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
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
In this paper, we study periodic waves in reaction-diffusion systems with limit cycle kinetics and weak diffusion. The results are based on the analysis of a nonlinear partial differential equation which is derived fr...In this paper, we study periodic waves in reaction-diffusion systems with limit cycle kinetics and weak diffusion. The results are based on the analysis of a nonlinear partial differential equation which is derived from singular perturbation techniques. We obtain the first order approximation expression of the dispersion curve for periodic wave trains and then show that in the generic case of limit cycle kinetics there is a one parameter family of target patterns and the rotating spiral waves of Archimedian type exist. Finally, we apply these results to the general λ-ω systems.展开更多
The human retina,a complex and highly specialized structure,includes multiple cell types that work synergistically to generate and transmit visual signals.However,genetic predisposition or age-related degeneration can...The human retina,a complex and highly specialized structure,includes multiple cell types that work synergistically to generate and transmit visual signals.However,genetic predisposition or age-related degeneration can lead to retinal damage that severely impairs vision or causes blindness.Treatment options for retinal diseases are limited,and there is an urgent need for innovative therapeutic strategies.Cell and gene therapies are promising because of the efficacy of delivery systems that transport therapeutic genes to targeted retinal cells.Gene delivery systems hold great promise for treating retinal diseases by enabling the targeted delivery of therapeutic genes to affected cells or by converting endogenous cells into functional ones to facilitate nerve regeneration,potentially restoring vision.This review focuses on two principal categories of gene delivery vectors used in the treatment of retinal diseases:viral and non-viral systems.Viral vectors,including lentiviruses and adeno-associated viruses,exploit the innate ability of viruses to infiltrate cells,which is followed by the introduction of therapeutic genetic material into target cells for gene correction.Lentiviruses can accommodate exogenous genes up to 8 kb in length,but their mechanism of integration into the host genome presents insertion mutation risks.Conversely,adeno-associated viruses are safer,as they exist as episomes in the nucleus,yet their limited packaging capacity constrains their application to a narrower spectrum of diseases,which necessitates the exploration of alternative delivery methods.In parallel,progress has also occurred in the development of novel non-viral delivery systems,particularly those based on liposomal technology.Manipulation of the ratios of hydrophilic and hydrophobic molecules within liposomes and the development of new lipid formulations have led to the creation of advanced non-viral vectors.These innovative systems include solid lipid nanoparticles,polymer nanoparticles,dendrimers,polymeric micelles,and polymeric nanoparticles.Compared with their viral counterparts,non-viral delivery systems offer markedly enhanced loading capacities that enable the direct delivery of nucleic acids,mRNA,or protein molecules into cells.This bypasses the need for DNA transcription and processing,which significantly enhances therapeutic efficiency.Nevertheless,the immunogenic potential and accumulation toxicity associated with non-viral particulate systems necessitates continued optimization to reduce adverse effects in vivo.This review explores the various delivery systems for retinal therapies and retinal nerve regeneration,and details the characteristics,advantages,limitations,and clinical applications of each vector type.By systematically outlining these factors,our goal is to guide the selection of the optimal delivery tool for a specific retinal disease,which will enhance treatment efficacy and improve patient outcomes while paving the way for more effective and targeted therapeutic interventions.展开更多
This paper is concerned with the spreading speeds of time dependent partially degenerate reaction-diffusion systems with monostable nonlinearity.By using the principal Lyapunov exponent theory,the author first proves ...This paper is concerned with the spreading speeds of time dependent partially degenerate reaction-diffusion systems with monostable nonlinearity.By using the principal Lyapunov exponent theory,the author first proves the existence,uniqueness and stability of spatially homogeneous entire positive solution for time dependent partially degenerate reaction-diffusion system.Then the author shows that such system has a finite spreading speed interval in any direction and there is a spreading speed for the partially degenerate system under certain conditions.The author also applies these results to a time dependent partially degenerate epidemic model.展开更多
The periodically forced spatially extended Brusselator is investigated in the oscillating regime. The temporal response and pattern formation within the 2：1 frequency-locking band where the system oscillates at one h...The periodically forced spatially extended Brusselator is investigated in the oscillating regime. The temporal response and pattern formation within the 2：1 frequency-locking band where the system oscillates at one half of the forcing frequency are examined. An hexagonal standing-wave pattern and other resonant patterns are observed. The detailed phase diagram of resonance structure in the forcing frequency and forcing amplitude parameter space is calculated. The transitions between the resonant standing-wave patterns are of hysteresis when control parameters are varied, and the presence of multiplicity is demonstrated. Analysis in the framework of amplitude equation reveals that the spatial patterns of the standing waves come out as a result of Turing bifurcation in the amplitude equation.展开更多
We present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many nat- ural phenomena in areas such as developmen...We present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many nat- ural phenomena in areas such as developmental and cancer biology, cell motility and material science. In many of these applications, often one is interested in identifying parameters which will lead to a particular pattern for a given reaction-diffusion model. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally, we show that in some cases the inhomogeneous steady state can be a linear combination of eigenfunctions. Finally,we show an example suggesting that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.展开更多
With the continuous advancement and maturation of technologies such as big data,artificial intelligence,virtual reality,robotics,human-machine collaboration,and augmented reality,many enterprises are finding new avenu...With the continuous advancement and maturation of technologies such as big data,artificial intelligence,virtual reality,robotics,human-machine collaboration,and augmented reality,many enterprises are finding new avenues for digital transformation and intelligent upgrading.Industry 5.0,a further extension and development of Industry 4.0,has become an important development trend in industry with more emphasis on human-centered sustainability and flexibility.Accordingly,both the industrial metaverse and digital twins have attracted much attention in this new era.However,the relationship between them is not clear enough.In this paper,a comparison between digital twins and the metaverse in industry is made firstly.Then,we propose the concept and framework of Digital Twin Systems Engineering(DTSE)to demonstrate how digital twins support the industrial metaverse in the era of Industry 5.0 by integrating systems engineering principles.Furthermore,we discuss the key technologies and challenges of DTSE,in particular how artificial intelligence enhances the application of DTSE.Finally,a specific application scenario in the aviation field is presented to illustrate the application prospects of DTSE.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.
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.
文摘In this paper, we study periodic waves in reaction-diffusion systems with limit cycle kinetics and weak diffusion. The results are based on the analysis of a nonlinear partial differential equation which is derived from singular perturbation techniques. We obtain the first order approximation expression of the dispersion curve for periodic wave trains and then show that in the generic case of limit cycle kinetics there is a one parameter family of target patterns and the rotating spiral waves of Archimedian type exist. Finally, we apply these results to the general λ-ω systems.
基金Hongguang Wu,Both authors contributed equally to this work and share first authorshipLing Dong,Both authors contributed equally to this work and share first authorship。
文摘The human retina,a complex and highly specialized structure,includes multiple cell types that work synergistically to generate and transmit visual signals.However,genetic predisposition or age-related degeneration can lead to retinal damage that severely impairs vision or causes blindness.Treatment options for retinal diseases are limited,and there is an urgent need for innovative therapeutic strategies.Cell and gene therapies are promising because of the efficacy of delivery systems that transport therapeutic genes to targeted retinal cells.Gene delivery systems hold great promise for treating retinal diseases by enabling the targeted delivery of therapeutic genes to affected cells or by converting endogenous cells into functional ones to facilitate nerve regeneration,potentially restoring vision.This review focuses on two principal categories of gene delivery vectors used in the treatment of retinal diseases:viral and non-viral systems.Viral vectors,including lentiviruses and adeno-associated viruses,exploit the innate ability of viruses to infiltrate cells,which is followed by the introduction of therapeutic genetic material into target cells for gene correction.Lentiviruses can accommodate exogenous genes up to 8 kb in length,but their mechanism of integration into the host genome presents insertion mutation risks.Conversely,adeno-associated viruses are safer,as they exist as episomes in the nucleus,yet their limited packaging capacity constrains their application to a narrower spectrum of diseases,which necessitates the exploration of alternative delivery methods.In parallel,progress has also occurred in the development of novel non-viral delivery systems,particularly those based on liposomal technology.Manipulation of the ratios of hydrophilic and hydrophobic molecules within liposomes and the development of new lipid formulations have led to the creation of advanced non-viral vectors.These innovative systems include solid lipid nanoparticles,polymer nanoparticles,dendrimers,polymeric micelles,and polymeric nanoparticles.Compared with their viral counterparts,non-viral delivery systems offer markedly enhanced loading capacities that enable the direct delivery of nucleic acids,mRNA,or protein molecules into cells.This bypasses the need for DNA transcription and processing,which significantly enhances therapeutic efficiency.Nevertheless,the immunogenic potential and accumulation toxicity associated with non-viral particulate systems necessitates continued optimization to reduce adverse effects in vivo.This review explores the various delivery systems for retinal therapies and retinal nerve regeneration,and details the characteristics,advantages,limitations,and clinical applications of each vector type.By systematically outlining these factors,our goal is to guide the selection of the optimal delivery tool for a specific retinal disease,which will enhance treatment efficacy and improve patient outcomes while paving the way for more effective and targeted therapeutic interventions.
基金This work was supported by the National Natural Science Foundation of China(Nos.41801029,11701041)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2020JM-223).
文摘This paper is concerned with the spreading speeds of time dependent partially degenerate reaction-diffusion systems with monostable nonlinearity.By using the principal Lyapunov exponent theory,the author first proves the existence,uniqueness and stability of spatially homogeneous entire positive solution for time dependent partially degenerate reaction-diffusion system.Then the author shows that such system has a finite spreading speed interval in any direction and there is a spreading speed for the partially degenerate system under certain conditions.The author also applies these results to a time dependent partially degenerate epidemic model.
基金Supported by the National Natural Science Foundation of China under Grant No 10204002.
文摘The periodically forced spatially extended Brusselator is investigated in the oscillating regime. The temporal response and pattern formation within the 2：1 frequency-locking band where the system oscillates at one half of the forcing frequency are examined. An hexagonal standing-wave pattern and other resonant patterns are observed. The detailed phase diagram of resonance structure in the forcing frequency and forcing amplitude parameter space is calculated. The transitions between the resonant standing-wave patterns are of hysteresis when control parameters are varied, and the presence of multiplicity is demonstrated. Analysis in the framework of amplitude equation reveals that the spatial patterns of the standing waves come out as a result of Turing bifurcation in the amplitude equation.
文摘We present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many nat- ural phenomena in areas such as developmental and cancer biology, cell motility and material science. In many of these applications, often one is interested in identifying parameters which will lead to a particular pattern for a given reaction-diffusion model. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally, we show that in some cases the inhomogeneous steady state can be a linear combination of eigenfunctions. Finally,we show an example suggesting that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.
基金Supported by Beijing Municipal Natural Science Foundation of China(Grant No.24JL002)China Postdoctoral Science Foundation(Grant No.2024M754054)+2 种基金National Natural Science Foundation of China(Grant No.52120105008)Beijing Municipal Outstanding Young Scientis Program of Chinathe New Cornerstone Science Foundation through the XPLORER PRIZE。
文摘With the continuous advancement and maturation of technologies such as big data,artificial intelligence,virtual reality,robotics,human-machine collaboration,and augmented reality,many enterprises are finding new avenues for digital transformation and intelligent upgrading.Industry 5.0,a further extension and development of Industry 4.0,has become an important development trend in industry with more emphasis on human-centered sustainability and flexibility.Accordingly,both the industrial metaverse and digital twins have attracted much attention in this new era.However,the relationship between them is not clear enough.In this paper,a comparison between digital twins and the metaverse in industry is made firstly.Then,we propose the concept and framework of Digital Twin Systems Engineering(DTSE)to demonstrate how digital twins support the industrial metaverse in the era of Industry 5.0 by integrating systems engineering principles.Furthermore,we discuss the key technologies and challenges of DTSE,in particular how artificial intelligence enhances the application of DTSE.Finally,a specific application scenario in the aviation field is presented to illustrate the application prospects of DTSE.
