Nonlinear Violence in Nonlinear Oscillations at High Energy

This paper focuses on the characteristics of solutions of nonlinear oscillatory systems in the limit of very high oscillation energy, E;specifically, systems, in which the nonlinear driving force grows with energy much faster for x(t) close to the turning point, a(E), than at any position, x(t), that is not too close to a(E). This behavior dominates important aspects of the solutions. It will be called “nonlinear violence”. In the vicinity of a turning point, the solution of a nonlinear oscillatory systems that is affected by nonlinear violence exhibits the characteristics of boundary-layer behavior (independently of whether the equation of motion of the system can or cannot be cast in the traditional form of a boundary-layer problem.): close to a(E), x(t) varies very rapidly over a short time interval (which vanishes for E → ∞). In traditional boundary layer systems this would be called the “inner” solution. Outside this interval, x(t) soon evolves into a moderate profile (e.g. linear in time, or constant)—the “outer” solution. In (1 + 1)-dimensional nonlinear energy-conserving oscillators, if the solution is reflection-invariant, nonlinear violence determines the characteristics of the whole solution. For large families of nonlinear oscillatory systems, as E → ∞, the solutions for x(t) tend to common, indistinguishable profiles, such as periodic saw-tooth profiles or step-functions. If such profiles are observed experimentally in high-energy oscillations, it may be difficult to decipher the dynamical equations that govern the motion. The solution of motion in a central field with a non-zero angular momentum exhibits extremely fast rotation around a turning point that is affected by nonlinear violence. This provides an example for the possibility of interesting phenomena in (1 + 2)-dimensional oscillatory systems.

Necessary and Sufficient Conditions for Oscillations of the Generalized Liénard Systems

In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.

The de Haas-van Alphen quantum oscillations in the kagome metal RbTi_(3)Bi_(5)

The kagome system has attracted great interest in condensed matter physics due to its unique structure that canhost various exotic states such as superconductivity(SC),charge density waves(CDWs)and nontrivial topological states.The topological semimetal RbTi_(3)Bi_(5)consisting of a Ti kagome layer shares a similar crystal structure to the topologicalcorrelated materials AV_(3)Sb_(5)(A=K,Rb,Cs)but without the absence of CDW and SC.Systematic de Haas-van Alphenoscillation measurements are performed on single crystals of RbTi_(3)Bi_(5)to pursue nontrivial topological physics and exoticstates.Combining this with theoretical calculations,the detailed Fermi surface topology and band structure are investigated.A two-dimensional Fermi pocket b is revealed with a light effective mass,consistent with the semimetal predictions.TheLandau fan diagram of RbTi_(3)Bi_(5)reveals a zero Berry phase for the b oscillation in contrast to that of CsTi_(3)Bi_(5).Theseresults suggest that kagome RbTi_(3)Bi_(5)is a good candidate for exploring nontrivial topological exotic states and topologicalcorrelated physics.

Two-dimensional Sb net generated nontrivial topological states in SmAgSb_(2) probed by quantum oscillations

The REAgSb_(2)(RE = rare earth and Y) family has drawn considerable research interest because the two-dimensional Sb net in their crystal structures hosts topological fermions and hence rich topological properties. We report herein the magnetization and magnetotransport measurements of SmAgSb_(2) single crystal, which unveil very large magnetoresistance and high carrier mobility up to 6.2 × 10^(3)% and 5.58 × 10^(3)cm^(2)·V^(-1)·s^(-1), respectively. The analysis of both Shubnikov–de Haas and de Haas–van Alphen quantum oscillations indicates nontrivial Berry phases in the paramagnetic state while trivial Berry curvature in the antiferromagnetic state, indicating a topological phase transition induced by the antiferromagnetic order. It is also supported by the first-principles calculations. The results not only provide a new interesting topological material but also offer valuable insights into the correlation between magnetism and nontrivial topological states.

Review of the Analysis and Suppression for High-frequency Oscillations of the Grid-connected Wind Power Generation System

High-frequency oscillation(HFO)of gridconnected wind power generation systems(WPGS)is one of the most critical issues in recent years that threaten the safe access of WPGS to the grid.Ensuring the WPGS can damp HFO is becoming more and more vital for the development of wind power.The HFO phenomenon of wind turbines under different scenarios usually has different mechanisms.Hence,engineers need to acquire the working mechanisms of the different HFO damping technologies and select the appropriate one to ensure the effective implementation of oscillation damping in practical engineering.This paper introduces the general assumptions of WPGS when analyzing HFO,systematically summarizes the reasons for the occurrence of HFO in different scenarios,deeply analyses the key points and difficulties of HFO damping under different scenarios,and then compares the technical performances of various types of HFO suppression methods to provide adequate references for engineers in the application of technology.Finally,this paper discusses possible future research difficulties in the problem of HFO,as well as the possible future trends in the demand for HFO damping.

Detection of Oscillations in Process Control Loops From Visual Image Space Using Deep Convolutional Networks

Oscillation detection has been a hot research topic in industries due to the high incidence of oscillation loops and their negative impact on plant profitability.Although numerous automatic detection techniques have been proposed,most of them can only address part of the practical difficulties.An oscillation is heuristically defined as a visually apparent periodic variation.However,manual visual inspection is labor-intensive and prone to missed detection.Convolutional neural networks(CNNs),inspired by animal visual systems,have been raised with powerful feature extraction capabilities.In this work,an exploration of the typical CNN models for visual oscillation detection is performed.Specifically,we tested MobileNet-V1,ShuffleNet-V2,Efficient Net-B0,and GhostNet models,and found that such a visual framework is well-suited for oscillation detection.The feasibility and validity of this framework are verified utilizing extensive numerical and industrial cases.Compared with state-of-theart oscillation detectors,the suggested framework is more straightforward and more robust to noise and mean-nonstationarity.In addition,this framework generalizes well and is capable of handling features that are not present in the training data,such as multiple oscillations and outliers.

Impact of a Bumpy Nonuniform Electric Field on Oscillations of a Massive Point-Like Charged Particle

As a general feature, the electric field of a localized electric charge distribution diminishes as the distance from the distribution increases;there are exceptions to this feature. For instance, the electric field of a charged ring (being a localized charge distribution) along its symmetry axis perpendicular to the ring through its center rather than as expected being a diminishing field encounters a local maximum bump. It is the objective of this research-oriented study to analyze the impact of this bump on the characteristics of a massive point-like charged particle oscillating along the symmetry axis. Two scenarios with and without gravity along the symmetry axis are considered. In addition to standard kinematic diagrams, various phase diagrams conducive to a better understanding are constructed. Applying Computer Algebra System (CAS), [1] [2] most calculations are carried out symbolically. Finally, by assigning a set of reasonable numeric parameters to the symbolic quantities various 3D animations are crafted. All the CAS codes are included.

The Reality of Baryonic Acoustic Oscillations

The initial idea for baryonic acoustic oscillations (BAO) came about during early efforts to understand the origin of galaxies by studying perturbed versions of the Friedmann-Robertson-Walker (FRW) model. In more recent times, the emphasis has shifted to the idea that 2-point galaxy correlations embedded in the distribution of matter by the BAO could be used as a standard ruler to fix the parameters of cosmological models. In this paper, we first consider the actual business of extracting the correlation length from large data sets of measured galaxy locations. To facilitate this process, we introduce a much-improved method for extracting the correlation peak from the data set. Fundamental to this process in any model is the use of a fiducial cosmological model to transition from redshift space to comoving coordinate space where the correlations actually exist. The belief is that the correlation length so determined can then be reverted to redshift space to fix the parameters of cosmological models. We show, however, that this process is circular and hence of no value whatsoever for fixing model parameters. All one obtains are the parameters of the model used to transition to comoving space in the first place. Finally, we present simple arguments that show that the idea of BAO being responsible for the structure of the universe, i.e. the cosmic web, is unworkable.

Cortico-striatal gamma oscillations are modulated by dopamine D3 receptors in dyskinetic rats

Long-term levodopa administration can lead to the development of levodopa-induced dyskinesia.Gamma oscillations are a widely recognized hallmark of abnormal neural electrical activity in levodopa-induced dyskinesia.Currently,studies have reported increased oscillation power in cases of levodopa-induced dyskinesia.However,little is known about how the other electrophysiological parameters of gamma oscillations are altered in levodopa-induced dyskinesia.Furthermore,the role of the dopamine D3 receptor,which is implicated in levodopa-induced dyskinesia,in movement disorder-related changes in neural oscillations is unclear.We found that the cortico-striatal functional connectivity of beta oscillations was enhanced in a model of Parkinson’s disease.Furthermore,levodopa application enhanced cortical gamma oscillations in cortico-striatal projections and cortical gamma aperiodic components,as well as bidirectional primary motor cortex(M1)↔dorsolateral striatum gamma flow.Administration of PD128907(a selective dopamine D3 receptor agonist)induced dyskinesia and excessive gamma oscillations with a bidirectional M1↔dorsolateral striatum flow.However,administration of PG01037(a selective dopamine D3 receptor antagonist)attenuated dyskinesia,suppressed gamma oscillations and cortical gamma aperiodic components,and decreased gamma causality in the M1→dorsolateral striatum direction.These findings suggest that the dopamine D3 receptor plays a role in dyskinesia-related oscillatory activity,and that it has potential as a therapeutic target for levodopa-induced dyskinesia.

Derivation of a Revised Tsiolkovsky Rocket Equation That Predicts Combustion Oscillations

Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx1, and slow-jet, vx2. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.

Numerical Investigations on Harbor Oscillations Induced by Falling Objects

In this paper,the open-sourced computational fluid dynamics software,OpenFOAM~?,is used to study the fluctuation phenomenon of the water body inside a horizontally one-dimensional enclosed harbor basin with constant water depth triggered by falling wedges with various horizontal falling positions,initial falling velocities and masses.Based on both Fourier transfo rm analysis and wavelet spectrum analysis for the time series of the free surface elevations inside the harbor basin,it is found for the first time that the wedge falling inside the harbor can directly trigger harbor resonance.The influences of the three factors(including the horizontal falling position,the initial falling velocity,and the mass)on the response amplitudes of the lowest three resonant modes are also investigated.The results show that when the wedge falls on one of the nodal points of a resonant mode,the mode would be remarkably suppressed.Conversely,when the wedge falls on one of the anti-nodal points of a resonant mode,the mode would be evidently triggered.The initial falling velocity of the wedge mainly has a remarkable effect on the response amplitude of the most significant mode,and the latter shows a gradual increase trend with the increase of the former.While for the other two less significant modes,their response amplitudes fluctuate around certain constant values as the initial falling velocity rises.In general,the response amplitudes of all the lowest three modes are shown to gradually increase with the mass of the wedge.

Observation of free oscillations after the 2010 Chile and 2011 Japan earthquakes by superconducting gravimeter in Kutch,Gujarat,India

In this paper,we present observations of free oscillations of the Earth after major earthquakes in Chile(February 27,2010,Mw8.8)and Japan(March 11,2011,Mw9.1)using data from the dual-sphere superconducting gravimeter(SG-055),installed at Badargadh(23°0.47 N,70°0.62 E),Kutch,Gujarat,India in March 2009.To see the noise characteristics,we calculated the power spectral density of the gravity time series of 5 quiet days in the frequency band 0.05-20 mHz using the new low noise model(NLNM)as a reference.We compared the noise level of the Badargadh site to other SG sites around the world.This shows that the Badargadh SG is in a low noise state.We find that the noise increases at frequencies below 1 mHz.Such a characteristic is also observed in Djougou(Afrique,Benin)and Strasbourg(France).Using theoretical tides for Gujarat,we estimated a scale factor of about-814 nm/s~2/V for Gravl(lowersphere)and about-775 nm/s~2/V for Grav2(upper-sphere).We corrected the influence of atmospheric pressure from the one-second gravity data before switching to the frequency domain.We extracted a total of 53 Earth’s Free Oscillations(EFO)modes during the earthquake in Japan and about 47 EFO modes during the earthquake in Chile.We are able to extract the lowest0S2spheroidal mode(0.30945 mHz or54 min)and0S0radial mode(0.81439 mHz or 20 min).The longer time series shows individual0S2singlets and0S3(0.46855 mHz)singlets due to the Coriolis splitting effect.We cross-referenced the frequencies of these modes using the PREM model and previous global observations.The correlation coefficient between the observed and the PREM model for these two events are 0.999 for Japan earthquake and 0.993 for Chile earthquake.This validates the quality of the data useful for low-frequency studies in seismology.We also calculated the relative deviations of our observed fundamental modes with previously determined observed and theoretical values.We found that the relative deviations of our observed free oscillations do not exceed 0.5%,indicating good correlations.

Nonlinear current response and electric quantum oscillations in the Dirac semimetal Cd_(3)As_(2)

Chiral anomaly is a distinct quantum anomaly associated with chiral fermions in Dirac or Weyl semimetals.The use of negative magnetoresistance(negative MR)as a signature for this anomaly remains contentious,as trivial mechanisms such as current jetting and weak localization can also induce negative MR.In this study,we report a novel nonlinear behavior of the chiral anomaly in the longitudinal direction,which we observed by applying parallel current and magnetic field to the Dirac semimetal Cd_(3)A_(s_(2)).This nonlinear characteristic peaks at an intermediate magnetic field of approximately5 T,displaying a resistance-increasing property concomitant with strengthening of the current source.Through angledependence experiments,we were able to rule out trivial factors,such as thermal effects,geometric artifacts,and anisotropy.Furthermore,additional electric quantum oscillations were observed when the direct current(DC)was applied as high as300μA.Such an unusual phenomenon is ascribed to the formation of quantized levels due to Bloch oscillation in the high DC regime,suggesting that an oscillatory density distribution may arise as the electric field increases.The non-Ohmic electric quantum oscillations open a new avenue for exploring chiral anomaly and other nontrivial topological properties,which is also one of the salient features of nonequilibrium steady states in condensed matter physics.

Explanation of Ball Lightning by Plasma Oscillations

Ball Lightning (BL) is a “plasma bubble” that has very remarkable properties. Its membrane contains a higher density of charged particles than the ambient medium. They are held together by mutually attracting surface charges, generated by collective oscillations of all unbound electrons inside the membrane. Energy losses by collisions and emission of radiation, as well as losses of charged particles by recombination, are compensated by extracting other ones from atmospheric air. Since that occurs in a special rhythmic way, this leads to “parametric amplification” of the oscillations of all unbound electrons in the plasma membrane. Moreover, BL is attracted by higher concentrations of charged particles in atmospheric air. Too much of them leads to explosion and too few to extinction of visible BL. Since the electric charge of BL is oscillating, it is also attracted by metals, water and glass. It can then heat, melt and vaporize these materials without stored energy. BL is even able to pass through window panes in 3 different ways, but that can also be explained.

Semiannual oscillation,annual oscillation,quasibiennial oscillation,and solar cycle variation of the OH airglow emission in the mesopause region

The vertically integrated emission rate,centroid altitude,peak emission rate,and peak height of the hydroxyl(OH)airglow were calculated from Thermosphere Ionosphere Mesosphere Energetics and Dynamics(TIMED)/Sounding of the Atmosphere using Broadband Emission Radiometry(SABER)observations to study the seasonal and interannual variations in the intensity and location of the OH emission.The emission rate is inversely proportional to the height of the emission,with the semiannual oscillation dominating at low latitudes and the annual oscillation dominating at higher latitudes.The OH emission is modulated by the quasibiennial oscillation at the equator,and the quasibiennial oscillation signal is weak at other latitudes.We represented the vertical transport of atomic oxygen by using atomic oxygen concentrations obtained from a global atmospheric model,the Specified Dynamics Whole Atmosphere Community Climate Model with thermosphere and ionosphere eXtension simulations.Compared with the amplitudes of the migrating diurnal tide(DW1)calculated from temperature data observed by TIMED/SABER,we found that both the vertical transport of atomic oxygen and DW1 amplitudes in the equatorial region exhibit semiannual oscillation and quasibiennial oscillation,which have a strong correlation with the variations in the amplitude and phase of semiannual oscillation and quasibiennial oscillation in OH emission.It is likely that the DW1 affects the vertical transport of atomic oxygen that is involved in the reaction to produce O3,thus affecting the OH emission.We analyzed the relationship between OH emission and solar activity by using the solar radio flux at 10.7 cm as a proxy for solar activity.The results showed that the OH emission is well correlated with solar activity,and the modulation of OH emission by solar activity has a significant latitudinal variation.The small correlation between emission height and solar activity indicates that solar activity modulates OH emission mainly through chemical rather than dynamic processes.

Influence of the Atlantic Multidecadal Oscillation and Interdecadal Pacific Oscillation on Antarctic surface air temperature during 1900 to 2015

The importance of the Atlantic Multidecadal Oscillation(AMO)and Interdecadal Pacific Oscillation(IPO)in influencing zonally asymmetric changes in Antarctic surface air temperature(SAT)has been established.However,previous studies have primarily concentrated on examining the combined impact of the contrasting phases of the AMO and IPO,which have been dominant since the advent of satellite observations in 1979.This study utilizes long-term reanalysis data to investigate the impact of four combinations of+AMO+IPO,–AMO–IPO,+AMO–IPO,and–AMO+IPO on Antarctic SAT over the past 115 years.The+AMO phase is characterized by a spatial mean temperature amplitude of up to 0.5℃over the North Atlantic Ocean,accompanied by positive sea surface temperature(SST)anomalies in the tropical eastern Pacific and negative SST anomalies in the extratropical-mid-latitude western Pacific,which are indicative of the+IPO phase.The Antarctic SAT exhibits contrasting spatial patterns during the+AMO+IPO and+AMO–IPO periods.However,during the–AMO+IPO period,apart from the Antarctic Peninsula and the vicinity of the Weddell Sea,the entire Antarctic region experiences a warming trend.The most pronounced signal in the SAT anomalies is observed during the austral autumn,whereas the combination of–AMO and–IPO exhibits the smallest magnitude across all the combinations.The wavetrain excited by the SST anomalies associated with the AMO and IPO induces upper-level and surface atmospheric circulation anomalies,which alter the SAT anomalies.Furthermore,downward longwave radiation anomalies related to anomalous cloud cover play a crucial role.In the future,if the phases of AMO and IPO were to reverse(AMO transitioning to a negative phase and IPO transitioning to a positive phase),Antarctica could potentially face more pronounced warming and accelerated melting compared to the current observations.

Chimera states of phase oscillator populations with nonlocal higher-order couplings

The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order interactions encoded with simplicial complexes.Previous works have shown that higher-order interactions promote coherent states.However, we uncover the fact that the introduced higher-order couplings can significantly enhance the emergence of the incoherent state.Remarkably, we identify that the chimera states arise as a result of multi-attractors in dynamic states.Importantly, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera states.All the observed results can be well described in terms of the dimension reduction method.This study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatial-temporal patterns in networked systems.

Salinity effect-induced ENSO amplitude modulation in association with the interdecadal Pacific Oscillation

A 110-year ensemble simulation of an ocean general circulation model(OGCM)was analyzed to identify the modulation of salinity interdecadal variability on El Niño-Southern Oscillation(ENSO)amplitude in the tropical Pacific during 1901-2010.The simulating results show that sea surface salinity(SSS)variation in the region exhibits notable and coherent interdecadal variability signal,which is closely associated with the Interdecadal Pacific Oscillation(IPO).As salinity increases or reduces,the SSS modulations on ENSO amplitude during its warm/cold events vary asymmetrically with positive/negative IPO phases.Physically,salinity interdecadal variability can enhance or reduce ENSO-related conditions in upper-ocean stratification,contributing noticeably to ENSO variability.Salinity anomalies associated with the mixed layer depth and barrier layer thickness can modulate ENSO amplitude during positive and negative IPO phases,resulting in the asymmetry of sea surface temperature(SST)anomaly in the tropical Pacific.During positive IPO phases,SSS interdecadal variability contributes positively to El Niño amplitude but negatively to La Niña amplitude by enhancing or reducing SSS interannual variability,and vice versa during negative IPO phases.Quantitatively,the results indicate that the modulation of the ENSO amplitude by the SSS interdecadal variability is 15%-28%during negative IPO phases and 30%-20%during positive IPO phases,respectively.Evidently,the SSS interdecadal variability associated with IPO and its modulation on ENSO amplitude in the tropical Pacific are among factors essentially contributing ENSO diversity.

Changes in the Boreal Summer Intraseasonal Oscillation under Global Warming in CMIP6 Models

Changes in the activities of the Boreal Summer Intraseasonal Oscillation(BSISO)at the end of 21st century under the SSP5-8.5 scenario are assessed by adopting 17 CMIP6 models and the weak-temperature-gradient assumption.Results show that the intraseasonal variations become more structured.The BSISO-related precipitation anomaly shows a larger zonal scale and propagates further northward.However,there is no broad agreement among models on the changes in the eastward and northward propagation speeds and the frequency of individual phases.In the western North Pacific(WNP),the BSISO precipitation variance is significantly increased,at 4.62%K^(−1),due to the significantly increased efficiency of vertical moisture transport per unit of BSISO apparent heating.The vertical velocity variance is significantly decreased,at−3.51%K^(−1),in the middle troposphere,due to the significantly increased mean-state static stability.Changes in the lower-level zonal wind variance are relatively complex,with a significant increase stretching from the northwestern to southeastern WNP,but the opposite in other regions.This is probably due to the combined impacts of the northeastward shift of the BSISO signals and the reduced BSISO vertical velocity variance under global warming.Changes in strong and normal BSISO events in the WNP are also compared.They show same-signed changes in precipitation and large-scale circulation anomalies but opposite changes in the vertical velocity anomalies.This is probably because the precipitation anomaly of strong(normal)events changes at a rate much larger(smaller)than that of the meanstate static stability,causing enhanced(reduced)vertical motion.

Beam oscillating parameters on pore inhibition,recrystallization and grain boundary characteristics of laser-arc hybrid welded AZ31 magnesium alloy

Oscillating laser-arc hybrid welding of AZ31B magnesium alloy was carried out,the effects of beam oscillation parameters on pore inhibition,microstructure,grain boundary characteristics and tensile properties were investigated.The results showed that the pore formation can be inhibited with oscillating frequency higher than 75 Hz and radius smaller than 0.5 mm.The columnar grains neighboring the fusion line can be broken by the beam oscillation behavior,while the grain growth was promoted with the increase of frequency or radius.It should be noted that the coincidence site lattice(CSL)boundaries were mainlyΣ13b andΣ29 boundaries,which were contributed by{10■2}tensile twins and{11■2}compression twins,respectively.The total fraction of CSL boundaries reached maximum at radius of 0.25 mm and frequency of 75 Hz,which was also confirmed as the optimized parameters.In this case,the elongation rate increased up to 13.2%,12.8%higher than that of the weld without beam oscillation.Finally,the pore formation and inhibition mechanisms were illustrated according to the state of melt flow and keyhole formation,the abnormal growth was discussed basing on secondary recrystallization,and the relationship among the pore formation,grain size,boundary characteristics and weld toughness were finally established.