This paper is concerned with the spreading speed of a food-limited population model with delay.First,the existence of the solution of Cauchy problem is proved.Then,the spreading speed of solutions with compactly suppo...This paper is concerned with the spreading speed of a food-limited population model with delay.First,the existence of the solution of Cauchy problem is proved.Then,the spreading speed of solutions with compactly supported initial data is investigated by using the general Harnack inequality.Finally,we present some numerical simulations and investigate the dynamical behavior of the solution.展开更多
A reaction-diffusion model for a single species with age structure and nonlocal reaction for periodic time t is derived. Some results about the model with monotone birth function are firstly introduced, and then by co...A reaction-diffusion model for a single species with age structure and nonlocal reaction for periodic time t is derived. Some results about the model with monotone birth function are firstly introduced, and then by constructing two auxiliary equations and squeezing method, the spreading speed for the system with nonmonotone birth function is obtained.展开更多
This paper is concerned with the Fisher-KPP equation with diffusion and nonlocal delay.Firstly,we establish the global existence and uniform boundedness of solutions to the Cauchy problem.Then,we establish the spreadi...This paper is concerned with the Fisher-KPP equation with diffusion and nonlocal delay.Firstly,we establish the global existence and uniform boundedness of solutions to the Cauchy problem.Then,we establish the spreading speed for the solutions with compactly supported initial data.Finally,we investigate the long time behavior of solutions by numerical simulations.展开更多
Cortical spreading depression(CSD),which is a significant pathological phenomenon that correlates with migraines and cerebral ischemia,has been characterized by a wave of depolarization among neuronal cells and propag...Cortical spreading depression(CSD),which is a significant pathological phenomenon that correlates with migraines and cerebral ischemia,has been characterized by a wave of depolarization among neuronal cells and propagates across the cortex at a rate of 2–5mm/min.Although the propagation pattern of CSD was well-investigated using high-resolution optical imaging technique,the variation of propagation speed of CSD across different regions of cortex was not well-concerned,partially because of the lack of ideal approach to visualize two-dimensional distribution of propagation speed of CSD over the whole imaged cortex.Here,we have presented a method to compute automatically the propagation speed of CSD throughout every spots in the imaged cortex.In this method,temporal clustering analysis(TCA)and least square estimation(LSE)were first used to detect origin site where CSD was induced.Taking the origin site of CSD as the origin of coordinates,the data matrix of each image was transformed into the corresponding points based on the polar-coordinate representation.Then,two fixed-distance regions of interest(ROIs)are sliding along with the radial coordinate at each polar angle within the image for calculating the time lag with correlating algorithm.Finally,we could draw a twodimensional image,in which the value of each pixel represented the velocity of CSD when it spread through the corresponding area of the imaged cortex.The results demonstrated that the method can reveal the heterogeneity of propagation speed of CSD in the imaged cortex with high fidelity and intuition.展开更多
In the study a fire and fire environment model is set up and by using PHEONICS software 3 cases of surface fires are studied. The results fit the experimental studies well generally. The simulation reveals that (1) Th...In the study a fire and fire environment model is set up and by using PHEONICS software 3 cases of surface fires are studied. The results fit the experimental studies well generally. The simulation reveals that (1) The wind speed fields in front of fire front generally can be divided into 3 zones and there is always an eddy immediately at the corner between just in front of the fire and the ground. (2) The shape and dimension of the division of the 3 zones is mainly decided by slope angle and ambient wind speed given fire line intensity. (3) There exits an upwind zone in front of fire front. Ambient wind speeds have little effect on the magnitude of the upwind speed when slope angle is 0. But when the slope angle is negative, the upwind is apparently stronger.展开更多
Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. In this paper the assignment and theoretical investigations of the pro...Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. In this paper the assignment and theoretical investigations of the problems of crown forest fire spread in windy condition were carried out. In this context, a study—mathematical modeling—of the conditions of forest fire spreading that would make it possible to obtain a detailed picture of the change in the temperature and component concentration fields with time, and determine as well as the limiting condition of fire propagation in forest with fire break.展开更多
In this paper, we establish a mathematical model of the forest fire spread process based on a partial differential equation. We describe the distribution of time field and velocity field in the whole two-dimensional s...In this paper, we establish a mathematical model of the forest fire spread process based on a partial differential equation. We describe the distribution of time field and velocity field in the whole two-dimensional space by vector field theory. And we obtain a continuous algorithm to predict the dynamic behavior of forest fire spread in a short time. We use the algorithm to interpolate the fire boundary by cubic non-uniform rational B-spline closed curve. The fire boundary curve at any time can be simulated by solving the Eikonal equation. The model is tested in theory and in practice. The results show that the model has good accuracy and stability, and it’s compatible with most of the existing models, such as the elliptic model and the cellular automata model.展开更多
基金Supported by the National Natural Science Foundation of China(11371179)。
文摘This paper is concerned with the spreading speed of a food-limited population model with delay.First,the existence of the solution of Cauchy problem is proved.Then,the spreading speed of solutions with compactly supported initial data is investigated by using the general Harnack inequality.Finally,we present some numerical simulations and investigate the dynamical behavior of the solution.
基金Supported by the NSF of China(11171120)Supported by the Doctoral Program of Higher Education of China(20094407110001)Supported by the NSF of Guangdong Province(10151063101000003)
文摘A reaction-diffusion model for a single species with age structure and nonlocal reaction for periodic time t is derived. Some results about the model with monotone birth function are firstly introduced, and then by constructing two auxiliary equations and squeezing method, the spreading speed for the system with nonmonotone birth function is obtained.
基金Supported by National Natural Science Foundation of China(12071193,11731005)。
文摘This paper is concerned with the Fisher-KPP equation with diffusion and nonlocal delay.Firstly,we establish the global existence and uniform boundedness of solutions to the Cauchy problem.Then,we establish the spreading speed for the solutions with compactly supported initial data.Finally,we investigate the long time behavior of solutions by numerical simulations.
基金supported by the grants from the National Natural Science Foundation of China(Grant No.30801482,30800313)the National Postdoctoral Science Foundation of China(20080430-9970)+2 种基金Special Foundation(200902436)the Ph.D.Programs Foundation of Ministry of Education of China(Grant No.20070487058)the National High Technology Research and Development Program of China(Grant No.2007AA02-Z303).
文摘Cortical spreading depression(CSD),which is a significant pathological phenomenon that correlates with migraines and cerebral ischemia,has been characterized by a wave of depolarization among neuronal cells and propagates across the cortex at a rate of 2–5mm/min.Although the propagation pattern of CSD was well-investigated using high-resolution optical imaging technique,the variation of propagation speed of CSD across different regions of cortex was not well-concerned,partially because of the lack of ideal approach to visualize two-dimensional distribution of propagation speed of CSD over the whole imaged cortex.Here,we have presented a method to compute automatically the propagation speed of CSD throughout every spots in the imaged cortex.In this method,temporal clustering analysis(TCA)and least square estimation(LSE)were first used to detect origin site where CSD was induced.Taking the origin site of CSD as the origin of coordinates,the data matrix of each image was transformed into the corresponding points based on the polar-coordinate representation.Then,two fixed-distance regions of interest(ROIs)are sliding along with the radial coordinate at each polar angle within the image for calculating the time lag with correlating algorithm.Finally,we could draw a twodimensional image,in which the value of each pixel represented the velocity of CSD when it spread through the corresponding area of the imaged cortex.The results demonstrated that the method can reveal the heterogeneity of propagation speed of CSD in the imaged cortex with high fidelity and intuition.
基金TheresearchissupportedbyFoundationforDoctoralStudiesofMinistryofEducation (No .19980 0 2 2 0 6 )
文摘In the study a fire and fire environment model is set up and by using PHEONICS software 3 cases of surface fires are studied. The results fit the experimental studies well generally. The simulation reveals that (1) The wind speed fields in front of fire front generally can be divided into 3 zones and there is always an eddy immediately at the corner between just in front of the fire and the ground. (2) The shape and dimension of the division of the 3 zones is mainly decided by slope angle and ambient wind speed given fire line intensity. (3) There exits an upwind zone in front of fire front. Ambient wind speeds have little effect on the magnitude of the upwind speed when slope angle is 0. But when the slope angle is negative, the upwind is apparently stronger.
文摘Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. In this paper the assignment and theoretical investigations of the problems of crown forest fire spread in windy condition were carried out. In this context, a study—mathematical modeling—of the conditions of forest fire spreading that would make it possible to obtain a detailed picture of the change in the temperature and component concentration fields with time, and determine as well as the limiting condition of fire propagation in forest with fire break.
文摘In this paper, we establish a mathematical model of the forest fire spread process based on a partial differential equation. We describe the distribution of time field and velocity field in the whole two-dimensional space by vector field theory. And we obtain a continuous algorithm to predict the dynamic behavior of forest fire spread in a short time. We use the algorithm to interpolate the fire boundary by cubic non-uniform rational B-spline closed curve. The fire boundary curve at any time can be simulated by solving the Eikonal equation. The model is tested in theory and in practice. The results show that the model has good accuracy and stability, and it’s compatible with most of the existing models, such as the elliptic model and the cellular automata model.
