A brain tumor occurs when abnormal cells grow, sometimes very rapidly, into an abnormal mass of tissue. The tumor can infect normal tissue, so there is an interaction between healthy and infected cell. The aim of this...A brain tumor occurs when abnormal cells grow, sometimes very rapidly, into an abnormal mass of tissue. The tumor can infect normal tissue, so there is an interaction between healthy and infected cell. The aim of this paper is to propose some efficient and accurate numerical methods for the computational solution of one-dimensional continuous basic models for the growth and control of brain tumors. After computing the analytical solution, we construct approximations of the solution to the problem using a standard second order finite difference method for space discretization and the Crank-Nicolson method for time discretization. Then, we investigate the convergence behavior of Conjugate gradient and generalized minimum residual as Krylov subspace methods to solve the tridiagonal toeplitz matrix system derived.展开更多
The cluster-shaped plasmonic nanostructures are used to manage the incident light inside an ultra-thin silicon solar cell.Here we simulate spherical,conical,pyramidal,and cylindrical nanoparticles in a form of a clust...The cluster-shaped plasmonic nanostructures are used to manage the incident light inside an ultra-thin silicon solar cell.Here we simulate spherical,conical,pyramidal,and cylindrical nanoparticles in a form of a cluster at the rear side of a thin silicon cell,using the finite difference time domain(FDTD)method.By calculating the optical absorption and hence the photocurrent,it is shown that the clustering of nanoparticles significantly improves them.The photocurrent enhancement is the result of the plasmonic effects of clustering the nanoparticles.For comparison,first a cell with a single nanoparticle at the rear side is evaluated.Then four smaller nanoparticles are put around it to make a cluster.The photocurrents of 20.478 mA/cm2,23.186 mA/cm2,21.427 mA/cm2,and 21.243 mA/cm2 are obtained for the cells using clustering conical,spherical,pyramidal,cylindrical NPs at the backside,respectively.These values are 13.987 mA/cm2,16.901 mA/cm2,16.507 mA/cm2,17.926 mA/cm2 for the cell with one conical,spherical,pyramidal,cylindrical NPs at the backside,respectively.Therefore,clustering can significantly improve the photocurrents.Finally,the distribution of the electric field and the generation rate for the proposed structures are calculated.展开更多
The paper introduces a method for displaying cubic volume cells (voxels) resulting frompartitioning given objectS with orthogonal planes for finite difference calculation. The method representS ablock of voxels as a B...The paper introduces a method for displaying cubic volume cells (voxels) resulting frompartitioning given objectS with orthogonal planes for finite difference calculation. The method representS ablock of voxels as a B-rep solid model and conStrUcts the B-rep geometric clementS with an approach frombottom to up. Once the B-rep model is established, it is efficient in displaying because inner voxels areomitted and many coplanar facetS are merged together. By displaying the interSeCtion lines of theconstructed B-reP model and the partitioning planes, the tessellation image can be generated.展开更多
The rational design of the sample cell may improve the sensitivity of surface-enhanced Raman scattering （SERS） detection in a high degree. Finite difference time domain （FDTD） simulations of the configuration of A...The rational design of the sample cell may improve the sensitivity of surface-enhanced Raman scattering （SERS） detection in a high degree. Finite difference time domain （FDTD） simulations of the configuration of Ag film-Ag particles illuminated by plane wave and evanescent wave are performed to provide physical insight for design of the sample cell. Numerical solutions indicate that the sample cell can provide more ＂hot spots＂ and the massive field intensity enhancement occurs in these ＂hot spots＂. More information on the nanometer character of the sample can be got because of gradient-field Raman （GFR） of evanescent wave. OCIS codes： 290.5860, 240.0310, 240.6680, 999.9999 （surface-enhanced Raman scattering）.展开更多
A comprehensive heat and mass transfer model of dissolution process of non-agglomerated and agglomerated alumina particles was established in an aluminum reduction cell. An appropriate finite difference method was use...A comprehensive heat and mass transfer model of dissolution process of non-agglomerated and agglomerated alumina particles was established in an aluminum reduction cell. An appropriate finite difference method was used to calculate the size dissolution rate, dissolution time and mass of alumina dissolved employing commercial software and custom algorithm based on the shrinking sphere assumption. The effects of some convection and thermal condition parameters on the dissolution process were studied. The calculated results show that the decrease of alumina content or the increase of alumina diffusion coefficient is beneficial for the increase of size dissolution rate and the decrease of dissolution time of non-agglomerated particles. The increase of bath superheat or alumina preheating temperature results in the increase of size dissolution rate and the decrease of dissolution time of agglomerated particles. The calculated dissolution curve of alumina（mass fraction of alumina dissolved） for a 300 k A aluminum reduction cell is in well accordance with the experimental results. The analysis shows that the dissolution process of alumina can be divided into two distinct stages： the fast dissolution stage of non-agglomerated particles and the slow dissolution stage of agglomerated particles, with the dissolution time in the order of 10 and 100 s, respectively. The agglomerated particles were identified to be the most important factor limiting the dissolution process.展开更多
为准确计算渤海海冰的动力过程,本文将质点网格方法(Particle in cell,简称PIC),引入到渤海海冰数值模拟中。该方法首先在欧拉坐标系下对海冰动力方程和连续方程进行差分求解,并插值出各网格内海冰质点的速度和密集度,然后在拉格朗日... 为准确计算渤海海冰的动力过程,本文将质点网格方法(Particle in cell,简称PIC),引入到渤海海冰数值模拟中。该方法首先在欧拉坐标系下对海冰动力方程和连续方程进行差分求解,并插值出各网格内海冰质点的速度和密集度,然后在拉格朗日坐标系下对海冰质点的位移和各网格的平均冰厚进行确定。PIC方法将欧拉法与拉格朗日法相结合,避免了欧拉坐标下有限差分法的数值扩散和拉格朗日坐标下光滑质点流体动力学计算量大的缺点。在对渤海海冰动力过程的数值模拟中采用了Hibler的粘塑性本构模型,并考虑了海冰热力作用过程。利用PIC方法对辽东湾海冰进行了48h数值模拟,结果表明:该方法可成功地处理海冰流变过程,精确计算出冰缘线位置和海冰分布状况,对海冰厚度和密集度的计算精度均优于有限差分法。PIC方法在精确模拟海冰的重叠和堆积过程,以及为冰区油气作业提供详实的海冰信息方面都有良好的应用前景。展开更多
文摘A brain tumor occurs when abnormal cells grow, sometimes very rapidly, into an abnormal mass of tissue. The tumor can infect normal tissue, so there is an interaction between healthy and infected cell. The aim of this paper is to propose some efficient and accurate numerical methods for the computational solution of one-dimensional continuous basic models for the growth and control of brain tumors. After computing the analytical solution, we construct approximations of the solution to the problem using a standard second order finite difference method for space discretization and the Crank-Nicolson method for time discretization. Then, we investigate the convergence behavior of Conjugate gradient and generalized minimum residual as Krylov subspace methods to solve the tridiagonal toeplitz matrix system derived.
文摘The cluster-shaped plasmonic nanostructures are used to manage the incident light inside an ultra-thin silicon solar cell.Here we simulate spherical,conical,pyramidal,and cylindrical nanoparticles in a form of a cluster at the rear side of a thin silicon cell,using the finite difference time domain(FDTD)method.By calculating the optical absorption and hence the photocurrent,it is shown that the clustering of nanoparticles significantly improves them.The photocurrent enhancement is the result of the plasmonic effects of clustering the nanoparticles.For comparison,first a cell with a single nanoparticle at the rear side is evaluated.Then four smaller nanoparticles are put around it to make a cluster.The photocurrents of 20.478 mA/cm2,23.186 mA/cm2,21.427 mA/cm2,and 21.243 mA/cm2 are obtained for the cells using clustering conical,spherical,pyramidal,cylindrical NPs at the backside,respectively.These values are 13.987 mA/cm2,16.901 mA/cm2,16.507 mA/cm2,17.926 mA/cm2 for the cell with one conical,spherical,pyramidal,cylindrical NPs at the backside,respectively.Therefore,clustering can significantly improve the photocurrents.Finally,the distribution of the electric field and the generation rate for the proposed structures are calculated.
文摘The paper introduces a method for displaying cubic volume cells (voxels) resulting frompartitioning given objectS with orthogonal planes for finite difference calculation. The method representS ablock of voxels as a B-rep solid model and conStrUcts the B-rep geometric clementS with an approach frombottom to up. Once the B-rep model is established, it is efficient in displaying because inner voxels areomitted and many coplanar facetS are merged together. By displaying the interSeCtion lines of theconstructed B-reP model and the partitioning planes, the tessellation image can be generated.
文摘The rational design of the sample cell may improve the sensitivity of surface-enhanced Raman scattering （SERS） detection in a high degree. Finite difference time domain （FDTD） simulations of the configuration of Ag film-Ag particles illuminated by plane wave and evanescent wave are performed to provide physical insight for design of the sample cell. Numerical solutions indicate that the sample cell can provide more ＂hot spots＂ and the massive field intensity enhancement occurs in these ＂hot spots＂. More information on the nanometer character of the sample can be got because of gradient-field Raman （GFR） of evanescent wave. OCIS codes： 290.5860, 240.0310, 240.6680, 999.9999 （surface-enhanced Raman scattering）.
基金Project(2010AA065201)supported by the High-tech Research and Development Program of ChinaProject(2013zzts038)supported by the Fundamental Research Funds for the Central Universities of Central South University,ChinaProject(ZB2011CBBCe1)supported by the Major Program for Aluminum Corporation of China Limited
文摘A comprehensive heat and mass transfer model of dissolution process of non-agglomerated and agglomerated alumina particles was established in an aluminum reduction cell. An appropriate finite difference method was used to calculate the size dissolution rate, dissolution time and mass of alumina dissolved employing commercial software and custom algorithm based on the shrinking sphere assumption. The effects of some convection and thermal condition parameters on the dissolution process were studied. The calculated results show that the decrease of alumina content or the increase of alumina diffusion coefficient is beneficial for the increase of size dissolution rate and the decrease of dissolution time of non-agglomerated particles. The increase of bath superheat or alumina preheating temperature results in the increase of size dissolution rate and the decrease of dissolution time of agglomerated particles. The calculated dissolution curve of alumina（mass fraction of alumina dissolved） for a 300 k A aluminum reduction cell is in well accordance with the experimental results. The analysis shows that the dissolution process of alumina can be divided into two distinct stages： the fast dissolution stage of non-agglomerated particles and the slow dissolution stage of agglomerated particles, with the dissolution time in the order of 10 and 100 s, respectively. The agglomerated particles were identified to be the most important factor limiting the dissolution process.
文摘 为准确计算渤海海冰的动力过程,本文将质点网格方法(Particle in cell,简称PIC),引入到渤海海冰数值模拟中。该方法首先在欧拉坐标系下对海冰动力方程和连续方程进行差分求解,并插值出各网格内海冰质点的速度和密集度,然后在拉格朗日坐标系下对海冰质点的位移和各网格的平均冰厚进行确定。PIC方法将欧拉法与拉格朗日法相结合,避免了欧拉坐标下有限差分法的数值扩散和拉格朗日坐标下光滑质点流体动力学计算量大的缺点。在对渤海海冰动力过程的数值模拟中采用了Hibler的粘塑性本构模型,并考虑了海冰热力作用过程。利用PIC方法对辽东湾海冰进行了48h数值模拟,结果表明:该方法可成功地处理海冰流变过程,精确计算出冰缘线位置和海冰分布状况,对海冰厚度和密集度的计算精度均优于有限差分法。PIC方法在精确模拟海冰的重叠和堆积过程,以及为冰区油气作业提供详实的海冰信息方面都有良好的应用前景。
