This work extends the idea of the traditional complex-amplitude expanded phase field crystal (APFC) model using the Ginzburg-Landau approach. A fast structural APFC model is proposed as a quick and effective method for describing different crystal structures. Taking square and rectangular phases as examples, we systematically determine the structure-dependent parameters in the fast structure APFC model and validates its effectiveness through numerical simulations. In particular, when dealing with rectangular phases, it is found that this method not only solves the stability problem of the rectangular phase but also describes the structural phase transition between rectangular and orthorhombic layered phases, demonstrating the capability of the model in describing multiple structural phase transitions. Finally, through simulating the classic rotation-shrinking of a circular grain, we confirm the ability of the model for correctly predicting physical laws and reveal the roles of different crystal symmetries on the rotation-shrinking behavior of the grain. The proposed method in this paper can effectively promote the application of APFC models in the simulation research of more and larger material systems.

Taking the advantages of tracking discontinuous material surfaces explicitly within the continuous mechanics framework, the phase field method has been successfully applied to study crack propagation and damage in brittle materials. Considering that the complex micro-structural inclusion-matrix interaction dominates the damage nucleation for heterogeneous PBX, we develop a phase field inclusion model based on the Eshelby's inclusion theory, and carry out the numerical simulation study of damage initiation and evolution. The phase field energy consists of the elastic energy and the inclusion-matrix interaction energy. Combining with the Mori-Tanaka method, the effective elastic moduli of heterogeneous PBXs with different volume fractions are derived. For the proposed phase field inclusion model, the nonlinear debonding effects and damage distribution can be characterized by the phase field order parameter directly. It owns explicity in physical mechanism, and completeness in mathematical theory. We apply this model to compute the high volume fraction heterogeneous PBXs with typical circular and polygonal inclusions, and investigate the influences of loading, inclusion shape, volume fraction and computational parameters on the debonding mechanism. Numerical results indicate that the inclusion-matrix micro-structural evolution promotes interface debonding and the formation of macroscopic material failure, which coincides with experimental observations.

This paper studies numerical scheme and suppression method of wall heating error for elastic-plastic flow with cell-centered Lagrange Godunov method. Provide the viscosity correction equation of Godunov scheme, describe the procedure of a viscous shock formation and propagation with a jump type initial data, and analyze the relationship between the viscosity behavior of the correction equation and wall heating error. On this basis, a new HLLC-type approximate Riemann solver is proposed. In this solver, an adaptive heat conduction viscosity is introduced to suppress wall heating error of internal energy and density at the interface; What's more, an additional contact velocity is proposed to suppress the over-heating phenomenon of deviatoric stress.

The aim of the paper is to analyse the physical properties of liquid heavy metal fast reactor fuel rods and control rods from a neutronics point of view to support their structural design and material selection.In this paper, the liquid-uranium ratio selection, radial power distribution, cladding material selection, reflective layer material selection for fuel rods, radial structural design of control rods, absorber material selection, and moderated structural design are computationally analysed using the fast neutron reactor analysis program SARAX. Calculation results show that: the K_eff of the fuel rod grid element is linearly related to the liquid-uranium ratio, and the selection of the liquid-uranium ratio needs to consider the heat-carrying factor more. The fuel rod cladding is preferred to be made of ferritic/martensitic steel materials. The materials for the reflective layer at the axial ends of the fuel may be chosen to be made of steel materials.Based on the results of the analysis of the Pu migration phenomenon, none of the current physical calculation procedures are coupled with the Pu migration phenomenon, and the power distribution obtained from the calculation is relatively homogeneous, which leads to a bias of unconservative results in the calculation of the fuel centre temperature.The use of thin rod design for control rods can effectively reduce the self-screening effect, but the use of thin rod structure will lead to lower space utilisation. B₄C is commonly used as the absorber material in fast reactors.The wrapping of the control rod absorber with a moderator softens the neutron energy spectrum and increases the B-10 neutron absorption cross section significantly, increasing the value of the control rod. At the same outer diameter, the rod value of a pure absorber core block is less than that of a core block wrapped with a moderator (ZrH₂).

For the finite-difference time-domain (FDTD) solution of the half-space problem, the conventional total-field/scattered-field (TF/SF) technique cannot be directly applied to introduce excitation fields for electromagnetic scattering from the ground. In this paper, we extend the generalized total-field/scattered-field (G-TF/SF) method to accurately calculate the high altitude electromagnetic pulse (HEMP) environment in 3D ground scenarios and adopt the convolution perfectly matched layer (CPML) absorption boundary condition around it. The G-TF/SF method effectively eliminates edge effects in numerical calculations for finite ground, thereby improving accuracy in the calculation of the ground electromagnetic environment. Moreover, only the incident field needs to be introduced at the G-TF/SF boundary, avoiding the computation of reflected and transmitted fields.

The contact problem between the fuel core block and the cladding is a key point in the simulation of nuclear reactor fuel rods, and the inclusion of a contact model increases the difficulty of solving the set of algebraic equations. By analyzing the sparse structure of the Jacobi matrix before and after contact, a novel adaptive preprocessing method based on the contact pressure judgment criterion is constructed. The full Jacobi matrix is used as the preprocessing matrix for the Preconditioned Jacobian-free Newton-Krylov (PJFNK) method when the contact pressure is zero, and the block diagonal of the Jacobi matrix is used as the preprocessing matrix when the contact pressure is non-zero. Numerical experiments show that the adaptive preprocessing method in this paper can effectively improve the simulation efficiency, and the total solution time is reduced by 15.2%~33.1% compared with the existing methods in Multiphysics Object-Oriented Simulation Environment(MOOSE).

The MMALE (multi-material Arbitrary Lagrangian Eulerian method) is an effective method for the simulation of multi-material flow with large deformation. Traditional MMALE methods are mainly used in pure fluids and focus on two-dimensional problems. In this paper, we propose a three-dimensional MMALE algorithm for elastic-plastic fluids by developing three key technologies: a closure model for elastic-plastic flow, an interface reconstruction method adapted to three-dimensional grids with large deformation, and a physical property preserving remapping method for elastic-plastic quantities. Firstly, to solve the pressure imbalance problem caused by elastic-plastic fluids using traditional bulk modulus weighted closure models, a relaxation mechanism is introduced in our new closure model to achieve the balance of the pressure. At the same time, this model does not require iterations, avoiding the difficulties of non convergence that may be encountered during the iteration process; Secondly, in order to address the conservation issues caused by distorted three-dimensional polyhedral grids, a step-by-step surface triangulation algorithm is introduced to preserve the conservation during the interface reconstruction process. Thirdly, in the aspect of the remapping of elastic-plastic quantities, aiming at the problem that the tensor property is destroyed and the strain energy is not conserved after the deviator stress is remapped component by component, the remapping of invariants of the stress tensor is introduced to preserve the tensor property and maintain the conservation of the strain energy. Finally, the MMALE method is used to simulate several typical examples, and its correctness and robustness are verified.

This paper focuses on some efficient deflated preconditioners for static elastic crack problems modelled by the geometrical extended finite element method. We not only construct the deflation subspace matrix which is suitable for linear elastic crack problems, but also give the principle for selecting the deflated mesh nodes. To further accelerate the convergence, we combine the deflation technique with the "crack tip" domain decomposition preconditioners through multiplicative way, and propose efficient adapted deflated preconditioned conjugate gradient solvers which can eliminate the high-frequency and low-frequency errors simultaneously in the iterations. Numerical experiments demonstrate the effectiveness of our algorithm.

The fracture morphology of hydraulic fracturing is a key parameter for evaluating the fracturing effect and predicting the yield. At present, the fracture information of fractured cracks is mainly extracted by microseismic monitoring at home and abroad, and it is difficult to obtain the fracture morphology through the planar identification algorithm by utilizing the microseismic data due to the existence of complex noise. For this reason, this paper proposes a robust planar identification algorithm for hydraulic fracturing cracks, the sampling projection algorithm (RANSAC-MP), which weakens the outlier noise caused by irrelevant rupture events through random sampling, and proposes a maximal projection planar fitting algorithm to minimize the influence of environmental noise, and at the same time, combines the noise resistance of the RANSAC algorithm and the advantages of the projection method with the noise resistance of the RANSAC algorithm. noise immunity and the dimension reduction effect of the projection method. The results show that the RANSAC-MP algorithm shows stronger robustness and higher computational accuracy under the influence of multiple noises, and the algorithm can directly process the original data when only a single fracture is formed by fracturing.

In response to the complex coupling calculation of LBM (lattice Boltzmann method) local mesh refinement, a method of inverting macroscopic physical quantities to obtain particle distribution functions is proposed to avoid conversion of distribution functions. By rewriting the Boltzmann equation, the relationship (depends on Knudsen number) inside the distribution function is derived, and the inversion calculation equation of the distribution function is given. Based on this, a new multi-block mesh refinement algorithm is designed, and its performance is verified by applying the algorithm to an example. The results show that the algorithm can display the numerical characteristics of the flow field under different Reynolds numbers, and the streamline graph is continuous and complete. The position of the vortex center in the flow field obtained is consistent with literature data. This algorithm can be used for flow field simulations and provides guidance for the development of local mesh refinement.

Due to factors such as limited integral terms and approximations, solving integral equations using classical numerical methods is often more challenging than solving differential equations. This paper proposes a theory of solving linear integral equations through the transformation of primitive functions using deep learning. By transforming the integrand into a primitive function, the integral equation is converted into a purely differential equation. The paper also provides a method for determining the initial conditions of the primitive function and a technique for generating the neural network loss function. After approximating the primitive function using deep learning with neural networks, the derivative of the primitive function is calculated and transformed according to the form of the integral kernel, ultimately obtaining the numerical solution of the unknown function in the integral equation. Through numerical experiments on various typical examples, the paper demonstrates that the proposed theory and key techniques exhibit good accuracy and applicability, thereby opening up new technical approaches for the numerical solution of linear integral equations.

Based on NMQSD (non-Markovian quantum state diffusion) method, this paper studies containing dynamical evolution of geometric quantum discord in a system with X direction Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interaction in a hybrid non-Markovian/Markovian environment and a single non-Markovian/Markovian environment. The results show that the geometric quantum discord in the hybrid non-Markovian environment is higher than that in the single non-Markovian environment. When interaction with X direction KSEA in the same initial state and different directions of intensity, the geometric quantum discord of the system achieves better recovery in a hybrid non-Markov environment. And we find that the single bath in the Markovian environment is better than the hybrid bath.

The Luo Rudy phase I heart model is used in this paper to study the propagation of waves generated by point wave sources in one- and two-dimensional weakly coupled myocardial tissues. It is observed that the weak coupling can lead to the reduction of the wave propagation speed. When there is a large coupling intensity gradient in the myocardial tissue, weak coupling can lead to the frustration of wave propagation and early afterdepolarization showed by cardiomyocytes. When the coupling intensity between cardiomyocytes is low enough, circular motion of wave and complex wave propagation can be observed in myocardial tissues. In addition, we also study the propagation of planar wave in two-dimensional weakly coupled myocardial tissues by constructing two different two-dimensional myocardial tissues with different coupling structures. We find that spiral waves can be spontaneously generated when plane wave propagates in the two myocardial tissues. Increasing the coupling intensity between cells can effectively prevent the circus movement of wave and the spontaneous generation of spiral wave. The physical mechanism of the above phenomenon is analyzed in this paper.

In order to explore how to avoid Braess paradox when adding transmission lines in interconnected power grid, this study uses the second order Kuramoto-like model to model the dynamics of the power grid, and connects the subnets through the largest nodes to construct interconnected power grid. When there is power transmission between the two subnets, consider adding transmission lines inside and between subnets to explore the probability of Braess paradox in interconnected power grid and analyze its reasons. The results show that the probability of Braess paradox is related to the transmission power between the subnets. When the power between subnets reaches a critical value, adding transmission lines in the power receiving subnet or between two subnets, the probability of Braess paradox in interconnected power grid will be reduced to nearly zero. Therefore, the Braess paradox phenomenon should be avoided. The reasons for this phenomenon are analyzed in this paper.