Reaction-diffusion equations modeling Predator-Prey interaction are of current interest. Standard approaches such as first-order (in time) finite difference schemes for approximating the solution are widely spread. Th...Reaction-diffusion equations modeling Predator-Prey interaction are of current interest. Standard approaches such as first-order (in time) finite difference schemes for approximating the solution are widely spread. Though, this paper shows that recent advance methods can be more favored. In this work, we have incorporated, throughout numerical comparison experiments, spectral methods, for the space discretization, in conjunction with second and fourth-order time integrating methods for approximating the solution of the reaction-diffusion differential equations. The results have revealed that these methods have advantages over the conventional methods, some of which to mention are: the ease of implementation, accuracy and CPU time.展开更多
The influence of the ultra-short pulse wavelength on the populations in the three electronic states of CsI molecule is investigated using the time-dependent wave packet method. The calculated results show that the pop...The influence of the ultra-short pulse wavelength on the populations in the three electronic states of CsI molecule is investigated using the time-dependent wave packet method. The calculated results show that the populations in the two excited states approach to the maxima at the wavelengths of 369 nm and 297 nm, respectively. The photodissociation reaction channels of the CsI molecule can be chosen by controlling the pump pulse wavelength.展开更多
A closed form of an analytical expression of concentration in the single-enzyme, single-substrate system for the full range of enzyme activities has been derived. The time dependent analytical solution for substrate, ...A closed form of an analytical expression of concentration in the single-enzyme, single-substrate system for the full range of enzyme activities has been derived. The time dependent analytical solution for substrate, enzyme-substrate complex and product concentrations are presented by solving system of non-linear differential equation. We employ He’s Homotopy perturbation method to solve the coupled non-linear differential equations containing a non-linear term related to basic enzymatic reaction. The time dependent simple analytical expressions for substrate, enzyme-substrate and free enzyme concentrations have been derived in terms of dimensionless reaction diffusion parameters ε, λ1, λ2 and λ3 using perturbation method. The numerical solution of the problem is also reported using SCILAB software program. The analytical results are compared with our numerical results. An excellent agreement with simulation data is noted. The obtained results are valid for the whole solution domain.展开更多
Non-adiabatic dynamical calculations are carried out for the Na(3 p)+HD(ν = 1, j = 0)→NaH/NaD+D/H reaction on the diabatic potential energy surfaces of Wang et al.(Sci. Rep. 2018, 8, 17960) by using the time-depende...Non-adiabatic dynamical calculations are carried out for the Na(3 p)+HD(ν = 1, j = 0)→NaH/NaD+D/H reaction on the diabatic potential energy surfaces of Wang et al.(Sci. Rep. 2018, 8, 17960) by using the time-dependent wave packet method. The state-to-state integral cross sections and differential cross sections of two reaction channels(NaH/NaD+D/H)are calculated for collision energy up to 0.4 eV. The cross section branching ratio indicates that the dominant reaction channel changes from NaD+H to NaH+D when the collision energy is larger than 0.227 eV. The products from two reaction channels both prefer to form in vibrationally cold but rotationally hot states, and they both tend to forward scattering.展开更多
文摘Reaction-diffusion equations modeling Predator-Prey interaction are of current interest. Standard approaches such as first-order (in time) finite difference schemes for approximating the solution are widely spread. Though, this paper shows that recent advance methods can be more favored. In this work, we have incorporated, throughout numerical comparison experiments, spectral methods, for the space discretization, in conjunction with second and fourth-order time integrating methods for approximating the solution of the reaction-diffusion differential equations. The results have revealed that these methods have advantages over the conventional methods, some of which to mention are: the ease of implementation, accuracy and CPU time.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10674114 and 10604045)
文摘The influence of the ultra-short pulse wavelength on the populations in the three electronic states of CsI molecule is investigated using the time-dependent wave packet method. The calculated results show that the populations in the two excited states approach to the maxima at the wavelengths of 369 nm and 297 nm, respectively. The photodissociation reaction channels of the CsI molecule can be chosen by controlling the pump pulse wavelength.
文摘A closed form of an analytical expression of concentration in the single-enzyme, single-substrate system for the full range of enzyme activities has been derived. The time dependent analytical solution for substrate, enzyme-substrate complex and product concentrations are presented by solving system of non-linear differential equation. We employ He’s Homotopy perturbation method to solve the coupled non-linear differential equations containing a non-linear term related to basic enzymatic reaction. The time dependent simple analytical expressions for substrate, enzyme-substrate and free enzyme concentrations have been derived in terms of dimensionless reaction diffusion parameters ε, λ1, λ2 and λ3 using perturbation method. The numerical solution of the problem is also reported using SCILAB software program. The analytical results are compared with our numerical results. An excellent agreement with simulation data is noted. The obtained results are valid for the whole solution domain.
基金Project supported by the National Natural Science Foundation of China(Grant No.11774043)
文摘Non-adiabatic dynamical calculations are carried out for the Na(3 p)+HD(ν = 1, j = 0)→NaH/NaD+D/H reaction on the diabatic potential energy surfaces of Wang et al.(Sci. Rep. 2018, 8, 17960) by using the time-dependent wave packet method. The state-to-state integral cross sections and differential cross sections of two reaction channels(NaH/NaD+D/H)are calculated for collision energy up to 0.4 eV. The cross section branching ratio indicates that the dominant reaction channel changes from NaD+H to NaH+D when the collision energy is larger than 0.227 eV. The products from two reaction channels both prefer to form in vibrationally cold but rotationally hot states, and they both tend to forward scattering.
