Mechanism of internal thermal runaway propagation in blade batteries

Blade batteries are extensively used in electric vehicles,but unavoidable thermal runaway is an inherent threat to their safe use.This study experimentally investigated the mechanism underlying thermal runaway propagation within a blade battery by using a nail to trigger thermal runaway and thermocouples to track its propagation inside a cell.The results showed that the internal thermal runaway could propagate for up to 272 s,which is comparable to that of a traditional battery module.The velocity of the thermal runaway propagation fluctuated between 1 and 8 mm s^(-1),depending on both the electrolyte content and high-temperature gas diffusion.In the early stages of thermal runaway,the electrolyte participated in the reaction,which intensified the thermal runaway and accelerated its propagation.As the battery temperature increased,the electrolyte evaporated,which attenuated the acceleration effect.Gas diffusion affected thermal runaway propagation through both heat transfer and mass transfer.The experimental results indicated that gas diffusion accelerated the velocity of thermal runaway propagation by 36.84%.We used a 1D mathematical model and confirmed that convective heat transfer induced by gas diffusion increased the velocity of thermal runaway propagation by 5.46%-17.06%.Finally,the temperature rate curve was analyzed,and a three-stage mechanism for internal thermal runaway propagation was proposed.In Stage I,convective heat transfer from electrolyte evaporation locally increased the temperature to 100℃.In Stage II,solid heat transfer locally increases the temperature to trigger thermal runaway.In StageⅢ,thermal runaway sharply increases the local temperature.The proposed mechanism sheds light on the internal thermal runaway propagation of blade batteries and offers valuable insights into safety considerations for future design.

Heat transfer enhanced inorganic phase change material compositing carbon nanotubes for battery thermal management and thermal runaway propagation mitigation

Developing technologies that can be applied simultaneously in battery thermal management(BTM)and thermal runaway(TR)mitigation is significant to improving the safety of lithium-ion battery systems.Inorganic phase change material(PCM)with nonflammability has the potential to achieve this dual function.This study proposed an encapsulated inorganic phase change material(EPCM)with a heat transfer enhancement for battery systems,where Na_(2)HPO_(4)·12H_(2)O was used as the core PCM encapsulated by silica and the additive of carbon nanotube(CNT)was applied to enhance the thermal conductivity.The microstructure and thermal properties of the EPCM/CNT were analyzed by a series of characterization tests.Two different incorporating methods of CNT were compared and the proper CNT adding amount was also studied.After preparation,the battery thermal management performance and TR propagation mitigation effects of EPCM/CNT were further investigated on the battery modules.The experimental results of thermal management tests showed that EPCM/CNT not only slowed down the temperature rising of the module but also improved the temperature uniformity during normal operation.The peak battery temperature decreased from 76℃to 61.2℃at 2 C discharge rate and the temperature difference was controlled below 3℃.Moreover,the results of TR propagation tests demonstrated that nonflammable EPCM/CNT with good heat absorption could work as a TR barrier,which exhibited effective mitigation on TR and TR propagation.The trigger time of three cells was successfully delayed by 129,474 and 551 s,respectively and the propagation intervals were greatly extended as well.

Robust autofocusing propagation in turbulence

Turbulence in complex environments such as the atmosphere and biological media has always been a great challenge to the application of beam propagation in optical communication, optical trapping and manipulation. To overcome this challenge, this study comprehensively investigates the robust propagation of traditional Gaussian and autofocusing beams in turbulent environments. In order to select stable beams that exhibit high intensity and high field gradient at the focal position in complex environments, Kolmogorov turbulence theory is used to simulate the propagation of beams in atmospheric turbulence based on the multi-phase screen method. We systematically analyze the intensity fluctuations, the variation of the coherence factor and the change in the scintillation index with propagation distance. The analysis reveals that the intensity fluctuations of autofocusing beams are significantly smaller than those of Gaussian beams, and the coherence of autofocusing beams is better than that of Gaussian beams under turbulence. Moreover, autofocusing beams exhibit less oscillation than Gaussian beams, indicating that autofocusing beams propagate in complex environments with less distortion and intensity fluctuation. Overall, this work clearly demonstrates that autofocusing beams exhibit higher stability in propagation compared with Gaussian beams, showing great promise for applications such as optical trapping and manipulation in complex environments.

Low-frequency oscillation of train-network system considering traction power supply mode

The low-frequency oscillation(LFO)has occurred in the train-network system due to the introduction of the power electronics of the trains.The modeling and analyzing method in current researches based on electrified railway unilateral power supply system are not suitable for the LFO analysis in a bilateral power supply system,where the trains are supplied by two traction substations.In this work,based on the single-input and single-output impedance model of China CRH5 trains,the node admittance matrices of the train-network system both in unilateral and bilateral power supply modes are established,including three-phase power grid,traction transformers and traction network.Then the modal analysis is used to study the oscillation modes and propagation characteristics of the unilateral and bilateral power supply systems.Moreover,the influence of the equivalent inductance of the power grid,the length of the transmission line,and the length of the traction network are analyzed on the critical oscillation mode of the bilateral power supply system.Finally,the theoretical analysis results are verified by the time-domain simulation model in MATLAB/Simulink.

A seismic elastic moduli module for the measurements of low-frequency wave dispersion and attenuation of fluid-saturated rocks under different pressures

Knowledge about the seismic elastic modulus dispersion,and associated attenuation,in fluid-saturated rocks is essential for better interpretation of seismic observations taken as part of hydrocarbon identification and time-lapse seismic surveillance of both conventional and unconventional reservoir and overburden performances.A Seismic Elastic Moduli Module has been developed,based on the forced-oscillations method,to experimentally investigate the frequency dependence of Young's modulus and Poisson's ratio,as well as the inferred attenuation,of cylindrical samples under different confining pressure conditions.Calibration with three standard samples showed that the measured elastic moduli were consistent with the published data,indicating that the new apparatus can operate reliably over a wide frequency range of f∈[1-2000,10^(6)]Hz.The Young's modulus and Poisson's ratio of the shale and the tight sandstone samples were measured under axial stress oscillations to assess the frequency-and pressure-dependent effects.Under dry condition,both samples appear to be nearly frequency independent,with weak pressure dependence for the shale and significant pressure dependence for the sandstone.In particular,it was found that the tight sandstone with complex pore microstructure exhibited apparent dispersion and attenuation under brine or glycerin saturation conditions,the levels of which were strongly influenced by the increased effective pressure.In addition,the measured Young's moduli results were compared with the theoretical predictions from a scaled poroelastic model with a reasonably good agreement,revealing that the combined fluid flow mechanisms at both mesoscopic and microscopic scales possibly responsible for the measured dispersion.

Suppression of low-frequency ultrasound broadband vibration using star-shaped single-phase metamaterials

In order to suppress the low-frequency ultrasound vibration in the broadband range of 20 k Hz—100 k Hz,this paper proposes and discusses an acoustic metamaterial with low-frequency ultrasound vibration attenuation properties,which is configured by hybrid arc and sharp-angle convergent star-shaped lattices.The effect of the dispersion relation and the bandgap characteristic for the scatterers in star-shaped are simulated and analyzed.The target bandgap width is extended by optimizing the geometry parameters of arc and sharp-angle convergent lattices.The proposed metamaterial configured by optimized hybrid lattices exhibits remarkable broad bandgap characteristics by bandgap complementarity,and the simulation results verify a 99%vibration attenuation amplitude can be obtained in the frequency of20 k Hz—100 k Hz.After the fabrication of the proposed hybrid configurational star-shaped metamaterial by 3D printing technique,the transmission loss experiments are performed,and the experimental results indicate that the fabricated metamaterial has the characteristics of broadband vibration attenuation and an amplitude greater than 85%attenuation for the target frequency.These results demonstrate that the hybrid configurational star-shaped metamaterials can effectively widen the bandgap and realize high efficiency attenuation,which has capability for the vibration attenuation in the application of highprecise equipment.

Current optimization-based control of dual three-phase PMSM for low-frequency temperature swing reduction

In this paper,a control scheme based on current optimization is proposed for dual three-phase permanent-magnet synchronous motor(DTP-PMSM)drive to reduce the low-frequency temperature swing.The reduction of temperature swing can be equivalent to reducing maximum instantaneous phase copper loss in this paper.First,a two-level optimization aiming at minimizing maximum instantaneous phase copper loss at each electrical angle is proposed.Then,the optimization is transformed to a singlelevel optimization by introducing the auxiliary variable for easy solving.Considering that singleobjective optimization trades a great total copper loss for a small reduction of maximum phase copper loss,the optimization considering both instantaneous total copper loss and maximum phase copper loss is proposed,which has the same performance of temperature swing reduction but with lower total loss.In this way,the proposed control scheme can reduce maximum junction temperature by 11%.Both simulation and experimental results are presented to prove the effectiveness and superiority of the proposed control scheme for low-frequency temperature swing reduction.

High-order Bragg forward scattering and frequency shift of low-frequency underwater acoustic field by moving rough sea surface

Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation.And with the principles of grating and constructive interference,the mechanism of this acoustic scattering modulation is explained.The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles,which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field,respectively,which is a high-order Bragg scattering phenomenon.Unlike the conventional Doppler effect,the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency.Therefore,even if a low-frequency underwater acoustic field is incident,it will produce obvious frequency shifts.Moreover,under the action of ideal sinusoidal waves,swells,fully grown wind waves,unsteady wind waves,or mixed waves,different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics.For the swell wave,which tends to be a single harmonic wave,the moving rough sea surface produces more obvious high-order scattering and frequency shifts.The same phenomena are observed on the sea surface under fully grown wind waves,however,the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum.Comparing with the swell and fully-grown wind waves,the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.

Diagnosing ratio of electron density to collision frequency of plasma surrounding scaled model in a shock tube using low-frequency alternating magnetic field phase shift

A non-contact low-frequency(LF)method of diagnosing the plasma surrounding a scaled model in a shock tube is proposed.This method utilizes the phase shift occurring after the transmission of an LF alternating magnetic field through the plasma to directly measure the ratio of the plasma loop average electron density to collision frequency.An equivalent circuit model is used to analyze the relationship of the phase shift of the magnetic field component of LF electromagnetic waves with the plasma electron density and collision frequency.The applicable range of the LF method on a given plasma scale is analyzed.The upper diagnostic limit for the ratio of the electron density(unit:m^(-3))to collision frequency(unit:Hz)exceeds 1×10^(11),enabling an electron density to exceed 1×10^(20)m^(-3)and a collision frequency to be less than 1 GHz.In this work,the feasibility of using the LF phase shift to implement the plasma diagnosis is also assessed.Diagnosis experiments on shock tube equipment are conducted by using both the electrostatic probe method and LF method.By comparing the diagnostic results of the two methods,the inversion results are relatively consistent with each other,thereby preliminarily verifying the feasibility of the LF method.The ratio of the electron density to the collision frequency has a relatively uniform distribution during the plasma stabilization.The LF diagnostic path is a loop around the model,which is suitable for diagnosing the plasma that surrounds the model.Finally,the causes of diagnostic discrepancy between the two methods are analyzed.The proposed method provides a new avenue for diagnosing high-density enveloping plasma.

Improved Belief Propagation Decoder for LDPC-CRC-Polar Codes with Bit-Freezing

Though belief propagation bit-flip(BPBF)decoding improves the error correction performance of polar codes,it uses the exhaustive flips method to achieve the error correction performance of CA-SCL decoding,thus resulting in high decoding complexity and latency.To alleviate this issue,we incorporate the LDPC-CRC-Polar coding scheme with BPBF and propose an improved belief propagation decoder for LDPC-CRC-Polar codes with bit-freezing(LDPCCRC-Polar codes BPBFz).The proposed LDPCCRC-Polar codes BPBFz employs the LDPC code to ensure the reliability of the flipping set,i.e.,critical set(CS),and dynamically update it.The modified CS is further utilized for the identification of error-prone bits.The proposed LDPC-CRC-Polar codes BPBFz obtains remarkable error correction performance and is comparable to that of the CA-SCL(L=16)decoder under medium-to-high signal-to-noise ratio(SNR)regions.It gains up to 1.2dB and 0.9dB at a fixed BLER=10-4compared with BP and BPBF(CS-1),respectively.In addition,the proposed LDPC-CRC-Polar codes BPBFz has lower decoding latency compared with CA-SCL and BPBF,i.e.,it is 15 times faster than CA-SCL(L=16)at high SNR regions.

Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.

Modelling of debris-flow susceptibility and propagation: a case study from Northwest Himalaya

The geological and geographical position of the Northwest Himalayas makes it a vulnerable area for mass movements particularly landslides and debris flows. Mass movements have had a substantial impact on the study area which is extending along Karakorum Highway(KKH) from Besham to Chilas. Intense seismicity, deep gorges, steep terrain and extreme climatic events trigger multiple mountain hazards along the KKH, among which debris flow is recognized as the most destructive geohazard. This study aims to prepare a field-based debris flow inventory map at a regional scale along a 200 km stretch from Besham to Chilas. A total of 117 debris flows were identified in the field, and subsequently, a point-based debris-flow inventory and catchment delineation were performed through Arc GIS analysis. Regional scale debris flow susceptibility and propagation maps were prepared using Weighted Overlay Method(WOM) and Flow-R technique sequentially. Predisposing factors include slope, slope aspect, elevation, Topographic Roughness Index(TRI), Topographic Wetness Index(TWI), stream buffer, distance to faults, lithology rainfall, curvature, and collapsed material layer. The dataset was randomly divided into training data(75%) and validation data(25%). Results were validated through the Receiver Operator Characteristics(ROC) curve. Results show that Area Under the Curve(AUC) using WOM model is 79.2%. Flow-R propagation of debris flow shows that the 13.15%, 22.94%, and 63.91% areas are very high, high, and low susceptible to debris flow respectively. The propagation predicated by Flow-R validates the naturally occurring debris flow propagation as observed in the field surveys. The output of this research will provide valuable input to the decision makers for the site selection, designing of the prevention system, and for the protection of current infrastructure.

Effect of Blasting Stress Wave on Dynamic Crack Propagation

Stress waves affect the stress field at the crack tip and dominate the dynamic crack propagation.Therefore,evaluating the influence of blasting stress waves on the crack propagation behavior and the mechanical characteristics of crack propagation is of great significance for engineering blasting.In this study,ANSYS/LS-DYNA was used for blasting numerical simulation,in which the propagation characteristics of blasting stress waves and stress field distribution at the crack tip were closely observed.Moreover,ABAQUS was applied for simulating the crack propagation path and calculating dynamic stress intensity factors(DSIFs).The universal function was calculated by the fractalmethod.The results show that:the compressive wave causes the crack to close and the reflected tensile wave drives the crack to initiate and propagate,and failure mode is mainly tensile failure.The crack propagation velocity varies with time,which increases at first and then decreases,and the crack arrest occurs due to the attenuation of stress waves and dissipation of the blasting energy.In addition,crack arrest toughness is smaller than the crack initiation toughness,applied pressure waveforms(such as the peak pressure,duration,waveforms,wavelengths and loading rates)have a great influence on DSIFs.It is conducive to our deep understanding or the study of blasting stress waves dominated fracture,suggesting a broad reference for the further development of rock blasting in engineering practice.

Improved Segmented Belief Propagation List Decoding for Polar Codes with Bit-Flipping

Belief propagation list(BPL) decoding for polar codes has attracted more attention due to its inherent parallel nature. However, a large gap still exists with CRC-aided SCL(CA-SCL) decoding.In this work, an improved segmented belief propagation list decoding based on bit flipping(SBPL-BF) is proposed. On the one hand, the proposed algorithm makes use of the cooperative characteristic in BPL decoding such that the codeword is decoded in different BP decoders. Based on this characteristic, the unreliable bits for flipping could be split into multiple subblocks and could be flipped in different decoders simultaneously. On the other hand, a more flexible and effective processing strategy for the priori information of the unfrozen bits that do not need to be flipped is designed to improve the decoding convergence. In addition, this is the first proposal in BPL decoding which jointly optimizes the bit flipping of the information bits and the code bits. In particular, for bit flipping of the code bits, a H-matrix aided bit-flipping algorithm is designed to enhance the accuracy in identifying erroneous code bits. The simulation results show that the proposed algorithm significantly improves the errorcorrection performance of BPL decoding for medium and long codes. It is more than 0.25 d B better than the state-of-the-art BPL decoding at a block error rate(BLER) of 10^(-5), and outperforms CA-SCL decoding in the low signal-to-noise(SNR) region for(1024, 0.5)polar codes.

Fatigue Crack Propagation Law of Corroded Steel Box Girders in Long Span Bridges

In order to investigate the fatigue performance of orthotropic anisotropic steel bridge decks,this study realizes the simulation of the welding process through elastic-plastic finite element theory,thermal-structural sequential coupling,and the birth-death element method.The simulated welding residual stresses are introduced into the multiscale finite element model of the bridge as the initial stress.Furthermore,the study explores the impact of residual stress on crack propagation in the fatigue-vulnerable components of the corroded steel box girder.The results indicate that fatigue cracks at the weld toe of the top deck,the weld root of the top deck,and the opening of the transverse diaphragm will not propagate under the action of a standard vehicle load.However,the inclusion of residual stress leads to the propagation of these cracks.When considering residual stress,the fatigue crack propagation paths at the weld toe of the transverse diaphragm and the U-rib weld toe align with those observed in actual bridges.In the absence of residual stress,the cracks at the toe of the transverse diaphragm with a 15%mass loss rate are categorized as type I cracks.Conversely,when residual stress is considered,these cracks become I-II composite cracks.Residual stress significantly alters the cumulative energy release rate of the three fracturemodes.Therefore,incorporating the influence of residual stress is essential when assessing the fatigue performance of corroded steel box girders in long-span bridges.

Cutting Propagation Technique of Pennisetum purpureum Schum

[Objectives]The paper was to study the cutting propagation technique of Pennisetum purpureum Schum and to provide a technical reference for establishing an efficient cutting propagation method.[Methods]Six treatments were set up using P.purpureum cv.Guiminyin and P.purpureum cv.Guimu-1 as test materials,including 1-node oblique insertion,1-node oblique insertion+rooting powder,1-node transverse burial,2-node oblique insertion,2-node oblique insertion+rooting powder and 2-node transverse burial.The following indices were observed and determined for P.purpureum cuttings:emergence rate,rooting rate,root number,longest root length,fresh root weight,plant height,number of tillers,number of leaves,and fresh stem and leaf weight.[Results]In the 2-node cutting+rooting powder treatment,Guiminyin and Guimu-1 exhibited the highest survival rate,root growth indices,and stem and leaf growth indices,with the emergence rates of 94.29%and 90.26%,respectively.The 2-node cutting treatment followed closely behind,while the 1-node cutting treatment had the lowest indices.Under the same treatment,Guimuyin exhibited higher mean values for plant height,number of leaves,fresh stem and leaf weight,longest root length,and fresh root weight compared to Guimu-1.However,it had lower mean number of tillers,and emergence rate and rooting rate of the 1-node cutting treatment compared to Guimu-1.[Conclusions]The P.purpureum cuttings thrived in the 2-node cutting+rooting powder treatment,and the overall cutting effect of Guiminyin was superior to that of Guimu-1.

Impact Analysis of Microscopic Defect Types on the Macroscopic Crack Propagation in Sintered Silver Nanoparticles

Sintered silver nanoparticles(AgNPs)arewidely used in high-power electronics due to their exceptional properties.However,the material reliability is significantly affected by various microscopic defects.In this work,the three primary micro-defect types at potential stress concentrations in sintered AgNPs are identified,categorized,and quantified.Molecular dynamics(MD)simulations are employed to observe the failure evolution of different microscopic defects.The dominant mechanisms responsible for this evolution are dislocation nucleation and dislocation motion.At the same time,this paper clarifies the quantitative relationship between the tensile strain amount and the failure mechanism transitions of the three defect types by defining key strain points.The impact of defect types on the failure process is also discussed.Furthermore,traction-separation curves extracted from microscopic defect evolutions serve as a bridge to connect the macro-scale model.The validity of the crack propagation model is confirmed through tensile tests.Finally,we thoroughly analyze how micro-defect types influence macro-crack propagation and attempt to find supporting evidence from the MD model.Our findings provide a multi-perspective reference for the reliability analysis of sintered AgNPs.

Development of a Post Quantum Encryption Key Generation Algorithm Using Electromagnetic Wave Propagation Theory

In today’s rapid widespread of digital technologies into all live aspects to enhance efficiency and productivity on the one hand and on the other hand ensure customer engagement, personal data counterfeiting has become a major concern for businesses and end-users. One solution to ensure data security is encryption, where keys are central. There is therefore a need to find robusts key generation implementation that is effective, inexpensive and non-invasive for protecting and preventing data counterfeiting. In this paper, we use the theory of electromagnetic wave propagation to generate encryption keys.

RELATIONSHIP BETWEEN SUMMER LOW-FREQUENCY RAINFALL OVER SOUTHERN CHINA AND PROPAGATION OF TROPICAL INTRASEASONAL OSCILLATION

This study investigates the relationship between summer low-frequency rainfall over southern China and tropical intraseasonal oscillation(ISO) in the atmosphere by examining systematically the propagation features of the tropical ISO in terms of focusing on five large-scale low-frequency rainfall regimes in summer over southern China. It is demonstrated that there is a close linkage between the five rainfall regimes over southern China and the northward propagation of the tropical ISO. The moist ISO signals, which influence the low-frequency rainfall events in different regions of southern China, mainly propagate northwestward from the tropical ocean to the southeast of China. The southeast China rainfall regime is intimately associated with the moist ISO signals propagating northwestward from the equatorial mid-western Pacific Ocean. For both the Yangtze River regime and South of Yangtze River regime, the moist ISO signals over the northern South China Sea show an evident northward propagation towards the Yangtze River region, and then propagate westward. It is further found that the interaction between the northward propagation of low-latitude ISO signals and the southward propagation of high-latitude ISO signals can also make a clear influence on the low-frequency rainfall in southern China. For the Southern China regime, the moist ISO signals show a significant northward propagation from the Philippines. Moreover, for the rainless regime, southern China is under dry ISO signals' control, and the latter shows no clear propagation to southern China. This study may provide insights for the extended-range forecasting of summer rainfall in southern China.

The Propagation of Disturbances Excited by Low-Frequency Oscillations in the Tropics

The propagation of disturbances excited by low-frequency oscillations in the tropics is investigated by applying the theory of wave packet dynamics. For simplicity, a linearized barotropic model is adopted and the zonal circulation is taken as basic current. Suppose that the disturbances or waves are superimposed on jet-like westerly basic cur-rent and excited by the forcing in the tropics. We have (1) only the eastward propagating (m>0, n>0 and σ>0) low-frequency disturbances and the stationary (σ = 0) waves can propagate into the middle and high latitudes in the Northern Hemisphere; the others, such as the westward propagating low-frequency wave (m>0, n<0, σ<0) and the high-frequency waves, are restricted only in the vicinity of source region; (2) a stationary wave (σ = 0) reaches a given latitude even more quickly than some low-frequency ones (σ>0) due to the fact that the group velocity of stationary wave is larger; (3) there is a whole wave train excited by the forcing in the tropics and extended into the middle and high latitudes, if the amplitude of the source is independent on time, especially, the low-frequency wave (σ > 0) is of travelling type propagating along the ray; (4) if the source lasts only for an interval of time, namely, its amplitude also has the character of low-frequency oscillation, the excited wave train is not always a whole one, but is restricted in the vicinity of source region in the beginning, extended from the source region to the middle and high latitudes in its saturated stage, after that it gradually becomes weaker and weaker and is detectable only in some area at high latitude, and eventually disappears. Undoubtedly, case (4) is closer to the reality, even though case (3) gives a more impressive wavy pattern.