magnitude of viscosity (e.g. engine coolant flow), all have low Reynolds numbers. In these cases, viscous forces become very important and often the flows can be steady and laminar. The Mach number, which is the ratio of the velocity to the speed of sound in the medium, also helps to differentiate types of flows. At very low Mach numbers, acoustic waves travel much faster than the object, and the flow can be assumed to be incompressible (e.g. Cessna 172 aircraft). As the object speed approaches the speed of sound, the gas density can become variable (e.g. flow over wing of Learjet 85). When the object speed is higher than the speed of sound (Ma > 1), the presences of shock waves and other gas dynamic features can become important to the vehicle performance (e.g. SR-71 Blackbird). In the hypersonic flow regime (Ma > 5), large changes in temperature begin to affect flow properties, causing real-gas effects to occur (e.g. X-43 Scramjet). At even higher Mach numbers, chemistry and nonequilibrium effects come into play (e.g. Startdust re-entry capsule), further complicating the measurement. These limits can be predicted by calculating the ratio of chemical and thermal relaxation time to the flow time scales. Other non-dimensional numbers can be used to further differentiate types of aerospace flows.

Danehy, Paul M.↗

DOE OSTI2022

Initial transient stage of pin-to-pin nanosecond repetitively pulsed discharges in air

In this work, evolution of parameters of nanosecond repetitively pulsed (NRP) discharges in pin-to-pin configuration in air was studied during the transient stage of initial 20 discharge pulses. Gas and plasma parameters in the discharge gap were measured using coherent microwave scattering, optical emission spectroscopy, and laser Rayleigh scattering for NRP discharges at repetition frequencies of 1, 10, and 100 kHz. Memory effects (when perturbations induced by the previous discharge pulse would not decay fully until the subsequent pulse) were detected for the repetition frequencies of 10 and 100 kHz. For 10 kHz NRP discharge, the discharge parameters experienced significant change after the first pulse and continued to substantially fluctuate between subsequent pulses due to rapid evolution of gas density and temperature during the 100 μs inter-pulse time caused by intense redistribution of the flow field in the gap on that time scale. For 100 kHz NRP discharge, the discharge pulse parameters reached a new steady-state at about five pulses after initiation. Further, this new steady-state was associated with well-reproducible parameters between the discharge pulses and substantial reduction in breakdown voltage, discharge pulse energy, and electron number density in comparison to the first discharge pulse. For repetition frequencies 1–100 kHz considered in this work, the memory effects can be likely attributed to the reduction in gas number density and increase in the gas temperature that cannot fully recover to ambient conditions before subsequent discharge pulses.

42 ENGINEERING↗

DOE OSTI2023

Simulating dielectric spectra: A demonstration of the direct electric field method and a new model for the nonlinear dielectric response

Here we demonstrate a method to compute the dielectric spectra of fluids in molecular dynamics (MD) by directly applying electric fields to the simulation. We obtain spectra from MD simulations with low magnitude electric fields (≈0.01 V/Å) in agreement with spectra from the fluctuation–dissipation method for water and acetonitrile. We examine this method’s trade-off between noise at low field magnitudes and the nonlinearity of the response at higher field magnitudes. We then apply the Booth equation to describe the nonlinear response of both fluids at low frequency (0.1 GHz) and high field magnitude (up to 0.5 V/Å). We develop a model of the frequency-dependent nonlinear response by combining the Booth description of the static nonlinear dielectric response of fluids with the frequency-dependent linear dielectric response of the Debye model. We find good agreement between our model and the MD simulations of the nonlinear dielectric response for both acetonitrile and water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Momentum-resolved analysis of condensate dynamic and Higgs oscillations in quenched superconductors with time-resolved ARPES

Higgs oscillations in nonequilibrium superconductors provide a unique tool to obtain information about the underlying order parameter. Several properties like the absolute value, existence of multiple gaps, and the symmetry of the order parameter can be encoded in the Higgs oscillation spectrum. Studying Higgs oscillations with time-resolved angle-resolved photoemission spectroscopy (ARPES) has the advantage over optical measurements that a momentum-resolved analysis of the condensate dynamic is possible. In this paper, we investigate the time-resolved spectral function measured in ARPES for different quench protocols. We find that analyzing amplitude oscillations of the ARPES intensity in the whole Brillouin zone allows to understand how the condensate dynamic contributes to the emerging of collective Higgs oscillations. Furthermore, by evaluating the phase of these oscillations, the symmetry deformation dynamic of the condensate can be revealed, which gives insight about the ground state symmetry of the system. With such an analysis, time-resolved ARPES experiments might be used in the future as a powerful tool in the field of Higgs spectroscopy.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Ab initio calculations for void swelling bias in α - and δ -plutonium

Void swelling can develop in materials under persistent irradiation when nonequilibrium vacancy and self-interstitial populations migrate under sufficiently asymmetric interaction biases. In conventional metals, the propensity is determined to the first approximation by comparing point-defect relaxation strains. We thus present DFT-based calculations of structures and formation energies and volumes of point defects in the α and the δ phases of plutonium. Here we discuss the pros and cons of various levels of electronic structure theory: spin polarization, spin-orbit coupling, and orbital polarization. Our results show that lattice defects in δ-Pu, in contrast to most fcc metals, have surprisingly small formation volumes. Equally unexpected are the large defect formation volumes found in the low-symmetry α-Pu phase. Both these unusual properties can be satisfactorily explained from defect-induced spin/orbital moment formation and destruction in the Pu phases. Surprisingly, the point defects in α-Pu are found to induce far larger transformation of the local electronic structure than in δ-Pu. When we use the calculated defect properties to estimate the classic void swelling bias in each of the phases, we find it to be unusually small in δ-Pu but likely much larger in α-Pu. Hence, swelling rates and mechanisms can diverge dramatically between the different phases of Pu. Especially in the transient regime before the formation of large defect clusters, the swelling rate of α-Pu can reliably be expected to be much larger than δ-Pu. However, accurate forecasts over longer times will require the conventional void-swelling theory to be modified to handle the complexities presented by the different Pu phases. As a case in point, we show the possible anomalous temperature dependence of vacancy properties in δ-Pu, caused by entropic contributions from defect-induced spin-lattice fluctuations. Such complications may affect defect-defect interactions and thus alter the void swelling bias.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗