Simple power analysis is the most devastating attack on the security of elliptic curve scalar multiplication and can probably retrieve the secret key. In this paper,we analyze the formulas of point doubling and additi...Simple power analysis is the most devastating attack on the security of elliptic curve scalar multiplication and can probably retrieve the secret key. In this paper,we analyze the formulas of point doubling and addition on Jacobi-quartic Curve in projective coordination. In addition,a fast and secure side-channel atomic scalar multiplication algorithm is proposed using the side-channel atomic block. Compared with the previous methods,the new algorithm is more efficient. For 192 bits scalar using NAF recoding,the efficiency of the new algorithm is increased by about 6.7%～23% if S/M=0.8 or 12.7%～33.2% if S/M=0.6.展开更多
Platinum clusters(Pt_(n))are extensively used as electrocatalysts for oxygen reduction reaction(ORR)because they provide excellent performance together with a reduced Pt requirement.However,the precise synthesis and a...Platinum clusters(Pt_(n))are extensively used as electrocatalysts for oxygen reduction reaction(ORR)because they provide excellent performance together with a reduced Pt requirement.However,the precise synthesis and atomic-level insights into the structure-activity relationship of Pt_(n) remain a great challenge.Here,we present a combinatorial synthesis and analysis method to investigate the atomicity-activity relationships of Pt_(n) at the individual level.We employ single nanoparticle collision electrochemistry to facilitate the in-situ electrodeposition of a single precisely tunable Pt_(n) on the graphene quantum dot support,followed by instantaneous measurement of the intrinsic ORR activity of the resulting Pt_(n).By relying on highly sensitive electrochemical measurements,our investigations clarify the atomicity-specific ORR activity of Pt_(n),which is attributed to their distinct geometric and electronic structures at varying cluster sizes.Significantly,Pt_(n) with low atomicity,especially below 20,can reach extraordinarily high ORR activities due to atom-by-atom arrangement.Our work provides a simple and efficient method for investigating the atomicity-activity relationships of other nanoclusters under real reaction conditions,enabling a better design of the electrocatalysts at the atomic level.展开更多
In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale in...In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale inequalities of mixed quasi-martingale Hardy spaces.Moreover,we furnish sufficient conditions for the boundedness ofσ-sublinear operators in these spaces.These findings extend the existing conclusions regarding mixed quasi-martingale Hardy spaces defined with the help of the mixed L_(p)-norm.展开更多
Scalability remains a major challenge in building practical fault-tolerant quantum computers.Currently,the largest number of qubits achieved across leading quantum platforms ranges from hundreds to thousands.In atom a...Scalability remains a major challenge in building practical fault-tolerant quantum computers.Currently,the largest number of qubits achieved across leading quantum platforms ranges from hundreds to thousands.In atom arrays,scalability is primarily constrained by the capacity to generate large numbers of optical tweezers,and conventional techniques using acousto-optic deflectors or spatial light modulators struggle to produce arrays much beyond∼10,000 tweezers.Moreover,these methods require additional microscope objectives to focus the light into micrometer-sized spots,which further complicates system integration and scalability.Here,we demonstrate the experimental generation of an optical tweezer array containing 280×280 spots using a metasurface,nearly an order of magnitude more than most existing systems.The metasurface leverages a large number of subwavelength phase-control pixels to engineer the wavefront of the incident light,enabling both large-scale tweezer generation and direct focusing into micron-scale spots without the need for a microscope.This result shifts the scalability bottleneck for atom arrays from the tweezer generation hardware to the available laser power.Furthermore,the array shows excellent intensity uniformity exceeding 90%,making it suitable for homogeneous single-atom loading and paving the way for trapping arrays of more than 10,000 atoms in the near future.展开更多
Atomic spin gyroscopes are promising candidates for next-generation inertial navigation due to extremely high theoretical precision,relatively small size among atomic gyroscopes,and promising potential for miniaturiza...Atomic spin gyroscopes are promising candidates for next-generation inertial navigation due to extremely high theoretical precision,relatively small size among atomic gyroscopes,and promising potential for miniaturization.In particular,the spin-exchange relaxation-free(SERF)atomic gyroscope relies on optical pumping to polarize atoms,enabling rotation sensing through the Faraday optical rotation angle(FORA).However,fluctuations in atomic density introduce systematic errors in FORA measurements,limiting long-term stability.We present a data-driven decoupling method that isolates atomic density fluctuations from the FORA signal by modeling spatially resolved light absorption in the vapor cell.The model accounts for the spatial distribution of spin polarization in the pump-light interaction volume,density-dependent relaxation rates,wall-induced relaxation,and polarization diffusion,and is implemented within a finite-element framework.Compared to the conventional Lambert-Beer law,which assumes one-dimensional homogeneity,our approach captures the full threedimensional density and polarization distribution,significantly improving the accuracy of light absorption modeling.The resulting absorption-density maps are used to train a feedforward neural network,yielding a high-precision estimator for atomic density fluctuations.This estimator enables the construction of a decoupling equation that separates the density contribution from the FORA signal.Experimental validation shows that this method improves the bias instability atσ(100 s)of the gyroscope was improved by 73.1%compared to traditional platinum-resistance-based stabilization.The proposed framework is general and can be extended to other optical pumping-based sensors,such as optically pumped magnetometers.展开更多
We prepared Co_(x)Pt_(100-x)(x=40,45,50,55,60)nanoparticles by the sol-gel method.The phase composition and crystal structure,morphology and microstructure,and magnetic properties of the samples were characterized and...We prepared Co_(x)Pt_(100-x)(x=40,45,50,55,60)nanoparticles by the sol-gel method.The phase composition and crystal structure,morphology and microstructure,and magnetic properties of the samples were characterized and tested using X-ray diffraction(XRD),transmission electron microscopy(TEM),and vibrating sample magnetometer(VSM),respectively.The results demonstrate that the coercivity of CoPt nanoparticles can be effectively controlled by adjusting the atomic ratio of Co and Pt in the samples.Among the compositions studied,the Co_(45)Pt_(55)sample synthesized by the sol-gel method exhibits smaller grain size and a coercivity as high as 6.65×10^(5) A/m is achieved.The morphology and microstructure of the nanoparticles were analyzed by TEM images,indicating that a slight excess of Pt can effectively enhance the coercivity of CoPt nanoparticles.展开更多
Fenton-like technology based on peroxymonosulfate activation has shown great potential in refractory organics degradation.In this work,single Fe atom catalysts were synthesized through facile ball milling and exhibite...Fenton-like technology based on peroxymonosulfate activation has shown great potential in refractory organics degradation.In this work,single Fe atom catalysts were synthesized through facile ball milling and exhibited very high performance in peroxymonosulfate activation.The Fe single-atom filled an N vacancy on the triazine ring edge of C_(3)N_(4),as confirmed through X-ray absorption fine structure,density functional calculation and elec-tron paramagnetic resonance.The SAFe_(0.4)–C_(3)N_(4)/PMS system could completely remove phenol(20 mg/L)within 10 min and its first-order kinetic constant was 12.3 times that of the Fe_(3)O_(4)/PMS system.Under different ini-tial pH levels and in various anionic environments,SAFe_(0.4)–C_(3)N_(4) still demonstrated excellent catalytic activity,achieving a removal rate of over 90%for phenol within 12 min.In addition,SAFe_(0.4)–C_(3)N_(4) exhibited outstanding selectivity in reaction systems with different pollutants,showing excellent degradation effects on electron-rich pollutants only.Hydroxyl radicals(•OH),singlet oxygen(1O_(2))and high-valent iron oxide(Fe(Ⅳ)=O)were de-tected in the SAFe_(0.4)–C_(3)N_(4)/PMS system through free radical capture experiments.Further experiments on the quenching of active species and a methyl phenyl sulfoxide probe confirmed that 1O_(2) and Fe(Ⅳ)=O played dom-inant roles.Additionally,the change in the current response after adding PMS and phenol in succession proved that a direct electron transfer path between organic matter and the catalyst surface was unlikely to exist in the SAFe_(0.4)–C_(3)N_(4)/PMS/Phenol degradation system.This study provides a new demonstration of the catalytic mech-anism of single-atom catalysts.展开更多
Introduction of active centers,such as oxygen vacancy and metal single atoms,has emerged as a promising strategy to further improve the electrochemical properties of transition metal oxide electrodes for high-performa...Introduction of active centers,such as oxygen vacancy and metal single atoms,has emerged as a promising strategy to further improve the electrochemical properties of transition metal oxide electrodes for high-performance pseudocapacitors.Here,an unprecedented MoO_(3)with multiple active centers,Ni anchored reduced MoO_(3)with oxygen vacancy(NirMoO_(3-x)),was in situ synthesized via γ-ray radiationinduced one-pot strategy under ambient conditions.This approach leverages the synergistic effects of radiation activation,etching,and reduction.The characteristics of multiple valence states(Mo^(4+/5+/6+)and Ni^(0/2+)),oxygen vacancies,single atoms,and atomic clusters in NirMoO_(3-x) were determined by X-ray photoelectron spectroscopy(XPS),X-ray absorption fine structure spectroscopy(XAFS),and atomic-resolution aberrationcorrected high-angle annular dark-field scanning transmission electron microscopy(HAADF-STEM)measurements.Notably,Ni-rMoO_(3-x)exhibited exceptional pseudocapacitive performance,with ultrahigh specific charge(881.0 C·g^(-1)at 1 A·g^(-1),more than twice that of MoO_(3)),fast charge/discharge rates,and remarkable cycle life stability(98.5% capacitance retention after 10,000 cycles).Furthermore,a hybrid supercapacitor device(Ni-rMoO_(3-x)//activated carbon(AC))demonstrated a high energy density of 97.8 Wh·kg^(-1)at a power density of 0.90 kW·kg^(-1)and exhibited excellent mechanical flexibility for practical applications.展开更多
Fe-N-C catalysts,as promising non-precious metal alternatives for the oxygen reduction reaction(ORR),still suffer from severe mass transport limitations in proton exchange membrane fuel cells(PEMFCs)due to water flood...Fe-N-C catalysts,as promising non-precious metal alternatives for the oxygen reduction reaction(ORR),still suffer from severe mass transport limitations in proton exchange membrane fuel cells(PEMFCs)due to water flooding of active sites embedded in micropores.Although pore engineering through a selected template is a general strategy,the structural features of an ideal template,particularly those governing the exposure of active sites and thus affecting mass transport,remain elusive.Here,we demonstrate that low-porosity carbon templates maximize the ratio of active sites distributed at or near the surface,thereby enhancing their exposure and accessibility while reducing mass transport resistance during the ORR process.The C_(lp-1)@PPy and C_(lp-2)@PPy(PPy=polypyrrole)catalysts,derived from low-porosity carbon templates,achieve peak power densities of 0.96 and 1.03 W·cm^(-2) under H_(2)/O_(2)and 0.50 and 0.52 W·cm^(-2) under H_(2)/air,demonstrating excellent performance in PEMFC tests.Structural and electrochemical characterizations reveal that the enhanced surface exposure of active sites effectively mitigates mass transport resistance during the ORR,thereby offering a general design principle for overcoming mass transport limitations in Fe-N-C catalysts for PEMFC applications.展开更多
High-pressure electrides,characterized by the presence of interstitial quasi-atoms(ISQs),possess unique electronic structures and physical properties,such as diverse dimensions of electride states exhibiting different...High-pressure electrides,characterized by the presence of interstitial quasi-atoms(ISQs),possess unique electronic structures and physical properties,such as diverse dimensions of electride states exhibiting different superconductivity,which has attracted significant attention.Here,we report a new electron-deficient type of electride Li_(4)Al and identify its phase transition progress with pressurization,where the internal driving force behind phase transitions,bonding characteristics,and superconducting behaviors have been revealed based on first-principles density functional theory.Through analysis of the bonding properties of electride Li_(4)Al,we demonstrate that the ISQs exhibiting increasingly covalent characteristics between Al ions play a critical role in driving the phase transition.Our electron–phonon coupling calculations indicate that all phases exhibit superconducting behaviors.Importantly,we prove that the ISQs behave as free electrons and demonstrate that the factor governing T_(c) is primarily derived from Li-p-hybridized electronic states with ISQ compositions.These electronic states are scattered by low-frequency phonons arising from mixed vibrations of Li and Al affected by ISQs to enhance electron–phonon coupling.Our study largely expands the research scope of electrides,provides new insight for understanding phase transitions,and elucidates the effects of ISQs on superconducting behavior.展开更多
We report the results of the experiment on synthesizing ^(287,288)Mc isotopes (Z=115) using the fusionevaporation reaction ^(243)Am(^(48)Ca,4n,3n)^(287,288)Mc at the Spectrometer for Heavy Atoms and Nuclear Structure-...We report the results of the experiment on synthesizing ^(287,288)Mc isotopes (Z=115) using the fusionevaporation reaction ^(243)Am(^(48)Ca,4n,3n)^(287,288)Mc at the Spectrometer for Heavy Atoms and Nuclear Structure-2(SHANS2),a gas-filled recoil separator located at the China Accelerator Facility for Superheavy Elements(CAFE2).In total,20 decay chains are attributed to ^(288)Mc and 1 decay chain is assigned to ^(287)Mc.The measured oa-decay properties of ^(287,288)Mc as well as its descendants are consistent with the known data.No additional decay chains originating from the 2n or 5n reaction channels were detected.The excitation function of the ^(243)Am(^(48)Ca,3n)^(288)Mc reaction was measured at the cross-section level of picobarn,which indicates the promising capability for the study of heavy and superheavy nuclei at the facility.展开更多
Optical non-reciprocity is a fundamental phenomenon in photonics.It is crucial for developing devices that rely on directional signal control,such as optical isolators and circulators.However,most research in this fie...Optical non-reciprocity is a fundamental phenomenon in photonics.It is crucial for developing devices that rely on directional signal control,such as optical isolators and circulators.However,most research in this field has focused on systems in equilibrium or steady states.In this work,we demonstrate a room-temperature Rydberg atomic platform where the unidirectional propagation of light acts as a switch to mediate time-crystalline-like collective oscillations through atomic synchronization.展开更多
Single-atom catalysts based on graphitic carbon nitride(g-C_(3)N_(4))show high potential for hydrogen production photocatalytically.However,it is still a challenge to develop single-atom-based g-C_(3)N_(4)due to the c...Single-atom catalysts based on graphitic carbon nitride(g-C_(3)N_(4))show high potential for hydrogen production photocatalytically.However,it is still a challenge to develop single-atom-based g-C_(3)N_(4)due to the complex synthesis procedures,limited active sites,and insufficient mechanistic understanding.Herein,a facile oxygen-tolerant synthesis strategy was developed,which utilizes the nitrogen-rich structure of g-C_(3)N_(4)to capture Fe single atoms from ammonium iron citrate,successfully constructing an efficient photocatalytic composite.The resulting Fe single-atom-modified g-C_(3)N_(4)catalyst exhibited highly improved light absorption,charge carrier separation,and a substantially enhanced rate of H_(2)production photocatalytically under visible light irradiation.Experimental results demonstrated that the optimal sample achieves a H_(2)production rate of 683μmol·h-1·g^(-1),representing a 425% enhancement compared to pristine g-C_(3)N_(4).This study presents a facile oxygen-tolerant approach for metal immobilization using metal-organic precursors,where the nitrogen-rich framework of g-C_(3)N_(4)effectively captures Fe atoms as singular site within the composite.The developed synthesis strategy provides new insights for designing high-performance single-atom photocatalytic materials,potentially advancing the application and development of photocatalysis.展开更多
The design of cost-effective and efficient metal-free carbon-based catalysts for the hydrogen evolution reaction(HER)is of great significance for increasing the production of clean hydrogen by the electrolysis of alka...The design of cost-effective and efficient metal-free carbon-based catalysts for the hydrogen evolution reaction(HER)is of great significance for increasing the production of clean hydrogen by the electrolysis of alkaline water.Precise control of the electronic structure by heteroatom doping has proven to be efficient for increasing catalytic activity.Nevertheless,both the structural characteristics and the underlying mechanism are not well understood,especially for doping with two different atoms,thus limiting the use of these catalysts.We report the production of phosphorus and nitrogen co-doped hollow carbon nanospheres(HCNs)by the copolymerization of pyrrole and aniline at a Triton X-100 micelle-interface,followed by doping with phytic acid and carbonization.The unique pore structure and defect-rich framework of the HCNs expose numerous active sites.Crucially,the combined effect of graphitic nitrogen and phosphorus-carbon bonds modulate the local electronic structure of adjacent C atoms and facilitates electron transfer.As a res-ult,the HCN carbonized at 1100°C exhibited superior HER activity and an outstanding stability(70 h at a current density of 10 mA cm^(−2))in alkaline water,because of the large number of graphitic nitrogen and phosphorus-carbon bonds.展开更多
The regioselective carbon-hydrogen bond functionalization reaction in atom-and step-economy holds significant potential for the late-stage elaboration of complex molecules and natural products.In recent years,the hydr...The regioselective carbon-hydrogen bond functionalization reaction in atom-and step-economy holds significant potential for the late-stage elaboration of complex molecules and natural products.In recent years,the hydrogen atom transfer strategy involving radicals has garnered considerable attention from chemists due to its high chemoselectivity and regioselectivity.However,owing to the marginal differences in bond dissociation energies(BDEs)among C(sp^(3))—H bonds,hydrogen atom transfer reactions mediated by alkyl radicals remain less-developed.A copper-catalyzed sulfone-induced regioselective C(sp^(3))—H bond heteroarylation reaction was reported.This strategy utilizes theα-alkyl radical of sulfone as an intramolecular hydrogen abstraction reagent,enabling the regioselective formation of carbon-nitrogen bonds under copper catalysis.展开更多
Lithium-sulfur (Li-S) batteries have gained great attention due to the high theoretical energy density and low cost,yet their further commercialization has been obstructed by the notorious shuttle effect and sluggish ...Lithium-sulfur (Li-S) batteries have gained great attention due to the high theoretical energy density and low cost,yet their further commercialization has been obstructed by the notorious shuttle effect and sluggish redox dynamics.Herein,we supply a strategy to optimize the electron structure of Ni_(2)P by concurrently introducing B-doped atoms and P vacancies in Ni_(2)P (Vp-B-Ni_(2)P),thereby enhancing the bidirectional sulfur conversion.The study indicates that the simultaneous introduction of B-doped atoms and P vacancies in Ni_(2)P causes the redistribution of electron around Ni atoms,bringing about the upward shift of d-band center of Ni atoms and effective d-p orbital hybridization between Ni atoms and sulfur species,thus strengthening the chemical anchoring for lithium polysulfides (LiPSs) as well as expediting the bidirectional conversion kinetics of sulfur species.Meanwhile,theoretical calculations reveal that the incorporation of B-doped atoms and P vacancies in Ni_(2)P selectively promotes Li2S dissolution and nucleation processes.Thus,the Li-S batteries with Vp-B-Ni_(2)P-separators present outstanding rate ability of 777 m A h g^(-1)at 5 C and high areal capacity of 8.03 mA h cm^(-2)under E/S of 5μL mg^(-1)and sulfur loading of 7.20 mg cm^(-2).This work elucidates that introducing heteroatom and vacancy in metal phosphide collaboratively regulates the electron structure to accelerate bidirectional sulfur conversion.展开更多
Exploring efficient microwave absorbing materials(MAMs)has gradually become a hot topic in recent years because it is crucial in both civil and military fields.Metal-organic framework(MOF)has great potential due to it...Exploring efficient microwave absorbing materials(MAMs)has gradually become a hot topic in recent years because it is crucial in both civil and military fields.Metal-organic framework(MOF)has great potential due to its unique composition and bonding mode,which has advantages such as large specific surface area,high porosity,adjustable structure,and designable composition.Herein,MOF-derived MAMs are highlighted based on morphology and structure.The synthesis strategies of MOF-derived MAMs of different dimensions are discussed.On this basis,the structure-activity relationships can be deeply explored through the precise control of material structure and property by atomic engineering.Finally,perspectives are given for the existing problems of MOF-derived MAMs,which will open a new horizon and promote the development of MAMs.展开更多
Exploiting non-precious metal catalysts with excellent oxygen reduction reaction(ORR)performance for energy devices is paramount essential for the green and sustainable society development.Herein,low-cost,high-perform...Exploiting non-precious metal catalysts with excellent oxygen reduction reaction(ORR)performance for energy devices is paramount essential for the green and sustainable society development.Herein,low-cost,high-performance biomass-derived ORR catalysts with an asymmetric Fe-N_(3)P configuration was prepared by a simple pyrolysis-etching technique,where carboxymethyl cellulose(CMC)was used as the carbon source,urea and 1,10-phenanthroline iron complex(FePhen)as additives,and Na_(3)PO_(4)as the phosphorus dopant and a pore-forming agent.The CMC-derived FeNPC catalyst displayed a large specific area(BET:1235 m^(2)g^(-1))with atomically dispersed Fe-N_(3)P active sites,which exhibited superior ORR activity and stability in alkaline solution(E_(1/2)=0.90 V vs.RHE)and Zn-air batteries(P_(max)=149 mW cm^(-2))to commercial Pt/C catalyst(E_(1/2)=0.87 V,P_(max)=118 mW cm^(-2))under similar experimental conditions.This work provides a feasible and costeffective route toward highly efficient ORR catalysts and their application to Zn-air batteries for energy conversion.展开更多
The T_(1)(Al_(2) CuLi)phase is one of the most effective strengthening nanoscale-precipitate in Al-Cu alloys with Li.However,its formation and evolution still need to be further clarified during aging due to the compl...The T_(1)(Al_(2) CuLi)phase is one of the most effective strengthening nanoscale-precipitate in Al-Cu alloys with Li.However,its formation and evolution still need to be further clarified during aging due to the complex precipitation sequences.Here,a detailed investigation has been carried out on the atomic struc-tural evolution of T_(1) precipitate in an aged Al-Cu-Li-Mg-Ag alloy using state-of-the-art Cs-corrected high-angle annular dark field(HAADF)-coupled with integrated differential phase contrast(iDPC)-scanning transmission electron microscopy(STEM)and energy-dispersive X-ray spectroscopy(EDXS)techniques.An intermediate T_(1)’phase between T_(1p) and T_(1) phase,with a crystal structure and orientation rela-tionship consistent with T_(1),but exhibiting different atomic occupancy and chemical composition was found.We observed the atomic structural transformation from T_(1p) to T_(1)’phase(fcc→hcp),involving only 1/12<112>Al shear component.DFT calculation results validated our proposed structural models and the precipitation sequence.Besides,the distributions of minor solute elements(Ag,Mg,and Zn)in the pre-cipitates exhibited significant differences.These findings may contribute to a further understanding of the nucleation mechanism of T_(1) precipitate.展开更多
Combustion dynamics are a critical factor in determining the performance and reliabilityof a chemical propulsion engine.The underlying processes include liquid atomization,evaporation,mixing,and chemical reactions.Thi...Combustion dynamics are a critical factor in determining the performance and reliabilityof a chemical propulsion engine.The underlying processes include liquid atomization,evaporation,mixing,and chemical reactions.This paper presents a high-fidelity numerical study of liquidatomization and spray combustion under high-pressure conditions,emphasizing the effects of pres-sure oscillations on the flow evolution and combustion dynamics.The theoretical framework isbased on the three-dimensional conservation equations for multiphase flows and turbulent combus-tion.The numerical solution is achieved using a coupling method of volume-of-fluid and Lagran-gian particle tracking.The Zhuang-Kadota-Sutton(ZKS)high-pressure evaporation model andthe eddy breakup-Arrhenius combustion model are employed.Simulations are conducted for amodel combustion chamber with impinging-jet injectors using liquid oxygen and kerosene as pro-pellants.Both conditions with and without inlet and outlet pressure oscillations are considered.Thefindings reveal that pressure oscillations amplify flow fluctuations and can be characterized usingkey physical parameters such as droplet evaporation,chemical reaction,and chamber pressure.The spectral analysis uncovers the axial variations of the dominant and secondary frequenciesand their amplitudes in terms of the characteristic physical quantities.This research helps establisha methodology for exploring the coupling effect of liquid atomization and spray combustion.It alsoprovides practical insights into their responses to pressure oscillations during the occurrence ofcombustion instability.This information can be used to enhance the design and operation ofliquid-fueled propulsion engines.展开更多
基金sponsored and financial supported by National Natural Science Foundation of China (NSFC), grant No.61003121Sichuan Province High Technology Program under No.2009CD00014
文摘Simple power analysis is the most devastating attack on the security of elliptic curve scalar multiplication and can probably retrieve the secret key. In this paper,we analyze the formulas of point doubling and addition on Jacobi-quartic Curve in projective coordination. In addition,a fast and secure side-channel atomic scalar multiplication algorithm is proposed using the side-channel atomic block. Compared with the previous methods,the new algorithm is more efficient. For 192 bits scalar using NAF recoding,the efficiency of the new algorithm is increased by about 6.7%～23% if S/M=0.8 or 12.7%～33.2% if S/M=0.6.
基金financially supported by the National Natural Science Foundation of China(22272052)the Major Research Project(92061108)the Science and Technology Commission of Shanghai Municipality(24DX1400200)。
文摘Platinum clusters(Pt_(n))are extensively used as electrocatalysts for oxygen reduction reaction(ORR)because they provide excellent performance together with a reduced Pt requirement.However,the precise synthesis and atomic-level insights into the structure-activity relationship of Pt_(n) remain a great challenge.Here,we present a combinatorial synthesis and analysis method to investigate the atomicity-activity relationships of Pt_(n) at the individual level.We employ single nanoparticle collision electrochemistry to facilitate the in-situ electrodeposition of a single precisely tunable Pt_(n) on the graphene quantum dot support,followed by instantaneous measurement of the intrinsic ORR activity of the resulting Pt_(n).By relying on highly sensitive electrochemical measurements,our investigations clarify the atomicity-specific ORR activity of Pt_(n),which is attributed to their distinct geometric and electronic structures at varying cluster sizes.Significantly,Pt_(n) with low atomicity,especially below 20,can reach extraordinarily high ORR activities due to atom-by-atom arrangement.Our work provides a simple and efficient method for investigating the atomicity-activity relationships of other nanoclusters under real reaction conditions,enabling a better design of the electrocatalysts at the atomic level.
基金Supported by the National Natural Science Foundation of China(11871195)。
文摘In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale inequalities of mixed quasi-martingale Hardy spaces.Moreover,we furnish sufficient conditions for the boundedness ofσ-sublinear operators in these spaces.These findings extend the existing conclusions regarding mixed quasi-martingale Hardy spaces defined with the help of the mixed L_(p)-norm.
基金supported by the National Natural Science Foundation of China (Grant No.92576208)Tsinghua University Initiative Scientific Research Program+1 种基金Beijing Science and Technology Planning ProjectTsinghua University Dushi Program。
文摘Scalability remains a major challenge in building practical fault-tolerant quantum computers.Currently,the largest number of qubits achieved across leading quantum platforms ranges from hundreds to thousands.In atom arrays,scalability is primarily constrained by the capacity to generate large numbers of optical tweezers,and conventional techniques using acousto-optic deflectors or spatial light modulators struggle to produce arrays much beyond∼10,000 tweezers.Moreover,these methods require additional microscope objectives to focus the light into micrometer-sized spots,which further complicates system integration and scalability.Here,we demonstrate the experimental generation of an optical tweezer array containing 280×280 spots using a metasurface,nearly an order of magnitude more than most existing systems.The metasurface leverages a large number of subwavelength phase-control pixels to engineer the wavefront of the incident light,enabling both large-scale tweezer generation and direct focusing into micron-scale spots without the need for a microscope.This result shifts the scalability bottleneck for atom arrays from the tweezer generation hardware to the available laser power.Furthermore,the array shows excellent intensity uniformity exceeding 90%,making it suitable for homogeneous single-atom loading and paving the way for trapping arrays of more than 10,000 atoms in the near future.
基金supported by the Beijing Natural Science Foundation(Grant No.3252013)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0300402)+1 种基金the National Natural Science Foundation of China(Grant No.61673041)Key Area Research and Development Program of Guangdong Province(Grant No.2021B0101410005)。
文摘Atomic spin gyroscopes are promising candidates for next-generation inertial navigation due to extremely high theoretical precision,relatively small size among atomic gyroscopes,and promising potential for miniaturization.In particular,the spin-exchange relaxation-free(SERF)atomic gyroscope relies on optical pumping to polarize atoms,enabling rotation sensing through the Faraday optical rotation angle(FORA).However,fluctuations in atomic density introduce systematic errors in FORA measurements,limiting long-term stability.We present a data-driven decoupling method that isolates atomic density fluctuations from the FORA signal by modeling spatially resolved light absorption in the vapor cell.The model accounts for the spatial distribution of spin polarization in the pump-light interaction volume,density-dependent relaxation rates,wall-induced relaxation,and polarization diffusion,and is implemented within a finite-element framework.Compared to the conventional Lambert-Beer law,which assumes one-dimensional homogeneity,our approach captures the full threedimensional density and polarization distribution,significantly improving the accuracy of light absorption modeling.The resulting absorption-density maps are used to train a feedforward neural network,yielding a high-precision estimator for atomic density fluctuations.This estimator enables the construction of a decoupling equation that separates the density contribution from the FORA signal.Experimental validation shows that this method improves the bias instability atσ(100 s)of the gyroscope was improved by 73.1%compared to traditional platinum-resistance-based stabilization.The proposed framework is general and can be extended to other optical pumping-based sensors,such as optically pumped magnetometers.
基金Funded by the National Natural Science Foundation of China(No.52371169)。
文摘We prepared Co_(x)Pt_(100-x)(x=40,45,50,55,60)nanoparticles by the sol-gel method.The phase composition and crystal structure,morphology and microstructure,and magnetic properties of the samples were characterized and tested using X-ray diffraction(XRD),transmission electron microscopy(TEM),and vibrating sample magnetometer(VSM),respectively.The results demonstrate that the coercivity of CoPt nanoparticles can be effectively controlled by adjusting the atomic ratio of Co and Pt in the samples.Among the compositions studied,the Co_(45)Pt_(55)sample synthesized by the sol-gel method exhibits smaller grain size and a coercivity as high as 6.65×10^(5) A/m is achieved.The morphology and microstructure of the nanoparticles were analyzed by TEM images,indicating that a slight excess of Pt can effectively enhance the coercivity of CoPt nanoparticles.
基金supported by the National Natural Science Foundation of China(Nos.22406081,22276086,22306086)the Natural Science Foundation of Jiangxi Province(No.20232BAB213029),all of which are greatly acknowledged by the authors.
文摘Fenton-like technology based on peroxymonosulfate activation has shown great potential in refractory organics degradation.In this work,single Fe atom catalysts were synthesized through facile ball milling and exhibited very high performance in peroxymonosulfate activation.The Fe single-atom filled an N vacancy on the triazine ring edge of C_(3)N_(4),as confirmed through X-ray absorption fine structure,density functional calculation and elec-tron paramagnetic resonance.The SAFe_(0.4)–C_(3)N_(4)/PMS system could completely remove phenol(20 mg/L)within 10 min and its first-order kinetic constant was 12.3 times that of the Fe_(3)O_(4)/PMS system.Under different ini-tial pH levels and in various anionic environments,SAFe_(0.4)–C_(3)N_(4) still demonstrated excellent catalytic activity,achieving a removal rate of over 90%for phenol within 12 min.In addition,SAFe_(0.4)–C_(3)N_(4) exhibited outstanding selectivity in reaction systems with different pollutants,showing excellent degradation effects on electron-rich pollutants only.Hydroxyl radicals(•OH),singlet oxygen(1O_(2))and high-valent iron oxide(Fe(Ⅳ)=O)were de-tected in the SAFe_(0.4)–C_(3)N_(4)/PMS system through free radical capture experiments.Further experiments on the quenching of active species and a methyl phenyl sulfoxide probe confirmed that 1O_(2) and Fe(Ⅳ)=O played dom-inant roles.Additionally,the change in the current response after adding PMS and phenol in succession proved that a direct electron transfer path between organic matter and the catalyst surface was unlikely to exist in the SAFe_(0.4)–C_(3)N_(4)/PMS/Phenol degradation system.This study provides a new demonstration of the catalytic mech-anism of single-atom catalysts.
基金supported by the National Natural Science Foundation of China(Nos.22176194,22206016,and 12305397)the Natural Science Foundation of Jiangsu Province(No.BK20230511)+2 种基金Science Challenge Project(No.TZ2018004)Suzhou Fundamental Research Project(No.SJC2023001)Key Scientific Research Foundation of the Education Department of Province Anhui(No.2022AH051835).
文摘Introduction of active centers,such as oxygen vacancy and metal single atoms,has emerged as a promising strategy to further improve the electrochemical properties of transition metal oxide electrodes for high-performance pseudocapacitors.Here,an unprecedented MoO_(3)with multiple active centers,Ni anchored reduced MoO_(3)with oxygen vacancy(NirMoO_(3-x)),was in situ synthesized via γ-ray radiationinduced one-pot strategy under ambient conditions.This approach leverages the synergistic effects of radiation activation,etching,and reduction.The characteristics of multiple valence states(Mo^(4+/5+/6+)and Ni^(0/2+)),oxygen vacancies,single atoms,and atomic clusters in NirMoO_(3-x) were determined by X-ray photoelectron spectroscopy(XPS),X-ray absorption fine structure spectroscopy(XAFS),and atomic-resolution aberrationcorrected high-angle annular dark-field scanning transmission electron microscopy(HAADF-STEM)measurements.Notably,Ni-rMoO_(3-x)exhibited exceptional pseudocapacitive performance,with ultrahigh specific charge(881.0 C·g^(-1)at 1 A·g^(-1),more than twice that of MoO_(3)),fast charge/discharge rates,and remarkable cycle life stability(98.5% capacitance retention after 10,000 cycles).Furthermore,a hybrid supercapacitor device(Ni-rMoO_(3-x)//activated carbon(AC))demonstrated a high energy density of 97.8 Wh·kg^(-1)at a power density of 0.90 kW·kg^(-1)and exhibited excellent mechanical flexibility for practical applications.
基金the National Key R&D Program of China(No.2024YFA1509500)the National Natural Science Foundation of China(No.22479010)+5 种基金the financial support from the Chongqing Municipal Natural Science Foundation(No.CSTB2024NSCQJQX0034)Shenzhen Science and Technology Program(No.KJZD20240903101359020)the financial support from the National Natural Science Foundation of China(No.22372004)the support from the Experimental Center of Advanced Materials of the Beijing Institute of Technologythe technical support from Biological and Medical Engineering Core Facilities of Beijing Institute of Technologythe Analysis and Testing Center of Beijing Institute of Technology.
文摘Fe-N-C catalysts,as promising non-precious metal alternatives for the oxygen reduction reaction(ORR),still suffer from severe mass transport limitations in proton exchange membrane fuel cells(PEMFCs)due to water flooding of active sites embedded in micropores.Although pore engineering through a selected template is a general strategy,the structural features of an ideal template,particularly those governing the exposure of active sites and thus affecting mass transport,remain elusive.Here,we demonstrate that low-porosity carbon templates maximize the ratio of active sites distributed at or near the surface,thereby enhancing their exposure and accessibility while reducing mass transport resistance during the ORR process.The C_(lp-1)@PPy and C_(lp-2)@PPy(PPy=polypyrrole)catalysts,derived from low-porosity carbon templates,achieve peak power densities of 0.96 and 1.03 W·cm^(-2) under H_(2)/O_(2)and 0.50 and 0.52 W·cm^(-2) under H_(2)/air,demonstrating excellent performance in PEMFC tests.Structural and electrochemical characterizations reveal that the enhanced surface exposure of active sites effectively mitigates mass transport resistance during the ORR,thereby offering a general design principle for overcoming mass transport limitations in Fe-N-C catalysts for PEMFC applications.
基金supported by the National Key Research and Development Program of China (Grant Nos.2023YFA1406200 and 2022YFA-1405500)the National Natural Science Foundation of China (Grant Nos.12304021 and 52072188)+3 种基金Zhejiang Provincial Natural Science Foundation of China (Grant Nos.LQ23A040004 and MS26A040028)Natural Science Foundation of Ningbo (Grant Nos.2022J091 and ZX2025001430)the Program for Science and Technology Innovation Team in Zhejiang (Grant No.2021R01004)the Program for Changjiang Scholars and Innovative Research Team in University (Grant No.IRT_15R23)。
文摘High-pressure electrides,characterized by the presence of interstitial quasi-atoms(ISQs),possess unique electronic structures and physical properties,such as diverse dimensions of electride states exhibiting different superconductivity,which has attracted significant attention.Here,we report a new electron-deficient type of electride Li_(4)Al and identify its phase transition progress with pressurization,where the internal driving force behind phase transitions,bonding characteristics,and superconducting behaviors have been revealed based on first-principles density functional theory.Through analysis of the bonding properties of electride Li_(4)Al,we demonstrate that the ISQs exhibiting increasingly covalent characteristics between Al ions play a critical role in driving the phase transition.Our electron–phonon coupling calculations indicate that all phases exhibit superconducting behaviors.Importantly,we prove that the ISQs behave as free electrons and demonstrate that the factor governing T_(c) is primarily derived from Li-p-hybridized electronic states with ISQ compositions.These electronic states are scattered by low-frequency phonons arising from mixed vibrations of Li and Al affected by ISQs to enhance electron–phonon coupling.Our study largely expands the research scope of electrides,provides new insight for understanding phase transitions,and elucidates the effects of ISQs on superconducting behavior.
基金supported in part by the National Key R&D Program of China (Contract Nos.2023YFA1606500,2024YFE0109800,and 2024YFE0110400)Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB34010000)+5 种基金the Gansu Key Project of Science and Technology (Grant No.23ZDGA014)the Guangdong Major Project of Basic and Applied Basic Research (Grant No.2021B0301030006)the National Natural Science Foundation of China (Grant Nos.12105328,W2412040,12475126,12422507,12035011,12375118,12435008,and W2412043)the Chinese Academy of Sciences Project for Young Scientists in Basic Research(Grant No.YSBR-002)the Youth Innovation Promotion Association of the Chinese Academy of Sciences (Grant Nos.2020409 and 2023439)the Russian Science Foundation (Grant No.25-42-00003)。
文摘We report the results of the experiment on synthesizing ^(287,288)Mc isotopes (Z=115) using the fusionevaporation reaction ^(243)Am(^(48)Ca,4n,3n)^(287,288)Mc at the Spectrometer for Heavy Atoms and Nuclear Structure-2(SHANS2),a gas-filled recoil separator located at the China Accelerator Facility for Superheavy Elements(CAFE2).In total,20 decay chains are attributed to ^(288)Mc and 1 decay chain is assigned to ^(287)Mc.The measured oa-decay properties of ^(287,288)Mc as well as its descendants are consistent with the known data.No additional decay chains originating from the 2n or 5n reaction channels were detected.The excitation function of the ^(243)Am(^(48)Ca,3n)^(288)Mc reaction was measured at the cross-section level of picobarn,which indicates the promising capability for the study of heavy and superheavy nuclei at the facility.
基金supported by the National Natural Science Foundation of China (Grant No.12274131)the Innovation Program for Quantum Science and Technology (Grant No.2024ZD0300101)。
文摘Optical non-reciprocity is a fundamental phenomenon in photonics.It is crucial for developing devices that rely on directional signal control,such as optical isolators and circulators.However,most research in this field has focused on systems in equilibrium or steady states.In this work,we demonstrate a room-temperature Rydberg atomic platform where the unidirectional propagation of light acts as a switch to mediate time-crystalline-like collective oscillations through atomic synchronization.
基金financially supported by the National Natural Science Foundation of China(No.22272159)the Chinese Academy of Sciences(No.KFJ-XCZX-202304).
文摘Single-atom catalysts based on graphitic carbon nitride(g-C_(3)N_(4))show high potential for hydrogen production photocatalytically.However,it is still a challenge to develop single-atom-based g-C_(3)N_(4)due to the complex synthesis procedures,limited active sites,and insufficient mechanistic understanding.Herein,a facile oxygen-tolerant synthesis strategy was developed,which utilizes the nitrogen-rich structure of g-C_(3)N_(4)to capture Fe single atoms from ammonium iron citrate,successfully constructing an efficient photocatalytic composite.The resulting Fe single-atom-modified g-C_(3)N_(4)catalyst exhibited highly improved light absorption,charge carrier separation,and a substantially enhanced rate of H_(2)production photocatalytically under visible light irradiation.Experimental results demonstrated that the optimal sample achieves a H_(2)production rate of 683μmol·h-1·g^(-1),representing a 425% enhancement compared to pristine g-C_(3)N_(4).This study presents a facile oxygen-tolerant approach for metal immobilization using metal-organic precursors,where the nitrogen-rich framework of g-C_(3)N_(4)effectively captures Fe atoms as singular site within the composite.The developed synthesis strategy provides new insights for designing high-performance single-atom photocatalytic materials,potentially advancing the application and development of photocatalysis.
基金financially supported by the project of the National Natural Science Foundation of China(52322203)the Key Research and Development Program of Shaanxi Province(2024GHZDXM-21)。
文摘The design of cost-effective and efficient metal-free carbon-based catalysts for the hydrogen evolution reaction(HER)is of great significance for increasing the production of clean hydrogen by the electrolysis of alkaline water.Precise control of the electronic structure by heteroatom doping has proven to be efficient for increasing catalytic activity.Nevertheless,both the structural characteristics and the underlying mechanism are not well understood,especially for doping with two different atoms,thus limiting the use of these catalysts.We report the production of phosphorus and nitrogen co-doped hollow carbon nanospheres(HCNs)by the copolymerization of pyrrole and aniline at a Triton X-100 micelle-interface,followed by doping with phytic acid and carbonization.The unique pore structure and defect-rich framework of the HCNs expose numerous active sites.Crucially,the combined effect of graphitic nitrogen and phosphorus-carbon bonds modulate the local electronic structure of adjacent C atoms and facilitates electron transfer.As a res-ult,the HCN carbonized at 1100°C exhibited superior HER activity and an outstanding stability(70 h at a current density of 10 mA cm^(−2))in alkaline water,because of the large number of graphitic nitrogen and phosphorus-carbon bonds.
文摘The regioselective carbon-hydrogen bond functionalization reaction in atom-and step-economy holds significant potential for the late-stage elaboration of complex molecules and natural products.In recent years,the hydrogen atom transfer strategy involving radicals has garnered considerable attention from chemists due to its high chemoselectivity and regioselectivity.However,owing to the marginal differences in bond dissociation energies(BDEs)among C(sp^(3))—H bonds,hydrogen atom transfer reactions mediated by alkyl radicals remain less-developed.A copper-catalyzed sulfone-induced regioselective C(sp^(3))—H bond heteroarylation reaction was reported.This strategy utilizes theα-alkyl radical of sulfone as an intramolecular hydrogen abstraction reagent,enabling the regioselective formation of carbon-nitrogen bonds under copper catalysis.
基金Institute of Technology Research Fund Program for Young Scholars21C Innovation Laboratory Contemporary Amperex Technology Co.,Limited,Ninde, 352100, China (21C–OP-202314)。
文摘Lithium-sulfur (Li-S) batteries have gained great attention due to the high theoretical energy density and low cost,yet their further commercialization has been obstructed by the notorious shuttle effect and sluggish redox dynamics.Herein,we supply a strategy to optimize the electron structure of Ni_(2)P by concurrently introducing B-doped atoms and P vacancies in Ni_(2)P (Vp-B-Ni_(2)P),thereby enhancing the bidirectional sulfur conversion.The study indicates that the simultaneous introduction of B-doped atoms and P vacancies in Ni_(2)P causes the redistribution of electron around Ni atoms,bringing about the upward shift of d-band center of Ni atoms and effective d-p orbital hybridization between Ni atoms and sulfur species,thus strengthening the chemical anchoring for lithium polysulfides (LiPSs) as well as expediting the bidirectional conversion kinetics of sulfur species.Meanwhile,theoretical calculations reveal that the incorporation of B-doped atoms and P vacancies in Ni_(2)P selectively promotes Li2S dissolution and nucleation processes.Thus,the Li-S batteries with Vp-B-Ni_(2)P-separators present outstanding rate ability of 777 m A h g^(-1)at 5 C and high areal capacity of 8.03 mA h cm^(-2)under E/S of 5μL mg^(-1)and sulfur loading of 7.20 mg cm^(-2).This work elucidates that introducing heteroatom and vacancy in metal phosphide collaboratively regulates the electron structure to accelerate bidirectional sulfur conversion.
基金supported by the National Natural Science Foundation of China(Nos.52373280,52177014 and 52273257).
文摘Exploring efficient microwave absorbing materials(MAMs)has gradually become a hot topic in recent years because it is crucial in both civil and military fields.Metal-organic framework(MOF)has great potential due to its unique composition and bonding mode,which has advantages such as large specific surface area,high porosity,adjustable structure,and designable composition.Herein,MOF-derived MAMs are highlighted based on morphology and structure.The synthesis strategies of MOF-derived MAMs of different dimensions are discussed.On this basis,the structure-activity relationships can be deeply explored through the precise control of material structure and property by atomic engineering.Finally,perspectives are given for the existing problems of MOF-derived MAMs,which will open a new horizon and promote the development of MAMs.
基金supported by the National Natural Science Foundation of China(No.21571062)the Program for Professor of Special Appointment(Eastern Scholar)at the Shanghai Institutions of Higher Learning to JGL,and the Fundamental Research Funds for the Central Universities(No.222201717003)。
文摘Exploiting non-precious metal catalysts with excellent oxygen reduction reaction(ORR)performance for energy devices is paramount essential for the green and sustainable society development.Herein,low-cost,high-performance biomass-derived ORR catalysts with an asymmetric Fe-N_(3)P configuration was prepared by a simple pyrolysis-etching technique,where carboxymethyl cellulose(CMC)was used as the carbon source,urea and 1,10-phenanthroline iron complex(FePhen)as additives,and Na_(3)PO_(4)as the phosphorus dopant and a pore-forming agent.The CMC-derived FeNPC catalyst displayed a large specific area(BET:1235 m^(2)g^(-1))with atomically dispersed Fe-N_(3)P active sites,which exhibited superior ORR activity and stability in alkaline solution(E_(1/2)=0.90 V vs.RHE)and Zn-air batteries(P_(max)=149 mW cm^(-2))to commercial Pt/C catalyst(E_(1/2)=0.87 V,P_(max)=118 mW cm^(-2))under similar experimental conditions.This work provides a feasible and costeffective route toward highly efficient ORR catalysts and their application to Zn-air batteries for energy conversion.
基金supported by the Pre-research fund(No.412130024).
文摘The T_(1)(Al_(2) CuLi)phase is one of the most effective strengthening nanoscale-precipitate in Al-Cu alloys with Li.However,its formation and evolution still need to be further clarified during aging due to the complex precipitation sequences.Here,a detailed investigation has been carried out on the atomic struc-tural evolution of T_(1) precipitate in an aged Al-Cu-Li-Mg-Ag alloy using state-of-the-art Cs-corrected high-angle annular dark field(HAADF)-coupled with integrated differential phase contrast(iDPC)-scanning transmission electron microscopy(STEM)and energy-dispersive X-ray spectroscopy(EDXS)techniques.An intermediate T_(1)’phase between T_(1p) and T_(1) phase,with a crystal structure and orientation rela-tionship consistent with T_(1),but exhibiting different atomic occupancy and chemical composition was found.We observed the atomic structural transformation from T_(1p) to T_(1)’phase(fcc→hcp),involving only 1/12<112>Al shear component.DFT calculation results validated our proposed structural models and the precipitation sequence.Besides,the distributions of minor solute elements(Ag,Mg,and Zn)in the pre-cipitates exhibited significant differences.These findings may contribute to a further understanding of the nucleation mechanism of T_(1) precipitate.
基金supported by the National Natural Science Foundation of China(Nos.U23B6009 and 12272050)。
文摘Combustion dynamics are a critical factor in determining the performance and reliabilityof a chemical propulsion engine.The underlying processes include liquid atomization,evaporation,mixing,and chemical reactions.This paper presents a high-fidelity numerical study of liquidatomization and spray combustion under high-pressure conditions,emphasizing the effects of pres-sure oscillations on the flow evolution and combustion dynamics.The theoretical framework isbased on the three-dimensional conservation equations for multiphase flows and turbulent combus-tion.The numerical solution is achieved using a coupling method of volume-of-fluid and Lagran-gian particle tracking.The Zhuang-Kadota-Sutton(ZKS)high-pressure evaporation model andthe eddy breakup-Arrhenius combustion model are employed.Simulations are conducted for amodel combustion chamber with impinging-jet injectors using liquid oxygen and kerosene as pro-pellants.Both conditions with and without inlet and outlet pressure oscillations are considered.Thefindings reveal that pressure oscillations amplify flow fluctuations and can be characterized usingkey physical parameters such as droplet evaporation,chemical reaction,and chamber pressure.The spectral analysis uncovers the axial variations of the dominant and secondary frequenciesand their amplitudes in terms of the characteristic physical quantities.This research helps establisha methodology for exploring the coupling effect of liquid atomization and spray combustion.It alsoprovides practical insights into their responses to pressure oscillations during the occurrence ofcombustion instability.This information can be used to enhance the design and operation ofliquid-fueled propulsion engines.
