We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separat...We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x=x(t).We prove that this problem admits global Radon measure solutions for all kinds of initial data.The over-compressing condition on the discontinuity x=x(t)is not enough to ensure the uniqueness of the solution.However,there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve x=x(t)+0,in addition to the full adhesion condition on its left-side.As an application,we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas.In particular,we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas.This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field.展开更多
Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough ...Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.展开更多
Due to the limited uplink capability in heterogeneousnetworks (HetNets), the decoupled uplinkand downlink access (DUDA) mode has recently beenproposed to improve the uplink performance. In thispaper, the random discon...Due to the limited uplink capability in heterogeneousnetworks (HetNets), the decoupled uplinkand downlink access (DUDA) mode has recently beenproposed to improve the uplink performance. In thispaper, the random discontinuous transmission (DTX)at user equipment (UE) is adopted to reduce the interferencecorrelation across different time slots. By utilizingstochastic geometry, we analytically derive themean local delay and energy efficiency (EE) of an uplinkHetNet with UE random DTX scheme under theDUDA mode. These expressions are further approximatedas closed forms under reasonable assumptions.Our results reveal that under the DUDA mode, there isan optimal EE with respect to mute probability underthe finite local delay constraint. In addition, with thesame finite mean local delay as under the coupled uplinkand downlink access (CUDA) mode, the HetNetsunder the DUDA mode can achieve a higher EE witha lower mute probability.展开更多
Since its introduction,discontinuous deformation analysis(DDA)has been widely used in different areas of rock mechanics.By dividing large blocks into subblocks and introducing artificial joints,DDA can be applied to r...Since its introduction,discontinuous deformation analysis(DDA)has been widely used in different areas of rock mechanics.By dividing large blocks into subblocks and introducing artificial joints,DDA can be applied to rock fracture simulation.However,parameter calibration,a fundamental issue in discontinuum methods,has not received enough attention in DDA.In this study,the parameter calibration of DDA for intact rock is carefully studied.To this end,a subblock DDA with Voronoi tessellation is presented first.Then,a modified contact constitutive law is introduced,in which the tensile and shear meso-strengths are modified to be independent of the bond lengths.This improvement can prevent the unjustified preferential failure of short edges.A method for imposing confining pressure is also introduced.Thereafter,sensitivity analysis is performed to investigate the influence of the calculated parameters and meso-parameters on the mechanical properties of modeled rock.Based on the sensitivity analysis,a unified calibration procedure is suggested for both cases with and without confining pressure.Finally,the calibration procedure is applied to two examples,including a biaxial compression test.The results show that the proposed Voronoi-based DDA can simulate rock fracture with and without confining pressure very well after careful parameter calibration.展开更多
Accurate wave propagation simulation in anisotropic media is important for forward modeling, migration and inversion. In this study, the weighted Runge-Kutta discontinuous Galerkin (RKDG) method is extended to solve t...Accurate wave propagation simulation in anisotropic media is important for forward modeling, migration and inversion. In this study, the weighted Runge-Kutta discontinuous Galerkin (RKDG) method is extended to solve the elastic wave equations in 2D transversely isotropic media. The spatial discretization is based on the numerical flux discontinuous Galerkin scheme. An explicit weighted two-step iterative Runge-Kutta method is used as time-stepping algorithm. The weighted RKDG method has good flexibility and applicability of dealing with undulating geometries and boundary conditions. To verify the correctness and effectiveness of this method, several numerical examples are presented for elastic wave propagations in vertical transversely isotropic and tilted transversely isotropic media. The results show that the weighted RKDG method is promising for solving wave propagation problems in complex anisotropic medium.展开更多
The effect of the inlet gas pressure,supplementary gas pressure and nozzle channel dispersion angle on the pre-breakup behavior of Ti-6Al-4V(TC4)discontinuous droplets during EIGA was investigated by combining numeric...The effect of the inlet gas pressure,supplementary gas pressure and nozzle channel dispersion angle on the pre-breakup behavior of Ti-6Al-4V(TC4)discontinuous droplets during EIGA was investigated by combining numerical simulation with experiments.The results show that the axial velocity at the recirculation zone before the stagnation location was first increased and decreased then increased significantly after the peak value,while the pressure of the recirculation zone increased with the increase in inlet pressure.With the supplementary pressure increasing,the velocity magnitude and range of the recirculation zone gradually decreased.As the dispersion angle of the nozzle channel increased,the pre-breakup efficiency of droplets gradually decreased,but the adhesion phenomenon of droplets on the inner wall surface of the nozzle channel(IWSNC)gradually weakened.Under the inlet pressure of 4 MPa,a supplementary pressure of 0.05 MPa,and the dispersion angle of 15°,the uniform and spherical TC4 powders with diameter of 70μm were prepared,which was consistent with the simulation results.The optimized process parameters is a balance between the size of the pre-atomized particles and the back-spraying and bonding phenomenons of droplets.展开更多
Magnesium alloys are lightweight materials with great potential,and plasma electrolytic oxidation(PEO)is effective surface treatment for necessary improvement of corrosion resistance of magnesium alloys.However,the∼1...Magnesium alloys are lightweight materials with great potential,and plasma electrolytic oxidation(PEO)is effective surface treatment for necessary improvement of corrosion resistance of magnesium alloys.However,the∼14µm thick and rough PEO protection layer has inferior wear resistance,which limits magnesium alloys as sliding or reciprocating parts,where magnesium alloys have special advantages by their inherent damping and denoising properties and attractive light-weighting.Here a novel super wear-resistant coating for magnesium alloys was achieved,via the discontinuous sealing(DCS)of a 1.3µm thick polytetrafluoroethylene(PTFE)polymer layer with an initial area fraction(A_(f))of 70%on the necessary PEO protection layer by selective spraying,and the wear resistance was exceptionally enhanced by∼5500 times in comparison with the base PEO coating.The initial surface roughness(Sa)under PEO+DCS(1.54µm)was imperfectly 59%higher than that under PEO and conventional continuous sealing(CS).Interestingly,DCS was surprisingly 20 times superior for enhancing wear resistance in contrast to CS.DCS induced nano-cracks that splitted DCS layer into multilayer nano-blocks,and DCS also provided extra space for the movement of nano-blocks,which resulted in rolling friction and nano lubrication.Further,DCS promoted mixed wear of the PTFE polymer layer and the PEO coating,and the PTFE layer(HV:6 Kg·mm^(−2),A_(f):92.2%)and the PEO coating(HV:310 Kg·mm^(−2),A_(f):7.8%)served as the soft matrix and the hard point,respectively.Moreover,the dynamic decrease of Sa by 29%during wear also contributed to the super wear resistance.The strategy of depositing a low-frictional discontinuous layer on a rough and hard layer or matrix also opens a window for achieving super wear-resistant coatings in other materials.展开更多
The fixed-time synchronization and preassigned-time synchronization are investigated for a class of quaternion-valued neural networks with time-varying delays and discontinuous activation functions. Unlike previous ef...The fixed-time synchronization and preassigned-time synchronization are investigated for a class of quaternion-valued neural networks with time-varying delays and discontinuous activation functions. Unlike previous efforts that employed separation analysis and the real-valued control design, based on the quaternion-valued signum function and several related properties, a direct analytical method is proposed here and the quaternion-valued controllers are designed in order to discuss the fixed-time synchronization for the relevant quaternion-valued neural networks. In addition, the preassigned-time synchronization is investigated based on a quaternion-valued control design, where the synchronization time is preassigned and the control gains are finite. Compared with existing results, the direct method without separation developed in this article is beneficial in terms of simplifying theoretical analysis, and the proposed quaternion-valued control schemes are simpler and more effective than the traditional design, which adds four real-valued controllers. Finally, two numerical examples are given in order to support the theoretical results.展开更多
In automotive industries,panel acoustic contribution analysis(PACA)is used to investigate the contributions of the body panels to the acoustic pressure at a certain point of interest.Currently,PACA is implementedmostl...In automotive industries,panel acoustic contribution analysis(PACA)is used to investigate the contributions of the body panels to the acoustic pressure at a certain point of interest.Currently,PACA is implementedmostly by either experiment-based methods or traditional numerical methods.However,these schemes are effort-consuming and inefficient in solving engineering problems,thereby restraining the further development of PACA in automotive acoustics.In this work,we propose a PACA scheme using discontinuous isogeometric boundary element method(IGABEM)to build an easily implementable and efficient method to identify the relative acoustic contributions of each automotive body panel.Discontinuous IGABEMis more accurate and converges faster than continuous BEM and IGABEM in the interior sound pressure evaluation of automotive compartments.In this work,a contribution ratio is defined to estimate the relative acoustic contribution of the structure panels;it can be calculated by reusing the coefficient matrix that has already been generated in the sound pressure evaluation process.The utilization of the parallel technique enables the proposed method to be more efficient than conventional methods;it is validated in two numerical examples,including a car passenger compartment subjected to realistic boundary conditions.A sound pressure response experiment based on a steel box is conducted to verify the accuracy of the interior sound pressure calculation using discontinuous IGABEM.This work is expected to promote the practical process of IGABEM for application in automotive acoustic problems.展开更多
Fixed-time synchronization(FTS)of delayed memristor-based neural networks(MNNs)with discontinuous activations is studied in this paper.Both continuous and discontinuous activations are considered forMNNs.And the mixed...Fixed-time synchronization(FTS)of delayed memristor-based neural networks(MNNs)with discontinuous activations is studied in this paper.Both continuous and discontinuous activations are considered forMNNs.And the mixed delays which are closer to reality are taken into the system.Besides,two kinds of control schemes are proposed,including feedback and adaptive control strategies.Based on some lemmas,mathematical inequalities and the designed controllers,a few synchronization criteria are acquired.Moreover,the upper bound of settling time(ST)which is independent of the initial values is given.Finally,the feasibility of our theory is attested by simulation examples.展开更多
In this paper,a local discontinuous Galerkin(LDG)scheme for the time-fractional diffusion equation is proposed and analyzed.The Caputo time-fractional derivative(of orderα,with 0<α<1)is approximated by a finit...In this paper,a local discontinuous Galerkin(LDG)scheme for the time-fractional diffusion equation is proposed and analyzed.The Caputo time-fractional derivative(of orderα,with 0<α<1)is approximated by a finite difference method with an accuracy of order3-α,and the space discretization is based on the LDG method.For the finite difference method,we summarize and supplement some previous work by others,and apply it to the analysis of the convergence and stability of the proposed scheme.The optimal error estimate is obtained in the L2norm,indicating that the scheme has temporal(3-α)th-order accuracy and spatial(k+1)th-order accuracy,where k denotes the highest degree of a piecewise polynomial in discontinuous finite element space.The numerical results are also provided to verify the accuracy and efficiency of the considered scheme.展开更多
The complex structure and strong heterogeneity of advanced nuclear reactor systems pose challenges for high-fidelity neutron-shielding calculations. Unstructured meshes exhibit strong geometric adaptability and can ov...The complex structure and strong heterogeneity of advanced nuclear reactor systems pose challenges for high-fidelity neutron-shielding calculations. Unstructured meshes exhibit strong geometric adaptability and can overcome the deficiencies of conventionally structured meshes in complex geometry modeling. A multithreaded parallel upwind sweep algorithm for S_(N) transport was proposed to achieve a more accurate geometric description and improve the computational efficiency. The spatial variables were discretized using the standard discontinuous Galerkin finite-element method. The angular flux transmission between neighboring meshes was handled using an upwind scheme. In addition, a combination of a mesh transport sweep and angular iterations was realized using a multithreaded parallel technique. The algorithm was implemented in the 2D/3D S_(N) transport code ThorSNIPE, and numerical evaluations were conducted using three typical benchmark problems:IAEA, Kobayashi-3i, and VENUS-3. These numerical results indicate that the multithreaded parallel upwind sweep algorithm can achieve high computational efficiency. ThorSNIPE, with a multithreaded parallel upwind sweep algorithm, has good reliability, stability, and high efficiency, making it suitable for complex shielding calculations.展开更多
In this paper,a new strategy for a sub-element-based shock capturing for discontinuous Galerkin(DG)approximations is presented.The idea is to interpret a DG element as a col-lection of data and construct a hierarchy o...In this paper,a new strategy for a sub-element-based shock capturing for discontinuous Galerkin(DG)approximations is presented.The idea is to interpret a DG element as a col-lection of data and construct a hierarchy of low-to-high-order discretizations on this set of data,including a first-order finite volume scheme up to the full-order DG scheme.The dif-ferent DG discretizations are then blended according to sub-element troubled cell indicators,resulting in a final discretization that adaptively blends from low to high order within a single DG element.The goal is to retain as much high-order accuracy as possible,even in simula-tions with very strong shocks,as,e.g.,presented in the Sedov test.The framework retains the locality of the standard DG scheme and is hence well suited for a combination with adaptive mesh refinement and parallel computing.The numerical tests demonstrate the sub-element adaptive behavior of the new shock capturing approach and its high accuracy.展开更多
Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions.These methods have been used in partial differential equation(PDE)-solve...Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions.These methods have been used in partial differential equation(PDE)-solvers and have demonstrated high-order convergence and spectrally accurate dispersion relations in numerical experiments.Discontinuous Galerkin(DG)methods are increasingly used for solving PDEs and,as all Galerkin formulations,come with a strong framework for proving the stability and the convergence.Here we propose the use of FC in forming a new basis for the DG framework.展开更多
In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered in...In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and linear functionals is investigated. So, the problem is not pure boundary-value. The authors single out a class of linear functionals and find simple algebraic conditions on coefficients, which garantee the existence of innnit number eigenvalues. Also the asymptotic formulas for eigenvalues are found.展开更多
The key-blocks are the main reason accounting for structural failure in discontinuous rock slopes, and automated identification of these block types is critical for evaluating the stability conditions. This paper pres...The key-blocks are the main reason accounting for structural failure in discontinuous rock slopes, and automated identification of these block types is critical for evaluating the stability conditions. This paper presents a classification framework to categorize rock blocks based on the principles of block theory. The deep convolutional neural network(CNN) procedure was utilized to analyze a total of 1240 highresolution images from 130 slope masses at the South Pars Special Zone, Assalouyeh, Southwest Iran.Based on Goodman’s theory, a recognition system has been implemented to classify three types of rock blocks, namely, key blocks, trapped blocks, and stable blocks. The proposed prediction model has been validated with the loss function, root mean square error(RMSE), and mean square error(MSE). As a justification of the model, the support vector machine(SVM), random forest(RF), Gaussian naïve Bayes(GNB), multilayer perceptron(MLP), Bernoulli naïve Bayes(BNB), and decision tree(DT) classifiers have been used to evaluate the accuracy, precision, recall, F1-score, and confusion matrix. Accuracy and precision of the proposed model are 0.95 and 0.93, respectively, in comparison with SVM(accuracy = 0.85, precision = 0.85), RF(accuracy = 0.71, precision = 0.71), GNB(accuracy = 0.75,precision = 0.65), MLP(accuracy = 0.88, precision = 0.9), BNB(accuracy = 0.75, precision = 0.69), and DT(accuracy = 0.85, precision = 0.76). In addition, the proposed model reduced the loss function to less than 0.3 and the RMSE and MSE to less than 0.2, which demonstrated a low error rate during processing.展开更多
In this paper, the existence of solutions for discontinuous nonlinear parabolic differential IBVP is proved by using a more generalized monotone iterative method. Moreover, the convergence of this method is discussed.
The Niumiangou landslide was the largest landslide triggered by the 2008 Wenchuan earthquake,which was significantly affected by the amplification effect of seismic acceleration.The ringshear experiments indicated tha...The Niumiangou landslide was the largest landslide triggered by the 2008 Wenchuan earthquake,which was significantly affected by the amplification effect of seismic acceleration.The ringshear experiments indicated that the materials in the source area of the Niumiangou landslide were subjected to friction degradation under a big shear displacement,which may result in rapid movement of the landslide.In order to better understand the landslide movement and study the effect of the friction degradation on movement mechanisms,the dynamic process of Niumiangou landslide was simulated with a new numerical method,which combines the finite difference method(FDM)and the discontinuous deformation analysis(DDA).First,the FDM was used to study the initiation time,amplification effect and velocity of the landslide.Afterwards,these initiation velocities were applied to the blocks in the DDA model by corresponding coordination in the FDM model.A displacementdependent friction model of the sliding surface was incorporated into DDA code to further understand the kinetic behavior of the landslide.The results show that the displacement-dependent friction strongly decreases the friction coefficient of sliding surface under a big displacement,which can obviously promote the run-out and velocity of landslide.The model output well matches the topographic map formed by the landslide.This implies that the proposed model can be applied to the simulation of earthquake-induced landslides with amplification effect,and the friction degradation model is important to clarify the movement mechanism of high-speed and long-distance landslides.展开更多
The discrete ordinates(S N)method requires numerous angular unknowns to achieve the desired accu-racy for shielding calculations involving strong anisotropy.Our objective is to develop an angular adaptive algorithm in...The discrete ordinates(S N)method requires numerous angular unknowns to achieve the desired accu-racy for shielding calculations involving strong anisotropy.Our objective is to develop an angular adaptive algorithm in the S N method to automatically optimize the angular distribution and minimize angular discretization errors with lower expenses.The proposed method enables linear dis-continuous finite element quadrature sets over an icosahe-dron to vary their quadrature orders in a one-twentieth sphere so that fine resolutions can be applied to the angular domains that are important.An error estimation that operates in conjunction with the spherical harmonics method is developed to determine the locations where more refinement is required.The adaptive quadrature sets are applied to three duct problems,including the Kobayashi benchmarks and the IRI-TUB research reactor,which emphasize the ability of this method to resolve neutron streaming through ducts with voids.The results indicate that the performance of the adaptive method is more effi-cient than that of uniform quadrature sets for duct transport problems.Our adaptive method offers an appropriate placement of angular unknowns to accurately integrate angular fluxes while reducing the computational costs in terms of unknowns and run times.展开更多
An h-adaptive method is developed for high-order discontinuous Galerkin methods(DGM)to solve the laminar compressible Navier-Stokes(N-S)equations on unstructured mesh.The vorticity is regarded as the indicator of adap...An h-adaptive method is developed for high-order discontinuous Galerkin methods(DGM)to solve the laminar compressible Navier-Stokes(N-S)equations on unstructured mesh.The vorticity is regarded as the indicator of adaptivity.The elements where the vorticity is larger than a pre-defined upper limit are refined,and those where the vorticity is smaller than a pre-defined lower limit are coarsened if they have been refined.A high-order geometric approximation of curved boundaries is adopted to ensure the accuracy.Numerical results indicate that highly accurate numerical results can be obtained with the adaptive method at relatively low expense.展开更多
基金supported by the National Natural Science Foundation of China(11871218,12071298)in part by the Science and Technology Commission of Shanghai Municipality(21JC1402500,22DZ2229014)。
文摘We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x=x(t).We prove that this problem admits global Radon measure solutions for all kinds of initial data.The over-compressing condition on the discontinuity x=x(t)is not enough to ensure the uniqueness of the solution.However,there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve x=x(t)+0,in addition to the full adhesion condition on its left-side.As an application,we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas.In particular,we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas.This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field.
基金supported by the National Natural Science Foundation of China(Grant No.42372310).
文摘Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.
基金supported in part by the National Key R&D Program of China under Grant 2021YFB 2900304the Shenzhen Science and Technology Program under Grants KQTD20190929172545139 and ZDSYS20210623091808025.
文摘Due to the limited uplink capability in heterogeneousnetworks (HetNets), the decoupled uplinkand downlink access (DUDA) mode has recently beenproposed to improve the uplink performance. In thispaper, the random discontinuous transmission (DTX)at user equipment (UE) is adopted to reduce the interferencecorrelation across different time slots. By utilizingstochastic geometry, we analytically derive themean local delay and energy efficiency (EE) of an uplinkHetNet with UE random DTX scheme under theDUDA mode. These expressions are further approximatedas closed forms under reasonable assumptions.Our results reveal that under the DUDA mode, there isan optimal EE with respect to mute probability underthe finite local delay constraint. In addition, with thesame finite mean local delay as under the coupled uplinkand downlink access (CUDA) mode, the HetNetsunder the DUDA mode can achieve a higher EE witha lower mute probability.
基金The authors would like to thank the National Natural Science Foundation of China(Grant Nos.51879184 and 52079091)for funding this work.
文摘Since its introduction,discontinuous deformation analysis(DDA)has been widely used in different areas of rock mechanics.By dividing large blocks into subblocks and introducing artificial joints,DDA can be applied to rock fracture simulation.However,parameter calibration,a fundamental issue in discontinuum methods,has not received enough attention in DDA.In this study,the parameter calibration of DDA for intact rock is carefully studied.To this end,a subblock DDA with Voronoi tessellation is presented first.Then,a modified contact constitutive law is introduced,in which the tensile and shear meso-strengths are modified to be independent of the bond lengths.This improvement can prevent the unjustified preferential failure of short edges.A method for imposing confining pressure is also introduced.Thereafter,sensitivity analysis is performed to investigate the influence of the calculated parameters and meso-parameters on the mechanical properties of modeled rock.Based on the sensitivity analysis,a unified calibration procedure is suggested for both cases with and without confining pressure.Finally,the calibration procedure is applied to two examples,including a biaxial compression test.The results show that the proposed Voronoi-based DDA can simulate rock fracture with and without confining pressure very well after careful parameter calibration.
基金supported by the National Natural Science Foundation of China(Grant Nos.41974114,41604105)the Fundamental Research Funds for the Central Universities(2020YQLX01)+1 种基金supported in part by the Project of Cultivation for Young Top-notch Talents of Beijing Municipal Institutions under Grant BPHR202203047in part by the Young Elite Scientists Sponsorship Program by BAST.
文摘Accurate wave propagation simulation in anisotropic media is important for forward modeling, migration and inversion. In this study, the weighted Runge-Kutta discontinuous Galerkin (RKDG) method is extended to solve the elastic wave equations in 2D transversely isotropic media. The spatial discretization is based on the numerical flux discontinuous Galerkin scheme. An explicit weighted two-step iterative Runge-Kutta method is used as time-stepping algorithm. The weighted RKDG method has good flexibility and applicability of dealing with undulating geometries and boundary conditions. To verify the correctness and effectiveness of this method, several numerical examples are presented for elastic wave propagations in vertical transversely isotropic and tilted transversely isotropic media. The results show that the weighted RKDG method is promising for solving wave propagation problems in complex anisotropic medium.
基金Funded by the National Natural Science Foundation of China(No.51627805)the Natural Scienceof Guangdong Province,China(No.2015A030312003)the Science and Technology Research Project of Guangdong Province,China(No.2014B010129003)。
文摘The effect of the inlet gas pressure,supplementary gas pressure and nozzle channel dispersion angle on the pre-breakup behavior of Ti-6Al-4V(TC4)discontinuous droplets during EIGA was investigated by combining numerical simulation with experiments.The results show that the axial velocity at the recirculation zone before the stagnation location was first increased and decreased then increased significantly after the peak value,while the pressure of the recirculation zone increased with the increase in inlet pressure.With the supplementary pressure increasing,the velocity magnitude and range of the recirculation zone gradually decreased.As the dispersion angle of the nozzle channel increased,the pre-breakup efficiency of droplets gradually decreased,but the adhesion phenomenon of droplets on the inner wall surface of the nozzle channel(IWSNC)gradually weakened.Under the inlet pressure of 4 MPa,a supplementary pressure of 0.05 MPa,and the dispersion angle of 15°,the uniform and spherical TC4 powders with diameter of 70μm were prepared,which was consistent with the simulation results.The optimized process parameters is a balance between the size of the pre-atomized particles and the back-spraying and bonding phenomenons of droplets.
基金This work was financially supported by the Jiangsu Distinguished Professor Project,the Innovate UK(Project reference:10004694)the National Key R&D Program of China 2021YFB3401200.The Experimental Techniques Centre at Brunel University London and Nanjing University of Aeronautics and Astronautics are acknowledged.The authors also acknowledge the characterization facility at Shanghai Jiao Tong University,Central South University,University of Birmingham and University of Lille.
文摘Magnesium alloys are lightweight materials with great potential,and plasma electrolytic oxidation(PEO)is effective surface treatment for necessary improvement of corrosion resistance of magnesium alloys.However,the∼14µm thick and rough PEO protection layer has inferior wear resistance,which limits magnesium alloys as sliding or reciprocating parts,where magnesium alloys have special advantages by their inherent damping and denoising properties and attractive light-weighting.Here a novel super wear-resistant coating for magnesium alloys was achieved,via the discontinuous sealing(DCS)of a 1.3µm thick polytetrafluoroethylene(PTFE)polymer layer with an initial area fraction(A_(f))of 70%on the necessary PEO protection layer by selective spraying,and the wear resistance was exceptionally enhanced by∼5500 times in comparison with the base PEO coating.The initial surface roughness(Sa)under PEO+DCS(1.54µm)was imperfectly 59%higher than that under PEO and conventional continuous sealing(CS).Interestingly,DCS was surprisingly 20 times superior for enhancing wear resistance in contrast to CS.DCS induced nano-cracks that splitted DCS layer into multilayer nano-blocks,and DCS also provided extra space for the movement of nano-blocks,which resulted in rolling friction and nano lubrication.Further,DCS promoted mixed wear of the PTFE polymer layer and the PEO coating,and the PTFE layer(HV:6 Kg·mm^(−2),A_(f):92.2%)and the PEO coating(HV:310 Kg·mm^(−2),A_(f):7.8%)served as the soft matrix and the hard point,respectively.Moreover,the dynamic decrease of Sa by 29%during wear also contributed to the super wear resistance.The strategy of depositing a low-frictional discontinuous layer on a rough and hard layer or matrix also opens a window for achieving super wear-resistant coatings in other materials.
基金supported by the National Natural Science Foundation of China (61963033, 61866036, 62163035)the Key Project of Natural Science Foundation of Xinjiang (2021D01D10)+1 种基金the Xinjiang Key Laboratory of Applied Mathematics (XJDX1401)the Special Project for Local Science and Technology Development Guided by the Central Government (ZYYD2022A05)。
文摘The fixed-time synchronization and preassigned-time synchronization are investigated for a class of quaternion-valued neural networks with time-varying delays and discontinuous activation functions. Unlike previous efforts that employed separation analysis and the real-valued control design, based on the quaternion-valued signum function and several related properties, a direct analytical method is proposed here and the quaternion-valued controllers are designed in order to discuss the fixed-time synchronization for the relevant quaternion-valued neural networks. In addition, the preassigned-time synchronization is investigated based on a quaternion-valued control design, where the synchronization time is preassigned and the control gains are finite. Compared with existing results, the direct method without separation developed in this article is beneficial in terms of simplifying theoretical analysis, and the proposed quaternion-valued control schemes are simpler and more effective than the traditional design, which adds four real-valued controllers. Finally, two numerical examples are given in order to support the theoretical results.
基金funded by the National Natural Science Foundation of China (Grant No.52175111)。
文摘In automotive industries,panel acoustic contribution analysis(PACA)is used to investigate the contributions of the body panels to the acoustic pressure at a certain point of interest.Currently,PACA is implementedmostly by either experiment-based methods or traditional numerical methods.However,these schemes are effort-consuming and inefficient in solving engineering problems,thereby restraining the further development of PACA in automotive acoustics.In this work,we propose a PACA scheme using discontinuous isogeometric boundary element method(IGABEM)to build an easily implementable and efficient method to identify the relative acoustic contributions of each automotive body panel.Discontinuous IGABEMis more accurate and converges faster than continuous BEM and IGABEM in the interior sound pressure evaluation of automotive compartments.In this work,a contribution ratio is defined to estimate the relative acoustic contribution of the structure panels;it can be calculated by reusing the coefficient matrix that has already been generated in the sound pressure evaluation process.The utilization of the parallel technique enables the proposed method to be more efficient than conventional methods;it is validated in two numerical examples,including a car passenger compartment subjected to realistic boundary conditions.A sound pressure response experiment based on a steel box is conducted to verify the accuracy of the interior sound pressure calculation using discontinuous IGABEM.This work is expected to promote the practical process of IGABEM for application in automotive acoustic problems.
基金supported by National Natural Science Foundation of China under(Grant Nos.62173175,12026235,12026234,61903170,11805091,61877033,61833005)by 111 Project under Grant B17040+2 种基金by the Natural Science Foundation of Shandong Province under Grant Nos.ZR2019BF045,ZR2019MF021,ZR2019QF004by the Project of Shandong Province Higher Educational Science and Technology Program No.J18KA354by the Key Research and Development Project of Shandong Province of China,No.2019GGX101003.
文摘Fixed-time synchronization(FTS)of delayed memristor-based neural networks(MNNs)with discontinuous activations is studied in this paper.Both continuous and discontinuous activations are considered forMNNs.And the mixed delays which are closer to reality are taken into the system.Besides,two kinds of control schemes are proposed,including feedback and adaptive control strategies.Based on some lemmas,mathematical inequalities and the designed controllers,a few synchronization criteria are acquired.Moreover,the upper bound of settling time(ST)which is independent of the initial values is given.Finally,the feasibility of our theory is attested by simulation examples.
基金supported by the State Key Program of National Natural Science Foundation of China(11931003)the National Natural Science Foundation of China(41974133)。
文摘In this paper,a local discontinuous Galerkin(LDG)scheme for the time-fractional diffusion equation is proposed and analyzed.The Caputo time-fractional derivative(of orderα,with 0<α<1)is approximated by a finite difference method with an accuracy of order3-α,and the space discretization is based on the LDG method.For the finite difference method,we summarize and supplement some previous work by others,and apply it to the analysis of the convergence and stability of the proposed scheme.The optimal error estimate is obtained in the L2norm,indicating that the scheme has temporal(3-α)th-order accuracy and spatial(k+1)th-order accuracy,where k denotes the highest degree of a piecewise polynomial in discontinuous finite element space.The numerical results are also provided to verify the accuracy and efficiency of the considered scheme.
文摘The complex structure and strong heterogeneity of advanced nuclear reactor systems pose challenges for high-fidelity neutron-shielding calculations. Unstructured meshes exhibit strong geometric adaptability and can overcome the deficiencies of conventionally structured meshes in complex geometry modeling. A multithreaded parallel upwind sweep algorithm for S_(N) transport was proposed to achieve a more accurate geometric description and improve the computational efficiency. The spatial variables were discretized using the standard discontinuous Galerkin finite-element method. The angular flux transmission between neighboring meshes was handled using an upwind scheme. In addition, a combination of a mesh transport sweep and angular iterations was realized using a multithreaded parallel technique. The algorithm was implemented in the 2D/3D S_(N) transport code ThorSNIPE, and numerical evaluations were conducted using three typical benchmark problems:IAEA, Kobayashi-3i, and VENUS-3. These numerical results indicate that the multithreaded parallel upwind sweep algorithm can achieve high computational efficiency. ThorSNIPE, with a multithreaded parallel upwind sweep algorithm, has good reliability, stability, and high efficiency, making it suitable for complex shielding calculations.
文摘In this paper,a new strategy for a sub-element-based shock capturing for discontinuous Galerkin(DG)approximations is presented.The idea is to interpret a DG element as a col-lection of data and construct a hierarchy of low-to-high-order discretizations on this set of data,including a first-order finite volume scheme up to the full-order DG scheme.The dif-ferent DG discretizations are then blended according to sub-element troubled cell indicators,resulting in a final discretization that adaptively blends from low to high order within a single DG element.The goal is to retain as much high-order accuracy as possible,even in simula-tions with very strong shocks,as,e.g.,presented in the Sedov test.The framework retains the locality of the standard DG scheme and is hence well suited for a combination with adaptive mesh refinement and parallel computing.The numerical tests demonstrate the sub-element adaptive behavior of the new shock capturing approach and its high accuracy.
文摘Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions.These methods have been used in partial differential equation(PDE)-solvers and have demonstrated high-order convergence and spectrally accurate dispersion relations in numerical experiments.Discontinuous Galerkin(DG)methods are increasingly used for solving PDEs and,as all Galerkin formulations,come with a strong framework for proving the stability and the convergence.Here we propose the use of FC in forming a new basis for the DG framework.
文摘In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and linear functionals is investigated. So, the problem is not pure boundary-value. The authors single out a class of linear functionals and find simple algebraic conditions on coefficients, which garantee the existence of innnit number eigenvalues. Also the asymptotic formulas for eigenvalues are found.
基金support provided by the National Natural Science Foundation of China(Grant No.42077235)the National Key Research and Development Program of China(Grant No.2018YFC1505104).
文摘The key-blocks are the main reason accounting for structural failure in discontinuous rock slopes, and automated identification of these block types is critical for evaluating the stability conditions. This paper presents a classification framework to categorize rock blocks based on the principles of block theory. The deep convolutional neural network(CNN) procedure was utilized to analyze a total of 1240 highresolution images from 130 slope masses at the South Pars Special Zone, Assalouyeh, Southwest Iran.Based on Goodman’s theory, a recognition system has been implemented to classify three types of rock blocks, namely, key blocks, trapped blocks, and stable blocks. The proposed prediction model has been validated with the loss function, root mean square error(RMSE), and mean square error(MSE). As a justification of the model, the support vector machine(SVM), random forest(RF), Gaussian naïve Bayes(GNB), multilayer perceptron(MLP), Bernoulli naïve Bayes(BNB), and decision tree(DT) classifiers have been used to evaluate the accuracy, precision, recall, F1-score, and confusion matrix. Accuracy and precision of the proposed model are 0.95 and 0.93, respectively, in comparison with SVM(accuracy = 0.85, precision = 0.85), RF(accuracy = 0.71, precision = 0.71), GNB(accuracy = 0.75,precision = 0.65), MLP(accuracy = 0.88, precision = 0.9), BNB(accuracy = 0.75, precision = 0.69), and DT(accuracy = 0.85, precision = 0.76). In addition, the proposed model reduced the loss function to less than 0.3 and the RMSE and MSE to less than 0.2, which demonstrated a low error rate during processing.
文摘In this paper, the existence of solutions for discontinuous nonlinear parabolic differential IBVP is proved by using a more generalized monotone iterative method. Moreover, the convergence of this method is discussed.
基金supported by the National Natural Science Foundation of China(Nos.4167230041902290)Opening fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection(Chengdu University of Technology)(No.SKLGP2017K015)。
文摘The Niumiangou landslide was the largest landslide triggered by the 2008 Wenchuan earthquake,which was significantly affected by the amplification effect of seismic acceleration.The ringshear experiments indicated that the materials in the source area of the Niumiangou landslide were subjected to friction degradation under a big shear displacement,which may result in rapid movement of the landslide.In order to better understand the landslide movement and study the effect of the friction degradation on movement mechanisms,the dynamic process of Niumiangou landslide was simulated with a new numerical method,which combines the finite difference method(FDM)and the discontinuous deformation analysis(DDA).First,the FDM was used to study the initiation time,amplification effect and velocity of the landslide.Afterwards,these initiation velocities were applied to the blocks in the DDA model by corresponding coordination in the FDM model.A displacementdependent friction model of the sliding surface was incorporated into DDA code to further understand the kinetic behavior of the landslide.The results show that the displacement-dependent friction strongly decreases the friction coefficient of sliding surface under a big displacement,which can obviously promote the run-out and velocity of landslide.The model output well matches the topographic map formed by the landslide.This implies that the proposed model can be applied to the simulation of earthquake-induced landslides with amplification effect,and the friction degradation model is important to clarify the movement mechanism of high-speed and long-distance landslides.
基金supported by the National Natural Science Foundation of China(No.11975097)the Fundamental Research Funds for the Central Universities(No.2019MS038).
文摘The discrete ordinates(S N)method requires numerous angular unknowns to achieve the desired accu-racy for shielding calculations involving strong anisotropy.Our objective is to develop an angular adaptive algorithm in the S N method to automatically optimize the angular distribution and minimize angular discretization errors with lower expenses.The proposed method enables linear dis-continuous finite element quadrature sets over an icosahe-dron to vary their quadrature orders in a one-twentieth sphere so that fine resolutions can be applied to the angular domains that are important.An error estimation that operates in conjunction with the spherical harmonics method is developed to determine the locations where more refinement is required.The adaptive quadrature sets are applied to three duct problems,including the Kobayashi benchmarks and the IRI-TUB research reactor,which emphasize the ability of this method to resolve neutron streaming through ducts with voids.The results indicate that the performance of the adaptive method is more effi-cient than that of uniform quadrature sets for duct transport problems.Our adaptive method offers an appropriate placement of angular unknowns to accurately integrate angular fluxes while reducing the computational costs in terms of unknowns and run times.
基金supported by the National Natural Science Foundation of China(11272152)
文摘An h-adaptive method is developed for high-order discontinuous Galerkin methods(DGM)to solve the laminar compressible Navier-Stokes(N-S)equations on unstructured mesh.The vorticity is regarded as the indicator of adaptivity.The elements where the vorticity is larger than a pre-defined upper limit are refined,and those where the vorticity is smaller than a pre-defined lower limit are coarsened if they have been refined.A high-order geometric approximation of curved boundaries is adopted to ensure the accuracy.Numerical results indicate that highly accurate numerical results can be obtained with the adaptive method at relatively low expense.
