The comparative study of the tensile plastic deformation of nano(n)-TiO2 ceramic prepared byphysical gas condensation (P) and chemical hydrolysis precipitation (C) methods was conductedby a gas pressure forming techni...The comparative study of the tensile plastic deformation of nano(n)-TiO2 ceramic prepared byphysical gas condensation (P) and chemical hydrolysis precipitation (C) methods was conductedby a gas pressure forming technique at 750~800℃. The results show that n-TiO2 (P) possessesexcellent property of tensile pIastic deformation comparing with n-TiO2(C). The reason for thisis attributed to the surface cleanness and soft agglomeration of n-TiO2 (P) particfe prepared inreIatively cIean vacuum condition.展开更多
INTRODUCTIONUrrets-Zavalia was first described as a syndrome consisting of a fixed,dilated pupil with iris atrophy following penetrating keratoplasty（PKP）in 1963 and back then it was thought that this syndrome was o...INTRODUCTIONUrrets-Zavalia was first described as a syndrome consisting of a fixed,dilated pupil with iris atrophy following penetrating keratoplasty（PKP）in 1963 and back then it was thought that this syndrome was only related to keratoconus patients.Other findings that were not essential for the diagnosis were posterior synechiae,ectropion uvea,pigment dispersion,anterior subcapsular lens opacities and secondary glaucoma syndrome.展开更多
Polysaccharides are the important biologically active components found in the peel of Dioscorea opposita Thunb.(DTTP).The influences of 4 extraction methods,namely hot water extraction(W),acidic extraction(HA),hot-com...Polysaccharides are the important biologically active components found in the peel of Dioscorea opposita Thunb.(DTTP).The influences of 4 extraction methods,namely hot water extraction(W),acidic extraction(HA),hot-compressed water extraction(HCW)and enzyme-assisted extraction(EAE),on the yields,physicochemical properties,hypoglycemic and antioxidant activities of polysaccharides from DTTP were studied and compared.Among these DTTP polysaccharides,DTTP-HA was outstanding in several respects.DTTP-HA was the most water soluble;it had the highest total carbohydrate content(85.08%),the highest uronic acid(13.20%)and the highest thermal stability.DTTP-HA and DTTP-W possessed a triple-helix structure.These 4 kinds of polysaccharides have the same types of monosaccharides,but in different molar percentages.Extraction method had a significant impact on the microstructures of the extracted polysaccharides.DTT-HA exhibited irregular structure with many holes.Among the 4 extracted methods,the DTTP-HA and DTTP-W initially exhibited higher hypoglycemic and antioxidant activities.The better bioactivities of DTTP-HA may be related to the above factors.The findings indicated that acid extraction is an effective method to extract polysaccharides with high biological activities from DTTP.展开更多
To screen new biological formulations, accurate and efficient application technology, field test was conducted with 72% Bacillus thuringiensis(Bt)·monosultap WP, 8% lambda-cyhalothrin·emamectin benzoate SA a...To screen new biological formulations, accurate and efficient application technology, field test was conducted with 72% Bacillus thuringiensis(Bt)·monosultap WP, 8% lambda-cyhalothrin·emamectin benzoate SA and 3.6% lambda-cyhalothrin·Bt SA through manual spraying and unmanned aerial vehicle spraying. Test results and comprehensive evaluation analysis demonstrated that 72% Bt·monosultap WP and 8%lambda-cyhalothrin·emamectin benzoate SA by manual spraying and unmanned aerial vehicle spraying had good prevention and control effect on strains and internodes damaged by Tryporyza intacta Snellen in middle and late stage, which were ideal new biological formulations with high effi-ciency and low risk for prevention and control of T. intacta in middle and late stage, and could be popularized in sugarcane area. 72% Bt·monosultap WP at the dose of 3 000 g/hectare and 8% lambda-cyhalothrin·emamectin benzoate SA at the dose of 750 mL/hectare could be sprayed in mid September at the peak occurrence period of the forth and fifth generations of T. intacta and Proceras venosatus. Agents were diluted with 900 kg water per hectare, and manually sprayed with electric knapsack sprayer; or agents were diluted with 15 kg of Haoyang aerial control special addi-tives and water per hectare, and sprayed with unmanned aerial vehicle. The control effect against borer-damaged strain rate was above 81.3% and that against borer-damaged internode rate was above 88.6%.展开更多
In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error...In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.展开更多
To establish a standard system for geneticstudies on sheath blight resistance, a field testwas conducted at the experimental farm ofYangzhou University to compare several pro-cedures for inoculating rice plants with R...To establish a standard system for geneticstudies on sheath blight resistance, a field testwas conducted at the experimental farm ofYangzhou University to compare several pro-cedures for inoculating rice plants with R.solani Kuhn (RH9). The varieties used wereJasmine 85, Teqing (resistant or moderatelyresistant), and Lemont (susceptible). They展开更多
Objective: to analyze the effect of Philips 256ict in different examination methods of coronary artery. Methods: 50 patients who received Philips 256ict coronary artery examination in our hospital from 2015 to Decembe...Objective: to analyze the effect of Philips 256ict in different examination methods of coronary artery. Methods: 50 patients who received Philips 256ict coronary artery examination in our hospital from 2015 to December 2019 were selected and divided into two groups according to the different examination methods. Group A (25 cases) and group B (25 cases). The results of the two groups were observed, mainly including the quality of blood vessel images and radiation dose. Results: there was no significant difference in vascular image quality between group A and group B, and the difference was not statistically significant (P > 0.05);the radiation dose of group A was significantly lower than that of group B (P < 0.05). Conclusion: the application of Philips 256iCT in different coronary artery examinations, prospective ECG control and retrospective ECG control can both obtain good vascular image quality, but the clinical application of the former can effectively reduce the radiation dose, so it has more significant application advantages.展开更多
Objective: to explore the value of different treatment methods in patients with pelvic inflammatory disease. Methods: through double-blind randomization, 78 cases of pelvic inflammatory disease were divided into two g...Objective: to explore the value of different treatment methods in patients with pelvic inflammatory disease. Methods: through double-blind randomization, 78 cases of pelvic inflammatory disease were divided into two groups (group A = 39 cases) and (Group B = 39 cases) from January 2020 to March 2021. Group B was treated with conventional drugs, and group A was treated with drugs + microwave combination. After the relevant treatment, the clinical efficacy of the two groups of cases was compared. Compared with the levels of IL-2 and TNF-A, the microwave binding method in group A was more advantageous than that in group B. In addition, in terms of the levels of inflammatory factors, group A tended to be more stable than group B, with significant differences in p-value data. Conclusion: targeted treatment of pelvic inflammatory disease, through drugs and microwave method to carry out comprehensive treatment, can promote the organic optimization of inflammatory level, and constantly improve the clinical efficacy, should be vigorously promoted in clinical.展开更多
Objective: to analyze the influence of different dissolution evaluation methods on the level of pharmaceutical preparations, and to sort out the application strategies for improving the level of pharmaceutical prepara...Objective: to analyze the influence of different dissolution evaluation methods on the level of pharmaceutical preparations, and to sort out the application strategies for improving the level of pharmaceutical preparations. Methods: 100 paracetamol tablets were screened out and then divided into 2 groups according to the blind selection method, specifically referring to: the observation group and the control group, each group is 50 tablets, among which, the observation group selected 0.04%NaOH solution as the dissolution medium, and then the dissolution was evaluated;In the control group, phosphate buffer with PH 6.8 was selected as the dissolution medium, and then the dissolution was evaluated. The dissolution amount and dissolution percentage (80%) of the two groups were determined separately. Results: in terms of the changes of dissolution volume, percentage of dissolution and other indicators, the observation group far exceeded the control group. However, in terms of the average dissolution time, the observation group was significantly smaller than the control group, and the difference between the two groups was significant, with a statistical advantage (P < 0.05). Conclusion: since the evaluation methods of dissolution are different, there are obvious differences in the changes in the level of pharmaceutical preparations. If the level of pharmaceutical preparations is to be gradually improved, the best dissolution evaluation method must be selected before the corresponding test results can be obtained.展开更多
Objective: to explore and compare the effects of different health education methods on blood pressure control level of patients with essential hypertension in physical examination center. Methods: 80 patients with ess...Objective: to explore and compare the effects of different health education methods on blood pressure control level of patients with essential hypertension in physical examination center. Methods: 80 patients with essential hypertension were divided into groups by touching the ball in the physical examination center. 40 patients in the control group received basic health education and 40 patients in the observation group received systematic health education. The results were observed and recorded. Results: the blood pressure index of the observation group was lower, and the score of quality of life and nursing satisfaction were higher (P < 0.05). Conclusion: systematic health education plays a very important role in stabilizing and controlling blood pressure. The quality of life of patients is generally improved. They are very satisfied with the nursing model, which is worthy of popularization and use.展开更多
This paper deals with numerical computation and analysis for the initial boundary problems of two dimensional(2D)Sobolev equations with piecewise continuous argument.Firstly,a two-level high-order compact difference m...This paper deals with numerical computation and analysis for the initial boundary problems of two dimensional(2D)Sobolev equations with piecewise continuous argument.Firstly,a two-level high-order compact difference method(HOCDM)with computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4))is suggested,whereτ,h_(x),h_(y) denote the temporal and spatial stepsizes of the method,respectively.In order to improve the temporal computational accuracy of this method,the Richardson extrapolation technique is used and thus a new two-level HOCDMis derived,which is proved to be convergent of order four both in time and space.Although the new two-level HOCDM has the higher computational accuracy in time than the previous one,it will bring a larger computational cost.To overcome this deficiency,a three-level HOCDM with computational accuracy O(τ^(4)+h_(x)^(4)+h_(y)^(4))is constructed.Finally,with a series of numerical experiments,the theoretical accuracy and computational efficiency of the above methods are further verified.展开更多
In this paper,we apply high-order finite difference(FD)schemes for multispecies and multireaction detonations(MMD).In MMD,the density and pressure are positive and the mass fraction of the ith species in the chemical ...In this paper,we apply high-order finite difference(FD)schemes for multispecies and multireaction detonations(MMD).In MMD,the density and pressure are positive and the mass fraction of the ith species in the chemical reaction,say zi,is between 0 and 1,withΣz_(i)=1.Due to the lack of maximum-principle,most of the previous bound-preserving technique cannot be applied directly.To preserve those bounds,we will use the positivity-preserving technique to all the zi'is and enforceΣz_(i)=1 by constructing conservative schemes,thanks to conservative time integrations and consistent numerical fluxes in the system.Moreover,detonation is an extreme singular mode of flame propagation in premixed gas,and the model contains a significant stiff source.It is well known that for hyperbolic equations with stiff source,the transition points in the numerical approximations near the shocks may trigger spurious shock speed,leading to wrong shock position.Intuitively,the high-order weighted essentially non-oscillatory(WENO)scheme,which can suppress oscillations near the discontinuities,would be a good choice for spatial discretization.However,with the nonlinear weights,the numerical fluxes are no longer“consistent”,leading to nonconservative numerical schemes and the bound-preserving technique does not work.Numerical experiments demonstrate that,without further numerical techniques such as subcell resolutions,the conservative FD method with linear weights can yield better numerical approximations than the nonconservative WENO scheme.展开更多
In this paper, three implicit finite difference methods are developed to solve one dimensional time fractional advection-diffusion equation. The fractional derivative is treated by applying right shifted Grünwald...In this paper, three implicit finite difference methods are developed to solve one dimensional time fractional advection-diffusion equation. The fractional derivative is treated by applying right shifted Grünwald-Letnikov formula of order α ∈(0, 1). We investigate the stability analysis by using von Neumann method with mathematical induction and prove that these three proposed methods are unconditionally stable. Numerical results are presented to demonstrate the effectiveness of the schemes mentioned in this paper.展开更多
In this work, we will derive numerical schemes for solving 3-coupled nonlinear Schrödinger equations using finite difference method and time splitting method combined with finite difference method. The result...In this work, we will derive numerical schemes for solving 3-coupled nonlinear Schrödinger equations using finite difference method and time splitting method combined with finite difference method. The resulting schemes are highly accurate, unconditionally stable. We use the exact single soliton solution and the conserved quantities to check the accuracy and the efficiency of the proposed schemes. Also, we use these methods to study the interaction dynamics of two solitons. It is found that both elastic and inelastic collision can take place under suitable parametric conditions. We have noticed that the inelastic collision of single solitons occurs in two different manners: enhancement or suppression of the amplitude.展开更多
An approach of solving the finite difference equations with Monte Carlo method was presented. The accuracy of algorithm is guaranteed by the Central Limit Theorem. The computation of the value on each single node is i...An approach of solving the finite difference equations with Monte Carlo method was presented. The accuracy of algorithm is guaranteed by the Central Limit Theorem. The computation of the value on each single node is independent of each other, which makes it easy to realize the algorithm in parallel processing and greatly improves the efficiency while dealing with local area computation. As long as different kinds of boundary conditions are statistics modeled,wide applications can the be made where the finite difference method is of competence.展开更多
Rotational components play an important role in natural earthquake research,engineering seismic investigation,building monitoring,seismic exploration and other fields.Traditional researches mainly focus on three trans...Rotational components play an important role in natural earthquake research,engineering seismic investigation,building monitoring,seismic exploration and other fields.Traditional researches mainly focus on three translational components,but less on rotational ones.As the precision of rotational sensing techniques has increased,many scholars have paid more attention to the seismic rotational motions.Because the rotational observations are not very popular before and now,approximately converting the translational components into rotational components is utilized in rotation analysis.Based on numerical six-component seismic data with the finite difference method,we compare three different conversion methods,the travelling-wave,frequency-domain and the difference method,to analyze their characteristics and feasibilities when they are applied to estimate rotational components with translational observations.展开更多
The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are...The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continnous time.展开更多
The value of a European option satisfies the Black-Scholes equation with appropriately specified final and boundary conditions.We transform the problem to an initial boundary value problem in dimensionless form.There ...The value of a European option satisfies the Black-Scholes equation with appropriately specified final and boundary conditions.We transform the problem to an initial boundary value problem in dimensionless form.There are two parameters in the coefficients of the resulting linear parabolic partial differential equation.For a range of values of these parameters,the solution of the problem has a boundary or an initial layer.The initial function has a discontinuity in the first-order derivative,which leads to the appearance of an interior layer.We construct analytically the asymptotic solution of the equation in a finite domain.Based on the asymptotic solution we can determine the size of the artificial boundary such that the required solution in a finite domain in x and at the final time is not affected by the boundary.Also,we study computationally the behaviour in the maximum norm of the errors in numerical solutions in cases such that one of the parameters varies from finite (or pretty large) to small values,while the other parameter is fixed and takes either finite (or pretty large) or small values. Crank-Nicolson explicit and implicit schemes using centered or upwind approximations to the derivative are studied.We present numerical computations,which determine experimentally the parameter-uniform rates of convergence.We note that this rate is rather weak,due probably to mixed sources of error such as initial and boundary layers and the discontinuity in the derivative of the solution.展开更多
The numerical solution of a singularly perturbed problem for the semilinear parabolic differential equation with parabolic boundary layers is discussed. A nonlinear two-level difference scheme is constructed on the sp...The numerical solution of a singularly perturbed problem for the semilinear parabolic differential equation with parabolic boundary layers is discussed. A nonlinear two-level difference scheme is constructed on the special non-uniform grids. The uniform con vergence of this scheme is proved and some numerical examples are given.展开更多
文摘The comparative study of the tensile plastic deformation of nano(n)-TiO2 ceramic prepared byphysical gas condensation (P) and chemical hydrolysis precipitation (C) methods was conductedby a gas pressure forming technique at 750~800℃. The results show that n-TiO2 (P) possessesexcellent property of tensile pIastic deformation comparing with n-TiO2(C). The reason for thisis attributed to the surface cleanness and soft agglomeration of n-TiO2 (P) particfe prepared inreIatively cIean vacuum condition.
文摘INTRODUCTIONUrrets-Zavalia was first described as a syndrome consisting of a fixed,dilated pupil with iris atrophy following penetrating keratoplasty（PKP）in 1963 and back then it was thought that this syndrome was only related to keratoconus patients.Other findings that were not essential for the diagnosis were posterior synechiae,ectropion uvea,pigment dispersion,anterior subcapsular lens opacities and secondary glaucoma syndrome.
基金the financial support provided by Zhengzhou 1125 Talents Gathering Project (2018)the Doctor startup fund of Henan Agricultural University (30500431)
文摘Polysaccharides are the important biologically active components found in the peel of Dioscorea opposita Thunb.(DTTP).The influences of 4 extraction methods,namely hot water extraction(W),acidic extraction(HA),hot-compressed water extraction(HCW)and enzyme-assisted extraction(EAE),on the yields,physicochemical properties,hypoglycemic and antioxidant activities of polysaccharides from DTTP were studied and compared.Among these DTTP polysaccharides,DTTP-HA was outstanding in several respects.DTTP-HA was the most water soluble;it had the highest total carbohydrate content(85.08%),the highest uronic acid(13.20%)and the highest thermal stability.DTTP-HA and DTTP-W possessed a triple-helix structure.These 4 kinds of polysaccharides have the same types of monosaccharides,but in different molar percentages.Extraction method had a significant impact on the microstructures of the extracted polysaccharides.DTT-HA exhibited irregular structure with many holes.Among the 4 extracted methods,the DTTP-HA and DTTP-W initially exhibited higher hypoglycemic and antioxidant activities.The better bioactivities of DTTP-HA may be related to the above factors.The findings indicated that acid extraction is an effective method to extract polysaccharides with high biological activities from DTTP.
基金Supported by Special Fund of China Agricultural (Sugar) Industry Research System(CARS-170303)Training Project of Yunling Industry and Technology Leading Talents "Control of Sugarcane Harm-ful Organisms"(2018LJRC56)Special Fund of Agricultural Industry Research System in Yunnan Province
文摘To screen new biological formulations, accurate and efficient application technology, field test was conducted with 72% Bacillus thuringiensis(Bt)·monosultap WP, 8% lambda-cyhalothrin·emamectin benzoate SA and 3.6% lambda-cyhalothrin·Bt SA through manual spraying and unmanned aerial vehicle spraying. Test results and comprehensive evaluation analysis demonstrated that 72% Bt·monosultap WP and 8%lambda-cyhalothrin·emamectin benzoate SA by manual spraying and unmanned aerial vehicle spraying had good prevention and control effect on strains and internodes damaged by Tryporyza intacta Snellen in middle and late stage, which were ideal new biological formulations with high effi-ciency and low risk for prevention and control of T. intacta in middle and late stage, and could be popularized in sugarcane area. 72% Bt·monosultap WP at the dose of 3 000 g/hectare and 8% lambda-cyhalothrin·emamectin benzoate SA at the dose of 750 mL/hectare could be sprayed in mid September at the peak occurrence period of the forth and fifth generations of T. intacta and Proceras venosatus. Agents were diluted with 900 kg water per hectare, and manually sprayed with electric knapsack sprayer; or agents were diluted with 15 kg of Haoyang aerial control special addi-tives and water per hectare, and sprayed with unmanned aerial vehicle. The control effect against borer-damaged strain rate was above 81.3% and that against borer-damaged internode rate was above 88.6%.
文摘In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.
文摘To establish a standard system for geneticstudies on sheath blight resistance, a field testwas conducted at the experimental farm ofYangzhou University to compare several pro-cedures for inoculating rice plants with R.solani Kuhn (RH9). The varieties used wereJasmine 85, Teqing (resistant or moderatelyresistant), and Lemont (susceptible). They
文摘Objective: to analyze the effect of Philips 256ict in different examination methods of coronary artery. Methods: 50 patients who received Philips 256ict coronary artery examination in our hospital from 2015 to December 2019 were selected and divided into two groups according to the different examination methods. Group A (25 cases) and group B (25 cases). The results of the two groups were observed, mainly including the quality of blood vessel images and radiation dose. Results: there was no significant difference in vascular image quality between group A and group B, and the difference was not statistically significant (P > 0.05);the radiation dose of group A was significantly lower than that of group B (P < 0.05). Conclusion: the application of Philips 256iCT in different coronary artery examinations, prospective ECG control and retrospective ECG control can both obtain good vascular image quality, but the clinical application of the former can effectively reduce the radiation dose, so it has more significant application advantages.
文摘Objective: to explore the value of different treatment methods in patients with pelvic inflammatory disease. Methods: through double-blind randomization, 78 cases of pelvic inflammatory disease were divided into two groups (group A = 39 cases) and (Group B = 39 cases) from January 2020 to March 2021. Group B was treated with conventional drugs, and group A was treated with drugs + microwave combination. After the relevant treatment, the clinical efficacy of the two groups of cases was compared. Compared with the levels of IL-2 and TNF-A, the microwave binding method in group A was more advantageous than that in group B. In addition, in terms of the levels of inflammatory factors, group A tended to be more stable than group B, with significant differences in p-value data. Conclusion: targeted treatment of pelvic inflammatory disease, through drugs and microwave method to carry out comprehensive treatment, can promote the organic optimization of inflammatory level, and constantly improve the clinical efficacy, should be vigorously promoted in clinical.
文摘Objective: to analyze the influence of different dissolution evaluation methods on the level of pharmaceutical preparations, and to sort out the application strategies for improving the level of pharmaceutical preparations. Methods: 100 paracetamol tablets were screened out and then divided into 2 groups according to the blind selection method, specifically referring to: the observation group and the control group, each group is 50 tablets, among which, the observation group selected 0.04%NaOH solution as the dissolution medium, and then the dissolution was evaluated;In the control group, phosphate buffer with PH 6.8 was selected as the dissolution medium, and then the dissolution was evaluated. The dissolution amount and dissolution percentage (80%) of the two groups were determined separately. Results: in terms of the changes of dissolution volume, percentage of dissolution and other indicators, the observation group far exceeded the control group. However, in terms of the average dissolution time, the observation group was significantly smaller than the control group, and the difference between the two groups was significant, with a statistical advantage (P < 0.05). Conclusion: since the evaluation methods of dissolution are different, there are obvious differences in the changes in the level of pharmaceutical preparations. If the level of pharmaceutical preparations is to be gradually improved, the best dissolution evaluation method must be selected before the corresponding test results can be obtained.
文摘Objective: to explore and compare the effects of different health education methods on blood pressure control level of patients with essential hypertension in physical examination center. Methods: 80 patients with essential hypertension were divided into groups by touching the ball in the physical examination center. 40 patients in the control group received basic health education and 40 patients in the observation group received systematic health education. The results were observed and recorded. Results: the blood pressure index of the observation group was lower, and the score of quality of life and nursing satisfaction were higher (P < 0.05). Conclusion: systematic health education plays a very important role in stabilizing and controlling blood pressure. The quality of life of patients is generally improved. They are very satisfied with the nursing model, which is worthy of popularization and use.
文摘This paper deals with numerical computation and analysis for the initial boundary problems of two dimensional(2D)Sobolev equations with piecewise continuous argument.Firstly,a two-level high-order compact difference method(HOCDM)with computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4))is suggested,whereτ,h_(x),h_(y) denote the temporal and spatial stepsizes of the method,respectively.In order to improve the temporal computational accuracy of this method,the Richardson extrapolation technique is used and thus a new two-level HOCDMis derived,which is proved to be convergent of order four both in time and space.Although the new two-level HOCDM has the higher computational accuracy in time than the previous one,it will bring a larger computational cost.To overcome this deficiency,a three-level HOCDM with computational accuracy O(τ^(4)+h_(x)^(4)+h_(y)^(4))is constructed.Finally,with a series of numerical experiments,the theoretical accuracy and computational efficiency of the above methods are further verified.
基金the National Natural Science Foundation of China under Grant Number NSFC 11801302Tsinghua University Initiative Scientific Research Program.Yang Yang is supported by the NSF Grant DMS-1818467.
文摘In this paper,we apply high-order finite difference(FD)schemes for multispecies and multireaction detonations(MMD).In MMD,the density and pressure are positive and the mass fraction of the ith species in the chemical reaction,say zi,is between 0 and 1,withΣz_(i)=1.Due to the lack of maximum-principle,most of the previous bound-preserving technique cannot be applied directly.To preserve those bounds,we will use the positivity-preserving technique to all the zi'is and enforceΣz_(i)=1 by constructing conservative schemes,thanks to conservative time integrations and consistent numerical fluxes in the system.Moreover,detonation is an extreme singular mode of flame propagation in premixed gas,and the model contains a significant stiff source.It is well known that for hyperbolic equations with stiff source,the transition points in the numerical approximations near the shocks may trigger spurious shock speed,leading to wrong shock position.Intuitively,the high-order weighted essentially non-oscillatory(WENO)scheme,which can suppress oscillations near the discontinuities,would be a good choice for spatial discretization.However,with the nonlinear weights,the numerical fluxes are no longer“consistent”,leading to nonconservative numerical schemes and the bound-preserving technique does not work.Numerical experiments demonstrate that,without further numerical techniques such as subcell resolutions,the conservative FD method with linear weights can yield better numerical approximations than the nonconservative WENO scheme.
文摘In this paper, three implicit finite difference methods are developed to solve one dimensional time fractional advection-diffusion equation. The fractional derivative is treated by applying right shifted Grünwald-Letnikov formula of order α ∈(0, 1). We investigate the stability analysis by using von Neumann method with mathematical induction and prove that these three proposed methods are unconditionally stable. Numerical results are presented to demonstrate the effectiveness of the schemes mentioned in this paper.
文摘In this work, we will derive numerical schemes for solving 3-coupled nonlinear Schrödinger equations using finite difference method and time splitting method combined with finite difference method. The resulting schemes are highly accurate, unconditionally stable. We use the exact single soliton solution and the conserved quantities to check the accuracy and the efficiency of the proposed schemes. Also, we use these methods to study the interaction dynamics of two solitons. It is found that both elastic and inelastic collision can take place under suitable parametric conditions. We have noticed that the inelastic collision of single solitons occurs in two different manners: enhancement or suppression of the amplitude.
文摘An approach of solving the finite difference equations with Monte Carlo method was presented. The accuracy of algorithm is guaranteed by the Central Limit Theorem. The computation of the value on each single node is independent of each other, which makes it easy to realize the algorithm in parallel processing and greatly improves the efficiency while dealing with local area computation. As long as different kinds of boundary conditions are statistics modeled,wide applications can the be made where the finite difference method is of competence.
基金This research is supported by the National Natural Science Foundation of China(grant No.U1839208).
文摘Rotational components play an important role in natural earthquake research,engineering seismic investigation,building monitoring,seismic exploration and other fields.Traditional researches mainly focus on three translational components,but less on rotational ones.As the precision of rotational sensing techniques has increased,many scholars have paid more attention to the seismic rotational motions.Because the rotational observations are not very popular before and now,approximately converting the translational components into rotational components is utilized in rotation analysis.Based on numerical six-component seismic data with the finite difference method,we compare three different conversion methods,the travelling-wave,frequency-domain and the difference method,to analyze their characteristics and feasibilities when they are applied to estimate rotational components with translational observations.
文摘The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continnous time.
基金partially supported by the Russian Foundation for Basic Research(grant No.07-01-00729)the Singapore Academic Research Funds R-146-000-064-112 and R-146-000-099-112the Boole Centre for Research in Informatics at the National University of Ireland,Cork and by the Mathematics Applications Consortium for Science and Industry in Ireland(MACSI)under the Science Foundation Ireland Mathematics Initiative.
文摘The value of a European option satisfies the Black-Scholes equation with appropriately specified final and boundary conditions.We transform the problem to an initial boundary value problem in dimensionless form.There are two parameters in the coefficients of the resulting linear parabolic partial differential equation.For a range of values of these parameters,the solution of the problem has a boundary or an initial layer.The initial function has a discontinuity in the first-order derivative,which leads to the appearance of an interior layer.We construct analytically the asymptotic solution of the equation in a finite domain.Based on the asymptotic solution we can determine the size of the artificial boundary such that the required solution in a finite domain in x and at the final time is not affected by the boundary.Also,we study computationally the behaviour in the maximum norm of the errors in numerical solutions in cases such that one of the parameters varies from finite (or pretty large) to small values,while the other parameter is fixed and takes either finite (or pretty large) or small values. Crank-Nicolson explicit and implicit schemes using centered or upwind approximations to the derivative are studied.We present numerical computations,which determine experimentally the parameter-uniform rates of convergence.We note that this rate is rather weak,due probably to mixed sources of error such as initial and boundary layers and the discontinuity in the derivative of the solution.
文摘The numerical solution of a singularly perturbed problem for the semilinear parabolic differential equation with parabolic boundary layers is discussed. A nonlinear two-level difference scheme is constructed on the special non-uniform grids. The uniform con vergence of this scheme is proved and some numerical examples are given.
