The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space (n= 1, 2 or 3) are derived by...The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space (n= 1, 2 or 3) are derived by means of the condition of mass conservation , the time-space similarity of the solution , Mellin transform and the properties of the Fox function . And the asymptotic behaviors for the solutions are also given .展开更多
The thermoelastic plane problems of two-dimensional decagonal quasicrystals(QCs)are systematically investigated.By introducing a displacement function,the problem of thermoelastic plane problems can be simplified to a...The thermoelastic plane problems of two-dimensional decagonal quasicrystals(QCs)are systematically investigated.By introducing a displacement function,the problem of thermoelastic plane problems can be simplified to an eighth-order partial differential governing equation,and then general solutions are presented through an operator method.By virtue of the Almansi′s theorem,the general solutions are further established,and all expressions for the phonon,phason and thermal fields are described in terms of the potential functions.As an application of the general solution,for a steady point heat source in a semi-infinite quasicrystal plane,the closed form solutions are presented by four newly induced harmonic functions.展开更多
In the description of the characteristic volume of fire behavior,fire intensity I<sub>r</sub>ate of spread R,and flame length L,etc.all have their scientific definitions,while the bound be-tween the fireli...In the description of the characteristic volume of fire behavior,fire intensity I<sub>r</sub>ate of spread R,and flame length L,etc.all have their scientific definitions,while the bound be-tween the fireline and the residual region of a fire scene is not yet scientifically defined.This pa-per tries to find out theoretically the basis for dividing the bound,to give the fireline thickness D a scientific definition,and to propose a method of quantitative calculation.According to the generality of fuels,the time-dependent curves of fuels combustion rate are utilized to work out a formula by experience.On the basis of defining scientifically the fireline thickness,the Byram’s formula is corrected,and a new one for calculating the fire intensity of slurface fire,i.e.I=0.788HWr,is presented.In this formula,H is the fuel low heat of combustion,the calculating method of the thermal cuyrrent intensity j is given,and J<sub>max</sub>=1.25HWR/D,the calculating formula of flame length is revised,and L=0.0775I<sup>0.46</sup>. In the展开更多
The evolution of the upward migration of the magma is a nonlinear and unstable problem in mathematics. It is difficult to solve it. And using the numerical method, the solution is relatively tedious and time-consuming...The evolution of the upward migration of the magma is a nonlinear and unstable problem in mathematics. It is difficult to solve it. And using the numerical method, the solution is relatively tedious and time-consuming. This paper introduces a method of the instantaneous point source to solve the linear and unstable heat conduction equation during the infinite period of time instead of the solution of the nonlinear and unstable heat conduction equation. The results obtained by this method coincide with those by the numerical method, meaning that this method offers a simple way to solve the nonlinear and unstable heat conduction equation.展开更多
基金the National Natural Science Foundation of China (10272067) the Doctoral Foundation of Education Ministry of China (1999042211)
文摘The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space (n= 1, 2 or 3) are derived by means of the condition of mass conservation , the time-space similarity of the solution , Mellin transform and the properties of the Fox function . And the asymptotic behaviors for the solutions are also given .
基金supported by the National Natural Sci-ence Foundation of China(11172319)the Chinese Univer-sities Scientific Fund(2011JS046,2013BH008)+2 种基金the Opening Fund of State Key Laboratory of Nonlinear Mechanicsthe Program for New Century Excellent Talents in Univer-sity(NCET-13-0552)the National Science Foundation for Post-doctoral Scientists of China(2013M541086)
文摘The thermoelastic plane problems of two-dimensional decagonal quasicrystals(QCs)are systematically investigated.By introducing a displacement function,the problem of thermoelastic plane problems can be simplified to an eighth-order partial differential governing equation,and then general solutions are presented through an operator method.By virtue of the Almansi′s theorem,the general solutions are further established,and all expressions for the phonon,phason and thermal fields are described in terms of the potential functions.As an application of the general solution,for a steady point heat source in a semi-infinite quasicrystal plane,the closed form solutions are presented by four newly induced harmonic functions.
文摘In the description of the characteristic volume of fire behavior,fire intensity I<sub>r</sub>ate of spread R,and flame length L,etc.all have their scientific definitions,while the bound be-tween the fireline and the residual region of a fire scene is not yet scientifically defined.This pa-per tries to find out theoretically the basis for dividing the bound,to give the fireline thickness D a scientific definition,and to propose a method of quantitative calculation.According to the generality of fuels,the time-dependent curves of fuels combustion rate are utilized to work out a formula by experience.On the basis of defining scientifically the fireline thickness,the Byram’s formula is corrected,and a new one for calculating the fire intensity of slurface fire,i.e.I=0.788HWr,is presented.In this formula,H is the fuel low heat of combustion,the calculating method of the thermal cuyrrent intensity j is given,and J<sub>max</sub>=1.25HWR/D,the calculating formula of flame length is revised,and L=0.0775I<sup>0.46</sup>. In the
文摘The evolution of the upward migration of the magma is a nonlinear and unstable problem in mathematics. It is difficult to solve it. And using the numerical method, the solution is relatively tedious and time-consuming. This paper introduces a method of the instantaneous point source to solve the linear and unstable heat conduction equation during the infinite period of time instead of the solution of the nonlinear and unstable heat conduction equation. The results obtained by this method coincide with those by the numerical method, meaning that this method offers a simple way to solve the nonlinear and unstable heat conduction equation.
