Dislocation theory of the fracture criterion for anisotropic solids

A dislocation theory of fracture criterion for the mixed dislocation emission and cleavage process in an anisotropic solid is developed in this paper. The complicated cases involving mixed-mode loading are considered here. The explicit formula for dislocations interaction with a semi-infinite crack is obtained. The governing equation for the critical condition of crack cleavage in an anisotropic solid after a number dislocation emissions is established. The effects of elastic anisotropy, crack geometry and load phase angle on the critical energy release rate and the total number of the emitted dislocations at the onset of cleavage are analysed in detail. The analyses revealed that the critical energy release rates can increase to one or two magnitudes larger than the surface energy because of the dislocation emission. It is also found elastic anisotropy and crystal orientation have significant effects on the critical energy release rates. The anisotropic values can be several times the isotropic value in one crack orientation. The values may be as much as 40% less than the isotropic value in another crack orientation and another anisotropy parameter. Then the theory is applied to a fee single crystal. An edge dislocation can emit from the crack tip along the most highly shear stressed slip plane. Crack cleavage can occur along the most highly stressed slip plane after a number of dislocation emissions. Calculation is carried out step by step. Each step we should judge by which slip system is the most highly shear stressed slip system and which slip system has the largest energy release rate. The calculation clearly shows that the crack orientation and the load phase angle have significant effects on the crystal brittle-ductile behaviours.

Variational approach to the closure problem of turbulence theory

A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin-Fokker-Planck (LFP) model. The dynamic damping coefficient eta of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for eta to replace the divergent response equation of Kraichnan's direct-interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko = 1.2, which is compatible with the experimental data given by Gibson and Schwartz, (1963).

Correcting the systematic error of the density functional theory calculation: the alternate combination approach of genetic algorithm and neural network

The alternate combinational approach of genetic algorithm and neural network (AGANN) has been presented to correct the systematic error of the density functional theory (DFT) calculation. It treats the DFT as a black box and models the error through external statistical information. As a demonstration, the AGANN method has been applied in the correction of the lattice energies from the DFT calculation for 72 metal halides and hydrides. Through the AGANN correction, the mean absolute value of the relative errors of the calculated lattice energies to the experimental values decreases from 4.93% to 1.20% in the testing set. For comparison, the neural network approach reduces the mean value to 2.56%. And for the common combinational approach of genetic algorithm and neural network, the value drops to 2.15%. The multiple linear regression method almost has no correction effect here.

Mandarin speech emotion recognition based on high dimensional geometry theory

In this paper, a novel approach for mandarin speech emotion recognition, that is mandarin speech emotion recognition based on high dimensional geometry theory, is proposed. The human emotions are classified into 6 archetypal classes: fear, anger, happiness, sadness, surprise and disgust. According to the characteristics of these emotional speech signals, the amplitude, pitch frequency and formant are used as the feature parameters for speech emotion recognition. The new method called high dimensional geometry theory is applied for recognition. Compared with traditional GSVM model, the new method has some advantages. It is noted that this method has significant values for researches and applications henceforth.

Applicability of the reaction window theory

Based on the molecular Coulombic over barrier model for description of slow ion-atom collisions, the reaction window theory related to projectile velocity is presented briefly. According to the theory, the state-selective differential cross sections of single electron capture in O8+ -H, A(8+) -H, Ar8+-He, Ne10+-He and Ar18+-He collisions at different collision velocities are calculated and compared with experimental results. Calculations are also done for single, double, and triple electron capture in N-15(7+)-Ne collisions at fixed velocity of 0.53 a.u., and are compared with experimental data. It is found that the predictions of the final electronic state distribution of captured electron(s) are in agreement with experimental data, and both theory and experiments show that the widths of the reaction window increase with the projectile velocity. The differential cross sections predicted by the theory are larger for smaller Q-values, vice versa, when compared with experimental data.

Calculations of cross sections of resonant two-photon transitions to the second excited 4f5d state in Pr3+: Y3Al5O12 using density matrix theory

The density matrix resonant two-photon absorption (TPA) theory applicable to laser crystals doped with rare earth ions is described. Using this theory, resonant TPA cross sections for transitions from the ground state to the second excited state of the 4f5d configuration in cm(4)s Pr3+:Y3Al5O12 are calculated. The peak value of TPA cross section calculated is 2.75 x 10(-50) cm(4)s which is very close to the previous experimental value 4 x 10(-50) cm(4) s. The good agreement of calculated data with measured values demonstrates that the density matrix resonant TPA theory can predict resonant TPA intensity much better than the standard second-order perturbation TPA theory.

Phase-separation behavior of the system PES/phenoxy: An application of the Sanchez-Lacombe lattice fluid theory

Cloud-point curves reported for the system polyethersulfone (PES)/phenoxy were calculated by means of the Sanchez-Lacombe (SL) lattice fluid theory. The one adjustable parameter epsilon(12)*/k (quantifying the interaction energy between mers of the different components) can be evaluated by comparison of the theoretical and experimental phase diagrams. The Flory-Huggins (FH) interaction parameters are computed based on the evaluated epsilon(12)*/k and are approximately a linear function of volume fraction and of inverse temperature. The calculated enthalpies of mixing of PES/phenoxy blends for different compositions are consistent with the experimental values obtained previously by Singh and Walsh [1].

Thermodynamics of blends of poly(ethylene oxide) with poly(methyl methacrylate) and poly(vinyl acetate): prediction of miscibility based on Flory solution theory modified by Hamada

Flory solution theory modified by Hamada et al. (Macromolecules, 1980, 13, 729) was used to predict the miscibility of blends of poly(ethylene oxide) with poly(methyl methacrylate) (PEO-aPMMA) and with poly(vinyl acetate) (PEO-PVAc). Interaction parameters of a PEO-aPMMA blend with the weight ratio of PEO/aPMMA = 50/50 at the temperature range of 393-433 K and PEO-PVAc blends with different compositions and temperatures were calculated from the determined equation-of-state parameters based on Flory solution theory modified by Hamada ed al. Results show that interaction parameters of the PEO-aPMMA blend are negative and can be comparable with values obtained from neutron-scattering measurements by Ito et al. (Macromolecules, 1987, 20, 2213). Also, interaction parameters and excess volumes of PEO-PVAc blends are negative and increase with enhancing the content of PEO and the temperature. (C) 1998 Elsevier Science Ltd. All rights reserved.

The application of the MPB4 theory to the interface between between two immiscible electrolyte solutions .4. The differential capacitance of the water/nitrobenzene interface in the presence of 2:2 electrolyte

We have developed a new theoretical model based on the MPB4 theory to calculate the differential capacitance of the interface of 0.05mol/L MgSO4 in water and 0.1mol/L TBATPB in nitrobenzene. Our results coincide with the experimental values very well. It indicates that our model may describe well the structure of ITIES not only in the presence of 1:1 electrolyte but also in the presence of 2:2 electrolyte.