Some dynamical property of the Tsallis distribution from a Fokker-Planck equation

This paper studies the possible dynamical property of the Tsallis distribution from a Fokker--Planck equation. For the Langevin dynamical system with an {arbitrary} potential function, Markovian friction and Gaussian white noise, it shows that the current form of Tsallis distribution cannot describe any nonequilibrium dynamics of the system, and it only stands for a simple isothermal situation of the system governed by a potential field. So the form of Tsallis distribution and many existing applications using the Tsallis distribution need to be reconsidered.

Deformation characteristics and damage ontologies of soft and hard composite rock masses under impact loading

As one of the most common occurring geological landforms in deep rock formations, the dynamic mechanical properties of layered composite rock bodies under impact loading have been widely studied by scholars. To study the dynamic properties of soft and hard composite rocks with different thickness ratios, this paper utilizes cement, quartz sand and gypsum powder to construct soft and hard composite rock specimens and utilizes a combination of indoor tests, numerical calculations, and theoretical analyses to investigate the mechanical properties of soft and hard composite rock bodies. The test results reveal that:(1) When the proportion of hard rock increases from 20% to 50%, the strength of the combined rock body increases by 69.14 MPa and 87 MPa when the hard rock face and soft rock face are loaded, respectively;however, when the proportion of hard rock is the same, the compressive strength of the hard rock face impact is 9%-17% greater than that of the soft rock face impact;(2) When a specimen of soft and hard combined rock body is subjected to impact loading, the damage mode involves mixed tension and shear damage, and the cracks generally first appear at the ends of the specimen, then develop on the laminar surface from the impact surface, and finally end in the overall damage of the soft rock part. The development rate and the total number of cracks in the same specimen when the hard rock face is impacted are significantly greater than those when the soft rock face is impacted;(3) By introducing Weibull’s statistical strength theory to establish the damage variables of soft-hard combined rock bodies, combined with the DP strength criterion, the damage model and the Kelvin body are concatenated to obtain a statistical damage constitutive model, which can better fit the full stress-strain curve of soft-hard combined rock body specimens under a single impact load.

Dynamic compressive property and failure behavior of extruded Mg-Gd-Y alloy under high temperatures and high strain rates

For the purpose of investigating the dynamic deformational behavior and failure mechanisms of magnesium under high strain rates,the Split Hopkinson Pressure Bar(SHPB)was used for investigating dynamic mechanical properties of extruded Mg-Gd-Y Magnesium alloy at ambient temperature(300 K),200℃(473 K)and 300℃(573 K)temperature.The samples after compression were analyzed by scanning electron microscope(SEM)and metallographic microscope.Dynamic mechanical properties,crack performance and plastic deformation mechanism of extruded Mg-Gd-Y Magnesium alloy along the extrusion direction(ED)were discussed.The results show that,extruded Mg-Gd-Y Magnesium alloy has the largest dynamic compressive strength which is 535 MPa at ambient temperature(300 K)and strain rate of 2826 s^(−1).When temperature increases,dynamic compressive strength decreases,while ductility increases.The dynamic compression fracture mechanism of extruded Mg-Gd-Y Magnesium alloy is multi-crack propagation and intergranular quasi-cleavage fracture at both ambient temperature and high temperature.The dynamic compressive deformation mechanism of extruded Mg-Gd-Y Magnesium alloy is a combination of twinning,slipping and dynamic recrystallization at both ambient temperature and high temperature.

Dynamical analysis and circuit simulation of a new three-dimensional chaotic system

This paper reports a new three-dimensional autonomous chaotic system. It contains six control parameters and three nonlinear terms. Two cross-product terms are respectively in two equations. And one square term is in the third equation. Basic dynamic properties of the new system are investigated by means of theoretical analysis, numerical simulation, sensitivity to initial, power spectrum, Lyapunov exponent, and Poincar~ diagrams. The dynamic properties affected by variable parameters are also analysed. Finally, the chaotic system is simulated by circuit. The results verify the existence and implementation of the system.

Lattice dynamical and thermodynamical properties of ReB_2,RuB_2,and OsB_2 compounds in the ReB_2 structure

Structural and lattice dynamical properties of ReB2,RuB2,and OsB2 in the ReB2 structure are studied in the framework of density functional theory within the generalized gradient approximation.The present results show that these compounds are dynamically stable for the considered structure.The temperature-dependent behaviors of thermodynamical properties such as internal energy,free energy,entropy,and heat capacity are also presented.The obtained results are in good agreement with the available experimental and theoretical data.

Property estimation of free-field sand in 1-g shaking table tests

Experimental data taken from free-field soil in 1-g shaking table tests are valuable for seismic studies on soil-structure interaction.But the available data from medium-to large-scale shaking table tests were not abundant enough to cover a large variety of types and conditions of the soil.In the study,1-g shaking table tests of a 3-m-height sand column were conducted to provide seismic experimental data about sand.The sand was directly collected in-situ,with the largest grain diameter being 2 cm and containing a water content of 6.3%.Properties of the sand were estimated under the influence of white noise plus pulse and earthquake motions,including the settlement,the dynamic properties of the sand column,and the three soil layers′shear modulus degradation relationships.The estimated properties were then indirectly verified by means of finite element analysis.Results show that the estimated parameters were effective and could be used in numerical modeling to reproduce approximate seismic responses of the sand column.

RESEARCH ON THE DYNAMIC PROPERTY OF PIEZOELECTRIC MICRO DISPLACEMENT ACTUATOR FOR BORING ERROR COMPENSATION

The dynamic property of piezoelectric micro displacement actuator (PMDA) isanalyzed, especially the mechanical characteristic, lag phase property and hysteresis phenomenon.The influence factors of static and dynamic mechanical characteristics and the lag phase propertyare analyzed systematically. Three main influence factors of lag phase property are discovered, Withcomparison to mechanical Coulomb friction, a generalized model of nonlinear hysteresis of PMDA isadvanced, based on the essential analysis of nonlinear phenomenon. Finally the application of PMDAin error compensation control system of boring is introduced, A good compensation result isachieved.

Effects of non-Gaussian noise on the dynamical properties of a logistic system

The dynamical properties of a tumor cell growth system described by the logistic system with coupling between non- Gaussian and Gaussian noise terms are investigated. The effects of the nonextensive index q on the stationary properties and the transient properties are discussed, respectively. The results show that the nonextensive index q can induce the tumor cell numbers to decrease greatly in the case of q 〉 1. Moreover, the switch from the steady stable state to the extinct state is speeded up as the increases of q, and the tumor cell numbers can be more obviously restrained for a large value of q. The numerical results are found to be in basic agreement with the theoretical predictions.

Ab initio study of dynamical properties of U-Nb alloy melt

The U-Nb alloy,as a kind of nuclear material with good corrosion resistance and mechanical properties,plays an important role in the nuclear industry.However,the experimental measurements and theoretical calculations of many parameters which are essential in describing the dynamical properties of this alloy melt,including density,diffusivity,and viscosity,have not been carried out yet.The lack of data on the dynamical properties of nuclear materials seriously hinders the high-performance nuclear materials from being developed and applied.In this work,the dynamical properties of the U-Nb alloy melt are systematically studied by means of ab initio molecular dynamics simulations and their corresponding mathematical models are established,thereby being able to rapidly calculate the densities,diffusion coefficients,viscosities,and their activation energies in the whole U-Nb liquid region.This work provides a new idea for investigating the dynamical properties of binary alloy melts,thereby promoting the development of melt research.

Dynamic fluid transport property of hydraulic fractures and its evaluation using acoustic logging

The existing acoustic logging methods for evaluating the hydraulic fracturing effectiveness usually use the fracture density to evaluate the fracture volume, and the results often cannot accurately reflect the actual productivity. This paper studies the dynamic fluid flow through hydraulic fractures and its effect on borehole acoustic waves. Firstly, based on the fractal characteristics of fractures observed in hydraulic fracturing experiments, a permeability model of complex fracture network is established. Combining the dynamic fluid flow response of the model with the Biot-Rosenbaum theory that describes the acoustic wave propagation in permeable formations, the influence of hydraulic fractures on the velocity dispersion of borehole Stoneley-wave is then calculated and analyzed, whereby a novel hydraulic fracture fluid transport property evaluation method is proposed. The results show that the Stoneley-wave velocity dispersion characteristics caused by complex fractures can be equivalent to those of the plane fracture model, provided that the average permeability of the complex fracture model is equal to the permeability of the plane fracture. In addition, for fractures under high-permeability(fracture width 10~100 μm, permeability ~100 μm^(2)) and reduced permeability(1~10 μm, ~10 μm^(2), as in fracture closure) conditions, the Stoneley-wave velocity dispersion characteristics are significantly different. The field application shows that this fluid transport property evaluation method is practical to assess the permeability and the connectivity of hydraulic fractures.

The Structural,Dielectric,Lattice Dynamical and Thermodynamic Properties of Zinc-Blende CdX(X=S,Se,Te) from First-Principles Analysis

The structural, dielectric, lattice dynamical and thermodynamic properties of zinc-blende CdX （X=S, Se, Te） are studied by using a plane-wave pseudopotential method within the density-functional theory. Our calculated lattice constants and bulk modulus are compared with the pubfished experimental and theoretical data. In addition, the Born effective charges, electronic dielectric tensors, phonon frequencies, and longitudinal opticaltransverse optical splitting are calculated by the linear-response approach. Some of the characteristics of the phonon-dispersion curves for zinc-blende CdX （X= S, Se, Te） are summarized. What is more, based on the lattice dynamical properties, we investigate the thermodynamic properties of CdX （X= S, Se, Te） and analyze the temperature dependences of the Helmholtz free energy F, the internal energy E, the entropy S and the constant-volume specific heat Cv. The results show that the heat capacities for CdTe, CdSe, and CdS approach approximately to the Petit-Dulong limit 6R.

Experimental study of the dynamic mechanical responses and failure characteristics of coal under true triaxial confinements

Investigations on the dynamic mechanical properties and failure mechanisms of coal under in-situ stress is essential for the prevention of dynamic disasters in deep coal mines.Thus,a modified true triaxial Hopkinson bar was employed to explore the dynamic mechanical behaviors of coal at different confining pressures(0–20 MPa)and strain rates(40–220 s^(-1)).The results show that the dynamic peak stress is positively correlated with lateral static pre-stressσy andσz,but negatively correlated with axial static prestressσx.At approximate strain rates,increasing the lateral static pre-stress facilitates increasing the dynamic peak stress,but the minimum lateral static pre-stress is the primary factor limiting a significant increase in dynamic peak stress of coal.Furthermore,the dynamic differential stress is linearly related to the logarithm of strain rate,and the peak strain varies linearly with strain rate.However,there is no significant correlation between confining pressure and peak strain.Moreover,X-ray CT images and photographic fracture observations of coal samples show the failure patterns under uniaxial and triaxial conditions are splitting failure and shear failure,respectively.The device provides a viable approach for fully comprehending the dynamic mechanical behaviors of rock-like material in complex stress conditions.

Dynamic mechanical characteristics of frozen subgrade soil subjected to freeze-thaw cycles

As a widely-applied engineering material in cold regions, the frozen subgrade soils are usually subjected to seismic loading, which are also dramatically influenced by the freeze-thaw(F-T)cycles due to the varying temperature. A series of dynamic cyclic triaxial experiments were conducted through a cryogenic triaxial apparatus for exploring the influences of F-T cycles on the dynamic mechanical properties of frozen subgrade clay.According to the experimental results of frozen clay at the temperature of-10℃, the dynamic responses and microstructure variation at different times of F-T cycles(0, 1, 5, and 20 cycles) were explored in detail.It is experimentally demonstrated that the dynamic stress-strain curves and dynamic volumetric strain curves of frozen clay are significantly sparse after 20F-T cycles. Meanwhile, the cyclic number at failure(Nf) of the frozen specimen reduces by 89% after 20freeze-thaw cycles at a low ratio of the dynamic stress amplitude. In addition, with the increasing F-T cycles,the axial accumulative strain, residual deformation,and the value of damage variable of frozen clay increase, while the dynamic resilient modulus and dynamic strength decrease. Finally, the influence of the F-T cycles on the failure mechanisms of frozen clay was discussed in terms of the microstructure variation. These studies contribute to a better understanding of the fundamental changes in the dynamic mechanical of frozen soils exposed to F-T cycles in cold and seismic regions.

Dynamic compressive response of porcine muscle measured using a split Hopkinson bar system with a pair of PVDF force transducers

The classic metallic Split Hopkinson Pressure Bar(SHPB)cannot capture the transmitted signal accurately when measuring soft biological tissue,because of the very low wave impedance and strength of this material.So the dynamic compressive response of porcine muscle has been investigated by using a modified SHPB.The forces on both ends of the sample measured using Polyvinylidene fluor(PVDF)transducers were applied to calculate the stress in the specimen instead of the strain gauge signal on the transmitted bar.Moreover,a circular cardboard disk pulse shaper was applied for generating a suitable incident pulse to achieve stress equilibrium and constant strain rates in the specimens.Then,the dynamic mechanical properties of porcine muscle parallel and perpendicular to the fiber directions were measured,and the stress equilibrium process during loading was analyzed,as well as the inertia-induced extra stress being corrected.Furthermore,quasi-static tests were conducted at two different strain rates to investigate the strain rate dependence using a universal material testing machine.The results show that the stress-strain curves are sensitive to strain rate in the two different loading directions.The compressive stress perpendicular to the fiber direction is stiffer than that parallel to the fiber direction.In addition,a strain rate-dependent constitutive model was developed based on the mechanical response of the muscle at different strain rates and fitted to the experimental data.The results show that the overall fit is good,and the constitutive model could describe the muscle's dynamic mechanical properties.

A NOTE ON THE JULIA SETS OF ENTIRE SOLUTIONS TO DELAY DIFFERENTIAL EQUATIONS

Let f be an entire solution of the Tumura-Clunie type non-linear delay differential equation.We mainly investigate the dynamical properties of Julia sets of f,and the lower bound estimates of the measure of related limiting directions is verified.

Theoretical study on dynamic effective electroelastic properties of random piezoelectric composites with aligned inhomogeneities

The closed-form solutions of the dynamic problem of heterogeneous piezoelectric materials are formulated by introducing polarizations into a reference medium and using the generalized reciprocity theorem.These solutions can be reduced to the ones of an elastodynamic problem.Based on the effective medium method,these closedform solutions can be used to establish the self-consistent equations about the frequencydependent effective parameters,which can be numerically solved by iteration.Theoretical predictions are compared with the experimental results,and good agreement can be found.Furthermore,the analyses on the effects of microstructure and wavelength on the effective properties,resonance frequencies,and attenuation are also presented,which may provide some guidance for the microstructure design and analysis of piezoelectric composites.

Dynamic behaviors of water-saturated and frozen sandstone subjected to freeze-thaw cycles

In high-altitude cold areas,freeze-thaw(F-T)cycles induced by day-night and seasonal temperature changes cause numerous rock mass slope engineering disasters.To investigate the dynamic properties of rock in the natural environment of a high-altitude cold area,standard specimens were drilled from the slope of the Jiama copper mine in Tibet,and dynamic compression tests were performed on watersaturated and frozen sandstone with different numbers of F-T cycles(0,10,20,30,and 40)by the split Hopkinson pressure bar(SHPB)system with a cryogenic control system.The influence of water-saturated and frozen conditions on the dynamic performance of sandstone was investigated.The following conclusions are drawn:(1)With increasing strain rate,the attenuation factor(la)of water-saturated sandstone and the intensifying factor(li)of frozen sandstone linearly increase.As the number of F-T cycles increases,the dependence factor(ld)of water-saturated sandstone linearly decreases,whereas the ld of frozen sandstone linearly increases.(2)The prediction equation of the dynamic compressive strength of water-saturated and frozen sandstone is obtained,which can be used to predict the dynamic compressive strength of sandstone after various F-T cycles based on the strain rate.(3)The mesoscopic mechanism of water-saturated and frozen sandstone’s dynamic compressive strength evolution is investigated.The water softening effect causes the dynamic compressive strength of water-saturated sandstone to decrease,whereas the strengthening effect of pore ice causes it to increase.(4)The decrease in the relative dynamic compressive strength of water-saturated sandstone and the increase in the relative dynamic compressive strength of frozen sandstone can be attributed to the increased porosity.

Numerical Approach to Simulate the Effect of Corrosion Damage on the Natural Frequency of Reinforced Concrete Structures

Corrosion of reinforcing steel in concrete elements causes minor to major damage in different aspects.It may lead to spalling of concrete cover,reduction of section’s capacity and can alter the dynamic properties.For the dynamic properties,natural frequency is to be a reliable indicator of structural integrity that can be utilized in non-destructive corrosion assessment.Although the correlation between natural frequency and corrosion damage has been reflected in different experimental programs,few attempts have been made to investigate this relationship in forward modeling and/or structural health monitoring techniques.This can be attributed to the limited available data,the complex nature of corrosion,and the involvement of multidisciplinaryfields.Therefore,this study presents a numerical attempt to simulate the effect of corrosion damage on the natural frequency of the structure.The approach relies on simulating the time history response of the structure using a modified Bouc-Wen model that incorporates the nonlinear effects of corrosion.Then,modal analysis is utilized to assess the change in dynamic properties in the frequency domain.Tofinish up,regression algorithms are employed tofind optimal relationship between involved parameters,including corrosion damage as input,and natural frequency as output.The efficiency of the suggested framework is illustrated in thirteen buildings with cantilevered column lateral force-resisting system and different levels of corrosion.

Dynamics of bubble-shaped Bose-Einstein condensates on two-dimensional cross-section in micro-gravity environment

We investigated the dynamic evolution and interference phenomena of bubble-shaped Bose-Einstein condensates achievable in a micro-gravity environment.Using numerical solutions of the Gross-Pitaevskii equation describing the dynamic evolution of the bubble-shaped Bose-Einstein condensates,we plotted the evolution of the wave function density distribution on its two-dimensional(2D)cross-section and analysed the resulting patterns.We found that changes in the strength of atomic interactions and initial momentum can affect the dynamic evolution of the bubble-shaped Bose-Einstein condensates and their interference fringes.Notably,we have observed that when the initial momentum is sufficiently high,the thickness of the bubble-shaped Bose-Einstein condensate undergoes a counterintuitive thinning,which is a counterintuitive result that requires further investigation.Our findings are poised to advance our comprehension of the physical essence of bubble-shaped Bose-Einstein condensates and to facilitate the development of relevant experiments in microgravity environments.

Experimental and numerical investigation on the dynamic shear failure mechanism of sandstone using short beam compression specimen

In this study,a novel testing method is proposed to characterize the dynamic shear property and failure mechanism of rocks by introducing the short beam compression(SBC)specimen into the split Hopkinson pressure bar(SHPB)system.Firstly,the stress distribution of SBC specimen is comprehensively analyzed by finite element method(FEM),and the results show that the optimal notch separation ratio of SBC specimen is C/H?0.2 to achieve successful dynamic simple-shear tests.Then,dynamic shear tests are conducted on sandstone using the SBC-SHPB method.Via careful pulse shaping technique,the dynamic force balance is guaranteed for SBC specimens,and the testing results show that the dynamic shear strength of sandstone is significantly rate-dependent.Combining the results of dynamic compression and tension tests,the failure envelopes of sandstone under different loading rates are obtained in the principle stress plane.It is found that the failure envelope of sandstone constantly expands outwards with increasing loading rate.Moreover,the energy partition of SBC specimen is quantified by virtue of high-speed digital image correlation(DIC)technique.The results show that the kinetic energy portion is non-negligible,and the shear fracture energy increases with increasing loading rate.In addition,the microscopic shear cracking mechanism of SBC specimen is analyzed by the thin section observation:the intra-granular(TG)fracture of minerals dominates the dynamic shear failure of sandstone,and the portion of TG fracture increases with increasing loading rate.This study provides a convenient and reliable method to investigate the dynamic shear property and failure mechanism of rocks.