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DOE OSTI2020

Nonlinear modeling and performance analysis of cracked beam microgyroscopes

Cracks constitute a common structural defect in microelectromechanical systems that may arise during manufacturing, mechanical fatigue, or shock loading. Areas weakened by cracks increase the flexibility of the microstructure. Furthermore, depending on the crack severity, the increased flexibility can cause dramatic changes in the static and dynamic behaviors of electrically actuated MEMS. In this study, a numerical investigation of the depth and location of multiple edge cracks on the performance of beam microgyroscopes is conducted. Applying the Griffith strain energy release theorem for an edge crack, the vibrational characteristics of microgyroscopes with multiple cracks including the static deflection, natural frequencies, and mode shapes are studied analytically. Then, the differential quadrature method is employed to model the nonlinear dynamic behaviors of the cracked gyroscope system. Cracks initiated along the driving or sensing directions of the microgyroscope are found to have differing effects on its nonlinear dynamic response. This numerical study reveals that the onset of severe single cracks or a series of multiple cracks can significantly affect the sensitivity of the microgyroscope to base rotations and therefore leads to a degradation in the performance of the damaged MEMS sensor. This study also shows that a potential design approach for broadband microgyroscope systems manufactured with cracks can be proposed.

42 ENGINEERING↗

DOE OSTI2023

Near-MHz temperature and H 2 O measurements in post-detonation fireballs of 25 g hemispherical explosives using scanned-wavelength-modulation spectroscopy

A laser absorption spectroscopy diagnostic integrated within a hardened optical probe was used to measure temperature and water mole fraction at 500 kHz in post-detonation fireballs of explosives. In the experiments, an exploding-bridgewire detonator initiated a 25 g hemisphere of explosive (N5 or PETN). This produced a hemispherical fireball that traveled radially towards a hardened measurement probe. The probe contained a pressure transducer and optical equipment to pitch fiber-coupled laser light across a 12.6 cm gap onto a detector. Tunable diode lasers emitting near 7185.6 and 6806 c m − <#comment/> 1 were used to measure the absorbance spectrum of H 2 O utilizing peak-picking scanned-wavelength-modulation spectroscopy with a scan frequency of 500 kHz and modulation frequencies of 35 and 45.5 MHz, respectively. This enabled measurements of temperature and X H 2 O in the shock-heated air and trailing fireball at 500 kHz. Time histories of pressure, temperature, and H 2 O mole fraction were acquired at different standoff distances to quantify how the fireball evolved in space and time as well as to compare measured quantities between PETN and N5 fireballs. The standard deviation of temperature and X H 2 O during one representative test were found to be 17 K (1.3%) and 0.011 (5%), respectively. These measurements demonstrate this diagnostic’s ability to provide rapid and reliable measurements in harsh, highly transient post-detonation environments produced by solid explosives.

Schwartz, Charles J.↗

NASA NTRS2004

Exhaust Nozzle for a Multitube Detonative Combustion Engine

An improved type of exhaust nozzle has been invented to help optimize the performances of multitube detonative combustion engines. The invention is applicable to both air-breathing and rocket engines used to propel some aircraft and spacecraft, respectively. In a detonative combustion engine, thrust is generated through the expulsion of combustion products from a detonation process in which combustion takes place in a reaction zone coupled to a shock wave. The combustion releases energy to sustain the shock wave, while the shock wave enhances the combustion in the reaction zone. The coupled shockwave/reaction zone, commonly referred to as a detonation, propagates through the reactants at very high speed . typically of the order of several thousands of feet per second (of the order of 1 km/s). The very high speed of the detonation forces combustion to occur very rapidly, thereby contributing to high thermodynamic efficiency. A detonative combustion engine of the type to which the present invention applies includes multiple parallel cylindrical combustion tubes, each closed at the front end and open at the rear end. Each tube is filled with a fuel/oxidizer mixture, and then a detonation wave is initiated at the closed end. The wave propagates rapidly through the fuel/oxidizer mixture, producing very high pressure due to the rapid combustion. The high pressure acting on the closed end of the tube contributes to forward thrust. When the detonation wave reaches the open end of the tube, it produces a blast wave, behind which the high-pressure combustion products are expelled from the tube. The process of filling each combustion tube with a detonable fuel/oxidizer mixture and then producing a detonation repeated rapidly to obtain repeated pulses of thrust. Moreover, the multiple combustion tubes are filled and fired in a repeating sequence. Hence, the pressure at the outlet of each combustion tube varies cyclically. A nozzle of the present invention channels the expansion of the pulsed combustion gases from the multiple combustion tubes into a common exhaust stream, in such a manner as to enhance performance in two ways: (1) It reduces the cyclic variations of pressure at the outlets of the combustion tubes so as to keep the pressure approximately constant near the optimum level needed for filling the tubes, regardless of atmospheric pressure at the altitude of operation; and (2) It maximizes the transfer of momentum from the exhaust gas to the engine, thereby maximizing thrust. The figure depicts a typical engine equipped with a nozzle according to the invention. The nozzle includes an interface section comprising multiple intake ports that couple the outlets of the combustion tubes to a common plenum. Proceeding from its upstream to its downstream end, the interface section tapers to a larger cross-sectional area for flow. This taper fosters expansion of the exhaust gases flowing from the outlets of the combustion tubes and contributes to the desired equalization of exhaust combustion pressure. The cross-sectional area for flow in the common plenum is greater than, or at least equal to, the combined cross-sectional flow areas of the combustor tubes. In the common plenum, the exhaust streams from the individual combustion tubes mix to form a single compound subsonic exhaust stream. Downstream of the common plenum is the throat that tapers to a smaller flow cross section. In this throat, the exhaust gases become compressed to form a compound sonic gas stream. Downstream of the throat is an expansion section, which typically has a bell or a conical shape. (The expansion section can be truncated or even eliminated in the case of an air-breathing engine.) After entering the expansion section, the exhaust gases expand rapidly from compound sonic to compound supersonic speeds and are then vented to the environment. The basic invention admits of numerous variations. For example, the combustion tubes can be arranged around the central axin a symmetrical or asymmetrical pattern other than the one shown in the figure. For another example, the flow cross-sectional area(s) of one or more of the intake ports in the interface section, of the common plenum, the throat, and/or the expansion section can be varied, either symmetrically or asymmetrically, to adjust dynamics of the exhaust stream or to direct the thrust vector away from the central axis.

Bratkovich, Thomas E.↗

NASA NTRS1992

An experimental/computational study of sharp fin induced shock wave/turbulent boundary layer interactions at Mach 5 - Experimental results

A combined experimental/computational study has been performed of sharp fin induced shock wave/turbulent boundary layer interactions at Mach 5. The current paper focuses on the experiments and analysis of the results. The experimental data include mean surface heat transfer, mean surface pressure distributions and surface flow visualization for fin angles of attack of 6, 8, 10, 12, 14 and 16-degrees at Mach 5 under a moderately cooled wall condition. Comparisons between the results and correlations developed earlier show that Scuderi's correlation for the upstream influence angle (recast in a conical form) is superior to other such correlations in predicting the current results, that normal Mach number based correlations for peak pressure heat transfer are adequate and that the initial heat transfer peak can be predicted using pressure-interaction theory.

Rodi, Patrick E.↗

NASA NTRS2005

Particle acceleration magnetic field generation, and emission in Relativistic pair jets

Plasma waves and their associated instabilities (e.g., the Buneman instability, two-streaming instability, and the Weibel instability) are responsible for particle acceleration in relativistic pair jets. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic pair jet propagating through a pair plasma. Simulations show that the Weibel instability created in the collisionless shock accelerates particles perpendicular and parallel to the jet propagation direction. Simulation results show that this instability generates and amplifies highly nonuniform, small-scale magnetic fields, which contribute to the electron's transverse deflection behind the jet head. The "jitter' I radiation from deflected electrons can have different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants. The growth rate of the Weibel instability and the resulting particle acceleration depend on the magnetic field strength and orientation, and on the initial particle distribution function. In this presentation we explore some of the dependencies of the Weibel instability and resulting particle acceleration on the magnetic field strength and orientation, and the particle distribution function.

Nishikawa, K.-I.↗

NASA NTRS2010

The Second Swift BAT Gamma-Ray Burst Catalog

We present the second Swift Burst Alert Telescope (BAT) catalog of gamma-ray bursts (GRBs), which contains 476 bursts detected by the BAT between 2004 December 19 and 2009 December 21. This catalog (hereafter the BAT2 catalog) presents burst trigger time, location, 90% error radius, duration, fluence, peak flux, time-averaged spectral parameters and time-resolved spectral parametert:; measured by the BAT. In the correlation study of various observed parameters extracted from the BAT prompt emission data, we distinguish among long-duration GRBs (L-GRBs), short-duration GRBs (S-GRBs), and short-duration GRBs with extended emission (S-GRBs with E.E.) to investigate differences in the prompt emission properties. The fraction of L-GRBs, S-GRBs and S-GRBs with E.E. in the catalog are 89%, 8% and 2% respectively. We compare the BAT prompt emission properties with the BATSE, BeppoSAX and HETE-2 GRB samples. We also correlate the observed prompt emission properties with the redshifts for the GRBs with known redshift. The BAT T90 and T50 durations peak at 70 s and 30 s, respectively. We confirm that the spectra of the BAT S-GRBs are generally harder than those of the L-GRBs. The time-averaged spectra of the BAT S GRBs with E.E. are similar to those of the L-GRBs. Whereas, the spectra of the initial short spikes of the S-GRBs with E.E. are similar to those of the S-GRBs. We show that the BAT GRB samples are significantly softer than the BATSE bright GRBs, and that the time-averaged E obs/peak of the BAT GRBs peaks at 80 keV which is significantly lower energy than those of the BATSE sample which peak at 320 keV. The time-averaged spectral properties of the BAT GRB sample are similar to those of the HETE-2 GRB samples. By time-resolved spectral analysis, we find that 10% of the BAT observed photon indices are outside the allowed region of the synchrotron shock model. The observed durations of the BAT high redshift GRBs are not systematically longer than those of the moderate red shift GRBs. Furthermore, the observed spectra of the BAT high red shift GRBs are similar to or harder than the moderate red shift GRBs. The T90 and T50 distributions measured at the 140-220 keY band in the GRB rest frame form the BAT known redshift GRBs peak at 19 sand 8 s, respectively. We also provide an update on the status of the on-orbit BAT calibrations.

Barthelmy, S. D.↗

NASA NTRS2004

Estimating Basic Preliminary Design Performances of Aerospace Vehicles

Aerodynamics and Performance Estimation Toolset is a collection of four software programs for rapidly estimating the preliminary design performance of aerospace vehicles represented by doing simplified calculations based on ballistic trajectories, the ideal rocket equation, and supersonic wedges through standard atmosphere. The program consists of a set of Microsoft Excel worksheet subprograms. The input and output data are presented in a user-friendly format, and calculations are performed rapidly enough that the user can iterate among different trajectories and/or shapes to perform "what-if" studies. Estimates that can be computed by these programs include: 1. Ballistic trajectories as a function of departure angles, initial velocities, initial positions, and target altitudes; assuming point masses and no atmosphere. The program plots the trajectory in two-dimensions and outputs the position, pitch, and velocity along the trajectory. 2. The "Rocket Equation" program calculates and plots the trade space for a vehicle s propellant mass fraction over a range of specific impulse and mission velocity values, propellant mass fractions as functions of specific impulses and velocities. 3. "Standard Atmosphere" will estimate the temperature, speed of sound, pressure, and air density as a function of altitude in a standard atmosphere, properties of a standard atmosphere as functions of altitude. 4. "Supersonic Wedges" will calculate the free-stream, normal-shock, oblique-shock, and isentropic flow properties for a wedge-shaped body flying supersonically through a standard atmosphere. It will also calculate the maximum angle for which a shock remains attached, and the minimum Mach number for which a shock becomes attached, all as functions of the wedge angle, altitude, and Mach number.

Luz, Paul L.↗

NASA NTRSDate not supplied

Ab Initio Electronic Structure Calculations of CNN for CN Excitation Studies

The CN molecule is an important contributor to radiative heat flux in shock layers around vehicles entering Titan’s atmosphere. Current data for heavy particle (de)excitation rate coefficients of CN leads to uncertainties in the population of CN in its first and second excited states. This in turn leads to uncertainties in the radiative heat flux predicted by Computational Fluid Dynamics (CFD) simulations of Titan atmospheric entry. This work performs ab initio electronic structure calculations of the CNN complex to create Potential Energy Surfaces (PESs) that correlate to the ground and first and second excited states of CN. Specifically, the state combinations of CN(X,A,B) + N(4S𝑜) correlate to six states of CNN (three Quintet A” and three Triplet A”). Initial calculations of these states suggest that heavy particle (de)excitation of CN by N atoms is likely to proceed through collinear geometries on triplet surfaces. Complete PESs will show all of the reaction pathways in detail, and will be used in nonadiabatic dynamics calculations to evaluate improved rate coefficients and reduce uncertainty in the radiative heat flux during Titan entry.

Eric C Geistfeld↗

NASA NTRSDate not supplied

Ab Initio Electronic Structure Calculations of CNN for CN Excitation Studies

Eric Geistfeld↗

DOE OSTI2021

Analytic solutions for Asay foil trajectories with implications for ejecta source models and mass measurements

We consider the trajectory of an Asay foil ejecta diagnostic for scenarios where ejecta are produced at a singly shocked planar surface and fly ballistically through a perfect vacuum to the sensor. We do so by building upon a previously established mathematical framework derived for the analytic study of stationary sensors. First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source model. The result is an integrodifferential equation of motion for the foil trajectory. This equation yields an easily calculable closed-form implicit solution for the foil trajectory in instant-production scenarios. From there, we derive a boundary condition that particle velocity distributions must satisfy if their associated foil trajectories are to exhibit a smooth initial acceleration, as occurs in some experiments. This condition is identical to one derived previously from a consideration of piezoelectric voltage data obtained in similar experiments. We also compare techniques for inferring accumulated ejecta masses from foil trajectories, first by deriving the exact solution, and then by quantifying the error imposed by a frequently used approximate solution (both subject to the assumption of instantaneous ejecta production). Finally, we examine the common practice of presenting inferred cumulative ejecta masses as a function of implied ejecta velocity, establishing the conditions under which this methodology is most meaningful.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1972

Investigation of mounting discrete chip components for hybrid microelectronic applications.

In the assembly of hybrid microcircuits, passive and active discrete chip components are attached by epoxy cements and by solders. This study was initiated to determine the integrity of such attachments. Alumina substrates were subjected to a group of thermal and mechanical test environments defined by test methods in MIL-STD-883. Lot samples of substrates with assembly variations were subjected to separately applied testing and to serial testing. These test methods were applied sequentially to the same lot of substrates. Epoxy cements were generally satisfactory with respect to separate tests, although sequential tests severely degraded epoxy bond strengths of all types. Bond strengths to unglazed substrates were slightly superior to those of the same components on glazed types. Solder joints were vulnerable to catastrophic failure in several environments, especially temperature cycling and thermal shock. Vibration and impact shock also produced solder joint failures.

Caruso, S. V.↗

NASA NTRS1975

Time-dependent transonic flow solutions for axial turbomachinery

Three-dimensional unsteady transonic flow through an axial turbomachine stage is described in terms of a pair of two-dimensional formulations pertaining to orthogonal surfaces, namely, a blade-to-blade surface and a hub-to-casing surface. The resulting systems of nonlinear, inviscid, compressible equations of motion are solved by an explicit finite-difference technique. The blade-to-blade program includes the periodic interaction between rotor and stator blade rows. Treatment of the boundary conditions and of the blade slipstream motion by a characteristic type procedure is discussed in detail. Harmonic analysis of the acoustic far field produced by the blade row interaction, including an arbitrary initial transient, is outlined. Results from the blade-to-blade program are compared with experimental measurements of the rotating pressure field at the tip of a high-speed fan. The hub-to-casing program determines circumferentially averaged flow properties on a meridional plane. Blade row interactions are neglected in this formulation, but the force distributions over the entire blade surface for both the rotor and stator are obtained. Results from the hub-to-casing program are compared with a relaxation method solution for a subsonic rotor. Results are also presented for a quiet fan stage which includes transonic flow in both the rotor and stator and a normal shock in the stator.

Erdos, J.↗

NASA NTRS2011

DBD Plasma Actuators for Flow Control in Air Vehicles and Jet Engines - Simulation of Flight Conditions in Test Chambers by Density Matching

Dielectric Barrier Discharge (DBD) Plasma actuators for active flow control in aircraft and jet engines need to be tested in the laboratory to characterize their performance at flight operating conditions. DBD plasma actuators generate a wall-jet electronically by creating weakly ionized plasma, therefore their performance is affected by gas discharge properties, which, in turn, depend on the pressure and temperature at the actuator placement location. Characterization of actuators is initially performed in a laboratory chamber without external flow. The pressure and temperature at the actuator flight operation conditions need to be simultaneously set in the chamber. A simplified approach is desired. It is assumed that the plasma discharge depends only on the gas density, while other temperature effects are assumed to be negligible. Therefore, tests can be performed at room temperature with chamber pressure set to yield the same density as in operating flight conditions. The needed chamber pressures are shown for altitude flight of an air vehicle and for jet engines at sea-level takeoff and altitude cruise conditions. Atmospheric flight conditions are calculated from standard atmosphere with and without shock waves. The engine data was obtained from four generic engine models; 300-, 150-, and 50-passenger (PAX) aircraft engines, and a military jet-fighter engine. The static and total pressure, temperature, and density distributions along the engine were calculated for sea-level takeoff and for altitude cruise conditions. The corresponding chamber pressures needed to test the actuators were calculated. The results show that, to simulate engine component flows at in-flight conditions, plasma actuator should be tested over a wide range of pressures. For the four model engines the range is from 12.4 to 0.03 atm, depending on the placement of the actuator in the engine. For example, if a DBD plasma actuator is to be placed at the compressor exit of a 300 PAX engine, it has to be tested at 12.4 atm for takeoff, and 6 atm for cruise conditions. If it is to be placed at the low-pressure turbine, it has to be tested at 0.5 and 0.2 atm, respectively. These results have implications for the feasibility and design of DBD plasma actuators for jet engine flow control applications. In addition, the distributions of unit Reynolds number, Mach number, and velocity along the engine are provided. The engine models are non-proprietary and this information can be used for evaluation of other types of actuators and for other purposes.

Ashpis, David E.↗

DOE OSTI2024

High-Entropy Alloy R&D for Accelerator Beam Window Applications

High-Entropy Alloys are a class of novel material that can offer improved resistance to beam-induced radiation damage and thermal shock. Development of these new alloys to serve as beam windows in multi-megawatt accelerator target applications is ongoing at Fermilab. Currently we are investigating AlCoCrMnTiV alloy systems of 4-6 components for service as beam windows; these compositions are predicted by CALPHAD simulation to have a low density and single-phase BCC crystal structure. The microstructures of these systems are being studied by electron microscopy techniques such as energy dispersive X-ray spectroscopy (EDS) to determine elemental homogeneity and composition, electron backscatter diffraction (EBSD) to quantify grain structure and orientation, and transmission electron microscopy (TEM) to observe defect structures and precipitate formation; nanoindentation is used to probe microstructural mechanical properties. Initial bulk property characterization utilizes differential scanning calorimetry to quantify specific heat capacity (cp), dilatometry to determine the coefficient of thermal expansion (CTE), and time-domain thermoreflectance (TDTR) to measure thermal conductivity (K). A miniature tensile testing apparatus is also being developed to test tensile properties. Post-irradiation examination is currently ongoing for several of these compositions that have been irradiated by low-energy ions to damage levels and at a temperature relevant to beam window applications at future next-generation accelerator facilities. This talk will briefly describe the alloy design and synthesis before going into more depth covering microstructural pre-characterization, and post-irradiation examination results from low-energy ion irradiated specimens. This will be followed by the plans for alloy down selection and future prototypic proton irradiations.

43 PARTICLE ACCELERATORS↗

NASA NTRS1992

Cosmic-ray-modified supernova remnant shocks

The evolution of cosmic-ray-modified SNRs during the early Sedov phase is investigated using the time-dependent, two-fluid model for diffusive shock acceleration. Consideration is given to the sensitivity of net acceleration efficiency to model assumptions regarding density structure of the external medium as well as time dependence in the diffusion coefficient and the cosmic-ray adiabatic index. Of the model assumptions explored, the greatest sensitivity was found to time variations in the specific heat ratio to cosmic rays. It was found that if tau is greater than or approximately equal to few times 100, dynamically significant cosmic-ray pressures are produced early in the Sedov inefficient cosmic-ray accelerators. For the SNR models under consideration, the total energy channeled into the cosmic rays can be of order 10 percent of the initial blast energy for both the uniform density and inverse-square density interstellar medium models.

Jones, T. W.↗

NASA NTRS1997

UVI Auroral Observations During the January 10, 1997 Magnetic Cloud Event

Solar wind IMF and plasma conditions surrounding the January 10-11 magnetic cloud event provided very interesting observations relating to magnetospheric and ionospheric processes. Prior to the arrival of the magnetic cloud a shock front followed by abrupt swings in the IMF orientation were observed by the Wind spacecraft at about 100 Re upstream. The Polar Ultraviolet Imager (UVI) near apogee over the northern hemisphere recorded the encounter of the shock with the magnetosphere. Enhancement of dayside precipitation around noon MLT and progression of the enhancement along dawn and dusk flanks of the oval culminating in a very localized pseudo onset near midnight MLT were observed. During the following mainly northward IMF the polar cap region was the site of multiple sunward aligned arcs and curled arc structures that persisted until the IMF turned rapidly southward. While the IMF remained southward the polar cap cleared of arc structures and expanded, and the auroral oval became very thin. No substorms were observed for at least 25 minutes after the following northward turning contrary to what might be expected on the basis of recent reports of substorm initiation by northward turning of the IMF. These observations and others during the magnetic cloud event provide a clear case study of the effect of the solar wind on dayside precipitation, thickness of the boundary layer, magnetosphere-polar cap magnetic topology and sources of the polar cap precipitation, and triggering of substorms. These issues will be discussed along with the presentation of the UVI auroral observations and solar wind measurements.

Brittnacher, M. J.↗

NASA NTRS1993

Enhanced mixing of a rectangular supersonic jet by natural and induced screech

The influence of shear layer excitation on the mixing of supersonic rectangular jets was studied experimentally. Two methods of excitation were used to control the jet mixing. The first used the natural screech of an underexpanded supersonic jet from a converging nozzle. The level of the screech excitation was controlled by the use of a pair of baffles located to block the acoustic feedback path between the downstream shock structure and the nozzle lip. A screech level variation of over 30 decibels was achieved and the mixing was completely determined by the level of screech attained at the nozzle lip. The second form of self-excitation used the induced screech caused by obstacles or paddles located in the shear layers on either long side of the rectangular jet. With sufficient immersion of the paddles intense jet mixing occurred and large flapping wave motion was observed using a strobed focused Schlieren system. Each paddle was instrumented with a total pressure tap and strain gages to determine the pressure and drag force on the square cross-section paddle. Considerable drag was observed in this initial exploratory study. Future studies using alternate paddle geometries will be conducted to maximize jet mixing with minimum drag.

Rice, Edward J.↗

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↗