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At least 487 records · Page 27

Suppressing Cation Migration in Triple-Cation Lead Halide Perovskites

Ion migration represents an intrinsic instability of metal halide perovskite solar cells. In this work, we show that triple-cation FA x MA y Cs 1–x–y PbI 3 [FA + = (NH 2 ) 2 CH + , MA + = CH 3 NH 3 + ] active layers with mixed orthorhombic, post-perovskite (δ ortho -CsPbI 3 ), and cubic perovskite (α) phases (i.e., α/δ-phase FA x MA y Cs 1–x–y PbI 3 ) exhibit improved cation stability against applied bias relative to pure α-phase perovskites (i.e., FA 0.85 Cs 0.15 PbI 3 and FA 0.76 MA 0.15 Cs 0.09 PbI 3 ). Infrared photothermal heterodyne imaging and time-of-flight secondary ion mass spectrometry are used to visualize exclusive α-phase perovskite lateral device A + cation accumulation (depletion) at perovskite negative (positive) electrode interfaces. The resulting compositional heterogeneities lead to degradation. Operational stability testing of solar cells reveals similar degradation behavior; α/δ-phase FA x MA y Cs 1–x–y PbI 3 lateral devices/solar cells, by contrast, show improved stabilities. Enhanced α/δ-FA x MA y Cs 1–x–y PbI 3 stability is rationalized by δortho-phase inclusions, acting as barriers through which A + cations do not easily migrate. This study thus provides new insights into cation migration in FA x MAyCs 1–x–y PbI 3 perovskites and suggests a materials design strategy toward suppressing cation instabilities in hybrid perovskites.

14 SOLAR ENERGY↗

ELM-free H-mode phase and decoupling of peeling–ballooning stability boundary in the MAST Upgrade tokamak

A linear magnetohydrodynamic (MHD) peeling–ballooning stability analysis of the edge-localized mode (ELM)-free phase of a MAST Upgrade (MAST-U) H-mode plasma is presented. In contrast to other similar discharges, #47018 is found to have a significantly higher and wider pedestal during its ELM-free H-mode phase that lasts for approximately 80 ms; this is made possible by the reduced core MHD mode activity on the q = 2 surface. During this period, there is sustained decoupling of peeling and ballooning branches of the stability boundary on J–α space, opening an access channel to the second stability regime with higher peaks in pedestal current density $J_{\mathrm{N,ped}}$ and pressure gradient (α). Such decoupling of the stability boundary has not previously been observed in MAST-U H-modes, and if such a condition can be readily reproduced, it opens a wide range of opportunities for MAST-U to explore low-collisionality peeling-limited pedestal regimes as well as advanced scenarios such as quiescent H-modes that are relevant to future reactors such as STEP and ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Evolution of silicate coordination in architected amorphous and crystalline magnesium silicates during carbon mineralization

Advancing durable solutions for carbon storage and removal at the gigaton scale to produce solid carbonates via carbon mineralization requires harnessing earth abundant magnesium silicate resources. Calibrated insights linking the structural and morphological features of earth abundant amorphous and crystalline magnesium silicate phases to their reactivity are essential for scalable deployment but remain underdeveloped. To resolve the influence of silica coordination and mass transfer on carbon mineralization behavior, magnesium silicates bearing amorphous and crystalline phases (AC Mg-silicate) are synthesized. The structural and morphological transitions starting from colloidal precursors to their final synthesized form on heating are delineated using operando ultra small/small/wide angle X-ray scattering (USAXS/SAXS/WAXS) measurements. The evolution of the silicate phases on carbon mineralization of AC Mg-silicate is contrasted with that of highly crystalline Mg-silicate (HC Mg-silicate) when reacted at 200 °C and a CO 2 partial pressure of 20 atm in water and 1 M NaHCO 3 solution in stirred and unstirred environments. These experimental conditions are analogous to those of the water–gas-shift reaction for sustainable recovery of H 2 with inherent carbon mineralization. Enhancement in the extent of carbon mineralization by 13.3–19.5% noted in the presence of NaHCO 3 compared to water in AC and HC Mg-silicate with and without stirring, is attributed to the buffering effect which aids simultaneous silicate dissolution and carbon mineralization. Enhanced extents of carbon mineralization in the presence of NaHCO 3 correspond to the formation of MgSiO 3 and SiO 2 phases from the starting Mg 2 SiO 4 precursors in AC and HC Mg-silicate. Unlocking these silicate transformations during carbon mineralization by harnessing architected Mg-silicate precursors reveals the feasibility of integrating these chemical pathways with sustainable H 2 conversion pathways with inherent carbon mineralization.

Gao, Xun [Cornell Univ., Ithaca, NY (United States↗

Behavior of soda-lime silicate glass under laser-driven shock compression up to 315 GPa

Shock experiments give a unique insight into the behavior of matter subjected to extremely high pressures and temperatures. Understanding the behavior of materials under such extreme conditions is key to modeling material failure and deformation dynamics under impact. While studies on pure silica are extensive, the shock behavior of other commercial silicates that contain additional oxides has not been systematically investigated. To better understand the role of composition in the dynamic behavior of silicates, we performed laser-driven dynamic compression experiments on soda-lime glass (SLG) up to 315 GPa. Using the accurate pulse shaping offered by the long pulse laser system at the Matter in Extreme Conditions end-station at the Linac Coherent Light Source, SLG was shock compressed along the Hugoniot to multiple pressure-temperature points. Velocity Interferometer System for Any Reflector was used to measure the velocity and determine the pressure inside the SLG. The U s –u p relationship obtained agrees well with the previous parallel plate impact studies. Within the error bars, no transformation to the crystalline phase was observed up to 70 GPa, which is in contrast to the behavior of pure silica under shock compression. Our studies show that the glass composition strongly influences the shock compression behavior of the silicate glasses.

36 MATERIALS SCIENCE↗

Nonequilibrium universality of the nonreciprocally coupled 𝑂⁡(𝑛 1 ) × 𝑂⁡(𝑛 2 ) model

Nonequilibrium dynamics play an important role in all contexts of physics, both classical and quantum as well as living and nonliving, so it is crucial to develop a foundational understanding of nonequilibrium phase transitions. In this work we investigate an important class of nonequilibrium dynamics in the form of nonreciprocal interactions. In particular we study how nonreciprocal coupling between two 𝑂⁡(𝑛𝑖) order parameters (with 𝑖 = 1,2) affects the universality at a multicritical point, extending the analysis of J. T. Young et al. [Phys. Rev. X 10, 011039 (2020)], which considered the case 𝑛 1 = 𝑛 2 = 1, i.e., a ℤ 2 × ℤ 2 model. We show that nonequilibrium fixed points (NEFPs) emerge for a broad range of 𝑛 1 ,𝑛 2 and exhibit intrinsically nonequilibrium critical phenomena, namely a violation of fluctuation-dissipation relations at all scales and underdamped oscillations near criticality in contrast to the overdamped relaxational dynamics of the corresponding equilibrium models. Furthermore, the NEFPs exhibit an emergent discrete scale invariance in certain physically relevant regimes of 𝑛 1 ,𝑛 2 , but not others, depending on whether the critical exponent 𝜈 is real or complex. The boundary between these two regions is described by an exceptional point in the renormalization group (RG) flow, leading to distinctive features in correlation functions and the phase diagram. Another contrast with the previous work is the number and stability of the NEFPs as well as the underlying topology of the RG flow. Lastly, we investigate an extreme form of nonreciprocity where one order parameter is independent of the other order parameter but not vice versa. Unlike the ℤ 2 × ℤ 2 model, which becomes nonperturbative in this case, we identify a distinct nonequilibrium universality class whose dependent field similarly violates fluctuation-dissipation relations but does not exhibit discrete scale invariance or underdamped oscillations near criticality.

Critical phenomena↗

Boosting the use of bauxite residue (red mud) in cement - Production of an Fe-rich calciumsulfoaluminate-ferrite clinker and characterisation of the hydration

Highlights: • Incorporation of 35 wt% of bauxite residue for production of CSAF clinker • Thermochemical calculations as suitable tool for predicting phase assemblage • Hydration of the cement was found to be accelerated in contrast to other CSA cements. • High early compressive strengths of 40 MPa In the present work, calciumsulfoaluminate-ferrite clinker was produced using 35 wt% of bauxite residue in combination with alumina, clay, limestone and gypsum. At a temperature of 1300 °C, the hydraulic phases ye'elimite, ferrite and C{sub 2}S were formed. Computed thermochemical predictions were a significantly better match for the real mineralogy than modified Bogue equations. Hydration of the clinker led to the formation of ettringite and monosulfate, resulting in compressive strengths of 17 MPa after 28d. Compressive strengths of 40 MPa after 2d, and 28d-strengths exceeding 50 MPa, were reached in blends with 10 wt% of anhydrite. The strength development was due to the rapid formation of ettringite, mainly originating from ye'elimite, which did not convert to AFm phases and led to a compact microstructure. Only when the ye'elimite dissolution decreased, did the ferrite phase react. In pastes with additional sulfates, ferrite hydration led to the formation of ettringite and to hydrogarnet. Cement nomenclature is used in this work.{sup 1}.

36 MATERIALS SCIENCE↗

Synthesis and Properties of the Helium Clathrate and Defect Perovskite [He 2– x $^\square$ x ][CaNb]F 6

The defect double perovskite [He 2– x $^\square$ x ][CaNb]F 6 , with helium on its A-site, can be prepared by the insertion of helium into ReO 3 -type CaNbF 6 at high pressure. Upon cooling from 300 to 100 K under 0.4 GPa helium, ~60% of the A-sites become occupied. Helium uptake was quantified by both neutron powder diffraction and gas insertion and release measurements. After the conversion of gauge pressure to fugacity, the uptake of helium by CaNbF 6 can be described by a Langmuir isotherm. The enthalpy of absorption for helium in [He 2– x $^\square$ x ][CaNb]F 6 is estimated to be ~+3(1) kJ mol –1 , implying that its formation is entropically favored. Helium is able to diffuse through the material on a time scale of minutes at temperatures down to ~150 K but is trapped at 100 K and below. The insertion of helium into CaNbF 6 reduces the magnitude of its negative thermal expansion, increases the bulk modulus, and modifies its phase behavior. On compressing pristine CaNbF 6 , at 50 and 100 K, a cubic (Fm$\overline{3}$m) to rhombohedral (R$\overline{3}$) phase transition was observed at <0.20 GPa. However, a helium-containing sample remained cubic at 0.4 GPa and 50 K. CaNbF 6 , compressed in helium at room temperature, remained cubic to >3.7 GPa, the limit of our X-ray diffraction measurements, in contrast to prior reports that upon compression in a nonpenetrating medium, a phase transition is detected at ~0.4 GPa.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Elastocaloric evidence for a multicomponent superconductor stabilized within the nematic state in Ba(Fe 1− x Co x ) 2 As 2

The iron-based high-$T_c$ superconductors (SCs) exhibit rich phase diagrams with intertwined phases, including magnetism, nematicity, and superconductivity. The superconducting $T_c$ in many of these materials is maximized in the regime of strong nematic fluctuations, making the role of nematicity in influencing the superconductivity a topic of intense research. Here, in this study, we use the AC elastocaloric effect (ECE) to map out the phase diagram of Ba(Fe 1− x Co x ) 2 As 2 near optimal doping. The ECE signature at $T_c$ on the overdoped side, where superconductivity condenses without any nematic order, is quantitatively consistent with other thermodynamic probes that indicate a single-component superconducting state. In contrast, on the slightly underdoped side, where superconductivity condenses within the nematic phase, ECE reveals a second thermodynamic transition proximate to and below $T_c$. We rule out magnetism and reentrant tetragonality as the origin of this transition and find that our observations strongly suggest a phase transition into a multicomponent superconducting state. This implies the existence of a subdominant pairing instability that competes strongly with the dominant $s^±$ instability. Our results highlight the significant role of nematic order in determining the pairing symmetry close to optimal doping in this extensively studied iron-based SC, while also demonstrating the power of ECE in uncovering strain-tuned phase diagrams of quantum materials.

Ghosh, Sayak [Stanford University, CA (United Stat↗

Coalescence of GaP on V-Groove Si

With an increase of control over crystalline defects, metallorganic vapor phase epitaxy (MOVPE)-grown III-V-on-Si multijunction solar cells have seen rapid increases in efficiency in recent years, pointing to a promising path to lower cost III-V solar cells. However, the cost of chemo-mechanical polishing the Si wafers to prepare them for epitaxy is high. The use of V-groove nanopatterns enables similar defect reduction to that achieved on planar wafers, but the nanopatterns can be fabricated with a low-cost process. While V-grooves offer advantages over planar Si, they add complexity to the growth process. In particular, coalescence can cause the formation of threading dislocations, and the highly-directional growth conditions required for coalescence are unusual for MOVPE. We have studied the coalescence of GaP films nucleated directly on V-groove Si by MOVPE. We observed that for optimized growth conditions (V/III=5,000 and T=800 C) two growth modes were possible, and the resulting morphology depended on the exact geometry of the SiNx cap used to cover the (0 0 1)-oriented Si at the tops of the grooves. For caps with a width >100 nm, noncoalescing, nano ridge-like growth terminating in f1 1 1g facets was observed. For narrower caps, coalescence with an RMS roughness of 0.2 nm as measured by atomic force microscopy was observed. We will discuss mechanisms responsible for this phenomenon, including the role of Si from the substrate surface. The dislocation dynamics of this system were studied with electron channeling contrast imaging (ECCI) and transmission electron microscopy (TEM). We find that V-grooves do not block dislocation glide; ECCI measurements show misfit dislocations greater than 10 micrometers long observed to continue perpendicularly across neighboring V-grooves. In addition, all threading dislocations appear to lie on f1 1 1g planes, consistent with the GaP relaxing via glided-in glissile dislocations. The dislocation dynamics and morphological evolution of the coalescence of GaP on Si, possible mechanisms behind the observed phenomenons, and further dislocation mitigation strategies for these materials will be presented.

dislocation dynamics↗

Towards understanding the development and characteristics of under-expanded flash boiling jets

Here in this research, the n-hexane jets discharged from a straight channel were studied numerically to reveal the development and characteristics of under-expanded flashing jets. Firstly, the development of flash boiling jets was investigated and compared to that of two-phase jets without phase transition. It was shown that the two-phase jets without phase transition can be under-expanded only if the flow is choked. In contrast, flash boiling jets can be under-expanded whether or not the choked conditions are verified. Secondly, the factors affecting the flashing jet behaviors were discussed. The relaxation time in phase transition, the expansion ratio, and the injection pressure have been identified as three key factors determining the jet characteristics. With high enough expansion ratio and low enough relaxation time, the expansion was so strong that the flow became transonic and shock structures similar to those of under-expanded gaseous jets appeared near the orifice exit. Finally, two types of choking have been identified for flash boiling jets, i.e., vaporization-induced choking and expansion-induced choking. The former one is mainly ascribed to the vapor formation in the orifice which reduces the local speed of sound, while the latter one is due to the expansion of under-expanded two-phase flow and the resultant flow acceleration.

42 ENGINEERING↗

Continuous symmetry breaking in a two-dimensional Rydberg array

Spontaneous symmetry breaking underlies much of our classification of phases of matter and their associated transitions. The nature of the underlying symmetry being broken determines many of the qualitative properties of the phase; this is illustrated by the case of discrete versus continuous symmetry breaking. Indeed, in contrast to the discrete case, the breaking of a continuous symmetry leads to the emergence of gapless Goldstone modes controlling, for instance, the thermodynamic stability of the ordered phase. Here, we realize a two-dimensional dipolar XY model that shows a continuous spin-rotational symmetry using a programmable Rydberg quantum simulator. We demonstrate the adiabatic preparation of correlated low-temperature states of both the XY ferromagnet and the XY antiferromagnet. In the ferromagnetic case, we characterize the presence of a long-range XY order, a feature prohibited in the absence of long-range dipolar interaction. In conclusion, our exploration of the many-body physics of XY interactions complements recent works using the Rydberg-blockade mechanism to realize Ising-type interactions showing discrete spin rotation symmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Tuning the Radius Ratio to Enhance Thermoelectric Properties in the Zintl Compounds AM 2 Sb 2 (A = Ba, Sr; M = Zn, Cd)

Five novel Zintl phase solid solutions in the Ba 1–x Sr x Zn 2–y Cd y Sb 2 (0 ≤ x ≤ 0.13(1); 0 ≤ y ≤ 0.32(2)) system were successfully synthesized by the molten Pb metal-flux method, and the powder X-ray diffraction and single-crystal X-ray diffraction analyses proved that all five title compounds adopted the BaCu 2 S 2 -type phase having the orthorhombic Pnma space group (Z = 4, Pearson code oP20) with five crystallographically independent atomic sites. The previously studied BaCu 2 S 2 -type antimonides demonstrated a limited tolerance for doping in contrast to the CaAl 2 Si 2 -type antimonides. To understand the relatively narrower phase width and limited dopability of the title BaCu 2 S 2 -type phase than the CaAl 2 Si 2 -type phase in the overall Ba 1–x Sr x Zn 2–y Cd y Sb 2 system, the radius ratio of cations and anionic elements r + /r – for two structure types were thoroughly investigated. For the first time, the r + /r – ratio was identified as a critical factor for the phase selectivity: (1) r + /r – > 1 favored the BaCu 2 S 2 -type phase, and (2) r + /r – < 1 favored the CaAl 2 Si 2 -type phase. Further, we also revealed the structural transformation mechanism from the more widely observed CaAl 2 Si 2 -type phase to the title BaCu 2 S 2 -type phase as the relatively larger cationic elements were introduced to the system. A series of DFT calculations using the three hypothetical models indicated that a resonance peak near EF in the density of states curves was descended from the relatively flat band structure at several special symmetry points rationalizing the enhanced Seebeck coefficients of Ba 0.94(1) Sr 0.06 Zn 1.86(3) Cd 0.14 Sb 2 and Ba 0.96(1) Sr 0.04 Zn 1.68(2) Cd 0.32 Sb 2 . Electron localization function analysis rationalized the correlation between the polarity change of anionic Zn/Cd–Sb bonds and the charge carrier mobility on the anionic frameworks. Temperature-dependent thermoelectric properties were studied for the four title compounds, and the results proved that the Sr and Cd doping in the title Ba 1–x Sr x Zn 2–y Cd y Sb 2 system successfully enhanced the ZT values through the increased Seebeck coefficients and the reduced total thermal conductivities.

36 MATERIALS SCIENCE↗

The interpenetration polymer network in a cement paste–waterborne epoxy system

The formation of the interpenetrating polymer network (IPN) structure within the cement-polymer system has been revealed by experiments from 2 dimensional to 3-dimensional scales. However, the microstructure design and performance prediction of IPN as a function of specific C-S-H/polymer components or ingredients' parameters e.g. water to cement ratios (w/c), polymer to cement ratios (p/c), monomer components, degree of polymerization (DP), etc. is by far not available. Here we developed a mesoscale model for IPN visualization based on the Flory-Huggins interaction theory which was applied to cement science for the first time. All the ingredients in the micro-structure were considered as soluble beads with rational sizes based on their properties obtained by molecular dynamic methods. The interaction parameters of each bead were then determined based on their element ratios and chemical backbones. The model was validated with the waterborne epoxy-cement material (WECM) in which a novel waterborne epoxy resin (WEP) was prepared and impregnated. The verification results on the 2D-3D scale show that the developed model predicts the WECM's IPN structures by rule and line concerning DP, w/c, and p/c in the mixture. The C-S-H beads were progressively scaled in size which alters the C-S-H texture to have completely different dissolution characteristics. Beads of diameter ~6 Å are more unstable and soluble which enable them to form a continuous phase in water or a composite structure with WEP. In contrast, beads with diameters larger than 10 Å have different properties with stronger nucleation effects. The results also suggest the impregnation content of WEP in cement-based material should be limited to 10% vol. to prevent the polymer IPN from decomposing into discrete clusters. The application of Flory-Huggins theory in cement-based composites demonstrates great potential in performance prediction and microstructure design.

36 MATERIALS SCIENCE↗

High radiation tolerance of an ultrastrong nanostructured NiCoCr alloy with stable dispersed nanooxides and fine grain structure

The present paper reports the irradiation behavior of nanostructured NiCoCr medium entropy alloy enhanced by Y-Hf-O nanooxides and fine grains produced by powder metallurgy. Ion beam irradiation to a peak dose of 130 dpa at 580°C produced neither detectable void swelling nor irradiation-induced hardening, in contrast to significant void swelling and property degradation of single phase NiCoCr concentrated solid-solution alloy under the similar irradiation condition. The dispersed nanooxides and high density of grain boundaries act as defect sinks that effectively annihilate irradiation-induced interstitials and vacancies. Furthermore, high-density nanooxides maintain their crystalline structures and stabilize the grain boundaries during irradiation.

36 MATERIALS SCIENCE↗

Differentiating Hund from Mott physics in a three-band Hubbard-Hund model: Temperature dependence of spectral, transport, and thermodynamic properties

We study the interplay between Mott physics, driven by Coulomb repulsion U, and Hund physics, driven by Hund's coupling J, for a minimal model for Hund metals, the orbital-symmetric three-band Hubbard-Hund model (3HHM) for a lattice filling of 1/3. Hund-correlated metals are characterized by spin-orbital separation (SOS), a Hund's-rule-induced two-stage Kondo-type screening process, in which spin screening occurs at much lower energy scales than orbital screening. By contrast, in Mott-correlated metals, lying close to the phase boundary of a metal-insulator transition, the SOS window becomes negligibly small and the Hubbard bands are well separated. Using dynamical mean-field theory and the numerical renormalization group as real-frequency impurity solver, we identify numerous fingerprints distinguishing Hundness from Mottness in the temperature dependence of various physical quantities. Furthermore, These include ARPES-type spectra, the local self-energy, static local orbital and spin susceptibilities, resistivity, thermopower, and lattice and impurity entropies. Our detailed description of the behavior of these quantities within the context of a simple model Hamiltonian will be helpful for distinguishing Hundness from Mottness in experimental and theoretical studies of real materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Transformer quantum state: A multipurpose model for quantum many-body problems

Here, inspired by the advancements in large language models based on transformers, we introduce the transformer quantum state (TQS): a versatile machine learning model for quantum many-body problems. In sharp contrast to Hamiltonian/task specific models, TQS can generate the entire phase diagram, predict field strengths with experimental measurements, and transfer such a knowledge to new systems it has never been trained on before, all within a single model. With specific tasks, fine-tuning the TQS produces accurate results with small computational cost. Versatile by design, TQS can be easily adapted to new tasks, thereby pointing towards a general-purpose model for various challenging quantum problems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DC-Link Current Minimization Control for Current Source Converter-Based Solid-State Transformer

This article proposes a fast predictive control method and a small DC-link inductor to minimize the DC-link current in current-source converter (CSC)-based solid-state transformer. The DC-link current minimization can significantly reduce power loss and improve efficiency. The challenge of this problem is on improving both steady-state and dynamic performance. PI control methods and large DC-link inductors are conventionally used in the CSC but have limited dynamic performance. A model predictive control (MPC) method is proposed to achieve switching-cycle-level settling time, and the DC-link inductor is sized for 40% ripple to enable fast current change. Importantly, this article also proposes to minimize the DC-link current by varying the current even within a line cycle under single-phase load to improve the steady-state performance, in contrast with the reduction to a constant value in the literature. The proposed MPC features a constant switching frequency without weighting factors. The MPC does not have a high computational burden and is implemented in a regular digital controller for a prototype of soft-switching solid-state transformer (S4T) with reduced conduction loss. The effectiveness of the proposed method has been experimentally verified on the SiC S4T prototype during steady-state and dynamics under different multiport power flow conditions up to 2 kV peak. Here, the DC-link current in the experiments is close to the minimum current with a short zero-vector duration, which further verifies the performance of the proposed method.

14 SOLAR ENERGY↗

Experimental Investigation of Interactions Between Two Closely Spaced Azimuthal Modes in a Multinozzle Can Combustor

Thermoacoustic instabilities in annular or circular combustors are often coupled with azimuthal modes. These modes can be characterized by a spin ratio (SR), which quantifies the dominant mode between two counter-rotating waves, and a phase difference between them, which is directly related to the orientation of the antinodal line. This study investigates the instability amplitudes, SR, and phase difference of two closely spaced (3% of their mean frequency), yet distinct azimuthal modes; one is the first azimuthal (1A) mode, and the other is a combination of first azimuthal and first longitudinal (1A1L) mode. Each mode itself consists of two peaks that are spaced even more closely in frequency (0.8%). Furthermore, distinct harmonics at 2× and 3× of these frequencies, presumably associated with nonlinearities, are also evident in the spectra. Each mode is bandpass filtered in spectrum to analyze them separately. For the 1A mode, the SR and phase difference exhibit a variety of behaviors—including quasi-periodic standing waves, spinning waves, and intermittency—depending on operating conditions such as thermal power and azimuthal fuel staging. Similar trends are observed for the 1A1 L mode. Moreover, there is clear coupling between the 1A and 1A1 L modes, as their SRs are almost synchronized during the quasi-periodic standing wave. This synchronization is observed in phase differences as well, but not in the instability amplitude. For spinning dominant wave conditions, the SRs of each mode have similar average values, but they fluctuate in a seemingly random fashion. For the phase difference, both average and fluctuation are not correlated. In contrast, the instability amplitudes are strongly correlated, with modulation of the 1A mode leading to that of the 1A1 L mode. Furthermore, these results clearly indicate that complex coupling occurs across closely spaced frequencies under instability conditions, coupling that must be understood in order to capture limit cycle dynamics.

33 ADVANCED PROPULSION SYSTEMS↗