Search NASA⌕ Search

SEARCH · Search NASA

Results for “hydrodynamic coupling”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Classical-quantum simulation of non-equilibrium Marshak waves

In the radiation hydrodynamic simulations used to design inertial confinement fusion (ICF) and pulsed power experiments, nonlinear radiation diffusion tends to dominate CPU time. This raises the interesting question of whether a quantum algorithm can be found for nonlinear radiation diffusion which provides a quantum speedup. Recently, such a quantum algorithm was introduced based on a quantum algorithm for solving systems of nonlinear partial differential equations (PDEs) which provides a quadratic quantum speedup. Here, we apply this quantum PDE (QPDE) algorithm to the problem of a non-equilibrium Marshak wave propagating through a cold, semi-infinite, optically thick target, where the radiation and matter fields are not assumed to be in local thermodynamic equilibrium. The dynamics is governed by a coupled pair of nonlinear PDEs which are solved using the QPDE algorithm, as well as two standard PDE solvers: (i) Python's py-pde solver; and (ii) the KULL ICF simulation code developed at Lawrence-Livermore National Laboratory. We compare the simulation results obtained using the QPDE algorithm and the standard PDE solvers and find excellent agreement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Cross-beam energy transfer saturation by ion trapping-induced detuning

The performance of direct-drive inertial confinement fusion implosions relies critically on the coupling of laser energy to the target plasma. Cross beam energy transfer (CBET), the resonant exchange of energy between intersecting laser beams mediated by ponderomotively driven ion-acoustic waves (IAW), inhibits this coupling by scattering light into unwanted directions. Furthermore, the variety of beam intersection angles and varying plasma conditions in an implosion results in IAWs with a range of phase velocities. Here we show that CBET saturates through a resonance detuning that depends on the IAW phase velocity and that results from trapping-induced modifications to the ion distribution functions. For smaller phase velocities, the modifications to the distribution functions can rapidly thermalize in the presence of mid-Z ions, leading to a blueshift in the resonant frequency. For larger phase velocities, the modifications can persist, leading to a redshift in the resonant frequency. Ultimately, these results may reveal pathways towards CBET mitigation and inform reduced models for radiation hydrodynamics codes to improve their predictive capability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Mechanistic mass transfer in hollow fiber membrane solvent extraction for bio-based isobutanol

Membrane solvent extraction (MSE) has emerged as a promising method for selectively recovering bioproducts from complex aqueous streams. Bio-isobutanol, a next-generation feedstock for biofuel, remains challenging to recover because of its low concentration and the presence of inhibitory substances. This study explores the potential of hollow fiber (HF) MSE for bio-isobutanol recovery and systematically examines the coupled effects of fiber packing, shell-side flow dynamics, and aqueous chemistry on performance. A resistance-in-series model is applied to understand mass transfer in the HF MSE modules, quantify local resistances, and validate overall performance. The results show that increasing the fiber packing provides a larger interfacial area but induces poor flow distribution and channeling, hindering effective isobutanol transport. Meanwhile, increasing the shell-side velocity improves isobutanol recovery due to reductions in the boundary layer thickness. The presence of salts, added to mimic fermentation broth, increases the partition coefficient through salting-out effects, further improving isobutanol flux. A modified correlation for the shell-side mass transfer coefficient (k s,ϕ+v ), integrating geometric and hydrodynamic effects, was developed and validated. The proposed model achieves highly predictive accuracy (r 2 = 0.9808) across a wide range of conditions, outperforming previous models. The findings provide mechanistic insight into the interaction of geometric packing, hydrodynamics, and chemistry in governing mass transfer in HF MSE. Overall, this work demonstrates the potential of HF MSE for efficient bio-isobutanol recovery and also provides practical guidelines on critical factors (packing fraction, partition coefficient, and shell-side velocity), aiding in the design and scaling of MSE systems for resource recovery.

Aqueous chemistry↗
DOE OSTI2020

Transverse-momentum and event-shape dependence of D-meson flow harmonics in Pb–Pb collisions at s NN = 5.02 TeV

The elliptic and triangular flow coefficients v 2 and v 3 of prompt D 0 , D + , and D * + mesons were measured at midrapidity ( | y | < 0.8 ) in Pb–Pb collisions at the centre-of-mass energy per nucleon pair of s NN = 5.02 TeV with the ALICE detector at the LHC. The D mesons were reconstructed via their hadronic decays in the transverse momentum interval 1 < p T < 36 GeV / c in central (0–10%) and semi-central (30–50%) collisions. Compared to pions, protons, and J / ψ mesons, the average D-meson v n harmonics are compatible within uncertainties with a mass hierarchy for p T ≲ 3 GeV / c , and are similar to those of charged pions for higher p T . The coupling of the charm quark to the light quarks in the underlying medium is further investigated with the application of the event-shape engineering (ESE) technique to the D-meson v 2 and p T -differential yields. The D-meson v 2 is correlated with average bulk elliptic flow in both central and semi-central collisions. Within the current precision, the ratios of per-event D-meson yields in the ESE-selected and unbiased samples are found to be compatible with unity. All the measurements are found to be reasonably well described by theoretical calculations including the effects of charm-quark transport and the recombination of charm quarks with light quarks in a hydrodynamically expanding medium.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Mesoscopic two-point collective dynamics of glass-forming liquids

The collective density–density and hydrostatic pressure–pressure correlations of glass-forming liquids are spatiotemporally mapped out using molecular dynamics simulations. It is shown that the sharp rise of structural relaxation time below the Arrhenius temperature coincides with the emergence of slow, nonhydrodynamic collective dynamics on mesoscopic scales. The observed long-range, nonhydrodynamic mode is independent of wave numbers and closely coupled to the local structural dynamics. Below the Arrhenius temperature, it dominates the slow collective dynamics on length scales immediately beyond the first structural peak in contrast to the well-known behavior at high temperatures. Furthermore, these results highlight a key connection between the qualitative change in mesoscopic two-point collective dynamics and the dynamic crossover phenomenon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Explosively driven Richtmyer–Meshkov instability jet suppression and enhancement via coupling machine learning and additive manufacturing

The ability to control the behavior of fluid instabilities at material interfaces, such as the shock-driven Richtmyer–Meshkov instability, is a grand technological challenge with a broad number of applications ranging from inertial confinement fusion experiments to explosively driven shaped charges. In this work, we use a linear-geometry shaped charge as a means of studying methods for controlling material jetting that results from the Richtmyer–Meshkov instability. A shaped charge produces a high-velocity jet by focusing the energy from the detonation of high explosives. The interaction of the resulting detonation wave with a hollowed cavity lined with a thin metal layer produces the unstable jetting effect. By modifying the characteristics of the detonation wave prior to striking the lined cavity, the kinetic energy of the jet can be enhanced or reduced. Modifying the geometry of the liner material can also be used to alter jetting properties. We apply optimization methods to investigate several design parameterizations for both enhancing or suppressing the shaped-charge jet. This is accomplished using 2D and 3D hydrodynamic simulations to investigate the design space that we consider. We also apply new additive manufacturing methods for producing the shaped-charge assemblies, which allow for the experimental testing of complicated design geometries obtained through computational optimization. We present a direct comparison of our optimized designs with experimental results carried out at the High Explosives Application Facility at Lawrence Livermore National Laboratory.

36 MATERIALS SCIENCE↗
DOE OSTI2020

The αs and θs in Rayleigh–Taylor and Richtmyer–Meshkov instabilities

The alphas (α b , α s ) and thetas (θ b , θ s ) are the essential parameters describing the asymptotic growth behavior of the mixing layer driven by Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities at the interface between the fluids. Extensive simulations and experiments have been conducted in the determination of these parameters. The results depend on numerical algorithms, resolutions, and the accuracy of experimental measurements. In this article, we present a unique relationship between the alphas and thetas by applying a simple buoyancy-drag mixing model. Our first main result is that, for the same fluids, these parameters are not independent because they are fundamentally connected by physics principles and they all are functions of the drag coefficients of the fluids. As a consequence, the alphas and thetas are intrinsically coupled. All are functions of any single one of these. Additionally, our second main result is that the RT bubble growth rate (α b ) is determined by the bubble competition process – a merger model – at the edge of the mixing layer. Together, these two main results determine all the alphas and thetas by strictly theoretical reasoning. Applications to both hydro and laser driven experiments at OMEGA are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

An effective description of charge diffusion and energy transport in a charged plasma from holography

We discuss the physics of sound propagation and charge diffusion in a plasma with non-vanishing charge density. Our analysis culminates the program initiated in to construct an open effective field theory of low-lying modes of the stress tensor and charge current in such plasmas. We model the plasma holographically as a Reissner-Nordström-AdS d+1 black hole, and study linearized fluctuations of longitudinally polarized scalar gravitons and photons in this background. We demonstrate that the perturbations can be decoupled and repackaged into the dynamics of two designer scalars, whose gravitational coupling is modulated by a non-trivial dilatonic factor. The holographic analysis allows us to isolate the phonon mode from the charge diffusion mode, and identify the combination of currents that corresponds to each of them. We use these results to obtain the real-time Gaussian effective action, which includes both the retarded response and the associated stochastic (Hawking) fluctuations, accurate to quartic order in gradients.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Development of an x-ray radiography platform to study laser-direct-drive energy coupling at the National Ignition Facility

A platform has been developed to study laser-direct-drive energy coupling at the National Ignition Facility (NIF) using a plastic sphere target irradiated in a polar-direct-drive geometry to launch a spherically converging shock wave. To diagnose this system evolution, eight NIF laser beams are directed onto a curved Cu foil to generate Heα line emission at a photon energy of 8.4 keV. These x rays are collected by a 100-ps gated x-ray imager in the opposing port to produce temporally gated radiographs. The platform is capable of acquiring images during and after the laser drive launches the shock wave. A backlighter profile is fit to the radiographs, and the resulting transmission images are Abel inverted to infer radial density profiles of the shock front and to track its temporal evolution. Here, the measurements provide experimental shock trajectories and radial density profiles that are compared to 2D radiation-hydrodynamic simulations using cross-beam energy transfer and nonlocal heat-transport models.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

Multibody for Everybody (M4E): A Symbolic Dynamics Modeling Tool with Applications in Simulation, Control, and Optimization

Developing the analytical model of a multibody system is often the initial step in control and optimization. The analytical model (equations of motion) describes a system’s time evolution under specified forcing conditions. Although developing these equations is easy for simple systems, this process becomes more complex for systems composed of multiple bodies. Deriving equations of motion for complex multibody systems requires specialized expertise in multibody dynamics, is time-consuming, and is susceptible to error. To address this issue, this paper presents an open-source, easy-to-use, systematic framework to derive symbolic equations of motion in both Python and MATLAB using the joint coordinate formulation. This formulation results in a set of ordinary differential equations that use the minimum set of coordinates needed to model a system. The symbolic representation provides better insight into the influence of design parameters on system performance, facilitates sensitivity analysis and parameter studies, and supports direct implementation of control and optimization routines. The tool enables numerical simulation for specified parameter sets, is modular for straightforward integration with other tools and libraries, and allows incorporation of hydrodynamics, mooring, and other external forces. The result is a reproducible, extensible pipeline for modeling, simulation, and design of complex multibody systems. The proposed tool is versatile and can be applied to domains such as robotics, control, and design. In addition, we integrated external libraries that provide capabilities for modeling offshore systems such as underwater robots and marine energy converters.

16 TIDAL AND WAVE POWER↗
DOE OSTI2021

Coupled Boltzmann transport equations of heavy quarks and quarkonia in quark-gluon plasma

We develop a framework of coupled transport equations for open heavy flavor and quarkonium states, in order to describe their transport inside the quark-gluon plasma. Our framework is capable of studying simultaneously both open and hidden heavy flavor observables in heavy-ion collision experiments and can account for both, uncorrelated and correlated recombination. Our recombination implementation depends on real-time open heavy quark and antiquark distributions. We carry out consistency tests to show how the interplay among open heavy flavor transport, quarkonium dissociation and recombination drives the system to equilibrium. We then apply our framework to study bottomonium production in heavy-ion collisions. We include Υ(1S), Υ(2S), Υ(3S), χb (1P) and χb (2P) in the framework and take feed-down contributions during the hadronic gas stage into account. Cold nuclear matter effects are included by using nuclear parton distribution functions for the initial primordial heavy flavor production. A calibrated 2 + 1 dimensional viscous hydrodynamics is used to describe the bulk QCD medium. We calculate both the nuclear modification factor R AA of all bottomonia states and the azimuthal angular anisotropy coefficient v 2 of the Υ(1S) state and find that our results agree reasonably with experimental measurements. Our calculations indicate that correlated cross-talk recombination is an important production mechanism of bottomonium in current heavy-ion experiments. The importance of correlated recombination can be tested experimentally by measuring the ratio of R AA ( χb (1P)) and R AA (Υ(2S)).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Filaments in and between galaxy clusters at low and mid-frequency with the SKA

Context. Understanding the magnetised Universe is a major challenge in modern astrophysics, and cosmic magnetism has been acknowledged as one of the key scientific drivers of the most ambitious radio instrument ever planned, the Square Kilometre Array. Aims. With this work, we aim to investigate the potential of the Square Kilometre Array and its precursors and pathfinders in the study of magnetic fields in galaxy clusters and filaments through diffuse synchrotron radio emission. Galaxy clusters and filaments of the cosmic web are indeed unique laboratories in which to investigate turbulent fluid motions and large-scale magnetic fields in action, and much of what is known about magnetic fields in galaxy clusters comes from sensitive radio observations. Methods. Based on cosmological magneto-hydrodynamic simulations, we predict radio properties (total intensity and polarisation) of a pair of galaxy clusters connected by a cosmic-web filament. Results. We use our theoretical expectations to explore the potential of polarimetric observations to study large-scale structure magnetic fields in the frequency ranges 50–350 MHz and 950–1760 MHz. We also present predictions for galaxy cluster polarimetric observations with the Square Kilometre Array precursors and pathfinders, such as the LOw frequency ARray 2.0 and the MeerKAT+ telescope. Conclusions. Our findings point out that polarisation observations are particularly powerful for the study of large-scale magnetic fields, since they are not significantly affected by confusion noise. The unprecedented sensitivity and spatial resolution of the intermediatefrequency radio telescopes make them the favourite instruments for the study of these sources through polarimetric data, potentially allowing us to understand if the energy density of relativistic electrons is in equipartition with the magnetic field or rather coupled with the thermal gas density. Our results show that low-frequency instruments also represent a precious tool to study diffuse synchrotron emission in total intensity and polarisation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Gas and dust dynamics in γ Cephei-type disks

Context. Giant planets are observed orbiting the primary stars of close binary systems. Such planets may have formed in compact circumprimary disks, which once surrounded these stars, under conditions much different than those encountered around single stars. Aims. In order to quantify the effects of the strong gravitational perturbations exerted on circumprimary disk material, the three-dimensional (3D) dynamics of gas and dust in orbit around the primary star of a compact and eccentric binary system was modeled by applying the stellar and orbital parameters of γ Cephei, a well-known system that can be representative of a class of close binaries. Methods. Circumprimary gas was approximated as an Eulerian viscous and compressible fluid and modeled by means of 3D hydrodynamical simulations, assuming locally isothermal conditions in the medium around the primary star. Dust grains were modeled as Lagrangean particles, subjected to gravity and aerodynamic drag forces. Models that include a giant planet were also considered. Results. Models indicate that spiral density waves excited around pericenter passage propagate toward the inner boundary of the disk, through at least a few pressure scale-heights from the mid-plane, inducing radial and vertical mixing in the gas. However, perturbations imparted to gas, both in terms of eccentricity and precession, are far weaker than previously estimated by two-dimensional (2D) simulations. Models predict small eccentricities, ≲0.03, and slow retrograde precession. The addition of a giant planet does not change the low eccentricity state of the disk. The parameters applied to the disk would lead to the formation of a massive planet, many times the mass of Jupiter, in agreement with some observations. Micron to mm-size dust grains are well coupled to the gas, resulting in similar dynamics and statistically similar distributions of orbital elements. The planet only affects the dust distributions locally. In agreement with outcomes of recent 2D models, the lifetime of an isolated circumprimary disk would be brief, ~10 5 years, because of its compact nature, requiring a long-term external supply of mass to allow for the in situ formation of a giant planet.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Tree hydrodynamic modelling of the soil–plant–atmosphere continuum using FETCH3

Modelling the water transport along the soil–plant–atmosphere continuum is fundamental to estimating and predicting transpiration fluxes. A Finite-difference Ecosystem-scale Tree Crown Hydrodynamics model (FETCH3) for the water fluxes across the soil–plant–atmosphere continuum is presented here. The model combines the water transport pathways into one vertical dimension, and assumes that the water flow through the soil, roots, and above-ground xylem can be approximated as flow in porous media. This results in a system of three partial differential equations, resembling the Richardson–Richards equation, describing the transport of water through the plant system and with additional terms representing sinks and sources for the transfer of water from the soil to the roots and from the leaves to the atmosphere. The numerical scheme, developed in Python 3, was tested against exact analytical solutions for steady state and transient conditions using simplified but realistic model parameterizations. The model was also used to simulate a previously published case study, where observed transpiration rates were available, to evaluate model performance. With the same model setup as the published case study, FETCH3 results were in agreement with observations. Through a rigorous coupling of soil, root xylem, and stem xylem, FETCH3 can account for variable water capacitance, while conserving mass and the continuity of the water potential between these three layers. FETCH3 provides a ready-to-use open access numerical model for the simulation of water fluxes across the soil–plant–atmosphere continuum.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Development of an accelerator-based neutron source to prototype Mo-99 production, part I: A liquid LBE windowless target

In this article, Molybdenum-99 (Mo-99)’s decay product, technetium-99 (Tc-99 m), is one of the most critical isotopes for medical diagnostics. To provide U.S. domestic supply of Mo-99 without using high-enriched uranium (HEU), a subcritical uranium target assembly (UTA) is irradiated by an accelerator-based neutron source to create Mo-99 through fission. This study discusses the development of the accelerator-based neutron source. The high-energy electrons from the accelerator irradiate a liquid lead-bismuth eutectic (LBE) target to produce neutrons. Part I of this work focuses on numerical and experimental analysis towards the development of a liquid LBE windowless target. Unlike the existing windowless targets in literature, the current design creates a vertical free surface for a beam to irradiate. First, a hydrodynamic analysis of the LBE windowless target is performed. Simplified analytical calculations are assisted by 2D computational fluid dynamics (CFD) simulations to design the target, with the focus on eliminating recirculation zones and avoiding cavitation. With the optimized geometry, the experimental study is performed to investigate the flow hydrodynamics using liquid LBE. The experiments (1) compare pressure drop in the system to correlation predictions; (2) visualize the free surface liquid LBE flow from the beam view; (3) validate the LBE flow profile using temperature sensitive paint from the side view; and (4) validate the liquid LBE film thickness using gamma densitometer measurements. Second, the power handling capability of the designed windowless target is investigated. The divider plate in the current design is susceptible to overheating due to the thin LBE film in front. As LBE erosion and corrosion is likely to occur at an LBE velocity of 2.0 m/s and temperature above 500 °C, a power limit of 10 kW of beam power was established to prevent this corrosion from occurring, which is calculated by a Nusselt number correlation. The divider plate surface temperature at 10 kW agrees well with the 3D CFD simulation results. Part I demonstrates the fundamental physics in liquid LBE windowless target design and associated testing. A companion paper, Part II will demonstrate how to couple this windowless target into the Mo-99 production system, including an accelerator system operating under an ultra-high vacuum and the UTA cooled by water at room temperature.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Static and dynamic properties of multi-ionic plasma mixtures

Complex plasma mixtures with three or more components are often encountered in astrophysics or in inertial confinement fusion (ICF) experiments. For mixtures containing species with large differences in atomic number Z, the modeling needs to consider at the same time the kinetic theory for low-Z elements combined with the theory of strongly coupled plasma for high-Z elements, as well as all the intermediate situations that can appear in multi-component systems. For such cases, we study the pair distribution functions, self-diffusions, mutual diffusion and viscosity for ternary mixtures at extreme conditions. These quantities can be produced from first principles using orbital free molecular dynamics at the computational expense of very intensive simulations to reach good statistics. Utilizing the first-principles results as reference data, we assess the merit of a global analytic model for transport coefficients, "Pseudo-Ions in Jellium" (PIJ), based on an iso-electronic assumption (iso-n e ). With a multi-component hypernetted-chain integral equation, we verify the quality of the iso-n e prescription for describing the static structure of the mixtures. This semi-analytical modeling compares well with the simulation results and allows one to consider plasma mixtures not accessible to simulations. Further, applications are given for the mix of materials in ICF experiments. A reduction of a multicomponent mixture to an effective binary mixture is also established in the hydrodynamic limit and compared with PIJ estimations for ICF relevant mixtures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Validation of magnetized gas-jet experiments to investigate the effects of an external magnetic field on laser-plasma instabilities

Laser-plasma instabilities (LPI) play a detrimental role in energy coupling to the target in inertial confinement fusion (ICF). The recent development of applied strong magnetic fields for use in ICF and laboratory astrophysics experiments has opened opportunities to investigate the role of external magnetic fields on LPIs. Recent numerical studies have shown that stimulated Raman scattering (SRS) can be mitigated by external magnetic fields in the kinetic regime of the instability and warrant systematic experimental studies to validate modelling. To this end, we design experiments at the OMEGA-EP laser facility to investigate the effect of an external perpendicular B-field of 5–30 T on the backscattered light spectrum from a gas-jet target. We present measurements from a proof-of-principle experiment, where the backward-SRS (BSRS) is in the kinetic regime, for which the magnetization is expected to produce the greatest effects on instability growth. New simulations motivated by this experiment are used to inform the proposal of an upgraded experimental design. Our simulation predictions show that the new design is suited to experimentally demonstrating BSRS mitigation by an external magnetic field, despite the magnetization effects on the hydrodynamics, as well as the inherent temporal and spatial variations in plasma conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Fluid dynamic mathematical aspects of supernova remnants

Supernovae—explosions of stars—are a central problem in astrophysics since they contain information on the entire process of stellar evolution and nucleosynthesis. Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities, developing during the supernova blast, lead to intense interfacial RT/RM mixing of the star's materials and couple astrophysical to atomic scales. This work analyzes some fluid dynamic mathematical aspects of the titanic task of supernova's blast. We handle mathematical challenges of RT/RM dynamics in supernova relevant conditions by directly linking the conservation laws governing RT/RM dynamics to symmetry-based momentum model, by exactly deriving the model parameters in the scale-dependent and scale-invariant regimes, and by exploring the special self-similar class for RT/RM interfacial mixing with variable accelerations. Here we reveal that RT/RM dynamics is strongly influenced by deterministic (the initial and the flow) conditions in the scale-dependent linear and nonlinear regimes and in the self-similar mixing regime. The theory outcomes are consistent with the observations of supernova remnants, explain the results of the scaled laboratory experiments in high energy density plasmas, and yield the design of future experiments for the accurate quantification of RT/RM dynamics in supernova relevant conditions. We find that from fluid dynamic mathematical perspectives, supernovae can be regarded as an astrophysical initial value problem. Along with the guidance of what explodes at microscopic scales, supernova remnants encapsulate information on the explosion hydrodynamics and the associated deterministic conditions at macroscopic scales. We urge such effects be considered in interpretations of the observational data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗