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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow

We consider causal higher order theories of relativistic viscous hydrodynamics in the limit of one-dimensional boost-invariant expansion and study the associated dynamical attractor. We obtain evolution equations for the inverse Reynolds number as a function of Knudsen number. The solutions of these equations exhibit attractor behavior which we analyze in terms of Lyapunov exponents using several different techniques. We compare the attractors of the second-order Müller-Israel-Stewart (MIS), transient Denicol-Niemi-Molnar-Rischke (DNMR), and third-order theories with the exact solution of the Boltzmann equation in the relaxation-time approximation. It is shown that for Bjorken flow the third-order theory provides a better approximation to the exact kinetic theory attractor than both MIS and DNMR theories. For three different choices of the time dependence of the shear relaxation rate we find analytical solutions for the energy density and shear stress and use these to study the attractors analytically. By studying these analytical solutions at both small and large Knudsen numbers we characterize and uniquely determine the attractors and Lyapunov exponents. While for small Knudsen numbers the approach to the attractor is exponential, strong power-law decay of deviations from the attractor and rapid loss of initial state memory are found even for large Knudsen numbers. Implications for the applicability of hydrodynamics in far-off-equilibrium situations are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Numerical Investigation of a Central Fuel Property Hypothesis under Boosted Spark-ignition Conditions

In the present work, a central fuel property hypothesis (CFPH), which states that fuel properties are sufficient to provide an indication of a fuel's performance irrespective of its chemical composition, was numerically investigated In particular, the objective of the study was to determine whether Research Octane Number (RON) and Motor Octane Number (MON), as fuel properties, are sufficient to describe a fuel's knock-limited performance under boosted spark-ignition (SI) conditions within the framework of CFPH. To this end, four TPRF-bioblendstock surrogates having different compositions but matched RON (= 98) and MON (= 90), were first generated using a non-linear regression model based on artificial neural network (ANN). Three unconventional bioblendstocks were included in the analysis: Di-isobutylene (DIB), Isobutanol and Anisole. Skeletal reaction mechanisms were generated for the TPRF-DIB, TPRF-isobutanol and TPRF-anisole blends from a detailed kinetic mechanism. Thereafter, numerical simulations were performed for the fuel surrogates using the skeletal mechanisms and a virtual cooperative fuel research (CFR) engine model, under a representative boosted operating condition. In the computational fluid dynamics (CFD) model, the G-equation approach was employed to track the turbulent flame front and the well-stirred reactor model combined with multi-zone binning strategy was used to capture auto-ignition in the end-gas. In addition, laminar flame speed was tabulated for each blend as a function of pressure, temperature and equivalence ratio a priori, and the lookup tables were used to prescribe laminar flame speed as an input to the G-equation model. Parametric spark timing sweeps were performed for each fuel blend to determine the corresponding knock-limited spark advance (KLSA) and 50% burn point (CA50) at the respective KLSA timing. It was observed that despite same RON, MON and engine operating conditions, the TPRF-Anisole blend exhibited markedly different knock-limited performance from the other three blends. This deviation from the octane index (DI) expectation was shown to be caused by differences in laminar flame speed (LFS). However; it was found that relatively large fuel-specific differences in LFS (> 20%) would have to be present to cause any appreciable deviation from the 01 framework. Otherwise, RON and MON would still be robust enough to predict a fuel's knock-limited performance.

Pal, Pinaki↗
DOE OSTI2024

Magnetic structure and properties of the compositionally complex perovskite (Y 0.2 La 0.2 Pr 0.2 Nd 0.2 Tb 0.2 )MnO 3

Large configurational disorder in compositionally complex ceramics can lead to unique functional properties that deviate from traditional rules of alloy mixing. In recent years, compositionally complex oxides (CCOs) have shown intriguing magnetic behavior including long-range order, enhanced magnetic exchange couplings, and mixed phase magnetic structures. This work focuses on how large local spin disorder affects magnetic ordering in a CCO. Specifically, we investigated the A-site alloyed perovskite, (Y 0.2 La 0.2 Pr 0.2 Nd 0.2 Tb 0.2 )MnO 3 , or (5A)MnO 3 , using a combination of bulk magnetometry, synchrotron X-ray diffraction, and temperature-dependent neutron diffraction. The five A-site ions have an average spin and ionic radius nearly equal to that of Nd 3+ ions, which minimizes structural distortions and allows for an understanding of the local spin disorder effects through a direct comparison with NdMnO 3 . Our magnetometry data show that (5A)MnO 3 exhibits two distinct phase transitions associated with the A-site and B-site sublattices, as seen in NdMnO 3 , as well as the presence of domain pinning and exchange bias at low temperature, suggesting a mixed phase magnetic ground state, as seen in other magnetic CCOs. Neutron powder diffraction shows clear long-range antiferromagnetic ordering below 67 K and refines to a Pn'ma' magnetic structure at low temperature, in excellent agreement with the well-studied behavior of NdMnO 3 . The two most notable differences in (5A)MnO 3 magnetism apparent from our data are a slight suppression of the B-site ordering temperature, which is explained by a smaller Mn–O–Mn bond angle in (5A)MnO 3 than NdMnO 3 , and the presence of a magnetic susceptibility transition above the B-site ordering, which could indicate the formation of a cluster glass but requires further study. Finally, this work demonstrates a general method of isolated investigation of size and spin disorder in CCOs and motivates future work using local structure probes to better understand the effects of nanoscale clustering and local spin disorder in magnetic CCOs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Robust supermoiré pattern in large-angle single-twist bilayers

Forming long-wavelength moiré superlattices in van der Waals bilayers that have a small-angle twist between the two layers has been a key approach for creating moiré flat bands. However, for small twist angles, strong lattice reconstruction creates domain walls and other forms of disorder in the moiré pattern, posing considerable challenges for engineering such platforms. At large twist angles, the lattices are more rigid, but it is difficult to produce flat bands in shorter-wavelength moiré superlattices. Here, in this study, we introduce an approach for tailoring robust supermoiré structures in bilayers of transition-metal dichalcogenides using only a single twist near a commensurate angle. Structurally, we show the spontaneous formation of a periodic arrangement of three inequivalent commensurate moiré stackings, where the angle deviation from the commensurate angle determines the periodicity. Electronically, we reveal a large set of van Hove singularities that indicate strong band hybridization, leading to flat bands near the valence band maximum. Our study extends the study of the interplay among band topology, quantum geometry and moiré superconductivity to the large twist angle regime.

electronic properties and materials↗
DOE OSTI2014

Interior micro-CT with an offset detector

Purpose: The size of field-of-view (FOV) of a microcomputed tomography (CT) system can be increased by offsetting the detector. The increased FOV is beneficial in many applications. All prior investigations, however, have been focused to the case in which the increased FOV after offset-detector acquisition can cover the transaxial extent of an object fully. Here, the authors studied a new problem where the FOV of a micro-CT system, although increased after offset-detector acquisition, still covers an interior region-of-interest (ROI) within the object. Methods: An interior-ROI-oriented micro-CT scan with an offset detector poses a difficult reconstruction problem, which is caused by both detector offset and projection truncation. Using the projection completion techniques, the authors first extended three previous reconstruction methods from offset-detector micro-CT to offset-detector interior micro-CT. The authors then proposed a novel method which combines two of the extended methods using a frequency split technique. The authors tested the four methods with phantom simulations at 9.4%, 18.8%, 28.2%, and 37.6% detector offset. The authors also applied these methods to physical phantom datasets acquired at the same amounts of detector offset from a customized micro-CT system. Results: When the detector offset was small, all reconstruction methods showed good image quality. At large detector offset, the three extended methods gave either visible shading artifacts or high deviation of pixel value, while the authors’ proposed method demonstrated no visible artifacts and minimal deviation of pixel value in both the numerical simulations and physical experiments. Conclusions: For an interior micro-CT with an offset detector, the three extended reconstruction methods can perform well at a small detector offset but show strong artifacts at a large detector offset. When the detector offset is large, the authors’ proposed reconstruction method can outperform the three extended reconstruction methods by suppressing artifacts and maintaining pixel values.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Lyα emitter galaxies at z ∼ 2.8 in the extended Chandra Deep Field South. I. Tracing the large-scale structure via Lyα imaging

We present a narrowband survey with three adjacent filters for z = 2.8–2.9 Lyman alpha (Lyα) emitter (LAE) galaxies in the Extended Chandra Deep Field South (ECDFS), along with spectroscopic follow-up. With a complete sample of 96 LAE candidates in the narrowband NB466, we confirm the large-scale structure at z ∼ 2.8 suggested by previous spectroscopic surveys. Compared to the blank field detected with the other two narrowband filters NB470 and NB475, the LAE-density excess in NB466 (900 arcmin{sup 2}) is ∼ 6.0 ± 0.8 times the standard deviation expected at z ∼ 2.8, assuming a linear bias of 2. The overdense large-scale structure in NB466 can be decomposed into four protoclusters, whose overdensities (each within an equivalent comoving volume 15{sup 3} Mpc{sup 3}) relative to the blank field (NB470+NB475) are in the range of 4.6–6.6. These four protoclusters are expected to evolve into a Coma-like cluster (M ≥ 10{sup 15} M {sub ⊙}) at z ∼ 0. We also investigate the various properties of LAEs at z = 2.8–2.9 and their dependence on the environment. The average star formation rates derived from the Lyα, rest-frame UV, and X-ray bands are ∼4, 10, and <16 M {sub ⊙} yr{sup −1}, respectively, implying a Lyα escape fraction of 25% ≲ f{sub ESC}{sup Lyα} ≲ 40% and a UV continuum escape fraction of f{sub ESC}{sup UV,cont} ≳ 62% for LAEs at z ∼ 2.8. The Lyα photon density calculated from the integrated Lyα luminosity function in the overdense field (NB466) is ∼50% higher than that in the blank field (NB470+NB475), and more bright LAEs are found in the overdense field. The three brightest LAEs, including a quasar at z = 2.81, are all detected in the X-ray band and in NB466. These three LAE-active galactic nuclei contribute an extra 20%–30% Lyα photon density compared to other LAE galaxies. Furthermore, we find that LAEs in overdense regions have larger equivalent width values, bluer U − B and V − R (∼2–3σ) colors compared with those in lower density regions, indicating that LAEs in overdense regions are younger and possible less dusty. We conclude that the structure at z ∼ 2.8 in the ECDFS field is a very significant and rare density peak similar to the SSA22 protocluster, and narrowband imaging is an efficient method of detecting and studying such structures in the high-z universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

The LMC geometry and outer stellar populations from early DES data

The Dark Energy Camera has captured a large set of images as part of Science Verification (SV) for the Dark Energy Survey. The SV footprint covers a large portion of the outer Large Magellanic Cloud (LMC), providing photometry 1.5 magnitudes fainter than the main sequence turn-off of the oldest LMC stellar population. We derive geometrical and structural parameters for various stellar populations in the LMC disc. For the distribution of all LMC stars, we find an inclination of i = –38.14°±0.08° (near side in the North) and a position angle for the line of nodes of θ₀ = 129.51°±0.17°. We find that stars younger than ~4 Gyr are more centrally concentrated than older stars. Fitting a projected exponential disc shows that the scale radius of the old populations is R >4Gyr = 1.41 ± 0.01 kpc, while the younger population has R <4Gyr = 0.72 ± 0.01 kpc. However, the spatial distribution of the younger population deviates significantly from the projected exponential disc model. The distribution of old stars suggests a large truncation radius of R t = 13.5 ± 0.8 kpc. If this truncation is dominated by the tidal field of the Galaxy, we find that the LMC is ≃24 +9 –6 times less massive than the encircled Galactic mass. By measuring the Red Clump peak magnitude and comparing with the best-fit LMC disc model, we find that the LMC disc is warped and thicker in the outer regions north of the LMC centre. As a result, our findings may either be interpreted as a warped and flared disc in the LMC outskirts, or as evidence of a spheroidal halo component.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Quantum and classical behavior in interacting bosonic systems

It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories, especially on time scales longer than the dynamical relaxation time. Recently there have been claims that the quantum theory deviates spectacularly from the classical theory on this time scale, even if the occupancy numbers are extremely large. Furthermore, it is claimed that the quantum theory quickly thermalizes while the classical theory does not. The evidence for these claims comes from noticing a spectacular difference in the time evolution of expectation values of quantum operators compared to the classical micro-state evolution. If true, this would have dramatic consequences for many important phenomena, including laboratory studies of interacting BECs, dark matter axions, preheating after inflation, etc. In this work we critically examine these claims. We show that in fact the classical theory can describe the quantum behavior in the high occupancy regime, even when interactions are large. The connection is that the expectation values of quantum operators in a single quantum micro-state are approximated by a corresponding classical ensemble average over many classical micro-states. Furthermore, by the ergodic theorem, a classical ensemble average of local fields with statistical translation invariance is the spatial average of a single micro-state. So the correlation functions of the quantum and classical field theories of a single micro-state approximately agree at high occupancy, even in interacting systems. Furthermore, both quantum and classical field theories can thermalize, when appropriate coarse graining is introduced, with the classical case requiring a cutoff on low occupancy UV modes. We discuss applications of our results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Quantum Versus Classical Switching Dynamics of Driven Dissipative Kerr Resonators

Here, we report a first-principles study of the driven dissipative dynamics for Kerr oscillators in the mesoscopic regime. This regime is characterized by large Kerr nonlinearity, realized here using the nonlinear kinetic inductance of a large array of Josephson junctions. The experimentally measured nonlinear resonance lineshapes of the junction array modes show significant deviations from steady-state numerical predictions, and necessitate time-dependent numerical simulations indicative of strong measurement-induced dephasing in the system arising from the large cross-Kerr effect between array modes. Analytical and numerical calculations of switching rate corroborate this by showing the emergence of a slow time scale, which is much longer than the linear decay rate and is set by fluctuation-induced switching times in the bistable regime. Furthermore, our analysis shows that the usual quantum-activated escape treatment is inadequate for prediction of the switching rates at large frequency shifts caused by strong nonlinearities, necessitating a quantum treatment that utilizes the full system Liouvillian. Based on our analysis, we identify a universal crossover parameter that delineates the regimes of validity of semiclassical and quantum descriptions, respectively. Our work shows how dynamical switching effects in strongly nonlinear systems provide a platform to study quantum-to-classical transitions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Review of Onsite Temperature and Solar Forecasting Models to Enable Better Building Design and Operations

Advanced building controls and energy optimization for new constructions and retrofits rely on accurate weather data. Traditionally, most studies utilize airport weather information as the decision inputs. However, most buildings are in environments that are quite different than those at the airport miles away. Tree cover, adjacent buildings, and micro-climate effects caused by the larger surrounding area can all yield deviations in air temperature, humidity, solar irradiance, and wind that are large enough to influence design and operation decisions. In order to overcome this challenge, there are many prior studies on developing weather forecasting algorithms from micro-to meso-scales. Additionally, this paper reviews and complies knowledge on common weather data resources, data processing methodologies and forecasting techniques of weather information. Commonly used statistical, machine learning and physical-based models are discussed and presented as two major categories: deterministic forecasting and probabilistic forecasting. Finally, evaluation metrics for forecasting errors are listed and discussed.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2019

Frankenstein’s ROMster: Avoiding pitfalls of reduced-order model development

Reduced-order models (ROMs) are a widely used and powerful approach to reducing the complexity of predictive physics-based numerical simulations for a wide range of applications, including electronics and fluid mechanics such as geologic CO 2 sequestration (GCS). ROMs are critical for optimization, sensitivity analysis, model calibration and uncertainty quantification where full-order models cannot be feasibly executed many times. Traditional approaches generate a single ROM for each simulated response (e.g., CO 2 injection rates, pH changes) based on a set of training simulations. Here, we demonstrate that a single ROM can display excellent overall predictive statistics, but have predictions that dramatically and unacceptably deviate from simulator responses especially when the response variable has a large range (i.e., vary over multiple orders of magnitude). For example, we show that a traditional statistically-high-performing GCS ROM (coefficient of determination R 2 of 0.99) can have average absolute relative errors of over 200%. To address this, we propose a new and novel approach where a set of sub-ROMs are generated to overcome the potential pitfalls in traditional single ROM development. The effectiveness of the proposed approach—the ROMster framework—is demonstrated using a case study of predicted CO 2 injection rates for GCS. We find our approach is a robust and general framework for ROM development, reducing the average “error” from 200% to only 4% in our case study.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Constraint on the matter–antimatter symmetry-violating phase in neutrino oscillations

The charge-conjugation and parity-reversal (CP) symmetry of fundamental particles is a symmetry between matter and antimatter. Violation of this CP symmetry was first observed in 1964, and CP violation in the weak interactions of quarks was soon established. Sakharov proposed that CP violation is necessary to explain the observed imbalance of matter and antimatter abundance in the Universe. Yet, CP violation in quarks is too small to support this explanation. So far, CP violation has not been observed in non-quark elementary particle systems. It has been shown that CP violation in leptons could generate the matter–antimatter disparity through a process called leptogenesis. Leptonic mixing, which appears in the standard model’s charged current interactions, provides a potential source of CP violation through a complex phase δ CP , which is required by some theoretical models of leptogenesis. This CP violation can be measured in muon neutrino to electron neutrino oscillations and the corresponding antineutrino oscillations, which are experimentally accessible using accelerator-produced beams as established by the Tokai-to-Kamioka (T2K) and NOvA experiments. Until now, the value of δ CP has not been substantially constrained by neutrino oscillation experiments. Here we report a measurement using long-baseline neutrino and antineutrino oscillations observed by the T2K experiment that shows a large increase in the neutrino oscillation probability, excluding values of δ CP that result in a large increase in the observed antineutrino oscillation probability at three standard deviations (3σ). The 3σ confidence interval for δ CP , which is cyclic and repeats every 2π, is [-3.41, -0.03] for the so-called normal mass ordering and [-2.54, -0.32] for the inverted mass ordering. Our findings indicate CP violation in leptons and our method enables sensitive searches for matter–antimatter asymmetry in neutrino oscillations using accelerator-produced neutrino beams. Future measurements with larger datasets will test whether leptonic CP violation is larger than the CP violation in quarks.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Inverse design of equilibrium cluster fluids applied to a physically informed model

Inverse design strategies have proven highly useful for the discovery of interaction potentials that prompt self-assembly of a variety of interesting structures. However, often the optimized particle interactions do not have a direct relationship to experimental systems. In this work, we show that Relative Entropy minimization is able to discover physically meaningful parameter sets for a model interaction built from depletion attraction and electrostatic repulsion that yield self-assembly of size-specific clusters. Here, we then explore the sensitivity of the optimized interaction potentials with respect to deviations in the underlying physical quantities, showing that clustering behavior is largely preserved even as the optimized parameters are perturbed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Non-perturbative and self-consistent models of neutron stars in R-squared gravity

In the present paper we investigate non-perturbatively and self-consistently the structure of neutron stars in R-squared gravity by simultaneously solving the interior and exterior problem. The mass-radius relations are obtained for several equations of state and for wide range of the R-squared gravity parameter a. Even though the deviation from general relativity for nonzero values of a can be large, they are still comparable with the variations due to different modern realistic equations of state. That is why the current observations of the neutron star masses and radii alone can not put constraints on the value of the parameter a. We also compare our results with those obtained within the perturbative method and we discuss the differences between them.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Role of the likelihood for elastic scattering uncertainty quantification

In the last decade, uncertainty quantification (UQ) for optical model potentials (OMPs) has become a focal point for nuclear reaction theory, and several competing approaches for OMP UQ have recently been developed. Here, we clarify recent efforts to compare frequentist and Bayesian approaches in the context of OMP UQ [G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019)]. We replicate a portion of that OMP UQ study but use independent statistical tools. Specifically, we compare two methods for OMP parameter inference from elastic scattering data: the Levenberg-Marquardt algorithm for χ 2 minimization on one hand and Markov chain Monte Carlo (MCMC) sampling on the other. Separately, we assess the common practice of using a renormalized likelihood (χ 2 /N), N being the number of data points, instead of the canonical weighted-least-squares likelihood (χ 2 ), as a way of accounting for unknown data correlations. Here, we show that for a generic linear model and for a five-parameter OMP analysis, frequentist and uniform-prior Bayesian approaches recover the same optimum and uncertainty estimates—not systematically larger uncertainties for the Bayesian approach, as was concluded in G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019). Further, we show that if an additional, near-degenerate parameter is introduced into the same OMP analysis such that the parameter posterior becomes non-Gaussian, then covariance-based estimates of uncertainty become unreliable. Finally, we show that regardless of optimization approach, if χ 2 /N is used for the likelihood, the resulting parametric uncertainties increase by $\sqrt{N}$, and that this is responsible for the conclusions drawn in the revisited study. Based on our replication results, we find that a fortuitous cancellation of unreported errors and the renormalization factor can lead to improvement in empirical coverages, as was the case in the original comparative study. We emphasize that developing and applying a realistic likelihood function is an essential task in a UQ analysis, and that several recent UQ studies that employed a renormalized likelihood (i.e., including a 1/N factor) may have yielded unrealistically large uncertainties for elastic-scattering observables. If the parameter posterior deviates from multivariate-normal, a sampling-based approach like MCMC has a clear advantage over methods that assume the Laplace approximation holds. We note that empirical coverage can serve as an important internal check for the analyst whose model or data may have additional, unaccounted-for uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

THE EFFECTS OF ANGULAR MOMENTUM ON HALO PROFILES

The near universality of DM halo density profiles provided by N -body simulations proved to be robust against changes in total mass density, power spectrum, and some forms of initial velocity dispersion. Here we study the effects of coherently spinning up an isolated DM-only progenitor on halo structure. Halos with spins within several standard deviations of the simulated mean ( λ ≲ 0.20) produce profiles with negligible deviations from the universal form. Only when the spin becomes quite large ( λ ≳ 0.20) do departures become evident. The angular momentum distribution also exhibits a near universal form, which is also independent of halo spin up to λ ≲ 0.20. A correlation between these epidemic profiles and the presence of a strong bar in the virialized halo is also observed. These bar structures bear resemblance to the radial orbit instability in the rotationless limit.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

STAR FORMATION RELATIONS IN THE MILKY WAY

The relations between star formation and properties of molecular clouds (MCs) are studied based on a sample of star-forming regions in the Galactic Plane. Sources were selected by having radio recombination lines to provide identification of associated MCs and dense clumps. Radio continuum emission and mid-infrared emission were used to determine star formation rates (SFRs), while {sup 13}CO and submillimeter dust continuum emission were used to obtain the masses of molecular and dense gas, respectively. We test whether total molecular gas or dense gas provides the best predictor of SFR. We also test two specific theoretical models, one relying on the molecular mass divided by the free-fall time, the other using the free-fall time divided by the crossing time. Neither is supported by the data. The data are also compared to those from nearby star-forming regions and extragalactic data. The star formation “efficiency,” defined as SFR divided by mass, spreads over a large range when the mass refers to molecular gas; the standard deviation of the log of the efficiency decreases by a factor of three when the mass of relatively dense molecular gas is used rather than the mass of all of the molecular gas.

79 ASTRONOMY AND ASTROPHYSICS↗