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At least 199 records · Page 11

Estimating ionization states and continuum lowering from ab initio path integral Monte Carlo simulations for warm dense hydrogen

Warm dense matter (WDM) is an active field of research, with applications ranging from astrophysics to inertial confinement fusion. Ionization degree and continuum lowering are important quantities to understand how materials behave under these conditions, but can be difficult to diagnose since experimental campaigns are limited and often require model-dependent analysis. This is especially true for hydrogen, which has a comparably low scattering cross section, making high-quality data particularly difficult to obtain. Consequently, building equation of state tables often relies on simulations in combination with untested approximations to extract properties from experiments. Here, we investigate an approach for extracting the ionization potential depression and ionization degree—quantities which are otherwise not directly accessible from the physical model—from first-principles path integral Monte Carlo (PIMC) simulations utilizing a chemical model. In contrast to experimental measurements, where noise and nonequilibrium effects add to the uncertainty of the inferred parameters, PIMC simulations provide a clean signal with well-defined thermodynamic conditions. Comparisons against commonly used models show a qualitative agreement, but we find deviations primarily for the high-density and high-temperature cases. We also demonstrate the decreasing sensitivity of the dynamic structure factor with respect to both ionization and continuum lowering for increasing scattering angles in x-ray Thomson scattering experiments. Our work has important implications for the design of future experiments, but also offers qualitative understanding of structure factors and the imaginary-time correlation function obtained from first-principles quantum Monte Carlo simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

High-temperature phonon-mediated superconductivity in monolayer Mg 2 B 4 C 2

A two-dimensional material – Mg 2 B 4 C 2 , belonging to the family of the conventional superconductor MgB 2 , is theoretically predicted to exhibit superconductivity with critical temperature T c estimated in the 47–48 K range (predicted using the McMillian-Allen-Dynes formula) without any tuning of external parameters such as doping, strain, or substrate-induced effects. The origin of such a high intrinsic T c is ascribed to the presence of strong electron-phonon coupling and large density of states at the Fermi level. This system is obtained after replacing the chemically active boron-boron surface layers in a MgB 2 slab by chemically inactive boron-carbon layers. Hence, the surfaces of this material are inert. Our calculations confirm the stability of 2D Mg 2 B 4 C 2 . We also find that the key features of this material remain essentially unchanged when its thickness is increased by modestly increasing the number of inner MgB 2 layers.

36 MATERIALS SCIENCE↗

Transport coefficients of the quark-gluon plasma at the critical point and across the first-order line

A bottom-up Einstein-Maxwell-dilaton holographic model is used to compute, for the first time, the behavior of several transport coefficients of the hot and baryon-rich strongly coupled quark-gluon plasma at the critical point and also across the first-order phase transition line in the phase diagram. The observables under study are the shear and bulk viscosities, the baryon and thermal conductivities, the baryon diffusion, the jet quenching parameter $\hat{q}$, as well as the heavy-quark drag force and the Langevin diffusion coefficients. These calculations provide a phenomenologically promising estimate for these coefficients, given that our model quantitatively reproduces lattice QCD thermodynamics results, both at zero and finite baryon density, besides naturally incorporating the nearly perfect fluidity of the quark-gluon plasma. Here we find that the diffusion of baryon charge, and also the shear and bulk viscosities, are suppressed with increasing baryon density, indicating that the medium becomes even closer to perfect fluidity at large densities. On the other hand, the jet quenching parameter and the heavy-quark momentum diffusion are enhanced with increasing density. The observables display a discontinuity gap when crossing the first-order phase transition line, while developing an infinite slope at the critical point. The transition temperatures associated with different transport coefficients differ in the crossover region but are found to converge at the critical point.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A Quantum-mechanical Treatment of Electron Broadening in Strong Magnetic Fields

Abstract Spectral line-shape fitting is an extremely useful tool in determining the gravity of white dwarf stars. This method is so far limited to nonmagnetic white dwarfs largely because the theory of line broadening in high magnetic fields is not as complete as in the nonmagnetic case. Current Stark+Zeeman models treat plasma particles classically and ignore the motion of the nucleus. We develop the formalism for a quantum-mechanical treatment of the perturbing electrons and include the nuclear motion as part of the broadening and explore their relative importance. The conditions we explore are those found in white dwarf and neutron star atmospheres. We find that, contrary to previous studies, the quantized perturbing electrons create more broadening than perturbers on a straight-path trajectory. Additionally, the quantization of the plasma electrons gives rise to resonances away from the line center. The nuclear motion creates an additional electric field, which also leads to an increase in line broadening; however, this effect in neutron star atmospheres is not as large as previously estimated. This suggests that neutron star spectral lines are sensitive to density and that their mass and radius can be obtained from spectral line fitting, which would help constrain the neutron star equation of state.

79 ASTRONOMY AND ASTROPHYSICS↗

Iron(III)–Oxo Cluster Chemistry with Dimethylarsinate Ligands: Structures, Magnetic Properties, and Computational Studies

A program has been initiated to develop Fe III /oxo cluster chemistry with the ‘pseudo-carboxylate’ ligand dimethylarsinate (Me 2 AsO 2 - ) for comparison with the well investigated Fe III /oxo/carboxylate cluster area. The synthesis and characterization of three polynuclear Fe III complexes are reported, [Fe 12 O 4 (O 2 C t Bu) 8 (O 2 AsMe 2 ) 17 (H 2 O) 3 ]Cl 3 (1), Na 2 [Fe 12 Na 2 O 4 (O 2 AsMe 2 ) 20 (NO 3 ) 6 (Me 2 AsO 2 H) 2 (H 2 O) 4 ](NO 3 ) 6 (2) and [Fe 3 (O 2 AsMe 2 ) 6 (Me 2 AsO 2 H) 2 (hqn) 2 ](NO 3 ) (3), where hqn is 8-hydroxyquinoline. The Fe 12 core of 1 is a type never previously encountered in Fe III carboxylate chemistry, consisting of two Fe 6 units each of which comprises two {Fe 3 (μ 3 -O 2- )} units bridged by three Me 2 AsO 2 - groups and linked into an Fe 12 loop structure by two anti-anti η 1 :η 1 :μ Me 2 AsO 2 - groups, a bridging mode extremely rare with carboxylates. 2 also consists of two Fe 6 units, differing in their ligation from those in 1, and this time linked together into a linear structure by a central {Na 2 (NO 3 ) 2 } bridging unit. 3 is a linear Fe 3 complex with no monoatomic bridges between Fe III ions, a very rare situation in Fe III chemistry with any ligands, and unprecedented in Fe carboxylate chemistry. The distinct differences observed in arsinate vs carboxylate ligation modes are rationalized largely based on the greater basicity of the former vs the latter. Variable-temperature dc and ac magnetic susceptibility data reveal all Fe 2 pairwise interactions to be antiferromagnetic. For 1 and 2, the different J ij couplings were estimated by use of a magnetostructural correlation for high nuclearity Fe III -oxo clusters and by density functional theory calculations using broken symmetry methods, allowing identification of their relative spin vector alignments and thus rationalization of their S = 0 ground states. The J ij values were then used as input values to give excellent fits of the experimental χM T vs T data. For 3, the fits of the experimental χM T vs T data to the Van Vleck equation or with PHI gave a very weak J 12 = -0.8(1) cm -1 (H = –2JŠ i ·Š j convention) between adjacent Fe III ions, and an S = 5/2 ground state. Furthermore, these initial Fe III arsinate complexes also provide structural parameters that help validate literature assignments of arsinate binding modes to iron oxide/hydroxide minerals as part of environmental concerns of using arsenic-containing herbicides in agriculture.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Light quark Yukawas in triboson final states

Triple heavy vector boson production, pp → VVV (V = W, Z), has recently been observed for the first time. We propose that precision measurements of this process provide an excellent probe of the first generation light quark Yukawa couplings. Modified quark interactions with the off-shell Higgs in this process lead to a rapid growth of the partonic cross sections with energy, which manifests in an enhanced p T distribution of the final state leptons and quarks. We quantify this effect and estimate the present and future 2σ sensitivity to the up, down, and strange Yukawas. In particular, we find that HL-LHC can reach $\mathscr{O}$(400) sensitivity to the down Yukawa relative to the Standard Model value, improving the current sensitivity in this process by a factor of 10, and which can be further improved to $\mathscr{O}$(30) at FCC-hh. This is competitive with and complementary to constraints from global fits and other on-shell probes of the first generation Yukawas. The triboson sensitivity at HL-LHC corresponds to probing dimension-6 SMEFT operators suppressed by an $\mathscr{O}$(1) TeV scale, similarly to other LHC Higgs probes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Extracting a mixing parameter from 2D radiographic imaging of variable-density turbulent flow

We extract a suitably averaged fluctuating density from the two-dimensional radiographic image of a flow. The X-ray attenuation is given by the Beer–Lambert law which exponentially damps the incident beam intensity by a factor proportional to the density, opacity and thickness of the target. By making reasonable assumptions for the mean density, opacity and effective thickness of the target flow, we estimate the density fluctuation contribution to the attenuation. The extracted density fluctuations averaged across the thickness of the flow in the direction of the beam may be used to form the density–specific-volume correlation $b$. In a statistical description of variable-density turbulence, $b$ quantifies the degree of mixedness. The ability to extract a measure of mixedness from experimental data would be a powerful tool that could be used in the validation of mix models. The scheme proposed is tested for DNS data computed for variable density buoyancy-driven mixing. We quantify the deficits in the extracted value of $b$ due to target thickness, Atwood number and modeled signal noise. This analysis justifies using the proposed scheme to infer the mix parameter from thin targets at moderate to low Atwood numbers. Furthermore, to illustrate how the scheme might be used in a practical problem, we demonstrate its application to a radiographic image of counter-shear flow obtained from experiments at the National Ignition Facility.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Partial muon capture rates in A = 3 and A = 6 nuclei with chiral effective field theory

Searches for neutrinoless-double beta decay rates are crucial in addressing questions within fundamental symmetries and neutrino physics. The rates of these decays depend not only on unknown parameters associated with neutrinos, but also on nuclear properties. In order to reliably extract information about the neutrino, one needs an accurate treatment of the complex many-body dynamics of the nucleus. Neutrinoless-double beta decays take place at momentum transfers on the order of 100 MeV/$c$ and require both nuclear electroweak vector and axial current matrix elements. Muon capture, a process in the same momentum transfer regime, has readily available experimental data to validate these currents. In this work, we present results of {\it ab initio} calculations of partial muon capture rates for $^3$He and $^6$Li nuclei using variational and Green's Function Monte Carlo computational methods. We estimate the impact of the three-nucleon interactions, the cutoffs used to regularize two-nucleon ($2N$) interactions, and the energy range of $2N$ scattering data used to fit these interactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Breakdown characteristics of deep-ultraviolet Al 0.6 Ga 0.4 N p-i-n avalanche photodiodes

A top-illuminated deep-ultraviolet Al 0.6 Ga 0.4 N p-i-n avalanche photodiode (APD) structure was designed and grown by metalorganic chemical vapor deposition on an AlN bulk substrate and on two different quality AlN/sapphire templates, and APDs were fabricated and tested. The APD devices with a circular diameter of 20 μm have demonstrated a distinctive reverse-bias breakdown behavior. The reverse breakdown voltage of the APDs is approximately -140 V, which corresponds to a breakdown electric field of 6–6.2 MV/cm for the Al 0.6 Ga 0.4 N material as estimated by Silvaco TCAD simulation. The APDs grown on the AlN bulk substrate show the lowest leakage current density of < 1 × 10 -8 A/cm 2 (at low reverse bias) compared to that of the devices grown on the AlN templates. From the photocurrent measurement, a maximum gain (current limited) of 1.2 × 10 4 is calculated. The average temperature coefficients of the breakdown voltage are negative for APD devices fabricated from both the AlN bulk substrate and the AlN templates, but these data show that the coefficient is the least negative for the APD devices grown on the low-dislocation-density AlN bulk substrate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Orbits and Masses of Binaries from Speckle Interferometry at SOAR

We present results from Speckle inteferometric observations of 15 visual binaries and one double-line spectroscopic binary, carried out with the HRCam Speckle camera of the SOAR 4.1 m telescope. These systems were observed as a part of an on-going survey to characterize the binary population in the solar vicinity, out to a distance of 250 pc. We obtained orbital elements and mass sums for our sample of visual binaries. The orbits were computed using a Markov Chain Monte Carlo algorithm that delivers maximum likelihood estimates of the parameters, as well as posterior probability density functions that allow us to evaluate their uncertainty. Their periods cover a range from 5 yr to more than 500 yr; and their spectral types go from early A to mid M, implying total system masses from slightly more than 4M{sub ⊙} down to 0.2M {sub ⊙}. They are located at distances between approximately 12 and 200 pc, mostly at low Galactic latitude. For the double-line spectroscopic binary YSC8, we present the first combined astrometric/radial-velocity orbit resulting from a self-consistent fit, leading to individual component masses of 0.897 ± 0.027 M {sub ⊙} and 0.857 ± 0.026 M {sub ⊙}; and an orbital parallax of 26.61 ± 0.29 mas, which compares very well with the Gaia DR2 trigonometric parallax (26.55 ± 0.27 mas). In combination with published photometry and trigonometric parallaxes, we place our objects on an H-R diagram and discuss their evolutionary status. We also present a thorough analysis of the precision and consistency of the photometry available for them.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Optimizing ensemble NV − spin properties of fluorescent diamond microparticles by systematic low pressure high temperature annealing

Low pressure high temperature annealing is a means for driving nitrogen and defect diffusion in diamond to reduce internal lattice damage without the need for technically complicated high-pressure cells. Herein, we perform a systematic time (5, 15, and 30 min) and temperature (1200 °C–1800 °C) study of effects of low-pressure high temperature annealing on photoluminescence, spin concentrations, and spin relaxation properties of NV centers in ca. 3 μm synthetic type 1b diamond particles. Annealing in the temperature range of ca. 1400 °C–1700 °C for even 5 min leads to a higher optically detected magnetic resonance contrast as compared to standard annealing at 900 °C for 2 h. Particles annealed at 1700 °C for 5 min exhibit a contrast close to about 13% as compared to about 9% for those annealed at 900 °C for 2 h. A reduction in the zero-field splitting strain parameter from E ≈ 4.5 MHz to ≈ 2.5 MHz and spectral linewidth from Δν ≈ 7 MHz to ≈ 4 MHz are observed even after 5 min annealing at 1700 °C. Improvements in these spectral parameters resulted in a roughly 2-fold reduction in the noise level of temperature monitoring experiment utilizing an ensemble of NV centers in the particles. Annealing in the temperature range of 1600 °C for 15 or 30 min or 1700 °C for 5 min resulted in NV T 1 relaxation times approaching ca. 5 ms typically observed for bulk diamond. Quantitative electron paramagnetic resonance (EPR) allowed for estimations of thermal activation energies of paramagnetic center annihilation. Monitoring the primary defect concentration (P1 and other defects with half integer spins) and utilizing second order kinetic modeling, an activation energy of 3.63 ± 0.28 eV was estimated. Alternatively, using the NV half field EPR signal and first order kinetic modeling, a similar activation energy 3.89 ± 0.29 eV was estimated.

NV centers↗

Nucleon momentum fraction, helicity and transversity from 2+1-flavor lattice QCD

A detailed analysis of the systematic uncertainties in the calculation of the isovector momentum fraction, ( x ) u - d , helicity moment, ( x ) Δ u - Δ d , and the transversity moment, ( x ) δu - δd , of the nucleon is presented using high-statistics data on seven ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT collaborations using 2 + 1-flavors of dynamical Wilson-clover quarks. The much higher statistics have facilitated better control over all systematics compared to previous lattice calculations. The least understood systematic — excited-state contamination — is quantified by studying the variation of the results as a function of different estimates of the mass gap of the first excited state, obtained from two- and three-point correlation functions, and as a function of the pion mass M π . The final results are obtained using a simultaneous fit in the lattice spacing a , pion mass M π and the finite volume parameter M π L keeping leading order corrections. The data show no significant dependence on the lattice spacing and some evidence for finite-volume corrections. Our final results, in the $ \overline{\mathrm{MS}} $ scheme at 2 GeV, are ( x ) u - d = 0 . 155(17)(20), ( x ) Δ u - Δ d = 0 . 183(14)(20) and ( x ) δu - δd = 0 . 220(18)(20), where the first error is the overall analysis uncertainty assuming excited-state contributions have been removed, and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with phenomenological global fit values.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Comparing correlation components and approximations in Hartree–Fock and Kohn–Sham theories via an analytical test case study

The asymmetric Hubbard dimer is a model that allows for explicit expressions of the Hartree–Fock (HF) and Kohn–Sham (KS) states as analytical functions of the external potential, Δv, and of the interaction strength, U. We use this unique circumstance to establish a rigorous comparison between the individual contributions to the correlation energies stemming from the two theories in the {U, Δv} parameter space. Within this analysis of the Hubbard dimer, we observe a change in the sign of the HF kinetic correlation energy, compare the indirect repulsion energies, and derive an expression for the “traditional” correlation energy, i.e., the one that corrects the HF estimate, in a pure site-occupation function theory spirit [Eq. (45)]. Next, we test the performances of the Liu–Burke and the Seidl–Perdew–Levy functionals, which model the correlation energy based on its weak- and strong-interaction limit expansions and can be used for both the traditional and the KS correlation energies. Further, our results show that, in the Hubbard dimer setting, they typically work better for the HF reference, despite having been originally devised for KS. These conclusions are somewhat in line with prior assessments of these functionals on various chemical datasets. However, the Hubbard dimer model allows us to show the extent of the error that may occur in using the strong-interaction ingredient for the KS reference in place of the one for the HF reference, as has been carried out in most of the prior assessments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Study of $\langle {p}_{\text{T}}\rangle$ and its higher moments, and extraction of the speed of sound in Pb-Pb collisions with ALICE

Ultrarelativistic heavy-ion collisions produce a state of hot and dense strongly interacting QCD matter called quark-gluon plasma (QGP). On an event-by-event basis, the volume of the QGP in ultracentral collisions is mostly constant, while its total entropy can vary significantly due to quantum fluctuations, leading to variations in the temperature of the system. Exploiting this unique feature of ultracentral collisions allows for the interpretation of the correlation of the mean transverse momentum ($\langle$p T $\rangle$) of produced charged hadrons and the number of charged hadrons as a measure for the speed of sound, c s . This speed is related to the rate at which compression waves travel in the QGP and is determined by fitting the relative increase in $\langle$p T $\rangle$ with respect to the relative change in the average charged-particle density ($\langle$dN ch /dη$\rangle$) measured at mid-rapidity. This study reports the event-average $\langle$p T $\rangle$ of charged particles as well as the variance, skewness, and kurtosis of the event-by-event transverse momentum per charged particle ([p T ]) distribution in ultracentral Pb-Pb collisions at a center-of-mass energy of 5.02 TeV per nucleon pair using the ALICE detector. Different centrality estimators based on charged-particle multiplicity or the transverse energy of the event are used to select ultracentral collisions. By ensuring a pseudorapidity gap between the region used to define the centrality and the region used to perform the measurement, the influence of biases and their potential effects on the rise of the mean transverse momentum is tested. The measured c$^{2}_{s}$ is found to strongly depend on the exploited centrality estimator and ranges between 0.1146±0.0028 (stat.)±0.0065 (syst.) and 0.4374±0.0006 (stat.)±0.0184 (syst.) in natural units. The self-normalized variance shows a steep decrease towards ultracentral collisions, while the self-normalized skewness variables show a maximum, followed by a fast decrease. These non-Gaussian features are understood in terms of the vanishing of the impact-parameter fluctuations contributing to the event-to-event [p T ] distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Optimal Twirling Depth for Classical Shadows in the Presence of Noise

The classical shadows protocol is an efficient strategy for estimating properties of an unknown state p using a small number of state copies and measurements. In its original form, it involves twirling the state with unitaries from some ensemble and measuring the twirled state in a fixed basis. It was recently shown that for computing local properties, optimal sample complexity (copies of the state required) is remarkably achieved for unitaries drawn from shallow depth circuits composed of local entangling gates, as opposed to purely local (zero depth) or global twirling (infinite depth) ensembles. Here, we consider the sample complexity as a function of the depth of the circuit, in the presence of noise. We find that this noise has important implications for determining the optimal twirling ensemble. Under fairly general conditions, we (i) show that any single-site noise can be accounted for using a depolarizing noise channel with an appropriate damping parameter f, (ii) compute thresholds f th at which optimal twirling reduces to local twirling for Pauli operators, (iii) nth order Renyi entropies (n ≥2), and (iv) provide a meaningful upper bound t max on the optimal circuit depth for any finite noise strength f, which applies to observables and entanglement entropy measurements. In conclusion, these thresholds strongly constrain the search for optimal strategies to implement shadow tomography and are easily tailored to the experimental system at hand.

97 MATHEMATICS AND COMPUTING↗

Active- and transfer-learning applied to microscale-macroscale coupling to simulate viscoelastic flows

Active- and transfer-learning are applied to microscale dynamics of polymer flows for the multiscale discovery of effective constitutive approximations required in viscoelastic flow simulation. The result is macroscopic rheology directly connected to a microstructural model. Micro and macroscale simulations are adaptively coupled by means of Gaussian process regression (GPR) to run the expensive microscale computations only as necessary. This multiscale method is demonstrated with flows of a polymer solution as a model system. At the microscale level dissipative particle dynamics (DPD) is employed to model the fluid as a suspension of bead-spring micro-structures subjected to steady shear flow. The results yield the non-Newtonian viscosity and the first normal stress difference at strain rates as training data used in a GPR model. DPD parameters are calibrated with respect to experimental data for a real polymer solution. Compliance with these data requires adjustment of the DPD model's cutoff radius, which then becomes a function of the second invariant of the strain rate tensor. The FENE-P model is chosen for the macroscale description using the spectral element method (SEM) to simulate channel flow and flow past a circular cylinder. The DPD results at the lowest possible shear strain rate yield an estimate of the zero-shear rate viscosity, which allows the initiation of the macroscale flow by SEM as a Newtonian fluid. The resulting strain-rate field is surveyed to determine additional shear strain rate sampling points for the DPD system. This new information allows an initial fitting of parameters of the constitutive equation followed by new SEM simulations at the macroscale. Additionally, guided by active-learning GPR to select new sampling points, this process continues until convergence is achieved. The effectiveness of this new simulation paradigm for viscoelastic flows is tested with different macroscale operating conditions. The effective closure learned in the channel simulation is then transferred directly to the flow past a circular cylinder at low Reynolds number, where the results show that only two additional DPD simulations are required to achieve a satisfactory constitutive model. With an increase of the Reynolds number, the active-learning scheme automatically detects the inaccuracy of the learned constitutive model, and initiates additional DPD simulations for the extra data needed to once again close the microscale-macroscale coupled system. This new paradigm of active- and transfer-learning for multiscale modeling is readily applicable to other microscale-macroscale coupled simulations of complex fluids and other materials. Furthermore, the coupling between microscale and macroscale solvers can be seamlessly implemented with our open source multiscale universal interface (MUI) library.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Feasibility of DEIM for retrieving the initial field via dimensionality reduction

When parameter estimation is solved in a high-dimensional space, the dimensionality reduction strategy becomes the primary consideration for alleviating the tremendous computational cost. Here, the discrete empirical interpolation method (DEIM) is explored to retrieve the initial condition (IC) by combining the polynomial chaos (PC) based ensemble Kalman filter (i.e. PC-EnKF), where a non-intrusive PC expansion is considered as a surrogate model in place of the forward model in the prediction step of the ensemble Kalman filter, resulting in fewer forward model integrations but with a comparable accuracy as Monte Carlo-based approaches. The DEIM acts as a hyper-reduction tool to provide the low-dimensional input for the high-dimensional initial field, which can be reconstructed using the information on the sparse interpolation grid points that is adaptively obtained through PC-EnKF data assimilation method. Thus an innovative framework to reconstruct the IC is developed. The detailed procedure at each assimilation iteration includes: the determination of the spatial interpolation points, the estimation of the initial values on the interpolation locations using the optimal observations, and the reconstruction of IC in the full space. The current study uses the reconstruction field of initial conditions of the Navier-Stokes equations as an example to illustrate the efficacy of our method. The experimental results demonstrate the proposed algorithm achieves a satisfactory reconstruction for the initial field. The proposed method helps to extend the applicable area of DEIM in solving inverse problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Tutorial on Bayesian analysis of linear shock compression data

Gas gun and other shock compression experiments often produce shock wave velocity measurements that are linearly associated with particle velocity. Traditionally, this empirical relationship is quantified with a single Hugoniot curve that is estimated using least squares regression. However, for downstream modeling and simulation tasks, it is often more useful to have multiple Hugoniot curves in the pressure–volume plane that are consistent with the data. We employ Bayesian uncertainty quantification methods as a framework for propagating measurement uncertainty through to model parameters and predictions. Specifically, this Tutorial shows how to sample multiple Hugoniot curves in the pressure–volume plane that are consistent with the shock wave-particle velocity measurements in a two-step Bayesian approach. First, we obtain an analytical expression for the posterior distribution of the linear model parameters using Bayesian linear regression. Second, we propagate samples from the posterior distribution through the Rankine–Hugoniot equations to yield Hugoniot curves in the pressure–volume plane. The procedure is demonstrated with publicly available data on argon, copper, and nickel, and compared against bootstrapping and linear regression. The Bayesian procedure is shown to be interpretable, computationally inexpensive, and less sensitive than an alternative bootstrapping approach to the removal of the point in the copper dataset that has the largest particle velocity. As a Tutorial on Bayesian methodology for the shock compression community, we provide several derivations and explanations that make this paper self-contained, and make all code and data available at github.com/llnl/BALSCD.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗