Tensile Shock Physics in Compressible Thermoviscoelastic Solid Medium

This paper addresses tensile shock physics in thermoviscoelastic (TVE) solids without memory. The mathematical model is derived using conservation and balance laws (CBL) of classical continuum mechanics (CCM), incorporating the contravariant second Piola-Kirchhoff stress tensor, the covariant Green’s strain tensor, and its rates up to order n. This mathematical model permits the study of finite deformation and finite strain compressible deformation physics with an ordered rate dissipation mechanism. Constitutive theories are derived using conjugate pairs in entropy inequality and the representation theorem. The resulting mathematical model is both thermodynamically and mathematically consistent and has closure. The solution of the initial value problems (IVPs) describing evolutions is obtained using a variationally consistent space-time coupled finite element method, derived using space-time residual functional in which the local approximations are in hpk higher-order scalar product spaces. This permits accurate description problem physics over the discretization and also permits precise a posteriori computation of the space-time residual functional, an accurate measure of the accuracy of the computed solution. Model problem studies are presented to demonstrate tensile shock formation, propagation, reflection, and interaction. A unique feature of this research is that tensile shocks can only exist in solid matter, as their existence requires a medium to be elastic (presence of strain), which is only possible in a solid medium. In tensile shock physics, a decrease in the density of the medium caused by tensile waves leads to shock formation ahead of the wave. In contrast, in compressive shocks, an increase in density and the corresponding compressive waves result in the formation of compression shocks behind of the wave. Although these are two similar phenomena, they are inherently different in nature. To our knowledge, this work has not been reported in the published literature.

Analysis on Shock Wave Speed of Water Hammer of Lifting Pipes for Deep-Sea Mining

Water hammer occurs whenever the fluid velocity in vertical lifting pipe systems for deep-sea mining suddenly changes. In this work, the shock wave was proven to play an important role in changing pressures and periods, and mathematical and numerical modeling technology was presented for simulated transient pressure in the abnormal pump operation. As volume concentrations were taken into account of shock wave speed, the experiment results about the pressure-time history, discharge-time history and period for the lifting pipe system showed that： as its concentrations rose up, the maximum transient pressure went down, so did its discharges; when its volume concentrations increased gradually, the period numbers of pressure decay were getting less and less, and the corresponding shock wave speed decreased. These results have highly coincided with simulation results. The conclusions are important to design lifting transporting system to prevent water hammer in order to avoid potentially devastating consequences, such as damage to components and equipment and risks to personnel.

Shear Wave Speed Dispersion Characteristics of Seafloor Sediments in the Northern South China Sea

To accurately characterize the shear wave speed dispersion of seafloor sediments in the northern South China Sea,five types of sediments including silty clay,clayey silt,sandy silt,silty sand,and clayey sand were selected,on which the measurements of the shear wave speed at 0.5-2.0 kHz and related physical properties were performed.Results reveal that the shear wave speed of sediments increases as the frequency increases,and the dispersion enhanced in the sediments in the order of silty clay,clayey silt,sandy silt,silty sand,and clayey sand,at a linear change rate of 0.727,0.787,3.32,4.893,and 6.967 m s−1 kHz−1,respectively.Through regression analysis,linear and logarithmic regression equations for the correlation between shear wave speed and frequency were established for each sediment type and the determination coefficients of regression equations indicate that the correlation is closer to a logarithmic relationship.The Grain-Shearing(GS)and Biot-Stoll models were used to calculate the shear wave speed dispersion of the five sediment types,and the comparison between theoretical prediction and measured results of shear wave speeds shows that the GS model can more accurately describe the shear wave speed dispersion characteristics of these sediments in the frequency band of 0.5-2.0 kHz.In the same band,the predictions obtained by using the Biot-Stoll model are significantly different from the measured data.

Multiscale simulation of nanometric cutting of single crystal copper——effect of different cutting speeds

A multiscale simulation has been performed to determine the effect of the cutting speed on the deformation mechanism and cutting forces in nanometric cutting of single crystal copper. The multiscale simulation model, which links the finite element method and the molecular dynamics method, captures the atomistic mechanisms during nanometric cutting from the free surface without the computational cost of full atomistic simulations. Simulation results show the material deformation mechanism of single crystal copper greatly changes when the cutting speed exceeds the material static propagation speed of plastic wave. At such a high cutting speed, the average magnitudes of tangential and normal forces increase rapidly. In addition, the variation of strain energy of work material atoms in different cutting speeds is investigated.

Simulation and Experimental Analysis of Super High-Speed Grinding of Ductile Material

This study aims to reduce the work-affected layer of the machined surface by carrying out the grinding at the speed over static pr o pagation speed of plastic wave of ductile materials and also aims to clarify suc h super high-speed machining mechanism.This paper reports on the result obtain ed through the molecular dynamics simulations and experiments on the super-spee d grinding below and beyond static propagation speed of aluminum.From the simul ation results,it is verified that the plastic deformation is reduced when the m a chining speed exceeds the material static propagation speed of plastic wave and its mechanism is completely different from that of the ordinary grinding process .Experimental results also show the improvement of the surface integrity when t he machining speed exceeds the material static propagation speed of plastic wave .

Determination of the Minimum Wave Speed for the Modelling of Ventilated Cavitation

Ventilated cavitation plays an important role on the drag reduction of underwater vehicles and surface ships. For the modelling of ventilated cavitation, the minimum speed of the pressure wave is a crucial parameter for the closure of the pressure-density coupling relationship. In this study, the minimum wave speed is determined based on a theoretical model coupling the wave equation and the bubble interface motion equation. The influences of several paramount parameters （e.g., frequency, bubble radius and void fraction） on the minimum wave speed are quantitatively demonstrated and discussed. Compared with the minimum wave speed in the traditional cavitation, values for the ventilated cavitation are much higher. The physical mechanisms for the above difference are briefly discussed with the suggestions on the usage of the present findings.

引入强分层近似对含密度跃层情况下的大幅内孤立波计算误差研究

At present,studies on large-amplitude internal solitary waves mostly adopt strong stratification models,such as the twoand three-layer Miyata–Choi–Camassa(MCC)internal wave models,which omit the pycnocline or treat it as another fluid layer with a constant density.Because the pycnocline exists in real oceans and cannot be omitted sometimes,the computational error of a large-amplitude internal solitary wave within the pycnocline introduced by the strong stratification approximation is unclear.In this study,the two-and three-layer MCC internal wave models are used to calculate the wave profile and wave speed of large-amplitude internal solitary waves.By comparing these results with the results provided by the Dubreil–Jacotin–Long(DJL)equation,which accurately describes large-amplitude internal solitary waves in a continuous density stratification,the computational errors of large-amplitude internal solitary waves at different pycnocline depths introduced by the strong stratification approximation are assessed.Although the pycnocline thicknesses are relatively large(accounting for 8%–10%of the total water depth),the error is much smaller under the three-layer approximation than under the two-layer approximation.

Acoustic Prediction and Risk Evaluation of Shallow Gas in Deep-Water Areas

Shallow gas is a potential risk in deep-water drilling that must not be ignored,as it may cause major safety problems,such as well kicks and blowouts.Thus,the pre-drilling prediction of shallow gas is important.For this reason,this paper conducted deep-water shallow gas acoustic simulation experiments based on the characteristics of deep-water shallow soil properties and the theory of sound wave speed propagation.The results indicate that the propagation speed of sound waves in shallow gas increases with an in-crease in pressure and decreases with increasing porosity.Pressure and sound wave speed are basically functions of the power expo-nent.Combined with the theory of sound wave propagation in a saturated medium,this paper establishes a multivariate functional relationship between sound wave speed and formation pressure and porosity.The numerical simulation method is adopted to simulate shal-low gas eruptions under different pressure conditions.Shallow gas pressure coefficients that fall within the ranges of 1.0-1.1,1.1-1.2,and exceeding 1.2 are defined as low-,medium-,and high-risk,respectively,based on actual operations.This risk assessment me-thod has been successfully applied to more than 20 deep-water wells in the South China Sea,with a prediction accuracy of over 90%.

Development and validation of an ocean wave retrieval algorithm for VV-polarization Sentinel-1 SAR data

The purpose is to study the accuracy of ocean wave parameters retrieved from C-band VV-polarization Sentinel-1Synthetic Aperture Radar（SAR） images, including both significant wave height（SWH） and mean wave period（MWP）, which are both calculated from a SAR-derived wave spectrum. The wind direction from in situ buoys is used and then the wind speed is retrieved by using a new C-band geophysical model function（GMF） model,denoted as C-SARMOD. Continuously, an algorithm parameterized first-guess spectra method（PFSM） is employed to retrieve the SWH and the MWP by using the SAR-derived wind speed. Forty-five VV-polarization Sentinel-1 SAR images are collected, which cover the in situ buoys around US coastal waters. A total of 52 subscenes are selected from those images. The retrieval results are compared with the measurements from in situ buoys. The comparison performs good for a wind retrieval, showing a 1.6 m/s standard deviation（STD） of the wind speed, while a 0.54 m STD of the SWH and a 2.14 s STD of the MWP are exhibited with an acceptable error.Additional 50 images taken in China＇s seas were also implemented by using the algorithm PFSM, showing a 0.67 m STD of the SWH and a 2.21 s STD of the MWP compared with European Centre for Medium-range Weather Forecasts（ECMWF） reanalysis grids wave data. The results indicate that the algorithm PFSM works for the wave retrieval from VV-polarization Sentinel-1 SAR image through SAR-derived wind speed by using the new GMF C-SARMOD.

An investigation into natural vibrations of fluid-structure interaction systems subject to Sommerfeld radiation condition

A fluid-structure interaction system subject to Sommerfeld＇s condition is defined as a Sommerfeld system which is divided into three categories： Fluid Sommerfeld （FS） System, Solid Sommerfeld （SS） System and Fluid Solid Sommerfeld （FSS） System of which Sommerfeld conditions are imposed on a fluid boundary only, a solid boundary only and both fluid and solid boundaries, respectively. This paper follows the previous initial results claimed by simple examples to further mathematically investigate the natural vibrations of generalized Sommerfeld systems. A new parameter representing the speed of radiation wave for generalized 3-D problems with more complicated boundary conditions is introduced into the Sommerfeld condition which allows investigation of the natural vibrations of a Sommerfeld system involving both free surface and compressible waves. The mathematical demonstrations and selected examples confirm and reveal the natural behaviour of generalized Sommerfeld systems defined above. These generalized conclusions can be used in theoretical or engineering analysis of the vibrations of various Sommerfeld systems in engineering.

The temporal and spatial variations in the Pacific wind and wave fields for the period 2002–2011

The temporal and spatial variations in the wind and wave fields in the Pacific Ocean between 2002 and 2011 are analyzed using a third-generation wave model（WAVEWATCH III）. The model performance for a significant wave height is validated using in situ buoy data. The results show that the wave model effectively hindcasts the significant wave height in the Pacific Ocean, but the errors are relatively large in the mid- and low-latitude regions. The spatial distributions and temporal variations in a wind speed and the significant wave height in the Pacific Ocean are then considered after dividing the Pacific Ocean into five regions, which show meridional differences and seasonal cycles. Regional mean values are used to give yearly average time series for each separate zone. The high latitude region in the Southern Hemisphere had a stronger significant wave height trend in the model results than regions at other latitudes. The sources and sinks of wave energy are then investigated. Their regional mean values are used to quantify variations in surface waves. Finally, the spectral analyses of the daily mean wind speeds and the significant wave heights are obtained. The significant wave height and the wind speed spectra are found to be connected in some ways but also show certain differences.

An evaluation of input/dissipation terms in WAVEWATCH Ⅲ using in situ and satellite significant wave height data in the South China Sea

A WAVEWATCH III version 3.14（WW3） wave model is used to evaluate input/dissipation source term packages WAM3, WAM4 and TC96 considering the effect of atmospheric instability. The comparisons of a significant wave height acquired from the model with different packages have been performed based on wave observation radar and HY-2 altimetry significant wave height data through five experiments in the South China Sea domain spanning latitudes of 0°–35°N and longitudes of 100°–135°E. The sensitivity of the wind speed correction parameter in the TC96 package also has been analyzed. From the results, the model is unable to dissipate the wave energy efficiently during a swell propagation with either source packages. It is found that TC96 formulation with the ＂effective wind speed＂ strategy performs better than WAM3 and WAM4 formulations. The wind speed correction parameter in the TC96 source package is very sensitive and needs to be calibrated and selected before the WW3 model can be applied to a specific region.

Solving the Inverse Problems of Wave Equation by a Boundary Functional Method

The inverse problems of wave equation to recover unknown space-time dependent functions of wave speed and wave source are solved in this paper, without needing of initial conditions and no internal measurement of data being required. After a homogenization technique, a sequence of spatial boundary functions at least the fourth-order polynomials are derived, which satisfy the homogeneous boundary conditions. The boundary functions and the zero element constitute a linear space, and then a new boundary functional is proved in the linear space, of which the energy is preserved for each dynamic energetic boundary function. The linear systems and iterative algorithms used to recover unknown wave speed and wave source functions with the dynamic energetic boundary functions as bases are developed, which converge fast at each time step. The input data are parsimonious, merely the measured boundary strains and the boundary values and slopes of unknown functions to be recovered. The accuracy and robustness of present methods are confirmed by comparing exact solutions with estimated results under large noises up to 20%.

A Simple Approach to Compute Interatomic Force Constant for Mono and Diatomic Semiconductors

In this paper, a mathematical relation was found between interatomic Hooke’s force constant and both the bulk modulus and interatomic distance in solid crystals, considering that the forces which have effect on an atom are only those resulted from the neighboring atoms, and the forces are subject to Hooke’s law as the deflections of atoms from their equilibrium positions are very small. This work has been applied on some solid semiconducting crystals of diatomic primitive cell, including crystals of mono-atomic primitive cell automatically, by using linear statistical fitting with computer programming and, then, using mathematical analysis, proceeding from the vibrational dispersion relation of solid linear lattice, these two methods have been used in the process in order to support each other and for the result to be satisfying and reasonable. This is a contribution to the process of using computer programming in physics to facilitate mathematical analyses and obtain the required relations and functions by designing and developing appropriate computer programs in line with the macro and micro natures of materials. The importance of this is in enhancing our understanding of the interatomic actions in cells and of the crystal structure of materials in general and semiconductors in particular, as it is a step of the initial steps to facilitate the process of calculating energies and extracting mathematical relations between correlation energy and temperature as well as between sub-fusion and fusion energies with temperature.

On Propagation of Rayleigh Type Surface Wave in a Micropolar Piezoelectric Medium

In the present paper, the governing equations of a linear transversely isotropic micropolar piezoelectric medium are specialized for x-z plane after using symmetry relations in constitutive coefficients. These equations are solved for the general surface wave solutions in the medium. Following radiation conditions in the half-space, the particular solutions are obtained, which satisfy the appropriate boundary conditions at the stress-free surface of the half-space. A secular equation for Rayleigh type surface wave is obtained. An iteration method is applied to compute the non-dimensional wave speed of the Rayleigh surface wave for specific material parameters. The effects of piezoelectricity, non-dimensional frequency and non-dimensional material constant, charge free surface and electrically shorted surface are shown graphically on the wave speed of Rayleigh wave.

Speed selection of traveling waves to an epidemic model

This paper is devoted to investigating the selection mechanism of the minimal wave speed for traveling waves to an epidemic model.The determinacy of linear and nonlinear selections is further discussed by the upper-lower solutions and comparison principle.A threshold is defined by the eigenvalue problem of the linearized system.We show that the nonlinear determinacy is obtained as long as there exists a lower solution with a faster decay and a speed parameter that is larger than the threshold.When the speed parameter equals to the threshold,if there exists an upper solution satisfying proper limit behavior,then the linear selection is realized.For a special function of infection rate,we obtain a threshold parameter that determines the linear and nonlinear selections.

The dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria

In this paper,we mainly investigate the dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria.We first establish the existence of spreading speed,and show that the spreading speed coincides with the minimal wave speed of traveling wavefronts.Moreover,a lower bound estimate of the spreading speed is given.Then,we prove that the traveling wavefronts with large speeds are globally exponentially stable,when the initial perturbation around the traveling wavefronts decays exponentially asχ→-∞,but the initial perturbation can be arbitrarily large in other locations.The adopted methods are the weighted energy and the squeezing technique.

Asymptotic Speed of Wave Propagation for A Discrete Reaction-Diffusion Equation

We deal with asymptotic speed of wave propagation for a discrete reactlon-diffusion equation. We find the minimal wave speed c★ from the characteristic equation and show that c★ is just the asymptotic speed of wave propagation. The isotropic property and the existence of solution of the initial value problem for the given equation are also discussed.

ON THE MINIMAL WAVE SPEED OF WAVE FRONTS FOR REACTION-DIFFUSION EQUATIONS

In this paper, a variational description of the minimal wave speed c(m, f) of wave fronts forthe reaction diffusion equations u_t=u_(xx)+u^mf(u) is given, where m>1 and f(u)～1-u.The continuity of c(m, f) in m and f is also proved. Especially, for f(u)=1-u, the estimateof the minimal wave speed c(m, f) is obtained.

ON BASIC EQUATIONS OF WATER HAMMER

Based on the derivation of the continuity equation of water hammer, the modification coefficient used in the wave speed formula is discussed thoroughly. Mistakes presented in current formulas are analyzed. Finally in this paper a summarizing comment is given on the problem that whether or not the slope term Vsina should be included in the characteristic equations.