This paper mainly discusses some effective domain decomposition preconditioners for static elastic crack problems modeled by geometrical extended finite element method. To construct the Schwarz type preconditioners, we adopt a special crack-tip domain decomposition strategy. The finite element mesh is decomposed into "crack tip" subdomains, which contain all the degrees of freedom (DOFs) of the branch enrichment functions, and "regular" subdomains, which contain the standard DOFs and the DOFs of the Heaviside enrichment functions. Based on the crack-tip domain decomposition strategy, an effective class of multiplicative and restrict multiplicative Schwarz preconditioners are derived. In the preconditioners, the crack tip subproblems are solved exactly and the regular subproblems are solved by some inexact solvers. Numerical experiments demonstrate the effectiveness of the preconditioners.

Smoothed particle hydrodynamics (SPH) simulation of non-isothermal viscoelastic poiseuille flow is carried out, in which the viscoelastic properties of the fluid are modeled and calculated according to the eXtended Pom-Pom (XPP) constitutive model. The SPH discrete format of the temperature equation is derived, and the temperature dependence of viscoelastic properties of fluid is considered based on the principle of time temperature equivalence. The accuracy and effectiveness of the SPH method for simulating non-isothermal XPP poiseuille flow are verified by comparing the SPH results with those obtained by the finite volume method. The numerical convergence of the SPH method is discussed by performing simulations with four different initial particle spacings. The influence of the introduction of the temperature equation on poiseuille flow is studied. The influence of different physical parameters on the flow process is deeply analyzed.

The three-dimensional multi-relaxation (MRT) Shan-Chen Lattice Boltzmann method (LBM) is used to simulate the dynamic process of a droplet impacting small solid spheres with different wettability (The ratio of droplet diameter to small sphere diameter is greater than 1.) On the basis of verifying the accuracy of the calculation model by various methods, the influence of the Weber number of the droplet and the surface wettability of the small sphere on the dynamic process and the relationship of the geometry of the lamella formed with wettability are explored. The results show that the lamella formed after impacting the hydrophilic sphere is bell-shaped, When the surface wetting degree is constant, the maximum bottom diameter of the lamella increases with the increase of Weber number. When impacting the hydrophilic small sphere, the lamella completely closes after the formation of the lamella; the larger the Weber number, the earlier the lamella is completely closed, and the lamella is prone to break during the closing process. When impacting the hydrophobic small sphere, a larger Weber number leads to an earlier breakage of the lamella, and the broken lamellas fall down in a ring strip during the opening of the lamella. The geometric characteristics of the lamella are affected by the Weber number and wettability of the small sphere.

Based on the important effect of carrier recombination on the photovoltaic efficiency of organic solar cells, the intermolecular carrier recombination dynamics in organic solar cells is studied theoretically by using an extended Su-Schrieffer-Heeger tight binding model combined with the non-adiabatic quantum dynamical method in this article. Firstly, intermolecular charge recombination dynamics of the positive and negative carriers at the donor/acceptor interface is simulated and revealed, and it is found that the intermolecular carrier recombination exhibits fractional charge recombination along with energy loss. Subsequently, influence of the system energy offset Δ, electric field, thermal effect and aggregation of acceptor molecules on intermolecular carrier recombination dynamics is studied. The results show that the system energy offset Δ exhibits the carrier recombination barrier, and the larger the energy offset Δ, the more favorable it is to suppress the recombination of carriers. The electric field can inhibit the recombination of carriers by inducing spatial delocalization of positive and negative charges. Especially, as the electric field is strong enough, it can dissociate the recombined charge transfer state into free carriers. Thermal effects can cause random fluctuations of the potential energy of the donor/acceptor material, which can reduce the recombination barrier of carriers, and further to aggravate the carrier recombination. The aggregation of acceptor molecules will induce the expansion of electrons between acceptor molecules, increasing the distance between positive and negative charge centers at the interface, thereby inhibiting the recombination of carriers.

A coarse-grained molecular dynamics method coupled with umbrella sampling is developed to study the desorption process of SDS and CTAC surfactants from spherical micelles. The influence mechanisms of aggregation number, salt species and concentrations on the desorption process of surfactant from spherical micelles are revealed. We find that the radius and eccentricity of spherical micelles both increase with aggregation number rising, and the effects of salt concentration depend on the ionic radius and adsorption characteristics of the counterions. Larger salicylate ions with stronger adsorption ability have more significant effect on the micellar structures. Based on umbrella sampling method, we obtain the desorption free energy and time of surfactants from micelles. we find that the desorption free energy and desorption time of surfactant both show a non-monotonic variation with the increase of aggregation number and salt concentration, whose mechanisms are attributed to the electrostatic shielding induced by ion adsorption on micelle surface. Moreover, we reveal that the free energy plays a leading role in surfactant desorption process. Combing the theory of micelle thermodynamics, we further develop the critical micelle concentration prediction method, and obtain the distribution range of micelle size under the critical micelle concentration of surfactants.

In this work, water adsorbed in single-walled carbon nanotube (SWCNT) is simulated by the Grand Canonical Monte Carlo (GCMC) method. The effects of pore length, pore size and surface strength on water adsorption behaviors at 298 K are systematically studied, via the characterization of isotherms, local density distribution and isosteric heat. There are hysteresis loops observed for water adsorbed and desorbed in SWCNTs with relatively large pore radii (PR=0.8, 1.0 nm), and the hysteresis loop disappears as the pore radius decreases to 0.55 nm. In addition, the water molecule packing manners are in the arrangement form of single chain, double helix chain and water clusters due to the pore size effects. When the pore length is in the range of 4~8 nm, the initial adsorption pressure becomes smaller and smaller as the pore length increases, but this effect rule gradually disappears with increasing pore length to 10 nm. Finally, the initial pressure of water adsorption decreases with surface strength; and when surface strengths are 20, 28, 32 K, the capillary evaporation phase transitions completed instantaneously. While the surface strength increases to 40 K, the capillary evaporation phase transition is shown gradually desorbed steps. As surface strengths increased from 20 K to 40 K, the isosteric adsorption heat at the pressure points of capillary condensation phase transition is 127.47, 117.98, 84.04, 59.16 kJ·mol^-1, respectively.

In this study, threshold displacement energy of O and Ti in rutile TiO₂ along different directions is simulated by using the method of molecular dynamics. Simulation results show that threshold displacement energy of O atom in all directions is generally lower than that of Ti atom. The threshold displacement energy of O is basically between 27.50 and 77.50 eV, while that of Ti is between 90.00 and 120.00 eV. Meanwhile, this study also explores the cascade radiation damage caused by O PKA and Ti PKA with energy of 1.0, 5.0 and 10.0 keV. Cascade radiation damage results show that O PKA and Ti PKA with energy less than 10.0 keV mainly produced point defects. The number of point defects reached the peak within 0.10~0.20 ps. After several ps evolution, more than 90.0% of the defects are annealing, and only less than 10.0% defects remained. In other words, the defects in rutile TiO₂ have higher self-recovery ability at the initial stage of defect generation.

Using Gurtin-Murdoch theory and complex potential method, the problem of secondary multiple rips in one-dimensional hexagonal quasicrystals take nano n-edge polygon orifices is studied. The analytical solutions of phonon field, phasor field and electric field, as well as phonon field stress intensity factors and energy release rate are obtained. Some calculations are given to discuss the effects of secondary crack morphology of nano orifice on field intensity factor and energy release rate. The results indicate that when the defect size asymptotically the nanometer level, the surface effect produced by the coupling of phonon field, phase field and electric field, while the smaller the size of secondary crack at the orifice, the stronger surface effect. The more the number of cracks, the smaller the field intensity factor. With the amplify of defect size, the influence by surface influence will gradually weaken, and eventually tends to the existing outcome.

Based on the Monte Carlo (MC) method and the fast Fourier transform micromagnetism (FFTM) method, the magnetic dynamic properties of the stacked Co nanoring arrays with different thickness are simulated. It is found that the hysteresis loops of Co nanorings with different thickness have the bistable states, and the formation and stability of the "vortex state" are significantly related to the thickness. Further studies show that the thickness of the stacked Co nanoring arrays has a great influence on the external magnetic field required for the system to reach saturation. The step width of the hysteresis loop ΔH_fc is also related to the thickness. The simulation results are close to the experimental facts.

In order to improve the magnetic properties of permanent magnet films, based on the theory of micromagnetism, we have studied the magnetization properties of Ce_1.66Mg_1.34Co₃ and α″-Fe₁₆N₂ exchange coupled multilayer gradient films by using software OOMMF, and the influence of magnetic crystal anisotropy gradient on the properties of multilayer films systematically. We analyze the changes of remanence, coercivity, hysteresis loop and energy during magnetization reversal process. We find that the coercivity and residual magnetization of the films can be effectively increased by decreasing the anisotropic gradient of magnetic crystals or increasing the anisotropy difference at the interface, so as to improve the magnetic properties. A magnetic vortex state is found by calculating the magnetic moment distribution, and the generation of this magnetic vortex state is accompanied by the increase of system energy.

A random walk algorithm compulsive evolution with individual reconstruction strategy is proposed to solve the problem that the optimization of mass exchanger network is easily trapped in local extremum due to the weakening of the ability of structural variation and the loss of population diversity. In the process of receiving differential solutions, real-time monitoring is carried out on individuals, and different reconstruction methods are adopted to stimulate the network structure updating and variation of backward individuals, so as to improve the structural variation ability and population diversity of the algorithm. At the same time, according to the characteristics of the unstructured model with shunt nodes, a new individual network structure after cross reconstruction is repaired. Finally, the R2S2 and R4S2 examples are used to verify the effectiveness of the proposed strategy, and the optimization results are all lower than the results in the current literature, which proves that the proposed strategy can effectively enhance the structural variation ability and global optimization ability of the algorithm.

To help the network system restore with reasonable investment as soon as possible after cascading failure, using coupling map lattice as the basis of the restoration dynamics model, and the failure state and coupling coefficient under the cascade failure are taken as the input of the restoration dynamics. By further adding the external restoring force and the internal coupling to form the restoration dynamics method. The restoration effect is improved by 46.7%, 47.9% and 66.7% respectively compared with three groups of network restoration methods without considering continuity. In addition, the simulation results on six different networks show that this method can fit the real restoration scene, overcome the differences in network level, scale, network construction methods and so on. Specifically, in the three-layer transportation network, the marginal contribution rate of the initial restoration ratio to the restoration degree is 26.8%, and when the coupling coefficient of restoration is 0.5 and 10% of the nodes are restored for the first time, the restoration degree of the network is as high as 86.4%. The proposed restoration dynamics method can effectively describe the restoration process of various networks.

Memristor plays an important role in modeling nonlinear circuits and systems. Based on the proposed smooth quadratic generic memristor, this paper proposes a memristor-based Lorenz chaotic system. Different from the chaotic system on account of memristor feedback, this system takes a variable of the original Lorenz chaotic system as an inner state variable of memristor, so as to ensure that the system dimension does not increase. Stability analysis shows that the system has the same equilibrium point and stability as the original Lorenz system, namely, one unstable saddle point and two unstable saddle foci. By means of bifurcation diagram, Lyapunov exponent spectra, and phase plot, the dynamics of the proposed memristive system are revealed. The simulated results show that the memristive Lorenz chaotic system possesses coexisting bistable mode and self-similar bifurcation structures. What is more interesting is that the amplitude of the system can be regulated by changing the inner parameters of the generic memristor. Finally, the equivalent circuits of memristor and memristive system are designed and also synthesized by analog components. Simulation results confirm the correctness of the numerical simulations.