In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondl...In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.展开更多
Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay di...Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.展开更多
The pursuit of Ag-based alloys with both high strength and toughness has posed a longstanding chal-lenge.In this study,we investigated the cluster strengthening and grain refinement toughening mecha-nisms in fully oxi...The pursuit of Ag-based alloys with both high strength and toughness has posed a longstanding chal-lenge.In this study,we investigated the cluster strengthening and grain refinement toughening mecha-nisms in fully oxidized AgMgNi alloys,which were internally oxidized at 800℃ for 8 h under an oxy-gen atmosphere.We found that Mg-O clusters contributed to the hardening(138 HV)and strengthening(376.9 MPa)of the AgMg alloy through solid solution strengthening effects,albeit at the expense of duc-tility.To address this limitation,we introduced Ni nanoparticles into the AgMg alloy,resulting in signifi-cant grain refinement within its microstructure.Specifically,the grain size decreased from 67.2μm in the oxidized AgMg alloy to below 6.0μm in the oxidized AgMgNi alloy containing 0.3 wt%Ni.Consequently,the toughness increased significantly,rising from toughness value of 2177.9 MJ m^(-3) in the oxidized AgMg alloy to 6186.1 MJ m^(-3) in the oxidized AgMgNi alloy,representing a remarkable 2.8-fold enhancement.Furthermore,the internally oxidized AgMgNi alloy attained a strength of up to 387.6 MPa,comparable to that of the internally oxidized AgMg alloy,thereby demonstrating the successful realization of concurrent strengthening and toughening.These results collectively offer a novel approach for the design of high-performance alloys through the synergistic combination of cluster strengthening and grain refinement toughening.展开更多
Ammonia and nitric acid,versatile industrial feedstocks,and burgeoning clean energy vectors hold immense promise for sustainable development.However,Haber–Bosch and Ostwald processes,which generates carbon dioxide as...Ammonia and nitric acid,versatile industrial feedstocks,and burgeoning clean energy vectors hold immense promise for sustainable development.However,Haber–Bosch and Ostwald processes,which generates carbon dioxide as massive by-product,contribute to greenhouse effects and pose environmental challenges.Thus,the pursuit of nitrogen fixation through carbon–neutral pathways under benign conditions is a frontier of scientific topics,with the harnessing of solar energy emerging as an enticing and viable option.This review delves into the refinement strategies for scale-up mild photocatalytic nitrogen fixation,fields ripe with potential for innovation.The narrative is centered on enhancing the intrinsic capabilities of catalysts to surmount current efficiency barriers.Key focus areas include the in-depth exploration of fundamental mechanisms underpinning photocatalytic procedures,rational element selection,and functional planning,state-of-the-art experimental protocols for understanding photo-fixation processes,valid photocatalytic activity evaluation,and the rational design of catalysts.Furthermore,the review offers a suite of forward-looking recommendations aimed at propelling the advancement of mild nitrogen photo-fixation.It scrutinizes the existing challenges and prospects within this burgeoning domain,aspiring to equip researchers with insightful perspectives that can catalyze the evolution of cutting-edge nitrogen fixation methodologies and steer the development of next-generation photocatalytic systems.展开更多
Due to the low content of alloying elements and the lack of effective nucleation sites,the fusion zone(FZ)of tungsten inert gas(TIG)welded AZ31 alloy typically exhibits undesirable coarse columnar grains,which can res...Due to the low content of alloying elements and the lack of effective nucleation sites,the fusion zone(FZ)of tungsten inert gas(TIG)welded AZ31 alloy typically exhibits undesirable coarse columnar grains,which can result in solidification defects and reduced mechanical properties.In this work,a novel welding wire containing MgO particles has been developed to promote columnar-to-equiaxed transition(CET)in the FZ of TIG-welded AZ31 alloy.The results show the achievement of a fully equiaxed grain structure in the FZ,with a significant 71.9%reduction in grain size to 41 μm from the original coarse columnar dendrites.Furthermore,the combination of using MgO-containing welding wire and pulse current can further refine the grain size to 25.6 μm.Microstructural analyses reveal the homogeneous distribution of MgO particles in the FZ.The application of pulse current results in an increase in the number density of MgO(1-2 μm)from 5.16 × 10^(4) m^(-3) to 6.18 × 10^(4) m^(-3).The good crystallographic matching relationship between MgO and α-Mg matrix,characterized by the orientation relationship of[11(2)0]α-Mg//[0(1)1]MgO and(0002)_(α-Mg)//(111)_(MgO),indicates that the MgO particles can act as effective nucleation sites for α-Mg to reduce nucleation undercooling.According to the Hunt criteria,the critical temperature gradient for CET is greatly enhanced due to the significantly increased number density of MgO nucleation sites.In addition,the correlation with the thermal simulation results reveals a transition in the solidification conditions within the welding pool from the columnar grain zone to the equiaxed grain zone in the CET map,leading to the realization of CET.The exceptional grain refinement has contributed to a simultaneous improvement in the strength and plasticity of welded joints.This study presents a novel strategy for controlling equiaxed microstructure and optimizing mechanical properties in fusion welding or wire and arc additive manufacturing of Mg alloy components.展开更多
To investigate the effect of microstructure evolution on corrosion behavior and strengthening mechanism of Mg-1Zn-1Ca(wt.%)alloys,as-cast Mg-1Zn-1Ca alloys were performed by equal channel angular pressing(ECAP)with 1 ...To investigate the effect of microstructure evolution on corrosion behavior and strengthening mechanism of Mg-1Zn-1Ca(wt.%)alloys,as-cast Mg-1Zn-1Ca alloys were performed by equal channel angular pressing(ECAP)with 1 and 4 passes.The corrosion behavior and mechanical properties of alloys were investigated by optical microscopy(OM),scanning electron microscopy(SEM),electron backscatter diffraction(EBSD),electrochemical tests,immersion tests and tensile tests.The results showed that mechanical properties improved after ECAP 1 pass;however,the corrosion resistance deteriorated due to high-density dislocations and fragmented secondary phases by ECAP.In contrast,synchronous improvement in the mechanical properties and corrosion resistance was achieved though grain refinement after ECAP 4 passes;fine grains led to a significant improvement in the yield strength,ultimate tensile strength,elongation,and corrosion rate of 103 MPa,223 MPa,30.5%,and 1.5843 mm/a,respectively.The enhanced corrosion resistance was attributed to the formation of dense corrosion product films by finer grains and the barrier effect by high-density grain boundaries.These results indicated that Mg-1Zn-1Ca alloy has a promising potential for application in biomedical materials.展开更多
This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ...This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.展开更多
Three types of NdFeB magnets with the same composition and different grain sizes were prepared,and then the grain boundary diffusion was conducted using metal Tb under the same technical parameters.The effect of grain...Three types of NdFeB magnets with the same composition and different grain sizes were prepared,and then the grain boundary diffusion was conducted using metal Tb under the same technical parameters.The effect of grain size on the grain boundary diffusion process and properties of sintered NdFeB magnets was investigated.The diffusion process was assessed using X-ray diffractometer,field emission scanning electron microscope,and electron probe microanalyzer.The magnetic properties of the magnet before and after diffusion were investigated.The results show that the grain refinement of the magnet leads to higher Tb utilization efficiency and results in higher coercivity at different temperatures.It can be attributed to the formation of a deeper and more complete core-shell structure,resulting in better magnetic isolation and higher anisotropy of the Nd_(2)Fe_(14)B grains.This work may shed light on developing high coercivity with low heavy rare earth elements through grain refinement.展开更多
Al-Cu-Mg-Ag alloys have become a research hotspot because of its good heat resistance.Its excellent mechanical properties are inseparable from the regulation of the structure by researchers.The method of material stru...Al-Cu-Mg-Ag alloys have become a research hotspot because of its good heat resistance.Its excellent mechanical properties are inseparable from the regulation of the structure by researchers.The method of material structure simulation has become more and more perfect.This study employs numerical simulation to investigate the microstructure evolution of Al-Cu-Mg-Ag alloys during solidification with the aim of controlling its structure.The size distribution of Ti-containing particles in an Al-Ti-B master alloy was characterized via microstructure observation,serving as a basis for optimizing the nucleation density parameters for particles of varying radii in the phase field model.The addition of refiner inhibited the growth of dendrites and no longer produced coarse dendrites.With the increase of refiner,the grains gradually tended to form cellular morphology.The refined grains were about 100μm in size.Experimental validation of the simulated as-cast grain morphology was conducted.The samples were observed by metallographic microscope and scanning electron microscope.The addition of refiner had a significant effect on the refinement of the alloy,and the average grain size after refinement was also about 100μm.At the same time,the XRD phase identification of the alloy was carried out.The observation of the microstructure morphology under the scanning electron microscope showed that the precipitated phase was mainly concentrated on the grain boundary.The Al_(2)Cu accounted for about 5%,and the matrix phase FCC accounted for about 95%,which also corresponded well with the simulation results.展开更多
In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belon...In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belongs to the Sobolev space H'(R)for some s>2.In addition,we obtain the weak formulation of this equation and prove the existence of both single peakon solution and a multi-peakon dynamic system.展开更多
We study the Cauchy problem of the Kolmogorov-Fokker-Planck equations and show that the solution enjoys an analytic smoothing effect with L?initial datum for positive time.
With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixe...With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.展开更多
In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations,numerous tricks have been proposed.The goal of this short review is to explain how a theorem of Eremenko on meromorphic...In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations,numerous tricks have been proposed.The goal of this short review is to explain how a theorem of Eremenko on meromorphic solutions of some nonlinear ODEs together with some classical,19th-century results,can be turned into algorithms(thus avoiding ad hoc assumptions)which provide all(as opposed to some)solutions in a precise class.To illustrate these methods,we present some new such exact solutions,physically relevant.展开更多
In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary varia...In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.展开更多
In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat eq...In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat equation defined on[0,T]×[0,1]driven by double-parameter fractional noise.展开更多
In this paper,we study the following pseudo-relativistic Hartree equation i∂_(t)Ψ-(|x|^(-1)*|Ψ|^(2))Ψwith(t,x)∈R×R^(3)We mainly focus on the normalized ground state solitary waves of the formΨ(t,x)=e^(itμ)...In this paper,we study the following pseudo-relativistic Hartree equation i∂_(t)Ψ-(|x|^(-1)*|Ψ|^(2))Ψwith(t,x)∈R×R^(3)We mainly focus on the normalized ground state solitary waves of the formΨ(t,x)=e^(itμ)φm(x)with||φm||_(2)^(2)=N.We investigate limit behaviors of energy and minimizer of the corresponding frinetional of this equationas m→+∞.We prove that m_(k)^(-3/2)φm_(k)→φ∞(x)in H^(-1/2(R^(3)))by energy method and lim_(m→+∞)+m^(-1)e(N)=e(N),whereφ_(m)(β∞)is a minimizer of e(N)(e(N).展开更多
Let a_(1),a_(2),a_(3)be nonzero integers with gcd(a_(1),a_(2),a_(3))=1,and let k be any positive integer,K=max[3,|a_(1)|,|a_(2)|,|a_(3)|,k].Suppose that l_(1),l_(2),l_(3)are integers each coprime to k.Suppose further ...Let a_(1),a_(2),a_(3)be nonzero integers with gcd(a_(1),a_(2),a_(3))=1,and let k be any positive integer,K=max[3,|a_(1)|,|a_(2)|,|a_(3)|,k].Suppose that l_(1),l_(2),l_(3)are integers each coprime to k.Suppose further that b is any integer satisfying some necessary congruent conditions.The solvability of linear equation a_(1)p_(1)+a_(2)p_(2)+a_(3)p_(3)=b(p_(j)=l_(j)(mod k),1≤j≤3)with prime variables pi,p_(2),ps is investigated.It is proved that if ai,a_(2),a_(3)are all positive,then the above equation is solvable whenever b≥K^(25);if a,a_(2),a_(3)are not all of the same sign,then the above equation has a solution p_(1),p_(2),p_(3)satisfying max(p_(1),p_(2),p_(3))≤3|b|+K^(25).展开更多
This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–M...This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.展开更多
基金Supported by National Natural Science Foundation of China(12101482)Postdoctoral Science Foundation of China(2022M722604)+2 种基金General Project of Science and Technology of Shaanxi Province(2023-YBSF-372)The Natural Science Foundation of Shaan Xi Province(2023-JCQN-0016)Shannxi Mathmatical Basic Science Research Project(23JSQ042)。
文摘In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.
文摘Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.
基金supported by the National Natural Science Foundation of China(Nos.51977027 and 51967008)the Scientific and Technological Project of Yunnan Precious Metals Lab-oratory(Nos.YPML-2023050250 and YPML-2022050206).
文摘The pursuit of Ag-based alloys with both high strength and toughness has posed a longstanding chal-lenge.In this study,we investigated the cluster strengthening and grain refinement toughening mecha-nisms in fully oxidized AgMgNi alloys,which were internally oxidized at 800℃ for 8 h under an oxy-gen atmosphere.We found that Mg-O clusters contributed to the hardening(138 HV)and strengthening(376.9 MPa)of the AgMg alloy through solid solution strengthening effects,albeit at the expense of duc-tility.To address this limitation,we introduced Ni nanoparticles into the AgMg alloy,resulting in signifi-cant grain refinement within its microstructure.Specifically,the grain size decreased from 67.2μm in the oxidized AgMg alloy to below 6.0μm in the oxidized AgMgNi alloy containing 0.3 wt%Ni.Consequently,the toughness increased significantly,rising from toughness value of 2177.9 MJ m^(-3) in the oxidized AgMg alloy to 6186.1 MJ m^(-3) in the oxidized AgMgNi alloy,representing a remarkable 2.8-fold enhancement.Furthermore,the internally oxidized AgMgNi alloy attained a strength of up to 387.6 MPa,comparable to that of the internally oxidized AgMg alloy,thereby demonstrating the successful realization of concurrent strengthening and toughening.These results collectively offer a novel approach for the design of high-performance alloys through the synergistic combination of cluster strengthening and grain refinement toughening.
基金financially supported by the National Natural Science Foundation of China(No.21675131)the Volkswagen Foundation(Freigeist Fellowship No.89592)+1 种基金the Natural Science Foundation of Chongqing(No.2020jcyj-zdxmX0003,CSTB2023NSCQ-MSX0924)the National Research Foundation,Singapore,and A*STAR(Agency for Science Technology and Research)under its LCER Phase 2 Programme Hydrogen&Emerging Technologies FI,Directed Hydrogen Programme(Award No.U2305D4003).
文摘Ammonia and nitric acid,versatile industrial feedstocks,and burgeoning clean energy vectors hold immense promise for sustainable development.However,Haber–Bosch and Ostwald processes,which generates carbon dioxide as massive by-product,contribute to greenhouse effects and pose environmental challenges.Thus,the pursuit of nitrogen fixation through carbon–neutral pathways under benign conditions is a frontier of scientific topics,with the harnessing of solar energy emerging as an enticing and viable option.This review delves into the refinement strategies for scale-up mild photocatalytic nitrogen fixation,fields ripe with potential for innovation.The narrative is centered on enhancing the intrinsic capabilities of catalysts to surmount current efficiency barriers.Key focus areas include the in-depth exploration of fundamental mechanisms underpinning photocatalytic procedures,rational element selection,and functional planning,state-of-the-art experimental protocols for understanding photo-fixation processes,valid photocatalytic activity evaluation,and the rational design of catalysts.Furthermore,the review offers a suite of forward-looking recommendations aimed at propelling the advancement of mild nitrogen photo-fixation.It scrutinizes the existing challenges and prospects within this burgeoning domain,aspiring to equip researchers with insightful perspectives that can catalyze the evolution of cutting-edge nitrogen fixation methodologies and steer the development of next-generation photocatalytic systems.
基金supported by the National Natural Science Foundation of China(No.51871155).
文摘Due to the low content of alloying elements and the lack of effective nucleation sites,the fusion zone(FZ)of tungsten inert gas(TIG)welded AZ31 alloy typically exhibits undesirable coarse columnar grains,which can result in solidification defects and reduced mechanical properties.In this work,a novel welding wire containing MgO particles has been developed to promote columnar-to-equiaxed transition(CET)in the FZ of TIG-welded AZ31 alloy.The results show the achievement of a fully equiaxed grain structure in the FZ,with a significant 71.9%reduction in grain size to 41 μm from the original coarse columnar dendrites.Furthermore,the combination of using MgO-containing welding wire and pulse current can further refine the grain size to 25.6 μm.Microstructural analyses reveal the homogeneous distribution of MgO particles in the FZ.The application of pulse current results in an increase in the number density of MgO(1-2 μm)from 5.16 × 10^(4) m^(-3) to 6.18 × 10^(4) m^(-3).The good crystallographic matching relationship between MgO and α-Mg matrix,characterized by the orientation relationship of[11(2)0]α-Mg//[0(1)1]MgO and(0002)_(α-Mg)//(111)_(MgO),indicates that the MgO particles can act as effective nucleation sites for α-Mg to reduce nucleation undercooling.According to the Hunt criteria,the critical temperature gradient for CET is greatly enhanced due to the significantly increased number density of MgO nucleation sites.In addition,the correlation with the thermal simulation results reveals a transition in the solidification conditions within the welding pool from the columnar grain zone to the equiaxed grain zone in the CET map,leading to the realization of CET.The exceptional grain refinement has contributed to a simultaneous improvement in the strength and plasticity of welded joints.This study presents a novel strategy for controlling equiaxed microstructure and optimizing mechanical properties in fusion welding or wire and arc additive manufacturing of Mg alloy components.
基金financially supported by the National Natural Science Foundation of China(No.52374395)the Natural Science Foundation of Shanxi Province,China(Nos.20210302123135,202303021221143)+5 种基金the Scientific and Technological Achievements Transformation Guidance Special Project of Shanxi Province,China(Nos.202104021301022,202204021301009)the Central Government Guided Local Science and Technology Development Projects,China(No.YDZJSX20231B003)the Ministry of Science and Higher Education of the Russian Federation for financial support under the Megagrant(No.075-15-2022-1133)the National Research Foundation(NRF)grant funded by the Ministry of Science and ICT of Korea through the Research Institute of Advanced Materials(No.2015R1A2A1A01006795)the China Postdoctoral Science Foundation(No.2022M710541)the Research Project supported by Shanxi Scholarship Council of China(No.2022-038)。
文摘To investigate the effect of microstructure evolution on corrosion behavior and strengthening mechanism of Mg-1Zn-1Ca(wt.%)alloys,as-cast Mg-1Zn-1Ca alloys were performed by equal channel angular pressing(ECAP)with 1 and 4 passes.The corrosion behavior and mechanical properties of alloys were investigated by optical microscopy(OM),scanning electron microscopy(SEM),electron backscatter diffraction(EBSD),electrochemical tests,immersion tests and tensile tests.The results showed that mechanical properties improved after ECAP 1 pass;however,the corrosion resistance deteriorated due to high-density dislocations and fragmented secondary phases by ECAP.In contrast,synchronous improvement in the mechanical properties and corrosion resistance was achieved though grain refinement after ECAP 4 passes;fine grains led to a significant improvement in the yield strength,ultimate tensile strength,elongation,and corrosion rate of 103 MPa,223 MPa,30.5%,and 1.5843 mm/a,respectively.The enhanced corrosion resistance was attributed to the formation of dense corrosion product films by finer grains and the barrier effect by high-density grain boundaries.These results indicated that Mg-1Zn-1Ca alloy has a promising potential for application in biomedical materials.
基金Supported by National Science Foundation of China(11971027,12171497)。
文摘This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.
基金Key Research and Development Program of Shandong Province(2021CXGC010310)Shandong Province Science and Technology Small and Medium Sized Enterprise Innovation Ability Enhancement Project(2023TSGC0287,2024TSGC0519)+1 种基金Shandong Provincial Natural Science Foundation(ZR2022ME222)National Natural Science Foundation of China(51702187)。
文摘Three types of NdFeB magnets with the same composition and different grain sizes were prepared,and then the grain boundary diffusion was conducted using metal Tb under the same technical parameters.The effect of grain size on the grain boundary diffusion process and properties of sintered NdFeB magnets was investigated.The diffusion process was assessed using X-ray diffractometer,field emission scanning electron microscope,and electron probe microanalyzer.The magnetic properties of the magnet before and after diffusion were investigated.The results show that the grain refinement of the magnet leads to higher Tb utilization efficiency and results in higher coercivity at different temperatures.It can be attributed to the formation of a deeper and more complete core-shell structure,resulting in better magnetic isolation and higher anisotropy of the Nd_(2)Fe_(14)B grains.This work may shed light on developing high coercivity with low heavy rare earth elements through grain refinement.
文摘Al-Cu-Mg-Ag alloys have become a research hotspot because of its good heat resistance.Its excellent mechanical properties are inseparable from the regulation of the structure by researchers.The method of material structure simulation has become more and more perfect.This study employs numerical simulation to investigate the microstructure evolution of Al-Cu-Mg-Ag alloys during solidification with the aim of controlling its structure.The size distribution of Ti-containing particles in an Al-Ti-B master alloy was characterized via microstructure observation,serving as a basis for optimizing the nucleation density parameters for particles of varying radii in the phase field model.The addition of refiner inhibited the growth of dendrites and no longer produced coarse dendrites.With the increase of refiner,the grains gradually tended to form cellular morphology.The refined grains were about 100μm in size.Experimental validation of the simulated as-cast grain morphology was conducted.The samples were observed by metallographic microscope and scanning electron microscope.The addition of refiner had a significant effect on the refinement of the alloy,and the average grain size after refinement was also about 100μm.At the same time,the XRD phase identification of the alloy was carried out.The observation of the microstructure morphology under the scanning electron microscope showed that the precipitated phase was mainly concentrated on the grain boundary.The Al_(2)Cu accounted for about 5%,and the matrix phase FCC accounted for about 95%,which also corresponded well with the simulation results.
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
文摘In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belongs to the Sobolev space H'(R)for some s>2.In addition,we obtain the weak formulation of this equation and prove the existence of both single peakon solution and a multi-peakon dynamic system.
基金Supported by NSFC (No.12031006)Fundamental Research Funds for the Central Universities of China。
文摘We study the Cauchy problem of the Kolmogorov-Fokker-Planck equations and show that the solution enjoys an analytic smoothing effect with L?initial datum for positive time.
基金Supported by the National Natural Science Foundation of China(12201368,62376252)Key Project of Natural Science Foundation of Zhejiang Province(LZ22F030003)Zhejiang Province Leading Geese Plan(2024C02G1123882,2024C01SA100795).
文摘With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.
基金partially supported by RGC(No.17307420)supported by NSFC(No.12471077)。
文摘In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations,numerous tricks have been proposed.The goal of this short review is to explain how a theorem of Eremenko on meromorphic solutions of some nonlinear ODEs together with some classical,19th-century results,can be turned into algorithms(thus avoiding ad hoc assumptions)which provide all(as opposed to some)solutions in a precise class.To illustrate these methods,we present some new such exact solutions,physically relevant.
基金Supported by the Research Project Supported of Shanxi Scholarship Council of China(No.2021-029)Shanxi Provincial International Cooperation Base and Platform Project(202104041101019)Shanxi Province Natural Science Research(202203021211129)。
文摘In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.
基金Partially supported by Postgraduate Research and Practice Innovation Program of Jiangsu Province(Nos.KYCX22-2211,KYCX22-2205)。
文摘In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat equation defined on[0,T]×[0,1]driven by double-parameter fractional noise.
文摘In this paper,we study the following pseudo-relativistic Hartree equation i∂_(t)Ψ-(|x|^(-1)*|Ψ|^(2))Ψwith(t,x)∈R×R^(3)We mainly focus on the normalized ground state solitary waves of the formΨ(t,x)=e^(itμ)φm(x)with||φm||_(2)^(2)=N.We investigate limit behaviors of energy and minimizer of the corresponding frinetional of this equationas m→+∞.We prove that m_(k)^(-3/2)φm_(k)→φ∞(x)in H^(-1/2(R^(3)))by energy method and lim_(m→+∞)+m^(-1)e(N)=e(N),whereφ_(m)(β∞)is a minimizer of e(N)(e(N).
文摘Let a_(1),a_(2),a_(3)be nonzero integers with gcd(a_(1),a_(2),a_(3))=1,and let k be any positive integer,K=max[3,|a_(1)|,|a_(2)|,|a_(3)|,k].Suppose that l_(1),l_(2),l_(3)are integers each coprime to k.Suppose further that b is any integer satisfying some necessary congruent conditions.The solvability of linear equation a_(1)p_(1)+a_(2)p_(2)+a_(3)p_(3)=b(p_(j)=l_(j)(mod k),1≤j≤3)with prime variables pi,p_(2),ps is investigated.It is proved that if ai,a_(2),a_(3)are all positive,then the above equation is solvable whenever b≥K^(25);if a,a_(2),a_(3)are not all of the same sign,then the above equation has a solution p_(1),p_(2),p_(3)satisfying max(p_(1),p_(2),p_(3))≤3|b|+K^(25).
基金supported by the PhD Research Startup Foundation of Hubei University of Economics(Grand No.XJ23BS42).
文摘This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.
