A Java program in a GUI environment has been developed for the numerical solution of basic partial differential equations and applied to Au diffusion in Si affected by vacancies and self-interstitials. Text fields of ...A Java program in a GUI environment has been developed for the numerical solution of basic partial differential equations and applied to Au diffusion in Si affected by vacancies and self-interstitials. Text fields of selected parameters for the calculation are set on the display, and the calculation starts by checking the start button after putting values on the text fields. The calculated results are plotted immediately after the finish of the calculation as the concentration profiles of substitutional Au, interstitial Au, vacancies and self-interstitials, and their diffusion can be presented immediately, resulting in the identification of the diffusion mechanism. By changing the values of the text fields, new results can be represented immediately. The diffusion of Au in Si can be simulated correctly and easily by this program. Results from the program for one set of conditions are shown, including images produced on the display.展开更多
This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information avail...This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.展开更多
We classify initial-value problems for extended KdV-Burgers equations via generalized conditional symmetries. These equations can be reduced to Cauchy problems for some systems of first-order ordinary differential equ...We classify initial-value problems for extended KdV-Burgers equations via generalized conditional symmetries. These equations can be reduced to Cauchy problems for some systems of first-order ordinary differential equations. The obtained reductions cannot be derived within the framework of the standard Lie approach.展开更多
This work describes the deterministic interaction of a diffusing particle of efavirenz through concentration gradient. Simulated pharmacokinetic data from patients on efavirenz are used. The Fourier’s Equation is use...This work describes the deterministic interaction of a diffusing particle of efavirenz through concentration gradient. Simulated pharmacokinetic data from patients on efavirenz are used. The Fourier’s Equation is used to infer on transfer of movement between solution particles. The work investigates diffusion using Fick’s analogy, but in a different variable space. Two important movement fluxes of a solution particle are derived an absorbing one identified as conductivity and a dispersing one identified as diffusivity. The Fourier’s Equation can be used to describe the process of gain/loss of movement in formation of a solution particle in an individual.展开更多
In this paper,an orthogonal-directional forward diffusion Partial Differential Equation(PDE) image inpainting and denoising model which processes image based on variation problem is proposed.The novel model restores t...In this paper,an orthogonal-directional forward diffusion Partial Differential Equation(PDE) image inpainting and denoising model which processes image based on variation problem is proposed.The novel model restores the damaged information and smoothes the noise in image si-multaneously.The model is morphological invariant which processes image based on the geometrical property.The regularization item of it diffuses along and cross the isophote,and then the known image information is transported into the target region through two orthogonal directions.The cross isophote diffusion part is the TV(Total Variation) equation and the along isophote diffusion part is the inviscid Helmholtz vorticity equation.The equivalence between the Helmholtz equation and the inpainting PDEs is proved.The model with the fidelity item which is used in the whole image domain denoises while preserving edges.So the novel model could inpaint and denoise simultaneously.Both theoretical analysis and experiments have verified the validity of the novel model proposed in this paper.展开更多
A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that gov...A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.展开更多
In this article,non-linear time-fractional diffusion equations are considered to describe oil pollution in the water.The latest technique,fractional reduced differential transform method(FRDTM),is used to ac-quire app...In this article,non-linear time-fractional diffusion equations are considered to describe oil pollution in the water.The latest technique,fractional reduced differential transform method(FRDTM),is used to ac-quire approximate solutions of the time fractional-order diffusion equation and two cases of Allen-Cahn equations.The acquired results are collated with the exact solutions and other results from literature for integer-orderα,which reveal that the proposed method is effective.Hence,FRDTM can be employed to obtain solutions for different types of nonlinear fractional-order IVPs arising in engineering and science.展开更多
We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),...We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),their local times exist when d≤3.A Tanaka formula of the local time is also derived.展开更多
文摘A Java program in a GUI environment has been developed for the numerical solution of basic partial differential equations and applied to Au diffusion in Si affected by vacancies and self-interstitials. Text fields of selected parameters for the calculation are set on the display, and the calculation starts by checking the start button after putting values on the text fields. The calculated results are plotted immediately after the finish of the calculation as the concentration profiles of substitutional Au, interstitial Au, vacancies and self-interstitials, and their diffusion can be presented immediately, resulting in the identification of the diffusion mechanism. By changing the values of the text fields, new results can be represented immediately. The diffusion of Au in Si can be simulated correctly and easily by this program. Results from the program for one set of conditions are shown, including images produced on the display.
文摘This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.
基金Supported by the National Natural Science Foundation of China under Grant No 10447007, and the Natural Science Foundation of Shaanxi Province under Grant No 2005A13.
文摘We classify initial-value problems for extended KdV-Burgers equations via generalized conditional symmetries. These equations can be reduced to Cauchy problems for some systems of first-order ordinary differential equations. The obtained reductions cannot be derived within the framework of the standard Lie approach.
文摘This work describes the deterministic interaction of a diffusing particle of efavirenz through concentration gradient. Simulated pharmacokinetic data from patients on efavirenz are used. The Fourier’s Equation is used to infer on transfer of movement between solution particles. The work investigates diffusion using Fick’s analogy, but in a different variable space. Two important movement fluxes of a solution particle are derived an absorbing one identified as conductivity and a dispersing one identified as diffusivity. The Fourier’s Equation can be used to describe the process of gain/loss of movement in formation of a solution particle in an individual.
基金the National Natural Science Foundation of China(No.60472033, No.60672062)the National Grand Fundamental Research 973 Program of China(No. 2004CB318005)the Technological Innovation Fund of Excellent Doctorial Candidate of Beijing Jiaotong University(No.48026)
文摘In this paper,an orthogonal-directional forward diffusion Partial Differential Equation(PDE) image inpainting and denoising model which processes image based on variation problem is proposed.The novel model restores the damaged information and smoothes the noise in image si-multaneously.The model is morphological invariant which processes image based on the geometrical property.The regularization item of it diffuses along and cross the isophote,and then the known image information is transported into the target region through two orthogonal directions.The cross isophote diffusion part is the TV(Total Variation) equation and the along isophote diffusion part is the inviscid Helmholtz vorticity equation.The equivalence between the Helmholtz equation and the inpainting PDEs is proved.The model with the fidelity item which is used in the whole image domain denoises while preserving edges.So the novel model could inpaint and denoise simultaneously.Both theoretical analysis and experiments have verified the validity of the novel model proposed in this paper.
文摘A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.
文摘In this article,non-linear time-fractional diffusion equations are considered to describe oil pollution in the water.The latest technique,fractional reduced differential transform method(FRDTM),is used to ac-quire approximate solutions of the time fractional-order diffusion equation and two cases of Allen-Cahn equations.The acquired results are collated with the exact solutions and other results from literature for integer-orderα,which reveal that the proposed method is effective.Hence,FRDTM can be employed to obtain solutions for different types of nonlinear fractional-order IVPs arising in engineering and science.
基金Partial funding in support of this work was provided by the Natural Sciences and Engineering Research Council of Canada(NSERC)the Department of Mathematics at the University of Oregon。
文摘We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),their local times exist when d≤3.A Tanaka formula of the local time is also derived.
