Grouting has been the most effective approach to mitigate water inrush disasters in underground engineering due to its ability to plug groundwater and enhance rock strength.Nevertheless,there is a lack of potent numer...Grouting has been the most effective approach to mitigate water inrush disasters in underground engineering due to its ability to plug groundwater and enhance rock strength.Nevertheless,there is a lack of potent numerical tools for assessing the grouting effectiveness in water-rich fractured strata.In this study,the hydro-mechanical coupled discontinuous deformation analysis(HM-DDA)is inaugurally extended to simulate the grouting process in a water-rich discrete fracture network(DFN),including the slurry migration,fracture dilation,water plugging in a seepage field,and joint reinforcement after coagulation.To validate the capabilities of the developed method,several numerical examples are conducted incorporating the Newtonian fluid and Bingham slurry.The simulation results closely align with the analytical solutions.Additionally,a set of compression tests is conducted on the fresh and grouted rock specimens to verify the reinforcement method and calibrate the rational properties of reinforced joints.An engineering-scale model based on a real water inrush case of the Yonglian tunnel in a water-rich fractured zone has been established.The model demonstrates the effectiveness of grouting reinforcement in mitigating water inrush disaster.The results indicate that increased grouting pressure greatly affects the regulation of water outflow from the tunnel face and the prevention of rock detachment face after excavation.展开更多
Mechanism of discontinuous precipitation(DP) in AZ80 alloy was investigated by phase-orientation correlated characterization.The results show DPs nucleate by turning the original grain boundaries(GBs) as reaction fron...Mechanism of discontinuous precipitation(DP) in AZ80 alloy was investigated by phase-orientation correlated characterization.The results show DPs nucleate by turning the original grain boundaries(GBs) as reaction front(RF),and further driving the RF to realize their growth.The DPs regions retained the same orientations as their parent grains.The misorientation angle and rotation axis of RFs had strong influence on DPs nucleation.The low-angle GBs,twin boundaries(TBs) and the GBs with specific misorientation axis which are known as low energy and low mobility GBs can hardly initiate DPs.In addition,the TBs had a strong ability to inhibit the growth of DPs,but it should be noticed that the growth of DPs cannot be totally inhibited by TBs.DPs can engulf the twins when the growth direction is approximately parallel to the long axis of TBs.The inhibition behavior is related to the distribution of Al solute atoms near the RF,boundary interactions of the TBs and twin tips with the RF,and the morphology of the continuous precipitations within the twins.展开更多
In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabili...In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabilization of the addressed neural networks. In order to complete the targets, based on set-valued map, differential inclusions theory, coincidence theorem and Hölder inequality technique, some new proportional delay-dependent criteria shown by the inequalities are derived. Based on the fact of the existence of solution, further by applying the FXT stability lemmas and equivalent transformation, the zero solution of closed-loop system achieves FXT stabilization and the corresponding settling-times are estimated. Some previous related works on NTNNs are extended. Finally, one typical example is provided to show the effectiveness of the established results.展开更多
A discontinuous smoothed particle hydrodynamics(DSPH)method considering block contacts is originally developed to model the cracking,frictional slip and large deformation in rock masses,and is verified by theoretical,...A discontinuous smoothed particle hydrodynamics(DSPH)method considering block contacts is originally developed to model the cracking,frictional slip and large deformation in rock masses,and is verified by theoretical,numerical and/or experimental results.In the DSPH method,cracking is realized by breaking the virtual bonds via a pseudo-spring method based on Mohr–Coulomb failure criteria.The damaged particles are instantaneously replaced by discontinuous particles and the contact bond between the original and discontinuous particles is formed to simulate the frictional slip and separation/contraction between fracture surfaces based on the block contact algorithm.The motion of rock blocks and the contact force of discontinuous particles are determined following Newton's second law.The results indicate that the DSPH method precisely captures the cracking,contact formation and complete failure across six numerical benchmark tests.This single smoothed particle hydrodynamics(SPH)framework could significantly improve computational efficiency and is potentially applicable to broad multi-physical rock engineering problems of different scales.展开更多
Simultaneously achieving high strength and high electrical conductivity in Cu–Ni–Si alloys pose a significant challenge, which greatly constrains its applications in the electronics industry. This paper offers a new...Simultaneously achieving high strength and high electrical conductivity in Cu–Ni–Si alloys pose a significant challenge, which greatly constrains its applications in the electronics industry. This paper offers a new pathway to improve properties, by preparation of nanometer lamellar discontinuous precipitates(DPs) arranged with the approximate same direction through a combination of deformationaging and cold rolling process. The strengthening effect is primarily attributed to nanometer-lamellar DPs strengthening and dislocation strengthening mechanism. The accumulation of dislocations at the interface between nanometer lamellar DPs and matrix during cold deformation process can results in the decrease of dislocation density inside the matrix grains, leading to the acceptably slight reduction of electrical conductivity during cold rolling. The alloy exhibits an electrical conductivity of 45.32%IACS(international annealed copper standard, IACS), a tensile strength of 882.67 MPa, and a yield strength of 811.33 MPa by this method. This study can provide a guidance for the composition and microstructure design of a Cu–Ni–Si alloy in the future, by controlling the morphology and distribution of DPs.展开更多
Cu-Ti alloys are a kind of elastic copper alloys with excellent comprehensive properties.They are often used in electronic and electrical fields.However,discontinuous precipitation may occur during the preparation pro...Cu-Ti alloys are a kind of elastic copper alloys with excellent comprehensive properties.They are often used in electronic and electrical fields.However,discontinuous precipitation may occur during the preparation process of Cu-Ti alloys,and they can lead to the significant deterioration of mechanical properties.To solve this problem,three Cu-Ti alloys with various Fe contents(Cu-2.7Ti,Cu-2.7Ti-0.1Fe and Cu-2.7Ti-0.2Fe)were designed and prepared in this paper to investigate the effects of Fe on the discontinuous precipitation.The results showed that after aging at any given aging time and temperature,the area fraction of cellular structure decreased with the increase of Fe content.The addition of Fe into Cu-Ti alloys resulted in Fe doping inβ'-Cu_(4)Ti phase andβ-Cu_(4)Ti phase.For 450℃/144 h-aged Cu-2.7Ti-0.2Fe alloy,the Fe content inβ'-Cu_(4)Ti phase andβ-Cu_(4)Ti phase was 1.59 at%and 0.90 at%,respectively.The tensile tests showed that under the same aging treatment conditions,Cu-2.7Ti-0.2Fe alloy possessed better mechanical properties.First-principles calculation confirmed that the thermodynamic stability ofβ'-Cu_(4)Ti phase was enhanced by decreasing its cohesive energy through Fe doping.At the same time,the enthalpy of formation ofβ-Cu_(4)Ti phase was generally increased by Fe doping,making it difficult to generate.In short,Fe addition in Cu-Ti alloys suppressed discontinuous precipitation by Fe doping in the precipitates and helped to improve mechanical properties.展开更多
A unique discontinuous lamellar microstructure of titanium alloys consisting of lamellar colonies at prior β-Ti grain boundaries and internal interwoven α-laths is prepared by a TiH_(2)-based powder metallurgy metho...A unique discontinuous lamellar microstructure of titanium alloys consisting of lamellar colonies at prior β-Ti grain boundaries and internal interwoven α-laths is prepared by a TiH_(2)-based powder metallurgy method.The α-variants get various crystallographic orientations and become discontinuous during vacuum annealing at 700℃.Remarkably,nanoscale phase δ-TiH compound layers are generated between α-laths and β-strips,so that dislocations are piled up at the α/δ/βinterfaces during tensile deformation.This leads to dislocation slips being confined to individual α-laths,with differentslips and particularly pyramidal<c+a>slips being activated.The efficiency of wavy slip is promoted and the work hardening rate is enhanced.Finally,the combined effect of dispersed micro-shear bands and lath distortions is considered contributive for alleviating the stress concentration at grain boundaries,resulting in a high-promising synergy of enhanced ultimate tensile strength of 1080 MPa and good elongation to fracture of 13.6%.展开更多
In this paper,we design a new error estimator and give a posteriori error analysis for a poroelasticity model.To better overcome“locking phenomenon”on pressure and displacement,we proposed a new error estimators bas...In this paper,we design a new error estimator and give a posteriori error analysis for a poroelasticity model.To better overcome“locking phenomenon”on pressure and displacement,we proposed a new error estimators based on multiphysics discontinuous Galerkin method for the poroelasticity model.And we prove the upper and lower bound of the proposed error estimators,which are numerically demonstrated to be computationally very efficient.Finally,we present numerical examples to verify and validate the efficiency of the proposed error estimators,which show that the adaptive scheme can overcome“locking phenomenon”and greatly reduce the computation cost.展开更多
We present the approaches to implementing the k-√k L turbulence model within the framework of the high-order discontinuous Galerkin(DG)method.We use the DG discretization to solve the full Reynolds-averaged Navier-St...We present the approaches to implementing the k-√k L turbulence model within the framework of the high-order discontinuous Galerkin(DG)method.We use the DG discretization to solve the full Reynolds-averaged Navier-Stokes equations.In order to enhance the robustness of approaches,some effective techniques are designed.The HWENO(Hermite weighted essentially non-oscillatory)limiting strategy is adopted for stabilizing the turbulence model variable k.Modifications have been made to the model equation itself by using the auxiliary variable that is always positive.The 2nd-order derivatives of velocities required in computing the von Karman length scale are evaluated in a way to maintain the compactness of DG methods.Numerical results demonstrate that the approaches have achieved the desirable accuracy for both steady and unsteady turbulent simulations.展开更多
Accurate dynamic modeling of landslides could help understand the movement mechanisms and guide disaster mitigation and prevention.Discontinuous deformation analysis(DDA)is an effective approach for investigating land...Accurate dynamic modeling of landslides could help understand the movement mechanisms and guide disaster mitigation and prevention.Discontinuous deformation analysis(DDA)is an effective approach for investigating landslides.However,DDA fails to accurately capture the degradation in shear strength of rock joints commonly observed in high-speed landslides.In this study,DDA is modified by incorporating simplified joint shear strength degradation.Based on the modified DDA,the kinematics of the Baige landslide that occurred along the Jinsha River in China on 10 October 2018 are reproduced.The violent starting velocity of the landslide is considered explicitly.Three cases with different violent starting velocities are investigated to show their effect on the landslide movement process.Subsequently,the landslide movement process and the final accumulation characteristics are analyzed from multiple perspectives.The results show that the violent starting velocity affects the landslide motion characteristics,which is found to be about 4 m/s in the Baige landslide.The movement process of the Baige landslide involves four stages:initiation,high-speed sliding,impact-climbing,low-speed motion and accumulation.The accumulation states of sliding masses in different zones are different,which essentially corresponds to reality.The research results suggest that the modified DDA is applicable to similar high-level rock landslides.展开更多
The primary impediments impeding the implementation of high-order methods in simulating viscous flow over complex configurations are robustness and convergence.These challenges impose significant constraints on comput...The primary impediments impeding the implementation of high-order methods in simulating viscous flow over complex configurations are robustness and convergence.These challenges impose significant constraints on computational efficiency,particularly in the domain of engineering applications.To address these concerns,this paper proposes a robust implicit high-order discontinuous Galerkin(DG)method for solving compressible Navier-Stokes(NS)equations on arbitrary grids.The method achieves a favorable equilibrium between computational stability and efficiency.To solve the linear system,an exact Jacobian matrix solving strategy is employed for preconditioning and matrix-vector generation in the generalized minimal residual(GMRES)method.This approach mitigates numerical errors in Jacobian solution during implicit calculations and facilitates the implementation of an adaptive Courant-Friedrichs-Lewy(CFL)number increasing strategy,with the aim of improving convergence and robustness.To further enhance the applicability of the proposed method for intricate grid distortions,all simulations are performed in the reference domain.This practice significantly improves the reversibility of the mass matrix in implicit calculations.A comprehensive analysis of various parameters influencing computational stability and efficiency is conducted,including CFL number,Krylov subspace size,and GMRES convergence criteria.The computed results from a series of numerical test cases demonstrate the promising results achieved by combining the DG method,GMRES solver,exact Jacobian matrix,adaptive CFL number,and reference domain calculations in terms of robustness,convergence,and accuracy.These analysis results can serve as a reference for implicit computation in high-order calculations.展开更多
The cohesive zone model(CZM)has been used widely and successfully in fracture propagation,but some basic problems are still to be solved.In this paper,artificial compliance and discontinuous force in CZM are investiga...The cohesive zone model(CZM)has been used widely and successfully in fracture propagation,but some basic problems are still to be solved.In this paper,artificial compliance and discontinuous force in CZM are investigated.First,theories about the cohesive element(local coordinate system,stiffness matrix,and internal nodal force)are presented.The local coordinate system is defined to obtain local separation;the stiffness matrix for an eight-node cohesive element is derived from the calculation of strain energy;internal nodal force between the cohesive element and bulk element is obtained from the principle of virtual work.Second,the reason for artificial compliance is explained by the effective stiffnesses of zero-thickness and finite-thickness cohesive elements.Based on the effective stiffness,artificial compliance can be completely removed by adjusting the stiffness of the finite-thickness cohesive element.This conclusion is verified from 1D and 3D simulations.Third,three damage evolution methods(monotonically increasing effective separation,damage factor,and both effective separation and damage factor)are analyzed.Under constant unloading and reloading conditions,the monotonically increasing damage factor method without discontinuous force and healing effect is a better choice than the other two methods.The proposed improvements are coded in LS-DYNA user-defined material,and a drop weight tear test verifies the improvements.展开更多
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
We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across th...We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.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
This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis techniq...This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.展开更多
In this paper,we develop bound-preserving discontinuous Galerkin(DG)methods for chemical reactive flows.There are several difficulties in constructing suitable numerical schemes.First of all,the density and internal e...In this paper,we develop bound-preserving discontinuous Galerkin(DG)methods for chemical reactive flows.There are several difficulties in constructing suitable numerical schemes.First of all,the density and internal energy are positive,and the mass fraction of each species is between 0 and 1.Second,due to the rapid reaction rate,the system may contain stiff sources,and the strong-stability-preserving explicit Runge-Kutta method may result in limited time-step sizes.To obtain physically relevant numerical approximations,we apply the bound-preserving technique to the DG methods.Though traditional positivity-preserving techniques can successfully yield positive density,internal energy,and mass fractions,they may not enforce the upper bound 1 of the mass fractions.To solve this problem,we need to(i)make sure the numerical fluxes in the equations of the mass fractions are consistent with that in the equation of the density;(ii)choose conservative time integrations,such that the summation of the mass fractions is preserved.With the above two conditions,the positive mass fractions have summation 1,and then,they are all between 0 and 1.For time discretization,we apply the modified Runge-Kutta/multi-step Patankar methods,which are explicit for the flux while implicit for the source.Such methods can handle stiff sources with relatively large time steps,preserve the positivity of the target variables,and keep the summation of the mass fractions to be 1.Finally,it is not straightforward to combine the bound-preserving DG methods and the Patankar time integrations.The positivity-preserving technique for DG methods requires positive numerical approximations at the cell interfaces,while Patankar methods can keep the positivity of the pre-selected point values of the target variables.To match the degree of freedom,we use polynomials on rectangular meshes for problems in two space dimensions.To evolve in time,we first read the polynomials at the Gaussian points.Then,suitable slope limiters can be applied to enforce the positivity of the solutions at those points,which can be preserved by the Patankar methods,leading to positive updated numerical cell averages.In addition,we use another slope limiter to get positive solutions used for the bound-preserving technique for the flux.Numerical examples are given to demonstrate the good performance of the proposed schemes.展开更多
This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software implementation.The C++software package called AdaM-D...This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software implementation.The C++software package called AdaM-DG,implementing the aSG-DG method,is available on GitHub at https://github.com/JuntaoHuang/adaptive-multiresolution-DG.The package is capable of treating a large class of high dimensional linear and nonlinear PDEs.We review the essential components of the algorithm and the functionality of the software,including the multiwavelets used,assembling of bilinear operators,fast matrix-vector product for data with hierarchical structures.We further demonstrate the performance of the package by reporting the numerical error and the CPU cost for several benchmark tests,including linear transport equations,wave equations,and Hamilton-Jacobi(HJ)equations.展开更多
In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)system....In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)system.The LoMaC property refers to the exact local conservation of macroscopic mass,momentum,and energy at the discrete level.The recently developed LoMaC low rank tensor algorithm(arXiv:2207.00518)simultaneously evolves the macroscopic conservation laws of mass,momentum,and energy using the kinetic flux vector splitting;then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables.This paper is a generalization of our previous work,but with DG discretization to take advantage of its compactness and flexibility in handling boundary conditions and its superior accuracy in the long term.The algorithm is developed in a similar fashion as that for a finite difference scheme,by observing that the DG method can be viewed equivalently in a nodal fashion.With the nodal DG method,assuming a tensorized computational grid,one will be able to(i)derive differentiation matrices for different nodal points based on a DG upwind discretization of transport terms,and(ii)define a weighted inner product space based on the nodal DG grid points.The algorithm can be extended to the high dimensional problems by hierarchical Tucker(HT)decomposition of solution tensors and a corresponding conservative projection algorithm.In a similar spirit,the algorithm can be extended to DG methods on nodal points of an unstructured mesh,or to other types of discretization,e.g.,the spectral method in velocity direction.Extensive numerical results are performed to showcase the efficacy of the method.展开更多
基金supported by the China Scholarship Council(CSC,Grant No.202108050072)JSPS KAKENHI(Grant No.JP19KK0121)。
文摘Grouting has been the most effective approach to mitigate water inrush disasters in underground engineering due to its ability to plug groundwater and enhance rock strength.Nevertheless,there is a lack of potent numerical tools for assessing the grouting effectiveness in water-rich fractured strata.In this study,the hydro-mechanical coupled discontinuous deformation analysis(HM-DDA)is inaugurally extended to simulate the grouting process in a water-rich discrete fracture network(DFN),including the slurry migration,fracture dilation,water plugging in a seepage field,and joint reinforcement after coagulation.To validate the capabilities of the developed method,several numerical examples are conducted incorporating the Newtonian fluid and Bingham slurry.The simulation results closely align with the analytical solutions.Additionally,a set of compression tests is conducted on the fresh and grouted rock specimens to verify the reinforcement method and calibrate the rational properties of reinforced joints.An engineering-scale model based on a real water inrush case of the Yonglian tunnel in a water-rich fractured zone has been established.The model demonstrates the effectiveness of grouting reinforcement in mitigating water inrush disaster.The results indicate that increased grouting pressure greatly affects the regulation of water outflow from the tunnel face and the prevention of rock detachment face after excavation.
基金supported by National Natural Science Foundation of China (52201107)Research Program of Chongqing Municipal Education Commission (KJQN202201151)Natural Science Foundation of Chongqing (CSTB2023NSCQ-MSX0067).
文摘Mechanism of discontinuous precipitation(DP) in AZ80 alloy was investigated by phase-orientation correlated characterization.The results show DPs nucleate by turning the original grain boundaries(GBs) as reaction front(RF),and further driving the RF to realize their growth.The DPs regions retained the same orientations as their parent grains.The misorientation angle and rotation axis of RFs had strong influence on DPs nucleation.The low-angle GBs,twin boundaries(TBs) and the GBs with specific misorientation axis which are known as low energy and low mobility GBs can hardly initiate DPs.In addition,the TBs had a strong ability to inhibit the growth of DPs,but it should be noticed that the growth of DPs cannot be totally inhibited by TBs.DPs can engulf the twins when the growth direction is approximately parallel to the long axis of TBs.The inhibition behavior is related to the distribution of Al solute atoms near the RF,boundary interactions of the TBs and twin tips with the RF,and the morphology of the continuous precipitations within the twins.
基金supported by Social Science Fund of Hunan province(Grant No.22JD074)the Research Foundation of Education Bureau of Hunan province(Grant No.22B0912).
文摘In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabilization of the addressed neural networks. In order to complete the targets, based on set-valued map, differential inclusions theory, coincidence theorem and Hölder inequality technique, some new proportional delay-dependent criteria shown by the inequalities are derived. Based on the fact of the existence of solution, further by applying the FXT stability lemmas and equivalent transformation, the zero solution of closed-loop system achieves FXT stabilization and the corresponding settling-times are estimated. Some previous related works on NTNNs are extended. Finally, one typical example is provided to show the effectiveness of the established results.
基金financial support from the National Key Research and Development Program of China(Grant No.2019YFC1509702)the Fundamental Research Funds for the Central Universities in Chinathe National Natural Science Foundation of China(Grant No.42377162).
文摘A discontinuous smoothed particle hydrodynamics(DSPH)method considering block contacts is originally developed to model the cracking,frictional slip and large deformation in rock masses,and is verified by theoretical,numerical and/or experimental results.In the DSPH method,cracking is realized by breaking the virtual bonds via a pseudo-spring method based on Mohr–Coulomb failure criteria.The damaged particles are instantaneously replaced by discontinuous particles and the contact bond between the original and discontinuous particles is formed to simulate the frictional slip and separation/contraction between fracture surfaces based on the block contact algorithm.The motion of rock blocks and the contact force of discontinuous particles are determined following Newton's second law.The results indicate that the DSPH method precisely captures the cracking,contact formation and complete failure across six numerical benchmark tests.This single smoothed particle hydrodynamics(SPH)framework could significantly improve computational efficiency and is potentially applicable to broad multi-physical rock engineering problems of different scales.
基金supported by the National Key Research and Development Program of China (No. 2023YFB3812601)the National Natural Science Founda tion of China (Nos. 51925401, 92066205, and 92266301)。
文摘Simultaneously achieving high strength and high electrical conductivity in Cu–Ni–Si alloys pose a significant challenge, which greatly constrains its applications in the electronics industry. This paper offers a new pathway to improve properties, by preparation of nanometer lamellar discontinuous precipitates(DPs) arranged with the approximate same direction through a combination of deformationaging and cold rolling process. The strengthening effect is primarily attributed to nanometer-lamellar DPs strengthening and dislocation strengthening mechanism. The accumulation of dislocations at the interface between nanometer lamellar DPs and matrix during cold deformation process can results in the decrease of dislocation density inside the matrix grains, leading to the acceptably slight reduction of electrical conductivity during cold rolling. The alloy exhibits an electrical conductivity of 45.32%IACS(international annealed copper standard, IACS), a tensile strength of 882.67 MPa, and a yield strength of 811.33 MPa by this method. This study can provide a guidance for the composition and microstructure design of a Cu–Ni–Si alloy in the future, by controlling the morphology and distribution of DPs.
基金supported by the National Natural Science Foundation of China(No.U2202255)Hunan Provincial Natural Science Foundation of China(No.2024JJ2076)the Key Technology Research Program of Ningbo(No.2023Z092).
文摘Cu-Ti alloys are a kind of elastic copper alloys with excellent comprehensive properties.They are often used in electronic and electrical fields.However,discontinuous precipitation may occur during the preparation process of Cu-Ti alloys,and they can lead to the significant deterioration of mechanical properties.To solve this problem,three Cu-Ti alloys with various Fe contents(Cu-2.7Ti,Cu-2.7Ti-0.1Fe and Cu-2.7Ti-0.2Fe)were designed and prepared in this paper to investigate the effects of Fe on the discontinuous precipitation.The results showed that after aging at any given aging time and temperature,the area fraction of cellular structure decreased with the increase of Fe content.The addition of Fe into Cu-Ti alloys resulted in Fe doping inβ'-Cu_(4)Ti phase andβ-Cu_(4)Ti phase.For 450℃/144 h-aged Cu-2.7Ti-0.2Fe alloy,the Fe content inβ'-Cu_(4)Ti phase andβ-Cu_(4)Ti phase was 1.59 at%and 0.90 at%,respectively.The tensile tests showed that under the same aging treatment conditions,Cu-2.7Ti-0.2Fe alloy possessed better mechanical properties.First-principles calculation confirmed that the thermodynamic stability ofβ'-Cu_(4)Ti phase was enhanced by decreasing its cohesive energy through Fe doping.At the same time,the enthalpy of formation ofβ-Cu_(4)Ti phase was generally increased by Fe doping,making it difficult to generate.In short,Fe addition in Cu-Ti alloys suppressed discontinuous precipitation by Fe doping in the precipitates and helped to improve mechanical properties.
基金financially supported by the National Natural Science Foundation of China(Nos.52301145,52275329)the Applied Basic Research Program of Liaoning Province,China(No.2023JH2/101300158)+1 种基金the Fundamental Research Fund for the Central Universities,China(No.N2202010)the Key Research Programs of High Education Institutions in Henan Province,China(No.24A430017).
文摘A unique discontinuous lamellar microstructure of titanium alloys consisting of lamellar colonies at prior β-Ti grain boundaries and internal interwoven α-laths is prepared by a TiH_(2)-based powder metallurgy method.The α-variants get various crystallographic orientations and become discontinuous during vacuum annealing at 700℃.Remarkably,nanoscale phase δ-TiH compound layers are generated between α-laths and β-strips,so that dislocations are piled up at the α/δ/βinterfaces during tensile deformation.This leads to dislocation slips being confined to individual α-laths,with differentslips and particularly pyramidal<c+a>slips being activated.The efficiency of wavy slip is promoted and the work hardening rate is enhanced.Finally,the combined effect of dispersed micro-shear bands and lath distortions is considered contributive for alleviating the stress concentration at grain boundaries,resulting in a high-promising synergy of enhanced ultimate tensile strength of 1080 MPa and good elongation to fracture of 13.6%.
基金supported by the National Natural Science Foundation of China(Grant Nos.12371393 and 11971150)Natural Science Foundation of Henan(Grant No.242300421047).
文摘In this paper,we design a new error estimator and give a posteriori error analysis for a poroelasticity model.To better overcome“locking phenomenon”on pressure and displacement,we proposed a new error estimators based on multiphysics discontinuous Galerkin method for the poroelasticity model.And we prove the upper and lower bound of the proposed error estimators,which are numerically demonstrated to be computationally very efficient.Finally,we present numerical examples to verify and validate the efficiency of the proposed error estimators,which show that the adaptive scheme can overcome“locking phenomenon”and greatly reduce the computation cost.
基金supported by the National Natural Science Foundation of China(Grant Nos.92252201 and 11721202)the Fundamental Research Funds for the Central Universities.
文摘We present the approaches to implementing the k-√k L turbulence model within the framework of the high-order discontinuous Galerkin(DG)method.We use the DG discretization to solve the full Reynolds-averaged Navier-Stokes equations.In order to enhance the robustness of approaches,some effective techniques are designed.The HWENO(Hermite weighted essentially non-oscillatory)limiting strategy is adopted for stabilizing the turbulence model variable k.Modifications have been made to the model equation itself by using the auxiliary variable that is always positive.The 2nd-order derivatives of velocities required in computing the von Karman length scale are evaluated in a way to maintain the compactness of DG methods.Numerical results demonstrate that the approaches have achieved the desirable accuracy for both steady and unsteady turbulent simulations.
基金supported by the National Natural Science Foundations of China(grant numbers U22A20601 and 52209142)the Opening fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection(Chengdu University of Technology)(grant number SKLGP2022K018)+1 种基金the Science&Technology Department of Sichuan Province(grant number 2023NSFSC0284)the Science and Technology Major Project of Tibetan Autonomous Region of China(grant number XZ202201ZD0003G)。
文摘Accurate dynamic modeling of landslides could help understand the movement mechanisms and guide disaster mitigation and prevention.Discontinuous deformation analysis(DDA)is an effective approach for investigating landslides.However,DDA fails to accurately capture the degradation in shear strength of rock joints commonly observed in high-speed landslides.In this study,DDA is modified by incorporating simplified joint shear strength degradation.Based on the modified DDA,the kinematics of the Baige landslide that occurred along the Jinsha River in China on 10 October 2018 are reproduced.The violent starting velocity of the landslide is considered explicitly.Three cases with different violent starting velocities are investigated to show their effect on the landslide movement process.Subsequently,the landslide movement process and the final accumulation characteristics are analyzed from multiple perspectives.The results show that the violent starting velocity affects the landslide motion characteristics,which is found to be about 4 m/s in the Baige landslide.The movement process of the Baige landslide involves four stages:initiation,high-speed sliding,impact-climbing,low-speed motion and accumulation.The accumulation states of sliding masses in different zones are different,which essentially corresponds to reality.The research results suggest that the modified DDA is applicable to similar high-level rock landslides.
基金supported by the National Natural Science Foundation of China(Grant No.12102247)the Technology Development Program(Grant No.JCKY2022110C119).
文摘The primary impediments impeding the implementation of high-order methods in simulating viscous flow over complex configurations are robustness and convergence.These challenges impose significant constraints on computational efficiency,particularly in the domain of engineering applications.To address these concerns,this paper proposes a robust implicit high-order discontinuous Galerkin(DG)method for solving compressible Navier-Stokes(NS)equations on arbitrary grids.The method achieves a favorable equilibrium between computational stability and efficiency.To solve the linear system,an exact Jacobian matrix solving strategy is employed for preconditioning and matrix-vector generation in the generalized minimal residual(GMRES)method.This approach mitigates numerical errors in Jacobian solution during implicit calculations and facilitates the implementation of an adaptive Courant-Friedrichs-Lewy(CFL)number increasing strategy,with the aim of improving convergence and robustness.To further enhance the applicability of the proposed method for intricate grid distortions,all simulations are performed in the reference domain.This practice significantly improves the reversibility of the mass matrix in implicit calculations.A comprehensive analysis of various parameters influencing computational stability and efficiency is conducted,including CFL number,Krylov subspace size,and GMRES convergence criteria.The computed results from a series of numerical test cases demonstrate the promising results achieved by combining the DG method,GMRES solver,exact Jacobian matrix,adaptive CFL number,and reference domain calculations in terms of robustness,convergence,and accuracy.These analysis results can serve as a reference for implicit computation in high-order calculations.
文摘The cohesive zone model(CZM)has been used widely and successfully in fracture propagation,but some basic problems are still to be solved.In this paper,artificial compliance and discontinuous force in CZM are investigated.First,theories about the cohesive element(local coordinate system,stiffness matrix,and internal nodal force)are presented.The local coordinate system is defined to obtain local separation;the stiffness matrix for an eight-node cohesive element is derived from the calculation of strain energy;internal nodal force between the cohesive element and bulk element is obtained from the principle of virtual work.Second,the reason for artificial compliance is explained by the effective stiffnesses of zero-thickness and finite-thickness cohesive elements.Based on the effective stiffness,artificial compliance can be completely removed by adjusting the stiffness of the finite-thickness cohesive element.This conclusion is verified from 1D and 3D simulations.Third,three damage evolution methods(monotonically increasing effective separation,damage factor,and both effective separation and damage factor)are analyzed.Under constant unloading and reloading conditions,the monotonically increasing damage factor method without discontinuous force and healing effect is a better choice than the other two methods.The proposed improvements are coded in LS-DYNA user-defined material,and a drop weight tear test verifies the improvements.
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 National Natural Science Foundation of China(12061080,12161087 and 12261093)the Science and Technology Project of the Education Department of Jiangxi Province(GJJ211601)supported by National Natural Science Foundation of China(11871305).
文摘We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.
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supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12071214)the Natural Science Foundation for Colleges and Universities of Jiangsu Province of China(Grant No.20KJB110011)+1 种基金supported by the National Science Foundation(Grant No.DMS-1620335)and the Simons Foundation(Grant No.637716)supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12272347).
文摘This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.
基金supported by the NSF under Grant DMS-1818467Simons Foundation under Grant 961585.
文摘In this paper,we develop bound-preserving discontinuous Galerkin(DG)methods for chemical reactive flows.There are several difficulties in constructing suitable numerical schemes.First of all,the density and internal energy are positive,and the mass fraction of each species is between 0 and 1.Second,due to the rapid reaction rate,the system may contain stiff sources,and the strong-stability-preserving explicit Runge-Kutta method may result in limited time-step sizes.To obtain physically relevant numerical approximations,we apply the bound-preserving technique to the DG methods.Though traditional positivity-preserving techniques can successfully yield positive density,internal energy,and mass fractions,they may not enforce the upper bound 1 of the mass fractions.To solve this problem,we need to(i)make sure the numerical fluxes in the equations of the mass fractions are consistent with that in the equation of the density;(ii)choose conservative time integrations,such that the summation of the mass fractions is preserved.With the above two conditions,the positive mass fractions have summation 1,and then,they are all between 0 and 1.For time discretization,we apply the modified Runge-Kutta/multi-step Patankar methods,which are explicit for the flux while implicit for the source.Such methods can handle stiff sources with relatively large time steps,preserve the positivity of the target variables,and keep the summation of the mass fractions to be 1.Finally,it is not straightforward to combine the bound-preserving DG methods and the Patankar time integrations.The positivity-preserving technique for DG methods requires positive numerical approximations at the cell interfaces,while Patankar methods can keep the positivity of the pre-selected point values of the target variables.To match the degree of freedom,we use polynomials on rectangular meshes for problems in two space dimensions.To evolve in time,we first read the polynomials at the Gaussian points.Then,suitable slope limiters can be applied to enforce the positivity of the solutions at those points,which can be preserved by the Patankar methods,leading to positive updated numerical cell averages.In addition,we use another slope limiter to get positive solutions used for the bound-preserving technique for the flux.Numerical examples are given to demonstrate the good performance of the proposed schemes.
基金supported by the NSF grant DMS-2111383Air Force Office of Scientific Research FA9550-18-1-0257the NSF grant DMS-2011838.
文摘This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software implementation.The C++software package called AdaM-DG,implementing the aSG-DG method,is available on GitHub at https://github.com/JuntaoHuang/adaptive-multiresolution-DG.The package is capable of treating a large class of high dimensional linear and nonlinear PDEs.We review the essential components of the algorithm and the functionality of the software,including the multiwavelets used,assembling of bilinear operators,fast matrix-vector product for data with hierarchical structures.We further demonstrate the performance of the package by reporting the numerical error and the CPU cost for several benchmark tests,including linear transport equations,wave equations,and Hamilton-Jacobi(HJ)equations.
基金supported by the NSF(Grant Nos.the NSF-DMS-1818924 and 2111253)the Air Force Office of Scientific Research FA9550-22-1-0390 and Department of Energy DE-SC0023164+1 种基金supported by the NSF(Grant Nos.NSF-DMS-1830838 and NSF-DMS-2111383)the Air Force Office of Scientific Research FA9550-22-1-0390.
文摘In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)system.The LoMaC property refers to the exact local conservation of macroscopic mass,momentum,and energy at the discrete level.The recently developed LoMaC low rank tensor algorithm(arXiv:2207.00518)simultaneously evolves the macroscopic conservation laws of mass,momentum,and energy using the kinetic flux vector splitting;then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables.This paper is a generalization of our previous work,but with DG discretization to take advantage of its compactness and flexibility in handling boundary conditions and its superior accuracy in the long term.The algorithm is developed in a similar fashion as that for a finite difference scheme,by observing that the DG method can be viewed equivalently in a nodal fashion.With the nodal DG method,assuming a tensorized computational grid,one will be able to(i)derive differentiation matrices for different nodal points based on a DG upwind discretization of transport terms,and(ii)define a weighted inner product space based on the nodal DG grid points.The algorithm can be extended to the high dimensional problems by hierarchical Tucker(HT)decomposition of solution tensors and a corresponding conservative projection algorithm.In a similar spirit,the algorithm can be extended to DG methods on nodal points of an unstructured mesh,or to other types of discretization,e.g.,the spectral method in velocity direction.Extensive numerical results are performed to showcase the efficacy of the method.
