Solving the initial condition of the string relaxation equation of the string model for glass transition: part-I

The string model for the glass transition can quantitatively describe the universal α-relaxation in glassformers,including the average relaxation time,the distribution function of the relaxation time,and the relaxation strength as functions of temperature.The string relaxation equation(SRE) of the model,at high enough temperatures,simplifies to the well-known single particle mean-field Debye relaxation equation,and at low enough temperatures to the well-known Rouse-Zimm relaxation equation that describes the relaxation dynamics of linear macromolecules.However,its initial condition,necessary to the further model predictions of glassy dynamics,has not been solved.In this paper,the special initial condition(SIC) of the SRE,i.e.for straight strings and the dielectric spectrum technique that is one of the most common methods to measure the glassy dynamics,was solved exactly.It should be expected that the obtained SIC would benefit the solution of the general initial condition of the SRE of the string model,i.e.for stochastically spatially configurating strings,as will be described in separate publications.     

Phonon relaxation and heat conduction in one-dimensional Fermi-Pasta-Ulam β lattices by molecular dynamics simulations

The phonon relaxation and heat conduction in one-dimensional Fermi-Pasta-Ulam (FPU) β lattices are studied by using molecular dynamics simulations.The phonon relaxation rate,which dominates the length dependence of the FPU β lattice,is first calculated from the energy autocorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations.We find that the relaxation rate as a function of wave number k is proportional to k 1.688,which leads to a N 0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation.This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415.Our results confirm the N 2/5 divergence in one-dimensional FPU β lattices.The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices.We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions.It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.     

Analysis of characteristics of sound radiation from double cylindrical shell coated with viscoelastic layer

The characteristics of vibration and sound radiation from a double shell with the outer shell coated with viscoelastic layer are systematically studied. The shell‘s motion function is expressed by the classical Fliigge operator and the layer‘s motion function is described by three-dimensional Navier equations, whose displacement solutions are expressed by Taylor expansion along the layer thickness. The continuity conditions of displacement and stress between the shell and the layers are used in obtaining the vibration equations. The effects of layer thickness, modulus of elasticity, the loss factor, and the hydro-compressibility on the structural acoustic characteristic are discussed in detail. It showed that the higher the modulus of elasticity is, or the thinner the thickness of layer is, or the smaller the loss factor is, the higher the sound radiation power is.     

Temperature-frequency dependence and mechanism of dielectric properties for γ-Y2Si2O7

This paper reports that single-phase γ-Y2Si2O7 is prepared via a sufficient blending and cold-pressed sintering technique from Y2O3 powder and SiO2 nanopowder. It studies the dielectric properties of γ-Y2Si2O7 as a function of the temperature and frequency. The γ-Y2Si2O7 exhibits low dielectric loss and non-Debye relaxation behaviour from 25 to 1400℃ in the range of 7.3-18 GHz. The mechanism for polarization relaxation of the as-prepared γ-Y2Si2O7 differing from that of SiO 2 is explained. Such particular dielectric properties could potentially make specific attraction for extensive practical applications.     

Effects of cross-correlated noises on the relaxation time of the bistable system

The stationary correlation function and the associated relaxation time for a general system driven by cross-correlated white noises are derived, by virtue of a Stratonovich-like ansatz. The effects of correlated noises on the relaxation time of a bistable kinetic model coupled to an additive and a multiplicative white noises are studied. It is proved that for small fluctuations the relaxation time T_c as a function of λ (the correlated intensity between noises) exhibits very different behaviours for αD (α and D, respectively, stand for the ntensities of additive and multiplicative noises). When α>D, T_c increases with increasing λ. But when α相似文献   

Generalized thermoelsticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli

In this paper,we construct the equations of generalized thermoelasicity for a non-homogeneous isotropic hollow cylider with a variable modulus of elasticity and thermal conductivity based on the Lord and Shulman theory.The problem has been solved numerically using the finite element method.Numerical results for the displacement,the temperature,the radial stress,and the hoop stress distributions are illustrated graphically.Comparisons are made between the results predicted by the coupled theory and by the theory of generalized thermoelasticity with one relaxation time in the cases of temperature dependent and independent modulus of elasticity.     

Studies of diamond-like carbon （DLC） films deposited on stainless steel substrate with Si/SiC intermediate layers

In this work, diamond-like carbon （DLC） films were deposited on stainless steel substrates with Si/SiC intermediate layers by combining plasma enhanced sputtering physical vapour deposition （PEUMS-PVD） and microwave electron cyclotron resonance plasma enhanced chemical vapour deposition （MW-ECRPECVD） techniques. The influence of substrate negative self-bias voltage and Si target power on the structure and nano-mechanical behaviour of the DLC films were investigated by Raman spectroscopy, nano-indentation, and the film structural morphology by atomic force microscopy （AFM）. With the increase of deposition bias voltage, the G band shifted to higher wave-number and the integrated intensity ratio ID/IG increased. We considered these as evidences for the development of graphitization in the films. As the substrate negative self-bias voltage increased, particle bombardment function was enhanced and the sp^3-bond carbon density reducing, resulted in the peak values of hardness （H） and elastic modulus （E）. Silicon addition promoted the formation of sp^3 bonding and reduced the hardness. The incorporated Si atoms substituted sp^2- bond carbon atoms in ring structures, which promoted the formation of sp^3-bond. The structural transition from C-C to C-Si bonds resulted in relaxation of the residual stress which led to the decrease of internal stress and hardness. The results of AFM indicated that the films was dense and homogeneous, the roughness of the films was decreased due to the increase of substrate negative self-bias voltage and the Si target power.     

β-distribution for Reynolds stress and turbulent heat flux in relaxation turbulent boundary layer of compression ramp

A challenge in the study of turbulent boundary layers(TBLs) is to understand the non-equilibrium relaxation process after separation and reattachment due to shock-wave/boundary-layer interaction. The classical boundary layer theory cannot deal with the strong adverse pressure gradient, and hence, the computational modeling of this process remains inaccurate. Here, we report the direct numerical simulation results of the relaxation TBL behind a compression ramp, which reveal the presence of intense large-scale eddies, with significantly enhanced Reynolds stress and turbulent heat flux. A crucial finding is that the wall-normal profiles of the excess Reynolds stress and turbulent heat flux obey a β-distribution, which is a product of two power laws with respect to the wall-normal distances from the wall and from the boundary layer edge. In addition, the streamwise decays of the excess Reynolds stress and turbulent heat flux also exhibit power laws with respect to the streamwise distance from the corner of the compression ramp. These results suggest that the relaxation TBL obeys the dilation symmetry, which is a specific form of self-organization in this complex non-equilibrium flow. The β-distribution yields important hints for the development of a turbulence model.     

Mechanical properties of jammed packings of frictionless spheres under an applied shear stress

By minimizing a thermodynamic-like potential, we unbiasedly sample the potential energy landscape of soft and frictionless spheres under a constant shear stress. We obtain zero-temperature jammed states under desired shear stresses and investigate their mechanical properties as a function of the shear stress. As a comparison, we also obtain the jammed states from the quasistatic-shear sampling in which the shear stress is not well-controlled. Although the yield stresses determined by both samplings show the same power-law scaling with the compression from the jamming transition point J at zero temperature and shear stress, for finite size systems the quasistatic-shear sampling leads to a lower yield stress and a higher critical volume fraction at point J. The shear modulus of the jammed solids decreases with increasing shear stress. However, the shear modulus does not decay to zero at yielding. This discontinuous change of the shear modulus implies the discontinuous nature of the unjamming transition under nonzero shear stress, which is further verified by the observation of a discontinuous jump in the pressure from the jammed solids to the shear flows. The pressure jump decreases upon decompression and approaches zero at the critical-like point J, in analogy with the well-known phase transitions under an external field. The analysis of the force networks in the jammed solids reveals that the force distribution is more sensitive to the increase of the shear stress near point J. The force network anisotropy increases with increasing shear stress. The weak particle contacts near the average force and under large shear stresses it exhibit an asymmetric angle distribution.     

Final Governing Equation of Plane Elasticity of Icosahedral Quasicrystals and General Solution Based on Stress Potential Function

The stress potential function theory for plane elasticity of icosahedral quasicrystals is developed. By introducing stress functions, huge numbers of basic equations involving elasticity of icosahedral quasicrystals are reduced to a single partial differential equation of the 12th order. The general solution of the equation is expressed by 6 analytic functions of complex variable z = x ＋ iy.