A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the phys- ical parameters and initial/boundary conditions. In virtue...A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the phys- ical parameters and initial/boundary conditions. In virtue of the level-cut method, the difference discrete equations with fuzzy parameters are equivalently transformed into groups of interval equations. New stability analysis theory suited to fuzzy difference schemes is developed. Based on the parameter perturbation method, the interval ranges of the uncertain temperature field can be approximately predicted. Subsequently, fuzzy solutions to the original difference equations are obtained by the fuzzy resolution theorem. Two numerical examples are given to demonstrate the feasibility and efficiency of the presented method for solving both steady-state and transient heat conduction problems.展开更多
A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference sche...A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference scheme and the error bounds of optimal order of the difference solutions are obtained in L^2 × H^1 × H^2 over a finite time interval （0, T]. Finally, the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.展开更多
The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip fa...The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero （total adhesion） and infinity （full slip）. Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and temperature fields. It is interesting to find that the slip increases the momentum and thermal boundary layer thickness. As the slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid. The presence of a magnetic field has also substantial effects on velocity and temperature fields.展开更多
One of the main factors of laser induced damage is the modulation to incident laser which is caused by the defect in the subsurface of the fused silica. In this work, the repaired damage site irradiated by CO2 laser i...One of the main factors of laser induced damage is the modulation to incident laser which is caused by the defect in the subsurface of the fused silica. In this work, the repaired damage site irradiated by CO2 laser is simplified to a Gaussian rotation according to the corresponding experimental results. Then, the three-dimensional finite-difference time-domain method is employed to simulate the electric field intensity distribution in the vicinity of this kind of defect in fused silica front subsurface. The simulated results show that the modulation is notable, the Emax is about 2.6 times the irradiated electric field intensity in the fused silica with the damage site （the width is 1.5 μm and depth is 2.3 μm） though the damage site is repaired by CO2 laser. The phenomenon and the theoretical result of the annular laser enhancement existed on the rear surface are first verified effectively, which agrees well with the corresponding experimental results. The relations between the maximal electric field intensity in fused silica with defect depth and width are given respectively. Meanwhile, the corresponding physical mechanism is analysed theoretically in detail.展开更多
In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a s...In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a static solid wall and a free boundary connected to a vacuum state. We take the homogeneous boundary conditions for velocity, microrotation and heat flux on the solid border and that the normal stress, heat flux and microrotation are equal to zero on the free boundary. The proof of the global existence of the solution is based on a limit procedure. We define the finite difference approximate equations system and construct the sequence of approximate solutions that converges to the solution of our problem globally in time.展开更多
This paper is a continuation of Ref. [1]. It employs frist-order accurateTaylor-Galerkin-based finite element approach for casting solidification. Theapproach is based on expressing the finite-difference approximation...This paper is a continuation of Ref. [1]. It employs frist-order accurateTaylor-Galerkin-based finite element approach for casting solidification. Theapproach is based on expressing the finite-difference approximation of thetransient time derivative of temperature, while the expressions of the governingequations are discretized in space via the classical Galerkin scheme using finite-element formulations. The detailed technique is reported in this study. Severalcasting solidification examples are solved to demonstrate the excellentagreements in comparison with the results obtained by using the control volumemethod, and to show the availability of combination of the finite elementmethod and the finite difference method in multi-dimensional modeling ofcasting solidification.展开更多
The problem of two dimensional stagnation point flow of an electrically conducting micropolar fluid impinging normally on a heated surface in the presence of a uniform transverse magnetic field is analyzed. The govern...The problem of two dimensional stagnation point flow of an electrically conducting micropolar fluid impinging normally on a heated surface in the presence of a uniform transverse magnetic field is analyzed. The governing continuity, momentum, angular momentum, and heat equations together with the associated boundary conditions are reduced to dimensionless form using suitable similarity transformations. The reduced self similar non-linear equations are then solved numerically by an algorithm based on the finite difference discretization. The results are further refined by Richardson＇s extrapolation. The effects of the magnetic parameter, the micropolar parameters, and the Prandtl number on the flow and temperature fields are predicted in tabular and graphical forms to show the important features of the solution. The study shows that the velocity and thermal boundary layers become thinner as the magnetic parameter is increased. The micropolar fluids display more reduction in shear stress as well as heat transfer rate than that exhibited by Newtonian fluids, which is beneficial in the flow and thermal control of polymeric processing.展开更多
Here we report a web server,the DelPhi web server,which utilizes DelPhi program to calculate electrostatic energies and the corresponding electrostatic potential and ionic distributions,and dielectric map.The server p...Here we report a web server,the DelPhi web server,which utilizes DelPhi program to calculate electrostatic energies and the corresponding electrostatic potential and ionic distributions,and dielectric map.The server provides extra services to fix structural defects,as missing atoms in the structural file and allows for generation of missing hydrogen atoms.The hydrogen placement and the corresponding DelPhi calculations can be done with user selected force field parameters being either Charmm22,Amber98 or OPLS.Upon completion of the calculations,the user is given option to download fixed and protonated structural file,together with the parameter and Delphi output files for further analysis.Utilizing Jmol viewer,the user can see the corresponding structural file,to manipulate it and to change the presentation.In addition,if the potential map is requested to be calculated,the potential can be mapped onto the molecule surface.The DelPhi web server is available from http://compbio.clemson.edu/delphi webserver.展开更多
基金supported by the National Special Fund for Major Research Instrument Development(2011YQ140145)111 Project(B07009)+1 种基金the National Natural Science Foundation of China(11002013)Defense Industrial Technology Development Program(A2120110001 and B2120110011)
文摘A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the phys- ical parameters and initial/boundary conditions. In virtue of the level-cut method, the difference discrete equations with fuzzy parameters are equivalently transformed into groups of interval equations. New stability analysis theory suited to fuzzy difference schemes is developed. Based on the parameter perturbation method, the interval ranges of the uncertain temperature field can be approximately predicted. Subsequently, fuzzy solutions to the original difference equations are obtained by the fuzzy resolution theorem. Two numerical examples are given to demonstrate the feasibility and efficiency of the presented method for solving both steady-state and transient heat conduction problems.
基金Supported by the National Natural Science Foundation of China(10371077)
文摘A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference scheme and the error bounds of optimal order of the difference solutions are obtained in L^2 × H^1 × H^2 over a finite time interval （0, T]. Finally, the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.
文摘The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero （total adhesion） and infinity （full slip）. Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and temperature fields. It is interesting to find that the slip increases the momentum and thermal boundary layer thickness. As the slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid. The presence of a magnetic field has also substantial effects on velocity and temperature fields.
基金Project supported by the National High Technology Research and Development Program of China (Grant No.2008AA8040508)the Youth Foundation of University of Science and Technology of China (Grant Nos.L08010401JX0834 and L08010401JX0806)the Fundamental Research Funds for the Central Universities of China
文摘One of the main factors of laser induced damage is the modulation to incident laser which is caused by the defect in the subsurface of the fused silica. In this work, the repaired damage site irradiated by CO2 laser is simplified to a Gaussian rotation according to the corresponding experimental results. Then, the three-dimensional finite-difference time-domain method is employed to simulate the electric field intensity distribution in the vicinity of this kind of defect in fused silica front subsurface. The simulated results show that the modulation is notable, the Emax is about 2.6 times the irradiated electric field intensity in the fused silica with the damage site （the width is 1.5 μm and depth is 2.3 μm） though the damage site is repaired by CO2 laser. The phenomenon and the theoretical result of the annular laser enhancement existed on the rear surface are first verified effectively, which agrees well with the corresponding experimental results. The relations between the maximal electric field intensity in fused silica with defect depth and width are given respectively. Meanwhile, the corresponding physical mechanism is analysed theoretically in detail.
基金supported by Scientific Research of the University of Rijeka(13.14.1.3.03)
文摘In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a static solid wall and a free boundary connected to a vacuum state. We take the homogeneous boundary conditions for velocity, microrotation and heat flux on the solid border and that the normal stress, heat flux and microrotation are equal to zero on the free boundary. The proof of the global existence of the solution is based on a limit procedure. We define the finite difference approximate equations system and construct the sequence of approximate solutions that converges to the solution of our problem globally in time.
文摘This paper is a continuation of Ref. [1]. It employs frist-order accurateTaylor-Galerkin-based finite element approach for casting solidification. Theapproach is based on expressing the finite-difference approximation of thetransient time derivative of temperature, while the expressions of the governingequations are discretized in space via the classical Galerkin scheme using finite-element formulations. The detailed technique is reported in this study. Severalcasting solidification examples are solved to demonstrate the excellentagreements in comparison with the results obtained by using the control volumemethod, and to show the availability of combination of the finite elementmethod and the finite difference method in multi-dimensional modeling ofcasting solidification.
文摘The problem of two dimensional stagnation point flow of an electrically conducting micropolar fluid impinging normally on a heated surface in the presence of a uniform transverse magnetic field is analyzed. The governing continuity, momentum, angular momentum, and heat equations together with the associated boundary conditions are reduced to dimensionless form using suitable similarity transformations. The reduced self similar non-linear equations are then solved numerically by an algorithm based on the finite difference discretization. The results are further refined by Richardson＇s extrapolation. The effects of the magnetic parameter, the micropolar parameters, and the Prandtl number on the flow and temperature fields are predicted in tabular and graphical forms to show the important features of the solution. The study shows that the velocity and thermal boundary layers become thinner as the magnetic parameter is increased. The micropolar fluids display more reduction in shear stress as well as heat transfer rate than that exhibited by Newtonian fluids, which is beneficial in the flow and thermal control of polymeric processing.
基金supported by a grant from the Institute of General Medical Sciences,National Institutes of Health,award number 1R01GM093937.
文摘Here we report a web server,the DelPhi web server,which utilizes DelPhi program to calculate electrostatic energies and the corresponding electrostatic potential and ionic distributions,and dielectric map.The server provides extra services to fix structural defects,as missing atoms in the structural file and allows for generation of missing hydrogen atoms.The hydrogen placement and the corresponding DelPhi calculations can be done with user selected force field parameters being either Charmm22,Amber98 or OPLS.Upon completion of the calculations,the user is given option to download fixed and protonated structural file,together with the parameter and Delphi output files for further analysis.Utilizing Jmol viewer,the user can see the corresponding structural file,to manipulate it and to change the presentation.In addition,if the potential map is requested to be calculated,the potential can be mapped onto the molecule surface.The DelPhi web server is available from http://compbio.clemson.edu/delphi webserver.
