Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna...Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.展开更多
Streptococcus pneumonia is one of the leading causes of mobility and mortality in children under 6 years and the elderly especially in developing countries in which Ghana,the study area is not an exception.In this pap...Streptococcus pneumonia is one of the leading causes of mobility and mortality in children under 6 years and the elderly especially in developing countries in which Ghana,the study area is not an exception.In this paper,a model of the spread and control of bacterial pneumonia that include symptomatic carriers,asymptomatic carriers and vaccination is formulated and analyzed to determine the effect of the vaccination intervention.Analysis of the system show that the disease free equilibrium is stable if and only if the basic reproductive number R0<1.For R01,the endemic equilibrium is globally stable and the disease persist.Numerical simulation on the system show that with effective vaccine intervention pneumonia infection can be eradicated in the long term.展开更多
文摘Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.
文摘Streptococcus pneumonia is one of the leading causes of mobility and mortality in children under 6 years and the elderly especially in developing countries in which Ghana,the study area is not an exception.In this paper,a model of the spread and control of bacterial pneumonia that include symptomatic carriers,asymptomatic carriers and vaccination is formulated and analyzed to determine the effect of the vaccination intervention.Analysis of the system show that the disease free equilibrium is stable if and only if the basic reproductive number R0<1.For R01,the endemic equilibrium is globally stable and the disease persist.Numerical simulation on the system show that with effective vaccine intervention pneumonia infection can be eradicated in the long term.
