A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer.The transitions from stationary ...A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer.The transitions from stationary patterns to asynchronous and synchronous oscillatory patterns are obtained.A novel method based on decomposing coupled systems into two associated subsystems has been proposed to elucidate the mechanism of formation of oscillating patterns.Linear stability analysis of the associated subsystems reveals that the Turing pattern in one layer induces the other layer locally,undergoes a supercritical Hopf bifurcation and gives rise to localized oscillations.It is found that the sizes and positions of oscillations are determined by the spatial distribution of the Turing patterns.When the size is large,localized traveling waves such as spirals and targets emerge.These results may be useful for deeper understanding of pattern formation in complex systems,particularly multilayered systems.展开更多
In this paper, the problem of initial boundary value for nonlinear coupled reaction-diffusion systems arising in biochemistry, engineering and combustion_theory is considered.
Using the sign-invariant theory, we study the nonlinear reaction-diffusion systems. We also obtain some new explicit solutions to the nonlinear resulting systems.
Boundary control for a class of partial integro-differential systems with space and time dependent coefficients is consid- ered. A control law is derived via the partial differential equation （PDE） backstepping. The...Boundary control for a class of partial integro-differential systems with space and time dependent coefficients is consid- ered. A control law is derived via the partial differential equation （PDE） backstepping. The existence of kernel equations is proved. Exponential stability of the closed-loop system is achieved. Simulation results are presented through figures.展开更多
Differential method and homotopy analysis method are used for solving the two-dimensional reaction-diffusion model. And the structure of the solutions is analyzed. Finally, the homotopy series solutions are simulated ...Differential method and homotopy analysis method are used for solving the two-dimensional reaction-diffusion model. And the structure of the solutions is analyzed. Finally, the homotopy series solutions are simulated with the mathematical software Matlab, so the Turing patterns will be produced. Overall analysis and experimental simulation of the model show that the different parameters lead to different Turing pattern structures. As time goes on, the structure of Turing patterns changes, and the final solutions tend to stationary state.展开更多
This paper deals with an initial boundary value problem for the strongly coupledreaction-diffusion systems with a full matrix of diffusion coefficients. The global existence ofsolutions is proved by using the techniqu...This paper deals with an initial boundary value problem for the strongly coupledreaction-diffusion systems with a full matrix of diffusion coefficients. The global existence ofsolutions is proved by using the techniques based on invariant regions, Lyapunov functionalmethods, and local Lp prior estimates independent of time.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
In this paper we discuss the following nonlinear degenerate parabolic systems u_i=△a_i(u_i)+b_i(x,t,u_i)Du_i+f_i(x,t,u)for i = 1,2, …, m and u = (u_1,…, u_m) is a vector function, with Dirichlet boundary condition....In this paper we discuss the following nonlinear degenerate parabolic systems u_i=△a_i(u_i)+b_i(x,t,u_i)Du_i+f_i(x,t,u)for i = 1,2, …, m and u = (u_1,…, u_m) is a vector function, with Dirichlet boundary condition. Under some structure conditions on a_i,b_i and f_i and initial data u_i^o∈Li(Ω) for some pi>p_i^o = 1,2,…,m, the result on existence and uniquence of global solution is established.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
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
This paper is concerned with the existence of entire solutions of some reaction-diffusion systems. We first consider Belousov-Zhabotinskii reaction model. Then we study a general model. Using the comparing argument an...This paper is concerned with the existence of entire solutions of some reaction-diffusion systems. We first consider Belousov-Zhabotinskii reaction model. Then we study a general model. Using the comparing argument and sub-super-solutions method, we obtain the existence of entire solutions which behave as two wavefronts 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. At last, we give some examples to explain our results for the general models.展开更多
This work is concerned with the numerical simulations for two reactiondiffusion systems,i.e.,the Brusselator model and the Gray-Scott model.The numerical algorithm is based upon a moving finite element method which he...This work is concerned with the numerical simulations for two reactiondiffusion systems,i.e.,the Brusselator model and the Gray-Scott model.The numerical algorithm is based upon a moving finite element method which helps to resolve large solution gradients.High quality meshes are obtained for both the spot replication and the moving wave along boundaries by using proper monitor functions.Unlike[33],this work finds out the importance of the boundary grid redistribution which is particularly important for a class of problems for the Brusselator model.Several ways for verifying the quality of the numerical solutions are also proposed,which may be of important use for comparisons.展开更多
This survey presents a comprehensive examination of sensor fusion research spanning four decades,tracing the methodological evolution,application domains,and alignment with classical hierarchical models.Building on th...This survey presents a comprehensive examination of sensor fusion research spanning four decades,tracing the methodological evolution,application domains,and alignment with classical hierarchical models.Building on this long-term trajectory,the foundational approaches such as probabilistic inference,early neural networks,rulebasedmethods,and feature-level fusion established the principles of uncertainty handling andmulti-sensor integration in the 1990s.The fusion methods of 2000s marked the consolidation of these ideas through advanced Kalman and particle filtering,Bayesian–Dempster–Shafer hybrids,distributed consensus algorithms,and machine learning ensembles for more robust and domain-specific implementations.From 2011 to 2020,the widespread adoption of deep learning transformed the field driving some major breakthroughs in the autonomous vehicles domain.A key contribution of this work is the assessment of contemporary methods against the JDL model,revealing gaps at higher levels-especially in situation and impact assessment.Contemporary methods offer only limited implementation of higher-level fusion.The survey also reviews the benchmark multi-sensor datasets,noting their role in advancing the field while identifying major shortcomings like the lack of domain diversity and hierarchical coverage.By synthesizing developments across decades and paradigms,this survey provides both a historical narrative and a forward-looking perspective.It highlights unresolved challenges in transparency,scalability,robustness,and trustworthiness,while identifying emerging paradigms such as neuromorphic fusion and explainable AI as promising directions.This paves the way forward for advancing sensor fusion towards transparent and adaptive next-generation autonomous systems.展开更多
This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called...This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.展开更多
Radiative cooling systems(RCSs)possess the distinctive capability to dissipate heat energy via solar and thermal radiation,making them suitable for thermal regulation and energy conservation applications,essential for...Radiative cooling systems(RCSs)possess the distinctive capability to dissipate heat energy via solar and thermal radiation,making them suitable for thermal regulation and energy conservation applications,essential for mitigating the energy crisis.A comprehensive review connecting the advancements in engineered radiative cooling systems(ERCSs),encompassing material and structural design as well as thermal and energy-related applications,is currently absent.Herein,this review begins with a concise summary of the essential concepts of ERCSs,followed by an introduction to engineered materials and structures,containing nature-inspired designs,chromatic materials,meta-structural configurations,and multilayered constructions.It subsequently encapsulates the primary applications,including thermal-regulating textiles and energy-saving devices.Next,it highlights the challenges of ERCSs,including maximized thermoregulatory effects,environmental adaptability,scalability and sustainability,and interdisciplinary integration.It seeks to offer direction for forthcoming fundamental research and industrial advancement of radiative cooling systems in real-world applications.展开更多
The incidence of benign airway stenosis(BAS)is on the rise,and current treatment options are associated with a significant risk of restenosis.Therefore,there is an urgent need to explore new and effective prevention a...The incidence of benign airway stenosis(BAS)is on the rise,and current treatment options are associated with a significant risk of restenosis.Therefore,there is an urgent need to explore new and effective prevention and treatment methods.Animal models serve as essential tools for investigating disease mechanisms and assessing novel therapeutic strategies,and the scientific rigor of their construction and validation significantly impacts the reliability of research findings.This paper systematically reviews the research progress and evaluation systems of BAS animal models over the past decade,aiming to provide a robust foundation for the optimized construction of BAS models,intervention studies,and clinical translation.This effort is intended to facilitate the innovation and advancement in BAS prevention and treatment strategies.展开更多
Malignant pleural effusion(MPE) is a serious disease caused by malignant tumors with high morbidity and mortality.Chemotherapy,immunotherapy,and antiangiogenic therapy are common treatments for MPE at present.However,...Malignant pleural effusion(MPE) is a serious disease caused by malignant tumors with high morbidity and mortality.Chemotherapy,immunotherapy,and antiangiogenic therapy are common treatments for MPE at present.However,traditional chemotherapeutic drugs have many side effects and can easily lead to drug resistance in patients.The complex tumor microenvironment(TME) of MPE directly reduces the antitumor efficacy of immunotherapy.Fortunately,drug delivery systems(DDSs) based on biomaterials have the ability to overcome some of the drawbacks of conventional treatments by improving drug stability,increasing the accuracy of tumor cell targeting,reducing toxic side effects,and remodeling TME,ultimately improving drug efficacy.Therefore,the purpose of this review is to provide an overview and discussion of the latest progress in biomaterial-based DDSs for the treatment of MPE.We discuss the application of biomaterials in the treatment of MPE from multiple perspectives,including chemotherapy,immunotherapy,combination therapy,and pleurodesis,where microspheres,cell membrane-derived microparticles(MPs),micelles,nanoparticles,and liposomes,are involved.The application of these biomaterials has been proven to have great potential in the treatment of MPE,providing a new idea for follow-up research.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12275065,12275064,12475203)the Natural Science Foundation of Hebei Province(Grant Nos.A2021201010 and A2024201020)+3 种基金Interdisciplinary Research Program of Natural Science of Hebei University(Grant No.DXK202108)Hebei Provincial Central Government Guiding Local Science and Technology Development Funds(Grant No.236Z1501G)Scientific Research and Innovation Team Foundation of Hebei University(Grant No.IT2023B03)the Excellent Youth Research Innovation Team of Hebei University(Grant No.QNTD202402)。
文摘A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer.The transitions from stationary patterns to asynchronous and synchronous oscillatory patterns are obtained.A novel method based on decomposing coupled systems into two associated subsystems has been proposed to elucidate the mechanism of formation of oscillating patterns.Linear stability analysis of the associated subsystems reveals that the Turing pattern in one layer induces the other layer locally,undergoes a supercritical Hopf bifurcation and gives rise to localized oscillations.It is found that the sizes and positions of oscillations are determined by the spatial distribution of the Turing patterns.When the size is large,localized traveling waves such as spirals and targets emerge.These results may be useful for deeper understanding of pattern formation in complex systems,particularly multilayered systems.
文摘In this paper, the problem of initial boundary value for nonlinear coupled reaction-diffusion systems arising in biochemistry, engineering and combustion_theory is considered.
基金National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘Using the sign-invariant theory, we study the nonlinear reaction-diffusion systems. We also obtain some new explicit solutions to the nonlinear resulting systems.
文摘Boundary control for a class of partial integro-differential systems with space and time dependent coefficients is consid- ered. A control law is derived via the partial differential equation （PDE） backstepping. The existence of kernel equations is proved. Exponential stability of the closed-loop system is achieved. Simulation results are presented through figures.
文摘Differential method and homotopy analysis method are used for solving the two-dimensional reaction-diffusion model. And the structure of the solutions is analyzed. Finally, the homotopy series solutions are simulated with the mathematical software Matlab, so the Turing patterns will be produced. Overall analysis and experimental simulation of the model show that the different parameters lead to different Turing pattern structures. As time goes on, the structure of Turing patterns changes, and the final solutions tend to stationary state.
基金Supported by the Henan Innovation Project for University Prominent Research Talents (2003KJCX008)
文摘This paper deals with an initial boundary value problem for the strongly coupledreaction-diffusion systems with a full matrix of diffusion coefficients. The global existence ofsolutions is proved by using the techniques based on invariant regions, Lyapunov functionalmethods, and local Lp prior estimates independent of time.
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 ) .
基金Research supported by the Natural Science Foundation of Fujian Province Under Grant A92025.
文摘In this paper we discuss the following nonlinear degenerate parabolic systems u_i=△a_i(u_i)+b_i(x,t,u_i)Du_i+f_i(x,t,u)for i = 1,2, …, m and u = (u_1,…, u_m) is a vector function, with Dirichlet boundary condition. Under some structure conditions on a_i,b_i and f_i and initial data u_i^o∈Li(Ω) for some pi>p_i^o = 1,2,…,m, the result on existence and uniquence of global solution is established.
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.
文摘This paper is concerned with the existence of entire solutions of some reaction-diffusion systems. We first consider Belousov-Zhabotinskii reaction model. Then we study a general model. Using the comparing argument and sub-super-solutions method, we obtain the existence of entire solutions which behave as two wavefronts 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. At last, we give some examples to explain our results for the general models.
基金The first and the third authors are partially supported by HKBU FRG grants and the Hong Kong Research Grant CouncilThe second author is partially supported by the Hong Kong RGC grant(No.201710).
文摘This work is concerned with the numerical simulations for two reactiondiffusion systems,i.e.,the Brusselator model and the Gray-Scott model.The numerical algorithm is based upon a moving finite element method which helps to resolve large solution gradients.High quality meshes are obtained for both the spot replication and the moving wave along boundaries by using proper monitor functions.Unlike[33],this work finds out the importance of the boundary grid redistribution which is particularly important for a class of problems for the Brusselator model.Several ways for verifying the quality of the numerical solutions are also proposed,which may be of important use for comparisons.
文摘This survey presents a comprehensive examination of sensor fusion research spanning four decades,tracing the methodological evolution,application domains,and alignment with classical hierarchical models.Building on this long-term trajectory,the foundational approaches such as probabilistic inference,early neural networks,rulebasedmethods,and feature-level fusion established the principles of uncertainty handling andmulti-sensor integration in the 1990s.The fusion methods of 2000s marked the consolidation of these ideas through advanced Kalman and particle filtering,Bayesian–Dempster–Shafer hybrids,distributed consensus algorithms,and machine learning ensembles for more robust and domain-specific implementations.From 2011 to 2020,the widespread adoption of deep learning transformed the field driving some major breakthroughs in the autonomous vehicles domain.A key contribution of this work is the assessment of contemporary methods against the JDL model,revealing gaps at higher levels-especially in situation and impact assessment.Contemporary methods offer only limited implementation of higher-level fusion.The survey also reviews the benchmark multi-sensor datasets,noting their role in advancing the field while identifying major shortcomings like the lack of domain diversity and hierarchical coverage.By synthesizing developments across decades and paradigms,this survey provides both a historical narrative and a forward-looking perspective.It highlights unresolved challenges in transparency,scalability,robustness,and trustworthiness,while identifying emerging paradigms such as neuromorphic fusion and explainable AI as promising directions.This paves the way forward for advancing sensor fusion towards transparent and adaptive next-generation autonomous systems.
文摘This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.
基金support from the Contract Research(“Development of Breathable Fabrics with Nano-Electrospun Membrane”,CityU ref.:9231419“Research and application of antibacterial and healing-promoting smart nanofiber dressing for children’s burn wounds”,CityU ref:PJ9240111)+1 种基金the National Natural Science Foundation of China(“Study of Multi-Responsive Shape Memory Polyurethane Nanocomposites Inspired by Natural Fibers”,Grant No.51673162)Startup Grant of CityU(“Laboratory of Wearable Materials for Healthcare”,Grant No.9380116).
文摘Radiative cooling systems(RCSs)possess the distinctive capability to dissipate heat energy via solar and thermal radiation,making them suitable for thermal regulation and energy conservation applications,essential for mitigating the energy crisis.A comprehensive review connecting the advancements in engineered radiative cooling systems(ERCSs),encompassing material and structural design as well as thermal and energy-related applications,is currently absent.Herein,this review begins with a concise summary of the essential concepts of ERCSs,followed by an introduction to engineered materials and structures,containing nature-inspired designs,chromatic materials,meta-structural configurations,and multilayered constructions.It subsequently encapsulates the primary applications,including thermal-regulating textiles and energy-saving devices.Next,it highlights the challenges of ERCSs,including maximized thermoregulatory effects,environmental adaptability,scalability and sustainability,and interdisciplinary integration.It seeks to offer direction for forthcoming fundamental research and industrial advancement of radiative cooling systems in real-world applications.
基金National Natural Science Foundation of China,Grant/Award Number:82000102 and 82270112。
文摘The incidence of benign airway stenosis(BAS)is on the rise,and current treatment options are associated with a significant risk of restenosis.Therefore,there is an urgent need to explore new and effective prevention and treatment methods.Animal models serve as essential tools for investigating disease mechanisms and assessing novel therapeutic strategies,and the scientific rigor of their construction and validation significantly impacts the reliability of research findings.This paper systematically reviews the research progress and evaluation systems of BAS animal models over the past decade,aiming to provide a robust foundation for the optimized construction of BAS models,intervention studies,and clinical translation.This effort is intended to facilitate the innovation and advancement in BAS prevention and treatment strategies.
基金financial support from the Noncommunicable Chronic Diseases-National Science and Technology Major Project (Nos.2024ZD0522800,2024ZD0522803)the National Natural Science Foundation of China (Nos.U21A20417,31930067,31800797)+2 种基金the Natural Science Foundation of Sichuan Province (No.2024NSFSC0046)the Sichuan Science and Technology Program (No.2022YFS0333)the 1·3·5 Project for Disciplines of Excellence,West China Hospital,Sichuan University (No.ZYGD24003)。
文摘Malignant pleural effusion(MPE) is a serious disease caused by malignant tumors with high morbidity and mortality.Chemotherapy,immunotherapy,and antiangiogenic therapy are common treatments for MPE at present.However,traditional chemotherapeutic drugs have many side effects and can easily lead to drug resistance in patients.The complex tumor microenvironment(TME) of MPE directly reduces the antitumor efficacy of immunotherapy.Fortunately,drug delivery systems(DDSs) based on biomaterials have the ability to overcome some of the drawbacks of conventional treatments by improving drug stability,increasing the accuracy of tumor cell targeting,reducing toxic side effects,and remodeling TME,ultimately improving drug efficacy.Therefore,the purpose of this review is to provide an overview and discussion of the latest progress in biomaterial-based DDSs for the treatment of MPE.We discuss the application of biomaterials in the treatment of MPE from multiple perspectives,including chemotherapy,immunotherapy,combination therapy,and pleurodesis,where microspheres,cell membrane-derived microparticles(MPs),micelles,nanoparticles,and liposomes,are involved.The application of these biomaterials has been proven to have great potential in the treatment of MPE,providing a new idea for follow-up research.
