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Results for “in-plane relaxation”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Matrix dominated stress/strain behavior in polymeric composites: Effects of hold time, nonlinearity and rate dependency

In order to understand matrix dominated behavior in laminated polymer matrix composites, an elastic/viscoplastic constitutive model was developed and used to predict stress strain behavior of off-axis and angle-ply symmetric laminates under in-plane, tensile axial loading. The model was validated for short duration tests at elevated temperatures. Short term stress relaxation and short term creep, strain rate sensitivity, and material nonlinearity were accounted for. The testing times were extended for longer durations, and periods of creep and stress relaxation were used to investigate the ability of the model to account for long term behavior. The model generally underestimated the total change in strain and stress for both long term creep and long term relaxation respectively.

Gates, Thomas S.↗
DOE OSTI2025

Anisotropic strain relaxation-induced directional ultrafast carrier dynamics in RuO 2 films

Ultrafast light-matter interactions inspire potential functionalities in picosecond optoelectronic applications. However, achieving directional carrier dynamics in metals remains challenging due to strong carrier scattering within a multiband environment, typically expected for isotropic carrier relaxation. In this study, we demonstrate epitaxial RuO 2 /TiO 2 (110) heterostructures grown by hybrid molecular beam epitaxy to engineer polarization selectivity of ultrafast light-matter interactions via anisotropic strain engineering. Combining spectroscopic ellipsometry, x-ray absorption spectroscopy, and optical pump-probe spectroscopy, we revealed the strong anisotropic transient optoelectronic response at an excitation energy of 1.58 eV in strain-engineered RuO 2 /TiO 2 (110) heterostructures along both in-plane [001] and [1$\bar1$0] crystallographic directions. Theoretical analysis identifies strain-induced modifications in band nesting as the underlying mechanism for enhanced anisotropic carrier relaxation observed at this excitation energy. These findings establish epitaxial strain engineering as a powerful tool for tuning anisotropic optoelectronic responses with near-infrared excitations in metallic systems, paving the way for next-generation polarization-sensitive ultrafast optoelectronic devices.

Science & Technology - Other Topics↗
NASA NTRS1984

Verification and application of the Iosipescu shear test method

Finite element models were used to study the effects of notch angle variations on the stress state within an Iosipescu shear test speciment. These analytical results were also studied to determine the feasibility of using strain gage rosettes and a modified extensometer to measure shear strains in this test specimen. Analytical results indicate that notch angle variations produced only small differences in simulated shear properties. Both strain gage rosettes and the modified extensometer were shown to be feasible shear strain transducers for the test method. The Iosipoescu shear test fixture was redesigned to incorporate several improvements. These improvements include accommodation of a 50 percent larger specimen for easier measurement of shear train, a clamping mechanism to relax strict tolerances on specimen width, and a self contained alignment tool for use during specimen installation. A set of in-plane and interlaminar shear properties were measured for three graphite fabric/epoxy composites of T300/934 composite material. The three weave patterns were Oxford, 5-harness satin, and 8-harness satin.

Walrath, D. E.↗
NASA NTRS2002

Growth of Defect-Free 3C-Sic on 4H- and 6H-SIC Mesas Using Step-Free Surface Heteroepitaxy

A new growth process, herein named step-free surface heteroepitaxy, has achieved 3C-SiC films completely free of double positioning boundaries and stacking faults on 4H-SiC and 6H-SiC substrate mesas. The process is based upon the initial 2-dimensional nucleation and lateral expansion of a single island of 3C-SiC on a 4H- or 6H-SiC mesa surface that is completely free of bilayer surface steps. Our experimental results indicate that substrate-epilayer in-plane lattice mismatch (Delta/a = 0.0854% for 3C/4H) is at least partially relieved parallel to the interface in the initial bilayers of the heterofilm, producing an at least partially relaxed 3C-SiC film without dislocations that undesirably thread through the thickness of the epilayer. This result should enable realization of improved 3C-SiC devices.

Neudeck, Philip G.↗
NASA NTRS2001

Growth of Defect-Free 3C-SiC on 4H- and 6H-SiC Mesas Using Step-Free Surface Heteroepitaxy

A new growth process, herein named step-free surface heteroepitaxy, has achieved 3CSiC films completely free of double positioning boundaries and stacking faults on 4H-SiC and 6H-SiC substrate mesas. The process is based upon the initial 2-dimensional nucleation and lateral expansion of a single island of 3C-SiC on a 4H- or 6H-SiC mesa surface that is completely free of bilayer surface steps. Our experimental results indicate that substrate-epilayer in-plane lattice mismatch (delta a/a = 0.0854% for 3C/4H) is at least partially relieved parallel to the interface in the initial bilayers of the heterofilm, producing an at least partially relaxed 3C-SiC film without dislocations that undesirably thread through the thickness of the epilayer. This result should enable realization of improved 3C-SiC devices.

Neudeck, Philip G.↗
DOE OSTI2025

Cold air quench control of local crystallization environment in fully air-processed carbon-based perovskite solar cells

Carbon-based perovskite solar cells (C-PSCs) present a low-cost route to efficient photovoltaic technology. Gas quenching is an essential process commonly used for solvent extraction in scalable module fabrication using solution processes, but film quality remains highly sensitive to the localized environmental processing temperature, especially during intermediate phase transitions before perovskite film high temperature annealing. In this study, we introduce a cold air quench strategy to precisely control the local crystallization temperature that simultaneously promotes uniform crystallization and facilitates strain relaxation in fully air-processed C-PSCs. It is found that implementing dry air at 10 °C as the quenching gas yields a champion power conversion efficiency (PCE) of 20.52 %, with preferential (110) orientation and reduced, homogenized in-plane strain. This newly developed technique of a cost-effective low temperature air quenching process also enhances carrier lifetime, reduces interface recombination, and improves charge extraction. Furthermore, this work presents cold air quenching as a scalable, economic method to control perovskite crystallization and strain in C-PSC fabrication, advancing the industrial viability of high-performance perovskite modules.

14 SOLAR ENERGY↗
DOE OSTI2025

Sensitive dependence on initial conditions in a formation of magnetic vortices

The magnetic vortex exhibits promise as a true random number generator for hardware-based encryption and probabilistic computing due to its stochastic formation of energetically equivalent fourfold degenerate states, characterized by two topologies: polarity and chirality. However, a comprehensive understanding of the stochastic formation of magnetic vortices remains elusive. In this work, we show that the magnetization relaxation in asymmetric Permalloy disks evolves along a pitchfork bifurcation, with both bifurcation paths leading to the formation of magnetic vortices with the same chirality. In the bifurcation, one formation path is always chosen under weak in-plane magnetic fields, ultimately determining the final magnetic vortex state. By delaying the in-plane magnetic field, we quantitatively investigate when the final vortex state is determined and find that it is closely associated with the initial conditions rather than the bifurcation point itself. Our findings provide valuable insights into future spintronic-based encryption and probabilistic computing.

Jeong, Suyeong↗
NASA NTRS1988

Thermo-viscoelastic analysis of composite materials, volume 1

Advanced composite materials, especially graphite/epoxy, are being applied to aircraft structures in order to improve performance and save weight. An important consideration in composite design is the residual strength of a structure containing holes, delaminations, or interlaminar damage when subjected to compressive loads. Recent studies have revealed the importance of viscoelastic effects in polymer-based composites. The viscoelastic effect is particularly significant at elevated temperature/moisture conditions since the matrix material is strongly affected by the environment. The solution of viscoelastic problems in composites was limited to special cases which can be solved by classical lamination theory. A finite element procedure is presented for calculating time-dependent stresses and strains in composite structures with general configurations and complicated boundary conditions. Using this procedure the in-plane and interlaminar stress distributions and histories in notched and unnotched composites were obtained for mechanical and thermal loads. Both two-dimensional and three-dimensional viscoelastic problems are analyzed. The effects of layup orientation and load spectrum on creep response and stress relaxation were also studied.

Lin, K. Y.↗
DOE OSTI2026

Cooperative Charge Ordering Signature of Trimer Molecules in Infinite-Layer CaCoO 2

The infinite-layer compound CaCoO 2 provides a compelling platform to explore how local orbital distortions evolve into collective electronic order. Using resonant soft x-ray scattering (RSXS) and its time-resolved counterpart (tr-RSXS), we reveal a cooperative coupling between two intertwined orders at the same in-plane wave vector, 𝑞 ≈ (1/4, 1/4, 0), comprising a quasi-two-dimensional orbital order associated with the distorted Co (1) sites and a quasi-three-dimensional trimerlike charge order stabilized through Co-O-Ca hybridization. The charge-sensitive component exhibits a uniform relaxation time of ∼400 fs (391 ± 5 fs) across multiple Co resonances, evidencing a collective charge response. A comparable timescale observed in the orbital order associated with the highly distorted Co (1) sites indicates that this collective behavior naturally originates from the same orbital framework that mediates both charge and orbital degrees of freedom. Together, these findings establish CaCoO 2 as a model system in which Jahn-Teller distortions, orbital hybridization, and geometric frustration cooperate to form molecular trimer units that dictate the macroscopic electronic behavior.

Lee, J.-S. [SLAC National Accelerator Laboratory (↗
NASA NTRS2007

Modeling Creep-Induced Stress Relaxation at the Leading Edge of SiC/SiC Airfoils

Anticipating the implementation of advanced SiC/SiC composites into internally cooled airfoil components within the turbine section of future aero-propulsion engines, the primary objective of this study was to develop physics-based analytical and finite-element modeling tools to predict the effects of composite creep and stress relaxation at the airfoil leading edges, which will generally experience large thermal gradients at high temperatures. A second objective was to examine how some advanced NASA-developed SiC/SiC systems coated with typical EBC materials would behave as leading edge materials in terms of long-term steady-state operating temperatures. Because of the complexities introduced by mechanical stresses inherent in internally cooled airfoils, a simple cylindrical thin-walled tube model subjected to thermal stresses only is employed for the leading edge, thereby obtaining a best-case scenario for the material behavior. In addition, the SiC/SiC composite materials are assumed to behave as isotropic materials with temperature-dependent viscoelastic creep behavior as measured in-plane on thin-walled panels. Key findings include: (1) without mechanical stresses and for typical airfoil geometries, as heat flux is increased through the leading edge, life-limiting tensile crack formation will occur first in the hoop direction on the inside wall of the leading edge; (2) thermal gradients through all current SiC/SiC systems should be kept below approx.300 F at high temperatures to avoid this cracking; (3) at temperatures near the maximum operating temperatures of advanced SiC/SiC systems, thermal stresses induced by the thermal gradients will beneficially relax with time due to creep; (4) although stress relaxation occurs, the maximum gradient should still not exceed 300oF because of residual tensile stress buildup on the airfoil outer wall during cool-down; and (5) without film cooling and mechanical stresses, the NASA-developed N26 SiC/SiC system with thru-thickness Sylramic-iBN fiber reinforcement and a typical EBC coating has the potential of offering a maximum long-term steady-state operating temperature of approx.3100 F at the surface of the EBC.

Lang, Jerry↗
NASA NTRS2006

CFD Growth of 3C-SiC on 4H/6H Mesas

This article describes growth and characterization of the highest quality reproducible 3C-SiC heteroepitaxial films ever reported. By properly nucleating 3C-SiC growth on top of perfectly on-axis (0001) 4H-SiC mesa surfaces completely free of atomic scale steps and extended defects, growth of 3C-SiC mesa heterofilms completely free of extended crystal defects can be achieved. In contrast, nucleation and growth of 3C-SiC mesa heterofilms on top of 4H-SiC mesas with atomic-scale steps always results in numerous observable dislocations threading through the 3C-SiC epilayer. High-resolution X-ray diffraction and transmission electron microscopy measurements indicate non-trivial in-plane lattice mismatch between the 3C and 4H layers. This mismatch is somewhat relieved in the step-free mesa case via misfit dislocations confined to the 3C/4H interfacial region without dislocations threading into the overlying 3C-SiC layer. These results indicate that the presence or absence of steps at the 3C/4H heteroepitaxial interface critically impacts the quality, defect structure, and relaxation mechanisms of single-crystal heteroepitaxial 3C-SiC films.

Neudeck, Philip G.↗
NASA NTRS2004

Coating Development for GRCop-84 Liners for Reusable Launch Vehicles Aided by Modeling Studies

The design of the next generation of reusable launch vehicles calls for using GRCop-84 copper alloy liners based on a composition invented at the NASA Glenn Research Center. Despite its considerable advantage over other copper alloys, it is expected that GRCop-84 will suffer from environmental degradation depending on the type of rocket fuels used and on thermomechanical fatigue. Applying protective coatings on GRCop-84 substrates can minimize or eliminate many of these problems and extend the operational life of the combustion liner. This could increase component reliability, shorten depot maintenance turnaround times, and lower operating costs. Therefore, Glenn is actively pursuing the development of advanced coatings technology for GRCop-84 liners. Technology is being developed in four major areas: (1) new metallic coating compositions, (2) application techniques, (3) test methods, and (4) life prediction design methodology using finite element analysis. The role of finite element analysis in guiding the coating effort is discussed in this report. Thermal analyses were performed at Glenn for different combinations of top- and bondcoat compositions to determine the temperature variation across the coated cross section with the thickness of the top coat. These calculations were conducted for simulated LH2/LO2 booster engine conditions assuming that the bond coat had a constant thickness of 50 m. The preceding graphs show the predicted temperatures at the outer surface of the top coat (hot wall), at the top-coat/bond-coat interface, at the bond-coat/GRCop-84 interface, and at the GRCop-84 cold wall as a function of top-coat thickness for Cu- 26(wt%)Cr top coat (top graph), Ni-17(wt%)Cr-6%Al-0.5%Y top coat and Cu-26%Cr bond coat, and NiAl top coat and Ni bond coat. In all cases, the temperature of the top coat at the hot wall increased with increasing top-coat thickness and with corresponding decreases in the temperatures at the two interfaces and the cold wall. These temperatures are not acutely sensitive to the thermal conductivity of the top coat when it exceeds 25 and 50 W/m/K for low and high heat flux engines. This observation is significant for two reasons. First, several different top-coat compositions can be evaluated as potential protective coatings without loss in the heat-transfer efficiency of the coated system. Second, materials with thermal conductivities less than the critical values of 25 or 50 W/m/K are more likely to act as thermal barrier coatings. The deposition of overlay coatings on GRCop-84 substrates results in the development of residual stresses. The presence of these residual stresses influences the probability of coating spallation, the thermal cycling life, and the fatigue properties of the coated substrate during use. Since it is important to understand how these stresses develop during the vacuum-plasma-spraying coating deposition process, the nature and magnitudes of the cool-down residual stresses were calculated and compared with experimentally determined values across the coated cross section of a disk specimen. The calculations were conducted assuming that the specimen cools down to room temperature from vacuum plasma-spraying temperatures of either 250 or 650 C. The effects of coating the substrate with and without grit blasting were also theoretically examined. The final graph compares the predicted and the experimental results for a GRCop-84 disk coated with about a 50- m-thick Ni bond coat and a 75- to 100- m NiAl top coat, where the curves for NASA-2 assume the presence of a prior residual stress generated by grit blasting under conditions similar to the experimental situation. The predicted cool-down in-plane stresses were compressive in both the NiAl top coat and the Ni bond coat. They were also compressive in the substrate to a depth of about 0.25 mm from the Ni/GRCop-84 interface when the vacuum-plasma-spraying temperature was low. However, using a higher plasma spraying temperaturs likely to leave the substrate under a small tensile stress to counter the compressive stresses in the bond and top coats because of the relaxation of residual stresses generated in the substrate during the grit blasting of its surface prior to spraying. These results suggest that the NiAl and Ni coatings are unlikely to spall after spraying as confirmed by the microstructural observations shown in the following photomicrograph of an as-sprayed specimen. Finally, it is noted that the calculated and experimental results are not in complete agreement, which indicates that both the experimental and modeling techniques need further refinement.

Raj, Sai V.↗
DOE OSTI2026

Ultrafast solvent-to-solute proton transfer mediated by intermolecular coherent vibrations

Ultrafast photoinduced excited-state proton transfer (ESPT) plays a crucial role in protecting biomolecules and functional materials from photodamage. However, the influence of solute-solvent interactions on ESPT dynamics remains under active investigation. Here, we present an ultrafast spectroscopic study of ESPT in the photobase 2-(2´-pyridyl)benzimidazole (PBI) in methanol. Ultrafast absorption spectroscopy, supported by quantum chemical calculations, reveals three distinct kinetic steps: (1) a 2.2 ps solvent-to-solute proton transfer, (2) subsequent nonradiative relaxation to the ground state within 31 ps, producing a vibrationally hot ensemble with substantial excess kinetic energy, and (3) equilibration as this energy dissipates into the surrounding solvent bath over 186 ps. Femtosecond-resolved dynamics exhibit oscillatory signals indicative of coherent wavepacket motion on the S 1 potential energy surface. A phase flip in the excited-state absorption maximum confirms this assignment. Fourier analysis resolves two dominant periods (∼117 fs and ∼340 fs), corresponding to in-plane and out-of-plane vibrational modes coupled between PBI and the hydrogen-bonded methanol molecule. The rapid dephasing ( < 300 fs) suggests that the nuclear wavefunction evolves on an anharmonic potential energy surface while traversing the ESPT reaction coordinate.

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

Spin fluctuations, absence of magnetic order, and crystal electric field studies in the Yb 3+ -based triangular lattice antiferromagnet Rb 3 ⁢Yb⁢(VO 4 ) 2

Here, we report a comprehensive experimental investigation of the structural, thermodynamic, static, and dynamic properties of a triangular lattice antiferromagnet Rb 3 ⁢Yb(VO 4 ) 2 . Through the analysis of magnetic susceptibility, magnetization, and specific heat, complemented by crystal electric field (CEF) calculations, we confirm the Kramers' doublet with effective spin 𝐽 eff = 1/2 ground state. Magnetic susceptibility and isothermal magnetization analysis reveal a weak antiferromagnetic interaction among the 𝐽 eff = 1/2 spins, characterized by a small Curie-Weiss temperature (𝜃$^{\textrm{LT}}_{\textrm{CW}}$ ≃−0.26 K) or a reduced exchange coupling (𝐽/𝑘 B ≃ 0.18 K). The 51 V NMR spectra and spin-lattice relaxation rate (1/𝑇 1 ) show no evidence of magnetic long-range-order down to 1.6 K but reflect strong influence of CEF excitations in the intermediate temperatures. At low temperatures, 1/𝑇 1 ⁡(𝑇) shows pronounced frequency dependence and 1/𝑇 1 vs field at different temperatures follows the scaling behavior, highlighting the role of paramagnetic fluctuations. The CEF calculations using the point charge approximation divulge a large energy gap ( ∼18.61 meV) between the lowest and second lowest energy doublets, further establishing Kramers' doublet as the ground state. Our calculations also reproduce the experimental magnetization and specific heat data and indicate an in-plane magnetic anisotropy. These findings position Rb 3⁢ Yb(VO 4 ) 2 as an ideal candidate to explore intrinsic quantum fluctuations and possible quantum spin-liquid physics in a Yb 3+ -based triangular lattice antiferromagnet.

Sebastian, Sebin J. [Indian Institute of Science E↗
NASA NTRS2001

Structure-Property Correlations in Al-Li Alloy Integrally Stiffened Extrusions

The objective of this investigation was to establish the relationship between mechanical property anisotropy, microstructure and crystallographic texture in integrally 'T'-stiffened extruded panels fabricated from the Al-Li alloys 2195, 2098 and 2096. In-plane properties were measured as a function of orientation at two locations in the panels, namely mid-way between (Skin), and directly beneath (Base), the integral 'T' stiffeners. The 2195 extrusion exhibited the best combination of strength and toughness, but was the most anisotropic. The 2098 extrusion exhibited lower strength and comparable toughness, but was more isotropic than 2195. The 2096 extrusion exhibited the lowest strength and poor toughness, but was the most isotropic. All three alloys exhibited highly elongated grain structures and similar location-dependent variations in grain morphology. The textural characteristics comprised a beta + <100> fiber texture, similar to rolled product, in the Skin regions and alpha <111> + <100> fiber texture, comparable to axisymmetric extruded product, in the Base regions. In an attempt to quantitatively correlate texture with yield strength anisotropy, the original 'full constraint' Taylor model and a variant of the 'relaxed constraint' model, explored by Wert et al., were applied to the data. A comparison of the results revealed that the Wert model was consistently more accurate than the Taylor model.

Hales, Stephen J.↗
NASA NTRS2006

Recent Results from Epitaxial Growth on Step Free 4H-SiC Mesas

This paper updates recent progress made in growth, characterization, and understanding of high quality homoepitaxial and heteroepitaxial films grown on step-free 4H-SiC mesas. First, we report initial achievement of step-free 4H-SiC surfaces with carbon-face surface polarity. Next, we will describe further observations of how step-free 4H-SiC thin lateral cantilever evolution is significantly impacted by crystal faceting behavior that imposes non-uniform film thickness on cantilever undersides. Finally, recent investigations of in-plane lattice constant mismatch strain relief mechanisms observed for heteroepitaxial growth of 3C-SiC as well as 2H-AlN/GaN heterofilms on step-free 4H-SiC mesas will be reviewed. In both cases, the complete elimination of atomic heterointerface steps on the mesa structure enables uniquely well-ordered misfit dislocation arrays to form near the heterointerfaces with remarkable lack of dislocations threading vertically into the heteroepilayers. In the case of 3C-SiC heterofilms, it has been proposed that dislocation half-loops nucleate at mesa edges and glide laterally along the step-free 3C/4H interfaces. In contrast, 3C-SiC and 2H-AlN/GaN heterofilms grown on 4H-SiC mesas with steps exhibit highly disordered interface misfit dislocation structure coupled with 100X greater density of dislocations threading through the thickness of the heteroepilayers. These results indicate that the presence of steps at the heteroepitaxial interface (i.e., on the initial heteroepitaxial nucleation surface) plays a highly important role in the defect structure, quality, and relaxation mechanisms of single-crystal heteroepitaxial films.

Neudeck, Philip G.↗
DOE OSTI2024

Insulating moiré homobilayers lack a threefold symmetric second-harmonic generation

Atoms within moiré bilayers relax in plane to minimize elastic energy; such relaxation brings their space group symmetries down to P1. Here, the ab initio second harmonic generation (SHG) of twisted and atomistically optimized hBN bilayers was determined at four twist angles (θ = 38.21°, 60.00°, 73.17°, and 98.21°) and for three displacements τ measured away from the ground state AA' configuration. All moiré bilayers have a P1 space symmetry after structural optimization. This situation is quite different to monolayers with hexagonal lattices, which retain a threefold symmetry. We point out that the actual symmetries of the SHG reported for hBN bilayers on two experimental works do not coincide with the sixfold symmetric theoretical profiles they provide [either sin 2 ⁡(3⁢Φ) or cos 2 ⁡(3⁢Φ)], and show that the intrinsic low structural symmetry of (atomically optimized) hBN bilayer moirés can in fact be read out from experimental SHG intensity profiles—which are tunable by θ and by the frequency of light ω: The SHG is most definitely not sixfold symmetric because moirés do not retain a threefold symmetry. Furthermore, an extrinsic twofold symmetry of the SHG emission is realized by tilting the pump by an angle α away from the 2D material's normal, regardless of θ and ω. Furthermore, the design of in-plane and ultrathin sources of SHG with low symmetry could be useful for the eventual creation of entanglement sources from 2D materials.

2-dimensional systems↗
DOE OSTI2026

The Evolution of Magnetism in a Thin Film Pyrochlore Ferromagnetic Insulator

The pyrochlore vanadates are compelling candidates for next-generation dissipationless devices. Lu 2 V 2 O 7 and Y 2 V 2 O 7 are ferromagnetic insulators (T c ~ 70 K) that are believed to exhibit the magnon Hall effect and are expected to host topological magnons. Their completely dissipationless magnon edge states could be harnessed to realize low-power information transport in spintronic or magnonic devices. As a crucial step in the realization of devices, we synthesize the first thin films of pyrochlore Y 2 V 2 O 7 on isostructural Y 2 V 2 O 7 substrates and explore the evolution of their magnetic properties down to the ultrathin limit. All films are insulating ferromagnets with transition temperatures of up to the bulk value (T c ~ 68 K) that decrease with thickness according to finite-size effects. Our films also exhibit a change in anisotropy from in-plane to out-of-plane easy axis coincident with the development of partial strain relaxation and nonzero magnetic hysteresis in an applied field. Furthermore, this evolution demonstrates the impact of strain on magnetic anisotropy and paves the way to tunable magnon topology.

Anderson, Margaret A. [Harvard University, Cambrid↗