A class of nonlinear for singularly perturbed problems for reaction diffusion equations with time delays are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of ...A class of nonlinear for singularly perturbed problems for reaction diffusion equations with time delays are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied.展开更多
Photoelectrochemical(PEC) water splitting using solar energy has attracted great attention for generation of renewable hydrogen with less carbon footprint, while there are enormous challenges that still remain for imp...Photoelectrochemical(PEC) water splitting using solar energy has attracted great attention for generation of renewable hydrogen with less carbon footprint, while there are enormous challenges that still remain for improving solar energy water splitting efficiency, due to limited light harvesting, energy loss associated to fast recombination of photogenerated charge carriers, as well as electrode degradation. This overview focuses on the recent development about catalyst nanomaterials and nanostructures in different PEC water splitting systems. As photoanode, Au nanoparticle-decorated TiO_2 nanowire electrodes exhibited enhanced photoactivity in both the UV and the visible regions due to surface plasmon resonance of Au and showed the largest photocurrent generation of up to 710 nm. Pt/Cd S/CGSe electrodes were developed as photocathode. With the role of p–n heterojunction, the photoelectrode showed high stability and evolved hydrogen continuously for more than 10 days. Further, in the Z-scheme system(Bi_2S_3/TNA as photoanode and Pt/Si PVC as photocathode at the same time), a self-bias(open-circuit voltage Voc= 0.766 V) was formed between two photoelectrodes, which could facilitate photogenerated charge transfers and enhance the photoelectrochemical performance, and which might provide new hints for PEC water splitting. Meanwhile, the existing problems and prospective solutions have also been reviewed.展开更多
Understanding the reduction behaviors and characteristics of the end products of Fe-Cr-O systems is very important not only for maximizing the recovery of metals from stainless steel dust but also for the subsequent r...Understanding the reduction behaviors and characteristics of the end products of Fe-Cr-O systems is very important not only for maximizing the recovery of metals from stainless steel dust but also for the subsequent reuse in metallurgical process. The present work first predicted the possible products thermodynamically when FeCr204 was reduced by C. The reduction behaviors by graphite of three kinds of Fe-Cr-O systems, i.e., FeCr204, Fe203q-Cr203, and Feq-Cr203, were then investigated in 1350-1550℃. Further, the microstructures of final products and element distribution conditions were examined. The results suggest that, thermodynamically, the mass of products for the carbothermal reduction of FeCr204 is a strong function of temperature, and the initial carbon content is used. More Fe-Cr-C solution and less residual carbon content are obtained at higher temperatures and lower no：no ratios （the initial molar ratio of C to O in the sample）. Experimental data show that the sample amount tends to affect the reduction rate, and the residual carbon content strongly depends on nc：no. With regard to the phases present in products during the reaction process, metal carbides tend to form in the initial stage, whereas Fe-Cr-C solution forms when the degree of reduction is sufficiently high.展开更多
The integer-order interdependent calcium([Ca^(2+)])and nitric oxide(NO)systems are unable to shed light on the influences of the superdiffusion and memory in triggering Brownian motion(BM)in neurons.Therefore,a mathem...The integer-order interdependent calcium([Ca^(2+)])and nitric oxide(NO)systems are unable to shed light on the influences of the superdiffusion and memory in triggering Brownian motion(BM)in neurons.Therefore,a mathematical model is constructed for the fractional-order nonlinear spatiotemporal systems of[Ca^(2+)]and NO incorporating reaction-diffusion equations in neurons.The two-way feedback process between[Ca^(2+)]and NO systems through calcium feedback on NO production and NO feedback on calcium through cyclic guanosine monophosphate(cGMP)with plasmalemmal[Ca^(2+)]-ATPase(PMCA)was incorporated in the model.The Crank–Nicholson scheme(CNS)with Grunwald approximation along spatial derivatives and L1 scheme along temporal derivatives with Gauss–Seidel(GS)iterations were employed.The numerical outcomes were analyzed to get insights into superdiffusion,buffer,and memory exhibiting BM of[Ca^(2+)]and NO systems.The conditions,events and mechanisms leading to dysfunctions in calcium and NO systems and causing different diseases like Parkinson’s were explored in neurons.展开更多
The tandem catalytic functionalization/carboxylation of double as well as triple carbon-carbon bonds with CO_(2) represent an emerging research area in synthetic organic methodology.In particular,the combination of mi...The tandem catalytic functionalization/carboxylation of double as well as triple carbon-carbon bonds with CO_(2) represent an emerging research area in synthetic organic methodology.In particular,the combination of mild reaction conditions,stoichiometric acceptor/donorless conditions(visible light photoredox catalysis)and chiral catalysts contributed to a rapid development of this intriguing research area capable of creating chemical diversity/complexity from readily available unsaturated hydrocarbons and CO2 as a C1-buinding block.The most recent developments in the field have been collected in the present review article and organized,based on the different sets ofπ-systems/intermediates/reactive partners employed(i.e.,nickelalactones,organo-halides)as well as synthetic strategies(i.e.,visible-light photo redox catalysis).展开更多
This paper studies the reentry attitude tracking control problem for hypersonic vehicles(HSV)equipped with reaction control systems(RCS)and aerodynamic surfaces.The attitude dynamical model of the hypersonic vehicles ...This paper studies the reentry attitude tracking control problem for hypersonic vehicles(HSV)equipped with reaction control systems(RCS)and aerodynamic surfaces.The attitude dynamical model of the hypersonic vehicles is established,and the simplified longitudinal and lateral dynamic models are obtained,respectively.Then,the compound control allocation strategy is provided and the model predictive controller is designed for the pitch channel.Furthermore,considering the complicated jet interaction effect of HSV during RCS is working,an improved model predictive control approach is presented by introducing the online parameter estimation of the jet interaction coefficient for dealing with the uncertainty and disturbance.Moreover,considering the strong coupling effect between the yaw channel and roll channel,a coupled model predictive controller is designed by introducing the feedback of sideslip angle into the roll control channel to eliminate the coupling effect.Finally,the comparison simulations using the classical control method,MPC and IMPC approach are given to demonstrate the effectiveness and efficiency of the presented IMPC scheme.展开更多
This paper is devoted to the investigation of stability for a class of coupled impulsive Markovian jump reaction-diffusion systems on networks(CIMJRDSNs). By using graph theory, a systematic method is provided to cons...This paper is devoted to the investigation of stability for a class of coupled impulsive Markovian jump reaction-diffusion systems on networks(CIMJRDSNs). By using graph theory, a systematic method is provided to construct global Lyapunov functions for the CIMJRDSNs. Based on Lyapunov functions and stochastic analysis method, some novel stability principles associated with the topology property of the networks are established.展开更多
A thorough understanding of the fundamental electrochemical and chemical processes in batteries is crucial to advancing energy density and power density.However,the characterizations of such processes are complex.In-s...A thorough understanding of the fundamental electrochemical and chemical processes in batteries is crucial to advancing energy density and power density.However,the characterizations of such processes are complex.In-situ electrochemical nuclear magnetic resonance(EC-NMR)offers the capability to collect real-time data during battery operation,furnishing insights into the local structures and ionic dynamics of materials by monitoring changes in the chemical environment around the nuclei.EC-NMR also has the advantages of being both quantitative and non-destructive.This paper systematically reviews the design of EC-NMR approach,and delves into the applications and progress of EC-NMR concerning battery reaction mechanisms,failure mechanisms,and overall battery systems.The review culminates in a comprehensive summary of the perspective and challenges associated with EC-NMR.展开更多
Molybdenum disulfide (MoS_(2)) with low cost, high activity and high earth abundance has been found to be a promising catalyst for the hydrogen evolution reaction (HER), but its catalytic activity is considerably limi...Molybdenum disulfide (MoS_(2)) with low cost, high activity and high earth abundance has been found to be a promising catalyst for the hydrogen evolution reaction (HER), but its catalytic activity is considerably limited due to its inert basal planes. Here, through the combination of theory and experiment, we propose that doping Ni in MoS_(2) as catalyst can make it have excellent catalytic activity in different reaction systems. In the EY/TEOA system, the maximum hydrogen production rate of EY/Ni-Mo-S is 2.72 times higher than that of pure EY, which confirms the strong hydrogen evolution activity of Ni-Mo-S nanosheets as catalysts. In the lactic acid and Na_(2)S/Na_(2)SO_(3) systems, when Ni-Mo-S is used as co-catalyst to compound with ZnIn_(2)S_(4) (termed as Ni-Mo-S/ZnIn_(2)S_(4)), the maximum hydrogen evolution rates in the two systems are 5.28 and 2.33 times higher than those of pure ZnIn_(2)S_(4), respectively. The difference in HER enhancement is because different systems lead to different sources of protons, thus affecting hydrogen evolution activity. Theoretically, we further demonstrate that the Ni-Mo-S nanosheets have a narrower band gap than MoS_(2), which is conducive to the rapid transfer of charge carriers and thus result in multi-photocatalytic reaction systems with excellent activity. The proposed atomic doping strategy provides a simple and promising approach for the design of photocatalysts with high activity and stability in multi-reaction systems.展开更多
In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has a...In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has attracted a lot of attention and many new types of nonplanar traveling waves have been observed for scalar reaction-diffusion equations with various nonlinearities. In this paper, by using the comparison argument and constructing appropriate super- and subsolutions, we study the existence, uniqueness and stability of three- dimensional traveling fronts of pyramidal shape for monotone bistable systems of reaction-diffusion equations in R3. The pyramidal traveling fronts are characterized as either a combination of planar traveling fronts on the lateral surfaces or a combination of two-dimensional V-form waves on the edges of the pyramid. In particular, our results are applicable to some important models in biology, such as Lotk,u-Volterra competition-diffusion systems with or without spatio-temporal delays, and reaction-diffusion systems of multiple obligate mutualists.展开更多
Bulk-surface partial differential equations(BS-PDEs)are prevalent in manyapplications such as cellular,developmental and plant biology as well as in engineeringand material sciences.Novel numerical methods for BS-PDEs...Bulk-surface partial differential equations(BS-PDEs)are prevalent in manyapplications such as cellular,developmental and plant biology as well as in engineeringand material sciences.Novel numerical methods for BS-PDEs in three space dimensions(3D)are sparse.In this work,we present a bulk-surface virtual elementmethod(BS-VEM)for bulk-surface reaction-diffusion systems,a form of semilinearparabolic BS-PDEs in 3D.Unlike previous studies in two space dimensions(2D),the3D bulk is approximated with general polyhedra,whose outer faces constitute a flatpolygonal approximation of the surface.For this reason,the method is restricted tothe lowest order case where the geometric error is not dominant.The BS-VEM guaranteesall the advantages of polyhedral methods such as easy mesh generation andfast matrix assembly on general geometries.Such advantages are much more relevantthan in 2D.Despite allowing for general polyhedra,general nonlinear reaction kineticsand general surface curvature,the method only relies on nodal values without needingadditional evaluations usually associated with the quadrature of general reactionkinetics.This latter is particularly costly in 3D.The BS-VEM as implemented in thisstudy retains optimal convergence of second order in space.展开更多
This paper is concerned with the existence of entire solutions of Lotka Volterra competition-diffusion model. Using the comparing argument and sub-super solutions method, we obtain the existence of entire solutions wh...This paper is concerned with the existence of entire solutions of Lotka Volterra competition-diffusion model. Using the comparing argument and sub-super solutions method, we obtain the existence of entire solutions which behave as two wave fronts coming from the both sides of x-axis, where an entire solution is meant by a classical solution defined for all space and time variables.展开更多
The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved i...The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .展开更多
Zoning in ore bodies, ore deposits and ore regions are recognized as temporal-spatial structures generated by the dynamics of ore- forming processes. Viewed from the theory of dissipative structures, ore zoning is a k...Zoning in ore bodies, ore deposits and ore regions are recognized as temporal-spatial structures generated by the dynamics of ore- forming processes. Viewed from the theory of dissipative structures, ore zoning is a kind of self-organization phenomenon occurring in far from-equilibrium geochemical dynamic systems. Therefore,kinetic and dynamic approaches must be taken to reveal the mechanisms of ore zoning. Two dominant coupling processes leading to ore zoning——reaction-transport feedbacks and double-diffusive convection——are discussed.展开更多
基金The Project Supported by National Natural Science Foundation of China(10071045)
文摘A class of nonlinear for singularly perturbed problems for reaction diffusion equations with time delays are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied.
基金supported by the EU-China EcoFuel project(FP7,246772)from the European Commission
文摘Photoelectrochemical(PEC) water splitting using solar energy has attracted great attention for generation of renewable hydrogen with less carbon footprint, while there are enormous challenges that still remain for improving solar energy water splitting efficiency, due to limited light harvesting, energy loss associated to fast recombination of photogenerated charge carriers, as well as electrode degradation. This overview focuses on the recent development about catalyst nanomaterials and nanostructures in different PEC water splitting systems. As photoanode, Au nanoparticle-decorated TiO_2 nanowire electrodes exhibited enhanced photoactivity in both the UV and the visible regions due to surface plasmon resonance of Au and showed the largest photocurrent generation of up to 710 nm. Pt/Cd S/CGSe electrodes were developed as photocathode. With the role of p–n heterojunction, the photoelectrode showed high stability and evolved hydrogen continuously for more than 10 days. Further, in the Z-scheme system(Bi_2S_3/TNA as photoanode and Pt/Si PVC as photocathode at the same time), a self-bias(open-circuit voltage Voc= 0.766 V) was formed between two photoelectrodes, which could facilitate photogenerated charge transfers and enhance the photoelectrochemical performance, and which might provide new hints for PEC water splitting. Meanwhile, the existing problems and prospective solutions have also been reviewed.
基金financially supported by the National Natural Science Foundation of China(No.51074025)the Fundamental Research Funds for the Central Universities of China(No.FRF-SD-12-009A)
文摘Understanding the reduction behaviors and characteristics of the end products of Fe-Cr-O systems is very important not only for maximizing the recovery of metals from stainless steel dust but also for the subsequent reuse in metallurgical process. The present work first predicted the possible products thermodynamically when FeCr204 was reduced by C. The reduction behaviors by graphite of three kinds of Fe-Cr-O systems, i.e., FeCr204, Fe203q-Cr203, and Feq-Cr203, were then investigated in 1350-1550℃. Further, the microstructures of final products and element distribution conditions were examined. The results suggest that, thermodynamically, the mass of products for the carbothermal reduction of FeCr204 is a strong function of temperature, and the initial carbon content is used. More Fe-Cr-C solution and less residual carbon content are obtained at higher temperatures and lower no：no ratios （the initial molar ratio of C to O in the sample）. Experimental data show that the sample amount tends to affect the reduction rate, and the residual carbon content strongly depends on nc：no. With regard to the phases present in products during the reaction process, metal carbides tend to form in the initial stage, whereas Fe-Cr-C solution forms when the degree of reduction is sufficiently high.
文摘The integer-order interdependent calcium([Ca^(2+)])and nitric oxide(NO)systems are unable to shed light on the influences of the superdiffusion and memory in triggering Brownian motion(BM)in neurons.Therefore,a mathematical model is constructed for the fractional-order nonlinear spatiotemporal systems of[Ca^(2+)]and NO incorporating reaction-diffusion equations in neurons.The two-way feedback process between[Ca^(2+)]and NO systems through calcium feedback on NO production and NO feedback on calcium through cyclic guanosine monophosphate(cGMP)with plasmalemmal[Ca^(2+)]-ATPase(PMCA)was incorporated in the model.The Crank–Nicholson scheme(CNS)with Grunwald approximation along spatial derivatives and L1 scheme along temporal derivatives with Gauss–Seidel(GS)iterations were employed.The numerical outcomes were analyzed to get insights into superdiffusion,buffer,and memory exhibiting BM of[Ca^(2+)]and NO systems.The conditions,events and mechanisms leading to dysfunctions in calcium and NO systems and causing different diseases like Parkinson’s were explored in neurons.
基金Financial support by the National Key Research and Development Program of China(Grants 2017YFA0204503 and 2017YFA0207800)the National Natural Science Foundation of China(Grants 51903187,21734006 and 21975178)the China Postdoctoral Science Foundation(No.2020M670642)is gratefully acknowledged.
文摘The tandem catalytic functionalization/carboxylation of double as well as triple carbon-carbon bonds with CO_(2) represent an emerging research area in synthetic organic methodology.In particular,the combination of mild reaction conditions,stoichiometric acceptor/donorless conditions(visible light photoredox catalysis)and chiral catalysts contributed to a rapid development of this intriguing research area capable of creating chemical diversity/complexity from readily available unsaturated hydrocarbons and CO2 as a C1-buinding block.The most recent developments in the field have been collected in the present review article and organized,based on the different sets ofπ-systems/intermediates/reactive partners employed(i.e.,nickelalactones,organo-halides)as well as synthetic strategies(i.e.,visible-light photo redox catalysis).
基金National Natural Science Foundation of China under grants NSFC 61603363,61703383,61603056.
文摘This paper studies the reentry attitude tracking control problem for hypersonic vehicles(HSV)equipped with reaction control systems(RCS)and aerodynamic surfaces.The attitude dynamical model of the hypersonic vehicles is established,and the simplified longitudinal and lateral dynamic models are obtained,respectively.Then,the compound control allocation strategy is provided and the model predictive controller is designed for the pitch channel.Furthermore,considering the complicated jet interaction effect of HSV during RCS is working,an improved model predictive control approach is presented by introducing the online parameter estimation of the jet interaction coefficient for dealing with the uncertainty and disturbance.Moreover,considering the strong coupling effect between the yaw channel and roll channel,a coupled model predictive controller is designed by introducing the feedback of sideslip angle into the roll control channel to eliminate the coupling effect.Finally,the comparison simulations using the classical control method,MPC and IMPC approach are given to demonstrate the effectiveness and efficiency of the presented IMPC scheme.
基金supported by the National Natural Science Foundation of China under Grant Nos.61473097,11301090the State Key Program of Natural Science Foundation of China under Grant No.U1533202+2 种基金Shandong Independent Innovation and Achievements Transformation Fund under Grant No.2014CGZH1101Civil Aviation Administration of China under Grant No.MHRD20150104Guangxi Natural Science Foundation under Grant No.2016JJA110005
文摘This paper is devoted to the investigation of stability for a class of coupled impulsive Markovian jump reaction-diffusion systems on networks(CIMJRDSNs). By using graph theory, a systematic method is provided to construct global Lyapunov functions for the CIMJRDSNs. Based on Lyapunov functions and stochastic analysis method, some novel stability principles associated with the topology property of the networks are established.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences,Grant No:XDB0600300National Natural Science Foundation of China(22272175,22232005,21825202)+4 种基金National Key R&D Programof China(2022YFA1504002)“Scientist Studio Funding”from Tianmu Lake Institute of Advanced Energy Storage Technologies Co.,Ltd.,Dalian supports high-level talent innovation and entrepreneurship projects(2021RD14)Dalian Institute of Chemical Physics(DICP I202213)Magnetic Resonance Union of Chinese Academy of Sciences(MRU-CAS)(2022GZL001)21C Innovation Laboratory,Contemporary Amperex Technology Ltd by project No.21C-OP-202208.
文摘A thorough understanding of the fundamental electrochemical and chemical processes in batteries is crucial to advancing energy density and power density.However,the characterizations of such processes are complex.In-situ electrochemical nuclear magnetic resonance(EC-NMR)offers the capability to collect real-time data during battery operation,furnishing insights into the local structures and ionic dynamics of materials by monitoring changes in the chemical environment around the nuclei.EC-NMR also has the advantages of being both quantitative and non-destructive.This paper systematically reviews the design of EC-NMR approach,and delves into the applications and progress of EC-NMR concerning battery reaction mechanisms,failure mechanisms,and overall battery systems.The review culminates in a comprehensive summary of the perspective and challenges associated with EC-NMR.
基金financial support from the National Natural Science Foundation of China (Nos. 11974188,11304159)the China Postdoctoral Science Foundation (Nos. 2021T140339,2018M632345)+2 种基金the Qing Lan Project of Jiangsu Provincethe Natural Science Foundation of Jiangsu Province (Nos. BK20201381,BK20161512)NUPTSF (No. NY218022)。
文摘Molybdenum disulfide (MoS_(2)) with low cost, high activity and high earth abundance has been found to be a promising catalyst for the hydrogen evolution reaction (HER), but its catalytic activity is considerably limited due to its inert basal planes. Here, through the combination of theory and experiment, we propose that doping Ni in MoS_(2) as catalyst can make it have excellent catalytic activity in different reaction systems. In the EY/TEOA system, the maximum hydrogen production rate of EY/Ni-Mo-S is 2.72 times higher than that of pure EY, which confirms the strong hydrogen evolution activity of Ni-Mo-S nanosheets as catalysts. In the lactic acid and Na_(2)S/Na_(2)SO_(3) systems, when Ni-Mo-S is used as co-catalyst to compound with ZnIn_(2)S_(4) (termed as Ni-Mo-S/ZnIn_(2)S_(4)), the maximum hydrogen evolution rates in the two systems are 5.28 and 2.33 times higher than those of pure ZnIn_(2)S_(4), respectively. The difference in HER enhancement is because different systems lead to different sources of protons, thus affecting hydrogen evolution activity. Theoretically, we further demonstrate that the Ni-Mo-S nanosheets have a narrower band gap than MoS_(2), which is conducive to the rapid transfer of charge carriers and thus result in multi-photocatalytic reaction systems with excellent activity. The proposed atomic doping strategy provides a simple and promising approach for the design of photocatalysts with high activity and stability in multi-reaction systems.
基金supported by National Natural Science Foundation of China (Grant Nos. 11371179 and 11271172)National Science Foundation of USA (Grant No. DMS-1412454)
文摘In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has attracted a lot of attention and many new types of nonplanar traveling waves have been observed for scalar reaction-diffusion equations with various nonlinearities. In this paper, by using the comparison argument and constructing appropriate super- and subsolutions, we study the existence, uniqueness and stability of three- dimensional traveling fronts of pyramidal shape for monotone bistable systems of reaction-diffusion equations in R3. The pyramidal traveling fronts are characterized as either a combination of planar traveling fronts on the lateral surfaces or a combination of two-dimensional V-form waves on the edges of the pyramid. In particular, our results are applicable to some important models in biology, such as Lotk,u-Volterra competition-diffusion systems with or without spatio-temporal delays, and reaction-diffusion systems of multiple obligate mutualists.
基金Regione Puglia(Italy)through the research programme REFIN-Research for Innovation(protocol code 901D2CAA,project No.UNISAL026)MF acknowledges support from the Italian National Institute of High Mathematics(INdAM)through the INdAM-GNCS Project no.CUP E55F22000270001+3 种基金the Global Challenges Research Fund through the Engineering and Physical Sciences Research Council grant number EP/T00410X/1:UK-Africa Postgraduate Advanced Study Institute in Mathematical Sciences,the Health Foundation(1902431)the NIHR(NIHR133761)and by the Discovery Grant awarded by Canadian Natural Sciences and Engineering Research Council(2023-2028)AM acknowledges support from the Royal Society Wolfson Research Merit Award funded generously by the Wolfson Foundation(2016-2021)AM is a Distinguished Visiting Scholar to the Department of Mathematics,University of Johannesburg,South Africa,and the University of Pretoria in South Africa.IS and MF are members of the INdAM-GNCS activity group.The work of IS is supported by the PRIN 2020 research project(no.2020F3NCPX)”Mathematics for Industry 4.0”,and from the”National Centre for High Performance Computing,Big Data and Quantum Computing”funded by European Union-NextGenerationEU,PNRR project code CN00000013,CUP F83C22000740001.
文摘Bulk-surface partial differential equations(BS-PDEs)are prevalent in manyapplications such as cellular,developmental and plant biology as well as in engineeringand material sciences.Novel numerical methods for BS-PDEs in three space dimensions(3D)are sparse.In this work,we present a bulk-surface virtual elementmethod(BS-VEM)for bulk-surface reaction-diffusion systems,a form of semilinearparabolic BS-PDEs in 3D.Unlike previous studies in two space dimensions(2D),the3D bulk is approximated with general polyhedra,whose outer faces constitute a flatpolygonal approximation of the surface.For this reason,the method is restricted tothe lowest order case where the geometric error is not dominant.The BS-VEM guaranteesall the advantages of polyhedral methods such as easy mesh generation andfast matrix assembly on general geometries.Such advantages are much more relevantthan in 2D.Despite allowing for general polyhedra,general nonlinear reaction kineticsand general surface curvature,the method only relies on nodal values without needingadditional evaluations usually associated with the quadrature of general reactionkinetics.This latter is particularly costly in 3D.The BS-VEM as implemented in thisstudy retains optimal convergence of second order in space.
文摘This paper is concerned with the existence of entire solutions of Lotka Volterra competition-diffusion model. Using the comparing argument and sub-super solutions method, we obtain the existence of entire solutions which behave as two wave fronts coming from the both sides of x-axis, where an entire solution is meant by a classical solution defined for all space and time variables.
文摘The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .
文摘Zoning in ore bodies, ore deposits and ore regions are recognized as temporal-spatial structures generated by the dynamics of ore- forming processes. Viewed from the theory of dissipative structures, ore zoning is a kind of self-organization phenomenon occurring in far from-equilibrium geochemical dynamic systems. Therefore,kinetic and dynamic approaches must be taken to reveal the mechanisms of ore zoning. Two dominant coupling processes leading to ore zoning——reaction-transport feedbacks and double-diffusive convection——are discussed.
