ON THE CAUCHY PROBLEM FOR THE GENERALIZED BOUSSINESQ EQUATION WITH A DAMPED TERM

This paper is devoted to the Cauchy problem for the generalized damped Boussinesq equation with a nonlinear source term in the natural energy space.With the help of linear time-space estimates,we establish the local existence and uniqueness of solutions by means of the contraction mapping principle.The global existence and blow-up of the solutions at both subcritical and critical initial energy levels are obtained.Moreover,we construct the sufficient conditions of finite time blow-up of the solutions with arbitrary positive initial energy.

A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.

A reweighted damped singular spectrum analysis method for robust seismic noise suppression

(Multichannel)Singular spectrum analysis is considered as one of the most effective methods for seismic incoherent noise suppression.It utilizes the low-rank feature of seismic signal and regards the noise suppression as a low-rank reconstruction problem.However,in some cases the seismic geophones receive some erratic disturbances and the amplitudes are dramatically larger than other receivers.The presence of this kind of noise,called erratic noise,makes singular spectrum analysis(SSA)reconstruction unstable and has undesirable effects on the final results.We robustify the low-rank reconstruction of seismic data by a reweighted damped SSA(RD-SSA)method.It incorporates the damped SSA,an improved version of SSA,into a reweighted framework.The damping operator is used to weaken the artificial disturbance introduced by the low-rank projection of both erratic and random noise.The central idea of the RD-SSA method is to iteratively approximate the observed data with the quadratic norm for the first iteration and the Tukeys bisquare norm for the rest iterations.The RD-SSA method can suppress seismic incoherent noise and keep the reconstruction process robust to the erratic disturbance.The feasibility of RD-SSA is validated via both synthetic and field data examples.

Near resonance vibration isolation on a levered-dual response(LEDAR)Coulomb-damped system by differential preloads/offsets in linear springs

The levered-dual response(LEDAR)Coulomb-damped system attains near resonant vibration isolation by differential preloads/offsets in linear springs.It takes the advantages of both the preloads/offsets in linear springs and the guiderail friction for realizing different levels of vibration isolation.The isolation capacities are investigated on the strategies with both the horizontal and vertical guiderails,with the horizontal rail only,and without guiderails.The compressive preloads generally result in the consumption of most of the initial excitation energy so as to overcome the potential threshold.The isolation onsets at the frequency ratio of 1∓0.095 on the left-hand side(LHS)and the right-hand side(RHS)of the lever are relative to the load plate connector.The observed near resonant isolation thus makes the LEDAR system a candidate for the isolation of the mechanical systems about resonance while opening a path for simultaneous harvesterisolation functions and passive functions at extreme frequencies.

The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

山麦冬皂苷B调节DAMPs释放诱导免疫源性细胞死亡的抗肿瘤机制研究

目的探讨Spicatoside B对肺癌细胞的增殖、凋亡和DAMPs释放的影响,并明确凋亡与DAMPs释放之间的关系。方法将不同浓度的SP-B作用于A549和H1299细胞株24 h,CCK8检测细胞增殖活性;根据CCK8结果,选取药物浓度,干预细胞24 h,流式细胞仪检测细胞凋亡;ATP试剂盒检测ATP细胞外分泌;流式细胞仪检测CRT表达;ELISA检测HMGB1、HSP70、HSP90的细胞外分泌;凋亡抑制剂抑制凋亡后,再次检测CRT、ATP、HMGB1和HSP70/90的表达。结果SP-B显著抑制A549和H1299细胞的增殖活性,IC_(50)值分别为73.11μM和51.461μM;选取40μM浓度干预细胞,可显著促进凋亡;药物作用后显著提高了CRT的阳性比率,增加了ATP、HMGB1、HSP70、HSP90的细胞外释放。抑制凋亡后,CRT、ATP、HMGB1和HSP70/90的表达随之减少。结论Spicatoside B可抑制增殖,促凋亡,并显著促进DAMPs的释放,诱导免疫原性细胞死亡,其中凋亡对DAMPs的释放发挥着重要作用。

The Extended Non-Elementary Amplitude Functions as Solutions to the Damped Pendulum Equation, the Van der Pol Equation, the Damped Duffing Equation, the Lienard Equation and the Lorenz Equations

In this paper, we define some non-elementary amplitude functions that are giving solutions to some well-known second-order nonlinear ODEs and the Lorenz equations, but not the chaos case. We are giving the solutions a name, a symbol and putting them into a group of functions and into the context of other functions. These solutions are equal to the amplitude, or upper limit of integration in a non-elementary integral that can be arbitrary. In order to define solutions to some short second-order nonlinear ODEs, we will make an extension to the general amplitude function. The only disadvantage is that the first derivative to these solutions contains an integral that disappear at the second derivation. We will also do a second extension: the two-integral amplitude function. With this extension we have the solution to a system of ODEs having a very strange behavior. Using the extended amplitude functions, we can define solutions to many short second-order nonlinear ODEs.

Microstructure and damping properties of LPSO phase dominant Mg-Ni-Y and Mg-Zn-Ni-Y alloys

This work studied the microstructure,mechanical properties and damping properties of Mg_(95.34)Ni_(2)Y_(2.66) and Mg_(95.34)Zn_(1)Ni_(1)Y_(2.66)alloys systematically.The difference in the evolution of the long-period stacked ordered(LPSO)phase in the two alloys during heat treatment was the focus.The morphology of the as-cast Mg_(95.34)Ni_(2)Y_(2.66)presented a disordered network.After heat treatment at 773 K for 2 hours,the eutectic phase was integrated into the matrix,and the LPSO phase maintained the 18R structure.As Zn partially replaced Ni,the crystal grains became rounded in the cast alloy,and lamellar LPSO phases and more solid solution atoms were contained in the matrix after heat treatment of the Mg_(95.34)Zn_(1)Ni_(1)Y_(2.66)alloy.Both Zn and the heat treatment had a significant effect on damping.Obvious dislocation internal friction peaks and grain boundary internal friction peaks were found after temperature-dependent damping of the Mg_(95.34)Ni_(2)Y_(2.66)and Mg_(95.34)Zn_(1)Ni_(1)Y_(2.66)alloys.After heat treatment,the dislocation peak was significantly increased,especially in the alloy Mg_(95.34)Ni_(2)Y_(2).66.The annealed Mg_(95.34)Ni_(2)Y_(2.66)alloy with a rod-shaped LPSO phase exhibited a good damping performance of 0.14 atε=10^(−3),which was due to the difference between the second phase and solid solution atom content.These factors also affected the dynamic modulus of the alloy.The results of this study will help in further development of high-damping magnesium alloys.

Closed-form steady-state solutions for forced vibration of second-order axially moving systems

Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.

An internally damped inertial platform for marine gravimetry and a test case in the South China Sea

To dampen periodic off-levelling motions within an inertial platform while undergoing horizontal accelerations of the same period and to achieve a levelling accuracy of a few tens of arcseconds with that system,an internally damped inertial platform for a marine scalar gravity system was the developed.Methods for attenuating horizontal acceleration and reducing off-levelling error by a satisfactory gyro-levelling loop,which are fundamental to the internally damped inertial platform,were designed and implemented.In addition,phase delays are introduced by the levelling loop.The resulting off-levelling gravity errors were analyzed and modeled.A series of tests on a motion simulator were performed in laboratory for a variety of simulated sea conditions.We found that the motion of the platform is a function of the amplitude and period of the simulated ship motions and ranges between 10 and 40 arcseconds.In addition,the phase lag between platform motion and ship motion is not constant but ranges 180°-270°,depending on the period and amplitude of the motion.Then,the platform,on which a gravimeter was mounted,was installed on the R/V Shiyan 2 to conduct a gravity survey in the South China Sea.Despite rough sea conditions,it was shown that in short periods of 2-30 s,the off-levelling angle was less than 30 arcseconds,and the phase lagged the horizontal acceleration by 230°-260°.From a repeated survey line and intersecting survey points,the estimated errors of gravity measurements were between 1.3 and 1.7 mGal.The marine measurements results were compared with those of satellite altimetry data and show a mean value of 0.5 mGal in a standard deviation of 1.5 mGal.

Three-dimensional mixed convection stagnation-point fow past a vertical surface with second-order slip velocity

This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.

Six New Sets of the Non-Elementary Jef-Family-Functions that Are Giving Solutions to Some Second-Order Nonlinear Autonomous ODEs

In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of three functions that belong together. Differentiating these functions twice gives second-order nonlinear ODEs that have the defined set of functions as solutions. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles. Using the methods described in this paper, it is possible to define many other sets of non-elementary functions that are giving solutions to some second-order nonlinear autonomous ODEs.

Effects of air damping on quality factors of different probes in tapping mode atomic force microscopy

The AFM probe in tapping mode is a continuous process of energy dissipation,from moving away from to intermittent contact with the sample surfaces.At present,studies regarding the energy dissipation mechanism of this continuous process have only been reported sporadically,and there are no systematic explanations or experimental verifications of the energy dissipation mechanism in each stage of the continuous process.The quality factors can be used to characterize the energy dissipation in TM-AFM systems.In this study,the vibration model of the microcantilever beam was established,coupling the vibration and damping effects of the microcantilever beam.The quality factor of the vibrating microcantilever beam under damping was derived,and the air viscous damping when the probe is away from the sample and the air squeeze film damping when the probe is close to the sample were calculated.In addition,the mechanism of the damping effects of different shapes of probes at different tip–sample distances was analyzed.The accuracy of the theoretical simplified model was verified using both experimental and simulation methods.A clearer understanding of the kinetic characteristics and damping mechanism of the TM-AFM was achieved by examining the air damping dissipation mechanism of AFM probes in the tapping mode,which was very important for improving both the quality factor and the imaging quality of the TM-AFM system.This study’s research findings also provided theoretical references and experimental methods for the future study of the energy dissipation mechanism of micro-nano-electromechanical systems.

Aseismic performances of constrained damping lining structures made of rubber-sand-concrete

Flexible damping technology considering aseismic materials and aseismic structures seems be a good solution for engineering structures.In this study,a constrained damping structure for underground tunnel lining,using a rubber-sand-concrete(RSC)as the aseismic material,is proposed.The aseismic performances of constrained damping structure were investigated by a series of hammer impact tests.The damping layer thickness and shape effects on the aseismic performance such as effective duration and acceleration amplitude of time-domain analysis,composite loss factor and damping ratio of the transfer function analysis,and total vibration level of octave spectrum analysis were discussed.The hammer impact tests revealed that the relationship between the aseismic performance and damping layer thickness was not linear,and that the hollow damping layer had a better aseismic performance than the flat damping layer one.The aseismic performances of constrained damping structure under different seismicity magnitudes and geological conditions were investigated.The effects of the peak ground acceleration(PGA)and tunnel overburden depth on the aseismic performances such as the maximum principal stress and equivalent plastic strain(PEEQ)were discussed.The numerical results show the constrained damping structure proposed in this paper has a good aseismic performance,with PGA in the range(0.2-1.2)g and tunnel overburden depth in the range of 0-300 m.

Low Gilbert damping in Bi/In-doped YIG thin films with giant Faraday effect

Magnetic films with low Gilbert damping are crucial for magnonic devices,which provide a promising platform forrealizing ultralow-energy devices.In this study,low Gilbert damping and coercive field were observed in Bi/In-dopedyttrium iron garnet(BiIn:YIG)thin films.The BiIn:YIG(444)films were deposited onto different substrates using pulsedlaser deposition.Low coercivity(<1 Oe)with saturation magnetization of 125.09 emu/cc was achieved along the in-planedirection of BiIn:YIG film.The values of Gilbert damping and inhomogeneous broadening of ferromagnetic resonance inBiIn:YIG films were obtained to be as low as 4.05×10^(-4)and 5.62 Oe,respectively.In addition to low damping,the giantFaraday rotation angles(up to 2.9×10^(4)deg/cm)were also observed in the BiIn:YIG film.By modifying the magneticstructure and coupling effect between Bi^(3+)and Fe^(3+)of Bi:YIG,doped In^(3+)plays a key role on variation of the magneticproperties.The low damping and giant Faraday effect made the BiIn:YIG film an appealing candidate for magnonic andmagneto-optical devices.

Prediction of Damping Capacity Demand in Seismic Base Isolators via Machine Learning

Base isolators used in buildings provide both a good acceleration reduction and structural vibration control structures.The base isolators may lose their damping capacity over time due to environmental or dynamic effects.This deterioration of them requires the determination of the maintenance and repair needs and is important for the long-termisolator life.In this study,an artificial intelligence prediction model has been developed to determine the damage and maintenance-repair requirements of isolators as a result of environmental effects and dynamic factors over time.With the developed model,the required damping capacity of the isolator structure was estimated and compared with the previously placed isolator capacity,and the decrease in the damping property was tried to be determined.For this purpose,a data set was created by collecting the behavior of structures with single degrees of freedom(SDOF),different stiffness,damping ratio and natural period isolated from the foundation under far fault earthquakes.The data is divided into 5 different damping classes varying between 10%and 50%.Machine learning model was trained in damping classes with the data on the structure’s response to random seismic vibrations.As a result of the isolator behavior under randomly selected earthquakes,the recorded motion and structural acceleration of the structure against any seismic vibration were examined,and the decrease in the damping capacity was estimated on a class basis.The performance loss of the isolators,which are separated according to their damping properties,has been tried to be determined,and the reductions in the amounts to be taken into account have been determined by class.In the developed prediction model,using various supervised machine learning classification algorithms,the classification algorithm providing the highest precision for the model has been decided.When the results are examined,it has been determined that the damping of the isolator structure with the machine learning method is predicted successfully at a level exceeding 96%,and it is an effective method in deciding whether there is a decrease in the damping capacity.

Recent Progresses of the DAMPE Mission

The DArk Matter Particle Explorer(DAMPE)is a space high-energy particle andγ-ray detector whose major scientific goals are the indirect detection of dark matter particles,the origin of cosmic rays and highenergyγ-ray astronomy.Since its successful launch in December 2015,the DAMPE has been operated smoothly in orbit for more than 8 years.The direct measurements of the boron-to-carbon and boron-to-oxygen flux ratios,and the proton+Helium spectrum up to 316 TeV have been obtained,revealing new spectral features with very high significances.The search results ofγ-ray spectral line and fractionally charged particles indicate a good potential of DAMPE for indirect dark matter detection and new physical discovery in space.The DAMPE measurements are expected to significantly advance our understanding of the fundamental problems in astroparticle physics.

Microstructure,Mechanical Properties and Damping of SiC/Mg97Zn1Y2 Composites

SiC particles were added to the Mg97Zn1Y2 alloy to improve its mechanical properties and damping properties.The microstructure,mechanical properties,and strain amplitude dependence of high-damping and high-strength SiC/Mg97Zn1Y2 magnesium matrix composites were analyzed.The strain amplitude-dependent damping of SiC/Mg97Zn1Y2 composites and the effect of SiC on this property were discussed herein.In anelastic damping,the strain amplitude-dependent damping curves of the composites were mainly divided into two sections,dominated by the G-L model.When the strain amplitude reaches a certain value,the dislocation motion inside the matrix becomes complicated.Moreover,the damping of the material could not be explained using the G-L model,and a new damping model related to microplastic deformation was proposed.In the anelastic damping stage,with the increase in the amount of the added SiC particles,the damping performance first increases and then decreases.Moreover,the damping value of the composite material is larger than that of the matrix alloy.In the microplastic deformation stage,the damping properties of the composites and matrix alloys considerably increase with the strain amplitude.

Damping properties and mechanism of aluminum matrix composites reinforced with glass cenospheres

The damping properties were improved by preparing Al matrix composites reinforced with glass cenospheres through the pressure infiltration method.Transmission electron microscopy and scanning electron microscopy were employed to characterize the microstructure of the composites.The low-frequency damping properties were examined by using a dynamic mechanical thermal analyzer,aiming at exploring the changing trend of damping capacity with strain,temperature,and frequency.The findings demonstrated that the damping value rose as temperature and strain increased,with a maximum value of 0.15.Additionally,the damping value decreased when the frequency increased.Dislocation damping under strain and interfacial damping under temperature served as the two primary damping mechanisms.The increase in the density of dislocation strong pinning points following heat treatment reduced the damping value,which was attributed to the heat treatment enhancement of the interfacial bonding force of the composites.

Mechanical and damping performances of TPMS lattice metamaterials fabricated by laser powder bed fusion

Lattice metamaterials based on three-period minimum surface(TPMS)are an effective means to achieve lightweight and high-strength materials which are widely used in various fields such as aerospace and ships.However,its vibration and noise reduction,and damping properties have not been fully studied.Therefore,in this study,the TPMS structures with parameterization were designed by the method of surface migration,and the TPMS structures with high forming quality was manufactured by laser powder bed fusion(LPBF).The mechanical properties and energy absorption characteristics of the beam and TPMS structures were studied and compared by quasi-static compression.The modal shapes of the beam lattice structures and TPMS structures were obtained by the free modal analysis,and the damping properties of two structures were obtained by modal tests.For the two structures after heat treatment with the same porosity of 70%,the yield strength of the beam lattice structure reaches 40.76 MPa,elastic modulus is 20.38 GPa,the energy absorption value is 32.23 MJ·m^(-3),the damping ratio is 0.52%.The yield strength,elastic modulus,energy absorption value,and damping ratio of the TPMS structure are 50.74 MPa,25.37 GPa,47.34 MJ·m^(-3),and 0.99%,respectively.The results show that TPMS structures exhibit more excellent mechanical properties and energy absorption,better damping performance,and obvious advantages in structural load and vibration and noise reduction compared with the beam lattice structures under the same porosity.