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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.

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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Space environmental effects on LDEF composites: A leading edge coated graphite epoxy panel

The electronics module cover for the leading edge (Row D 9) experiment M0003-8 was fabricated from T300 graphite/934 epoxy unidirectional prepreg tape in a (O(sub 2), +/- 45, O(sub 2), +/- 45, 90, 0)(sub s) layup. This 11.75 in x 16.75 in panel was covered with thermal control coatings in three of the four quadrants with the fourth quadrant uncoated. The composite panel experienced different thermal cycling extremes in each quadrant due to the different optical properties of the coatings and bare composite. The panel also experienced ultraviolet (UV) and atomic oxygen (AO) attack as well as micrometeoroid and space debris impacts. An AO reactivity of 0.99 x 10(exp -24) cm(sup 3)/atom was calculated for the bare composite based on thickness loss. The white urethane thermal control coatings (A276 and BMS 1060) prevented AO attack of the composite substrate. However, the black urethane thermal control coating (Z306) was severely eroded by AO, allowing some AO attack of the composite substrate. An interesting banding pattern on the AO eroded bare composite surface was investigated and found to match the dimensions of the graphite fiber tow widths as prepregged. Also, erosion depths were greater in the darker bands. Five micrometeoroid/space debris impacts were cross sectioned to investigate possible structural damage as well as impact/AO interactions. Local crushing and delaminations were found to some extent in all of the impacts. No signs of coating undercutting were observed despite the extensive AO erosion patterns seen in the exposed composite material at the impact sites. An extensive microcrack study was performed on the panel along with modeling of the thermal environment to estimate temperature extremes and thermal shock. The white coated composite substrate displayed almost no microcracking while the black coated and bare composite showed extensive microcracking. Significant AO erosion was seen in many of the cracks in the bare composite.

George, Pete E.↗
NASA NTRS1983

Four-dimensional modulation and coding: An alternate to frequency-reuse

Four dimensional modulation as a means of improving communication efficiency on the band-limited Gaussian channel, with the four dimensions of signal space constituted by phase orthogonal carriers (cos omega sub c t and sin omega sub c t) simultaneously on space orthogonal electromagnetic waves are discussed. "Frequency reuse' techniques use such polarization orthogonality to reuse the same frequency slot, but the modulation is not treated as four dimensional, rather a product of two-d modulations, e.g., QPSK. It is well known that, higher dimensionality signalling affords possible improvements in the power bandwidth sense. Four-D modulations based upon subsets of lattice-packings in four-D, which afford simplification of encoding and decoding are described. Sets of up to 1024 signals are constructed in four-D, providing a (Nyquist) spectral efficiency of up to 10 bps/Hz. Energy gains over the reuse technique are in the one to three dB range t equal bandwidth.

Wilson, S. G.↗
NASA NTRS1984

Four-dimensional modulation and coding - An alternate to frequency-reuse

Four dimensional modulation as a means of improving communication efficiency on the band-limited Gaussian channel, with the four dimensions of signal space constituted by phase orthogonal carriers (cos omega sub c t and sin omega sub c t) simultaneously on space orthogonal electromagnetic waves are discussed. 'Frequency reuse' techniques use such polarization orthogonality to reuse the same frequency slot, but the modulation is not treated as four dimensional, rather a product of two-D modulations, e.g., QPSK. It is well known that, higher dimensionality signalling affords possible improvements in the power bandwidth sense. Four-D modulations based upon subsets of lattice-packings in four-D, which afford simplification of encoding and decoding are described. Sets of up to 1024 signals are constructed in four-D, providing a (Nyquist) spectral efficiency of up to 10 bps/Hz. Energy gains over the reuse technique are in the one to three dB range t equal bandwidth.

Wilson, S. G.↗
NASA NTRS1989

Space station Simulation Computer System (SCS) study for NASA/MSFC. Volume 4: Conceptual design report

The Simulation Computer System (SCS) is the computer hardware, software, and workstations that will support the Payload Training Complex (PTC) at Marshall Space Flight Center (MSFC). The PTC will train the space station payload scientists, station scientists, and ground controllers to operate the wide variety of experiments that will be onboard the Space Station Freedom. In the first step of this task, a methodology was developed to ensure that all relevant design dimensions were addressed, and that all feasible designs could be considered. The development effort yielded the following method for generating and comparing designs in task 4: (1) Extract SCS system requirements (functions) from the system specification; (2) Develop design evaluation criteria; (3) Identify system architectural dimensions relevant to SCS system designs; (4) Develop conceptual designs based on the system requirements and architectural dimensions identified in step 1 and step 3 above; (5) Evaluate the designs with respect to the design evaluation criteria developed in step 2 above. The results of the method detailed in the above 5 steps are discussed. The results of the task 4 work provide the set of designs which two or three candidate designs are to be selected by MSFC as input to task 5-refine SCS conceptual designs. The designs selected for refinement will be developed to a lower level of detail, and further analyses will be done to begin to determine the size and speed of the components required to implement these designs.

Source record↗
DOE OSTI2022

Canted antiferromagnetic phases in the candidate layered Weyl material EuMnSb 2

EuMnSb 2 is a candidate topological material which can be tuned towards a Weyl semimetal, but there are differing reports for its antiferromagnetic (AFM) phases. The coupling of bands dominated by pure Sb layers hosting topological fermions to Mn and Eu magnetic states provides a potential path to tune the topological properties. In this study we present single-crystal neutron diffraction, magnetization, and heat-capacity data as well as polycrystalline 151 Eu Mössbauer data which show that three AFM phases exist as a function of temperature, and we present a detailed analysis of the magnetic structure in each phase. The Mn magnetic sublattice orders into a C-type AFM structure below T N Mn = 323 (1) K with the ordered Mn magnetic moment μ Mn lying perpendicular to the layers. AFM ordering of the Eu sublattice occurs below T N Eu1 = 23 (1) K with the ordered Eu magnetic moment μ Eu canted away from the layer normal and μ Mn retaining its higher temperature order. μ Eu is ferromagnetically aligned within each Eu layer but exhibits a complicated AFM layer stacking. Both of these higher-temperature phases are described by magnetic space group (MSG) $\mathcal{Pn'm'a'}$ with the chemical and magnetic unit cells having the same dimensions. Cooling below T N Eu2 =9 (1) K reveals a third AFM phase where μ Mn remains unchanged but μ Eu develops an additional substantial in-plane canting. This phase has MSG $\mathcal{P11}$ $\frac{2_1}{a′}$. We also find some evidence of short-range magnetic correlations associated with the Eu between 12 K≲ T≲ 30 K . Using the determined magnetic structures, we postulate the signs of nearest-neighbor intralayer and interlayer exchange constants and the magnetic anisotropy within a general Heisenberg model. We then discuss implications of the various AFM states in EuMnSb 2 and their potential for tuning topological properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Theory of criticality for quantum ferroelectric metals

A variety of compounds, for example, doped paraelectrics and polar metals, exhibit both ferroelectricity and correlated electronic phenomena such as low-density superconductivity and anomalous transport. Characterizing such properties is tied to understanding the quantum dynamics of inversion symmetry breaking in the presence of itinerant electrons. Here, we present a comprehensive analysis of the properties of a metal near a quantum critical transition to a ferroelectric state, in both two and three dimensions. In this study, starting from a minimal model of electrons coupled to a transverse polar phonon via a Rashba-type spin-orbit interaction, we compute the dynamical response of both electrons and phonons. We find that the system can evince both Fermi and non-Fermi liquid phases, as well as enhanced pairing in both singlet and triplet channels. Furthermore, we systematically compute corrections to one-loop theory and find a tendency to quantum order-by-disorder, leading to a phase diagram that can include second-order, first-order, and finite-momentum phase transitions. Finally, we show that the entire phase diagram can be controlled via application of external strain, either compressive or volume-preserving. Our results provide a map of the dynamical and thermodynamical phase space of quantum ferroelectic metals, which can serve in characterizing existing materials and in seeking applications for quantum technologies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1987

COFS 3 multibody dynamics and control technology

One of the results from the model definition study showed that the maximum scale factor for a replica model is .25. This is dictated by the fixed dimensions of the Large Spacecraft Lab. Replica scaling laws were applied to simplified theoretical models of joints and the joint/tube/joint system. The practical interpretation of the results for the specific Space Station configuration under study yielded a number of conclusions which are briefly discussed. Detailed suspension analyses were conducted to evaluate the ability of the suspended scale model to emulate the dynamic behavior of the free-free Space Station. The results indicated only a slight preference for smaller scales. A candidate erectable Space Station joint was fabricated at full scale, 1/4 scale and 1/3 scale in order to assess the comparability of the scaled joints to the full scale behavior. Another important question discussed is how well the inherent damping characteristics of the scaled joints compare to those of the full scale joint. The preliminary definition study yielded three separate scale factor recommendations for the scale model.

Letchworth, Robert↗
DOE OSTI2024

Gauge-invariant renormalization of four-quark operators

We study the renormalization of four-quark operators in one-loop perturbation theory. We employ a coordinate-space gauge-invariant renormalization scheme (GIRS), which can be advantageous compared to other schemes, especially in nonperturbative lattice investigations. From our perturbative calculations, we extract the conversion factors between GIRS and the modified minimal subtraction scheme ( MS ¯ ) at the next-to-leading order. As a by-product, we also obtain the relevant anomalous dimensions in the GIRS scheme. A formidable issue in the study of the four-quark operators is that operators with different Dirac matrices mix among themselves upon renormalization. We focus on both parity-conserving and parity-violating four-quark operators, which change flavor numbers by two units ( Δ F = 2 ). The extraction of the conversion factors entails the calculation of two-point Green’s functions involving products of two four-quark operators, as well as three-point Green’s functions with one four-quark and two bilinear operators. The significance of our results lies in their potential to refine our understanding of QCD phenomena, offering insights into the precision of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and shedding light on the nonperturbative treatment of complex mixing patterns associated with four-quark operators. Published by the American Physical Society 2024

Constantinou, M. (ORCID:0000000269881745)↗
DOE OSTI2020

Anomalies in the space of coupling constants and their dynamical applications I

It is customary to couple a quantum system to external classical fields. One application is to couple the global symmetries of the system (including the Poincaré symmetry) to background gauge fields (and a metric for the Poincaré symmetry). Failure of gauge invariance of the partition function under gauge transformations of these fields reflects ’t Hooft anomalies. It is also common to view the ordinary (scalar) coupling constants as background fields, i.e. to study the theory when they are spacetime dependent. We will show that the notion of ’t Hooft anomalies can be extended naturally to include these scalar background fields. Just as ordinary ’t Hooft anomalies allow us to deduce dynamical consequences about the phases of the theory and its defects, the same is true for these generalized ’t Hooft anomalies. Specifically, since the coupling constants vary, we can learn that certain phase transitions must be present. We will demonstrate these anomalies and their applications in simple pedagogical examples in one dimension (quantum mechanics) and in some two, three, and four-dimensional quantum field theories. An anomaly is an example of an invertible field theory, which can be described as an object in (generalized) differential cohomology. We give an introduction to this perspective. Also, we use Quillen’s superconnections to derive the anomaly for a free spinor field with variable mass. In a companion paper we will study four-dimensional gauge theories showing how our view unifies and extends many recently obtained results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1995

Low-energy ion acceleration at quasi-perpendicular shocks: Transverse diffusion

The problem of ion injection and acceleration at quasi perpendicular shocks has been the subject of some debate over the past two decades. It is widely known that these shocks efficiently accelerate particles that are well in the high-energy tail of the distribution. However, the issue of injection, or the acceleration of low-energy ions, has yet to reach a consensus. The fundamental issue is whether there is enough diffusion normal to the magnetic field for the particles to remain near the shock. Since transverse diffusion is a physical process that is not well understood in space plasmas, this is an important, and difficult issue to address. In this report, we will investigate the ion injection problem by performing test particle orbit integrations using synthesized turbulent fields. These fields are fully three-dimensional so that transverse diffusion is possible (cross-field diffusion is not possible in geometries where the electromagnetic fields are less than three dimensional). The synthesized fields are produced by superimposing a three-dimensional wave field on a background field. For completeness, we will compare the results from this model with the more well-established theories, such as the diffusive approximation and scatter-free shock drift acceleration. We will also compare these results with other numerical simulation techniques such as the well known hybrid simulation, and other test-particle calculations in which the shock fields are specified to have less than three dimensions. We will also discuss some recent relevant observations and how these compare with our results.

Giacalone, J.↗
NASA NTRS1989

Solar flare gamma-ray and hard x ray imaging with the GRID-on-a-balloon

A primary scientific objective for solar flare research during the rapidly approaching maximum in solar activity is the imaging of gamma-ray and hard x ray sources of solar flare emissions. These goals will be pursued by the Gamma Ray Imaging Device (GRID) instrument, one of three instruments recently selected for NASA's Max '91 Solar Balloon Program. The GRID instrument is based on the technique of Fourier transform imaging and utilizes scanning modulation grid collimator optics to provide full-Sun imaging with 1.9-arcsecond resolution over the energy range from 20 to 700 keV at time resolutions from 0.1 to 2 s. The GRID telescope will employ 32 subcollimators, each composed of a matched pair of high-Z collimator grids separated by 5.2 meters and a phoswich scintillation spectrometer detector having no spatial resolution. The subcollimators and integrally-mounted fine aspect system are contained within a telescope canister which will be pointed to 0.1 degree accuracy and cyclically scanned to produce source modulation. The 32 subcollimators provide a uniform distribution of grid slit orientations and a logarithmic distribution of slit spacings corresponding to angular dimensions of 1.9 arcseconds to several arcminutes. The instrument is several orders of magnitude more sensitive than the HXIS instrument on the Solar Maximum Mission (SMM) and nearly 10 times more sensitive than any similar instrument scheduled to fly during the next solar maximum. The payload, designed for long-duration high-altitude balloon capability, is scheduled for its first science flight (8 to 14 days duration) from the Antarctic in January of 1992.

Orwig, Larry E.↗
NASA NTRS2011

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

Three heliophysics missions -- the Advanced Composition Explorer (ACE), Solar Heliospheric Observatory (SOHO), and the Global Geoscience WIND -- have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center (GSFC). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 36 targeted lunar flybys with excursions to both L1 and L2 before its final insertion in L1 orbit. A figure depicts the orbits of the three spacecraft, showing projections of the orbits onto the orthographic planes of a solar rotating ecliptic frame of reference. The SOHO orbit is a quasi-periodic halo orbit, where the frequencies of the in-plane and out-of-plane motions are practically equal. Such an orbit is seen to repeat itself with a period of approximately 178 days. For ACE and WIND, the frequencies of the in-plane and out-of-plane motions are unequal, giving rise to the characteristic Lissajous motion. ACE's orbit is of moderately small amplitude, whereas WIND's orbit is a large-amplitude Lissajous of dimensions close to those of the SOHO halo orbit. As motion about the collinear points is inherently unstable, stationkeeping maneuvers are necessary to prevent orbital decay and eventual escape from the L1 region. Though the three spacecraft are dissimilar (SOHO is a 3-axis stabilized Sun pointer, WIND is a spin-stabilized ecliptic pole pointer, and ACE is also spin-stabilized with its spin axis maintained between 4 and 20 degrees of the Sun), the stationkeeping technique for the three is fundamentally the same. The technique consists of correcting the energy of the orbit via a delta-V directed parallel or anti-parallel to the Spacecraft-to-Sun line. SOHO achieves this using thrusters oriented in line with the solar direction. WIND achieves the delta-V via pulsing radial thrusters when aligned with the Sun. ACE uses axial thrusters to apply delta-V with a component that is 94% or more aligned with the ACE-Sun line. Sunward thrust adds energy to the orbit preventing decay back toward Earth. Thrust directed anti-Sunward takes energy out of the L1 orbit, thereby preventing escape from the Earth-Moon system into independent heliocentric orbit. Libration point orbit stationkeeping delta-V costs grow exponentially with time elapsed from the last maneuver performed. The doubling time constant is approximately 16 days. For the sake of fuel conservation, and for limiting the absolute magnitude of propulsion performance errors, stationkeeping maneuvers should be performed before the delta-V grows too large; for our purposes 'too large' is considered to be greater than 0.5 m/sec. In practice, the typical interval between burns for this trio is about three months, and the typical delta-V is much smaller than 0.5 m/sec. Typical annual stationkeeping costs have been around 1.0 m/sec for ACE and WIND, and much less than that for SOHO. All three spacecraft have ample fuel remaining; barring contingencies all three could, in principle, be maintained at L1 for decades to come. This paper will review the L1 orbits and the mission history of ACE, WIND, and SOHO, and describe the stationkeeping techniques and orbit maneuver experience. The Lissajous phase control that was practiced for ACE during the period from 1999 to 2001 will also be briefly discussed. The final section will consider the future of these ongoing missions.

Roberts, Craig E.↗
NASA NTRS1993

Performance and mood-state parameters during 30-day 6 degrees head-down bed rest with exercise training

The study was designed to determine if performance and mood impairments occur in bed-rested subjects, and if different exercise-training regimens modify or prevent them. Eighteen normal, healthy men were divided on the basis of age, peak oxygen uptake, and maximal isometric knee extension strength into three similar groups: no exercise (NOE), isotonic exercise (ITE), and isokinetic exercise (IKE). A 15-min battery of 10 performance tests and 8 mood and 2 sleep scales were administered daily during ambulatory control, 30 d of absolute bed rest (BR), and 4 d of ambulatory recovery. Performance test proficiency increased (p < 0.05) for all three groups during BR in 7 of 10 tests and there were no consistent significant differences between the three groups. However, during BR, the ITE group was distinguished from the other groups by a decline (p < 0.05) in the activation mood dimension and in two of its constituent scales (motivation and concentration), and by improvement (p < 0.05) in the trouble-falling-asleep and psychological-tension scales. Since few deleterious changes in performance and mood occurred in the three groups and did not exceed baseline ambulatory levels, we conclude that mood and performance did not deteriorate in response to prolonged BR and were not altered by exercise training. However, the decline in activation mood scales in the ITE group may reflect overtraining or excess total workload in this group.

NASA Center ARC↗
NASA NTRS2016

Spheres: from Ground Development to ISS Operations

SPHERES (Synchronized Position Hold Engage and Reorient Experimental Satellites) is an internal International Space Station (ISS) Facility that supports multiple investigations for the development of multi-spacecraft and robotic control algorithms. The SPHERES National Lab Facility aboard ISS is managed and operated by NASA Ames Research Center (ARC) at Moffett Field California. The SPHERES Facility on ISS consists of three self-contained eight-inch diameter free-floating satellites which perform the various flight algorithms and serve as a platform to support the integration of experimental hardware. SPHERES has served to mature the adaptability of control algorithms of future formation flight missions in microgravity (6 DOF (Degrees of Freedom) / long duration microgravity), demonstrate key close-proximity formation flight and rendezvous and docking maneuvers, understand fault diagnosis and recovery, improve the field of human telerobotic operation and control, and lessons learned on ISS have significant impact on ground robotics, mapping, localization, and sensing in three-dimensions - among several other areas of study.

SPHERES↗
DOE OSTI2021

Dispersion curve regression – assisted wideband local wavenumber analysis for characterizing three-dimensional (3D) profile of hidden corrosion damage

Corrosion as common damage in civil, petrochemical, nuclear, and aerospace structures affects the integrity and safety of the structures and may lead to catastrophic failures. This paper presents dispersion curve regression-assisted local wavenumber analysis method, which can analyze the time–space wavefield containing wideband information of wave-damage interaction and further extract the structural information carried by such wavefield for characterizing hidden corrosion damage in an isotropic plate. To acquire the time–space wavefield, a noncontact scanning laser Doppler vibrometer is used. In our analysis method, the acquired time–space wavefield is firstly processed to generate a local wavenumber function. The derived wavenumber function is further analyzed with a dispersion curve regression step, which searches in a set of theoretical frequency-wavenumber dispersion curves for different plate thicknesses and identifies the optimal plate thickness whose theoretical curve best matches the frequency-wavenumber relation contained in the local wavenumber function. By this means, a 3D profile including both in plane and thickness dimensions of the structure can be constructed for corrosion visualization and quantification. The experimental study demonstrates that our method can quantify the profile of hidden uniform corrosion in metal plates in terms of its in-plane shape and size as well as its out-of-plane depth in the subwavelength scale. Moreover, compared to previous Lamb wave-based corrosion inspection methods, our technique allows for noncontact 3D characterization of hidden corrosion from a far distance to the structure. Finally, we believe this work will inspire new 3D damage quantification methods that are based on wavefield analysis as well as enable potential applications for the quantification of hidden corrosion in civil, petrochemical, nuclear, and aerospace structures.

42 ENGINEERING↗
NASA NTRS1992

Status report, June 1988 - April 1992

The Mars Mission Research Center (MMRC) is one of nine University Space Engineering Research Centers established in June 1988 by NASA's Office of Aeronautics and Space Technology to broaden the nation's engineering capability to meet the critical needs fo the civilian space program. It includes North Carolina State University (NCSU) at Raleigh and on North Carolina A&T State University at Greensboro. The goal of the Center is to focus on research and educational technologies necessary for planetary exploration, especially transportation to and from our moon and Mars. The research combines mission analysis and design, hypersonic aerodynamics, structures and controls, composite materials, and fabrications. Covered here are activities of the Center from June to April 1992. The Center supports 26 graduate students, 29 undergraduates, 27 faculty and 6 staff. An additional 88 undergraduates worked on four special projects. Three facilities at A&T were renovated and a new 7,000 square foot facility was occupied at NCSU in October 1991. Five laboratories have been developed for composite processing and fabrication facility (A&T), materials testing (A&T), weaving (NCSU), braiding (NCSU), and structures (NCSU). During the past two years, the Center added a new dimension to its program - special projects which involve analysis, design, construction, and testing. The first two projects were full-scale research models of a Mars aerobrake and the HL-20 Personnel Launch System. Both projects received considerable new coverage and appeared in national publications. Additional projects include a model of a Mars Exclusion Vehicle, an Orbiter Ejector, and a Remotely Operated Vehicle. The Orbiter Ejector is scheduled to fly on Shuttle Flight STS-47 in October 1992. Special projects have increased undergraduate student participation and provided a mechanism for more interaction between the universities, NASA centers, and industries. The faculty developed 26 new courses related to the activities of the Center. They conducted four workshops on interplanetary spacecraft, lunar/Mars aerobrakes, spacecraft controls, and aerodynamic heating. The Outreach Program developed into a significant component of the Center. Faculty and students have conducted 12 tours of facilities and given 67 lectures to schools (grade k-12) and civic organizations.

Source record↗
NASA NTRS2007

Science Objectives of the JEM EUSO Mission on International Space Station

JEM-EUSO space observatory is planned with a very large exposure factor which will exceed the critical exposure factor required for observing the most of the sources within the propagational horizon of about one hundred Mpc. The main science objective of JEM-EUSO is the source-identifying astronomy in particle channel with extremey-high-energy particles. Quasi-linear tracking of the source objects through galactic magnetic field should become feasible at energy > 10(exp 20) eV for all-sky. The individual GZK profile in high statistics experiments should differ from source to source due to different distance unless Lorentz invariance is somehow limited. hi addition, JEM-EUSO has three exploratory test observations: (i), extremely high energy neutrinos beginning at E > 10(exp 19) eV: neutrinos as being expected to have a slowly increasing cross section in the Standard Model, and in particular, hundreds of times more in the extra-dimension models. (ii). fundamental physics at extreme Super LHC (Large Hadronic Collider) energies with the hierarchical unified energy much below the GUT scale, and (iii). global atmospheric observation, including large-scale and local plasma discharges, night-glow, meteorites, and others..

Takahashi, Yoshiyuki↗
DOE OSTI2020

Bosonic crystalline symmetry protected topological phases beyond the group cohomology proposal

It is demonstrated by explicit construction that three-dimensional bosonic crystalline symmetry protected topological (cSPT) phases are classified by $H^5_\phi(G; \mathbb{Z})⊕H^1_\phi(G; \mathbb{Z})$ for all 230 space groups $\textit{G}$, where $H^n_\phi(G; \mathbb{Z})$ denotes the $\textit{n}$th twisted group cohomology of $\textit{G}$ with $\mathbb{Z}$ coefficients, and $\phi$ indicates that $\textit{g ε G}$ acts nontrivially on coefficients by sending them to their inverses if $\textit{g}$ reverses space-time orientation and acts trivially otherwise. The previously known summand $H^5_\phi(G;\mathbb{Z})$ corresponds only to crystalline phases built without the $E_8$ state or its multiples on 2-cells of space. It is the crystalline analog of the “group cohomology proposal” for classifying bosonic symmetry protected topological (SPT) phases, which takes the form $H^{d + 2}_\phi(G; \mathbb{Z}) ≅ H^{d + 1}_\phi(G; \text{U}(1))$ for finite internal symmetry groups in d spatial dimensions. The new summand $H^1_\phi(G; \mathbb{Z})$ classifies possible configurations of $E_8$ states on 2-cells that can be used to build crystalline phases beyond the group cohomology proposal. The completeness of our classification and the physical meaning of $H^1_\phi(G; \mathbb{Z})$ are established through a combination of dimensional reduction, surface topological order, and explicit cellular construction. The value of $H^1_\phi(G; \mathbb{Z})$ can be easily read off from the international symbol for $\textit{G}$. In this work, our classification agrees with the prediction of the “generalized cohomology hypothesis,” which concerns the general structure of the classification of SPT phases, and therefore provides strong evidence for the validity of the said hypothesis in the realm of crystalline symmetries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗