The approach of Li and Zhou(2014)is adopted to find the Laplace transform of occupation time over interval(0,a)and joint occupation times over semi-infinite intervals(-∞,a)and(b,∞)for a time-homogeneous diffusion pr...The approach of Li and Zhou(2014)is adopted to find the Laplace transform of occupation time over interval(0,a)and joint occupation times over semi-infinite intervals(-∞,a)and(b,∞)for a time-homogeneous diffusion process up to an independent exponential time e_(q)for 0<a<b.The results are expressed in terms of solutions to the differential equations associated with the diffusion generator.Applying these results,we obtain explicit expressions on the Laplace transform of occupation time and joint occupation time for Brownian motion with drift.展开更多
A semi-analytical solution is presented using method of Laplace transform for the transient pulse electroosmotic flow (EOF) of Maxwell fluid in a circular micro-channel. The driving mode of pulse EOF here is considere...A semi-analytical solution is presented using method of Laplace transform for the transient pulse electroosmotic flow (EOF) of Maxwell fluid in a circular micro-channel. The driving mode of pulse EOF here is considered as an ideal rectangle pulse. The solution involves solving the linearized Poisson-Boltzmann (P-B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. The results show that the profiles of pulse EOF velocity vary rapidly and gradually stabilize as the increase of time <img src="Edit_440fb0f5-5539-4a78-8311-93b2664c8117.png" alt="" /> within a half period. The velocity profiles at the center of the micro-channel increase significantly with relaxation time <img src="Edit_ffb813ed-0046-40bc-95e6-76057f46ce32.png" alt="" />, especially for the smaller pulse width <em>a</em>. However, as the pulse width <em>a </em>increases, this change will be less obvious. At the same time, the different change frequency of velocity profiles will slow down, which means a long cycle time. Additionally, the time needed to attain the steady status becomes longer with the increase of relaxation time <img src="Edit_d1b31535-84c1-417e-b987-6ca53ab1616b.png" alt="" /> and pulse width <em>a</em>.展开更多
The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models...The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models with fractional derivatives are investigated analytically, and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order.展开更多
Gas–liquid two-phase flow abounds in industrial processes and facilities. Identification of its flow pattern plays an essential role in the field of multiphase flow measurement. A bluff body was introduced in this s...Gas–liquid two-phase flow abounds in industrial processes and facilities. Identification of its flow pattern plays an essential role in the field of multiphase flow measurement. A bluff body was introduced in this study to recognize gas–liquid flow patterns by inducing fluid oscillation that enlarged differences between each flow pattern. Experiments with air–water mixtures were carried out in horizontal pipelines at ambient temperature and atmospheric pressure. Differential pressure signals from the bluff-body wake were obtained in bubble, bubble/plug transitional, plug, slug, and annular flows. Utilizing the adaptive ensemble empirical mode decomposition method and the Hilbert transform, the time–frequency entropy S of the differential pressure signals was obtained. By combining S and other flow parameters, such as the volumetric void fraction β, the dryness x, the ratio of density φ and the modified fluid coefficient ψ, a new flow pattern map was constructed which adopted S（1–x）φ and （1–β）ψ as the vertical and horizontal coordinates, respectively. The overall rate of classification of the map was verified to be 92.9% by the experimental data. It provides an effective and simple solution to the gas–liquid flow pattern identification problems.展开更多
The Fourier transformations are used mainly with respect to the space variables. In certain circumstances, however, for reasons of expedience or necessity, it is desirable to eliminate time as a variable in the proble...The Fourier transformations are used mainly with respect to the space variables. In certain circumstances, however, for reasons of expedience or necessity, it is desirable to eliminate time as a variable in the problem. This is achieved by means of the Laplace transformation. We specify the particular concepts of the q-Laplace transform. The convolution for these transforms is considered in some detail.展开更多
On the basis of Terzaghi's one-dimensional consolidation theory, the variation of effective stress ratio in layered saturated soils with impeded boundaries under time-dependent loading was studied. By the method o...On the basis of Terzaghi's one-dimensional consolidation theory, the variation of effective stress ratio in layered saturated soils with impeded boundaries under time-dependent loading was studied. By the method of Laplace transform, the solution was presented. Influences of different kinds of cyclic loadings and impeded boundaries conditions were discussed. Through numerical inversion of Laplace transform, useful illustrations were given considering several common time-dependent loadings. Pervious or impervious boundary condition is just the special case of the problem considered here. Compared with average index method,the results from the method illustrated are more accurate.展开更多
A hybrid finite element-Laplace transform method is implemented to analyze the time domain electromagnetic scattering induced by a 2-D overfilled cavity embedded in the infinite ground plane.The algorithm divides the ...A hybrid finite element-Laplace transform method is implemented to analyze the time domain electromagnetic scattering induced by a 2-D overfilled cavity embedded in the infinite ground plane.The algorithm divides the whole scattering domain into two,interior and exterior,sub-domains.In the interior sub-domain which covers the cavity,the problem is solved via the finite element method.The problem is solved analytically in the exterior sub-domain which slightly overlaps the interior subdomain and extends to the rest of the upper half plane.The use of the Laplace transform leads to an analytical link condition between the overlapping sub-domains.The analytical link guides the selection of the overlapping zone and eliminates the need to use the conventional Schwartz iteration.This dramatically improves the efficiency for solving transient scattering problems.Numerical solutions are tested favorably against analytical ones for a canonical geometry.The perfect link over the artificial boundary between the finite element approximation in the interior and analytical solution in the exterior further indicates the reliability of the method.An error analysis is also performed.展开更多
For a < r < b, the approach of Li and Zhou(2014) is adopted to find joint Laplace transforms of occupation times over intervals(a, r) and(r, b) for a time homogeneous diffusion process before it first exits from...For a < r < b, the approach of Li and Zhou(2014) is adopted to find joint Laplace transforms of occupation times over intervals(a, r) and(r, b) for a time homogeneous diffusion process before it first exits from either a or b. The results are expressed in terms of solutions to the differential equations associated with the diffusions generator. Applying these results, we obtain more explicit expressions on the joint Laplace transforms of occupation times for Brownian motion with drift, Brownian motion with alternating drift and skew Brownian motion, respectively.展开更多
The forces on rigid particles moving in relation to fluid having been studied and the equation of modifications of their expressions under different flow conditions discussed, a general form of equation for discrete p...The forces on rigid particles moving in relation to fluid having been studied and the equation of modifications of their expressions under different flow conditions discussed, a general form of equation for discrete particles' motion in arbitrary flow field is obtained. The mathematical features of the linear form of the equation are clarified and analytical solution of the linearized equation is gotten by means of Laplace transform. According to above theoretical results, the effects of particles' properties on its motion in several typical flow field are studied, with some meaningful conclusions being reached.展开更多
Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D G...Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.展开更多
基金Supported by the National Natural Science Foundation of China(12271062,11731012)by the Hunan Provincial National Natural Science Foundation of China(2019JJ50405)。
文摘The approach of Li and Zhou(2014)is adopted to find the Laplace transform of occupation time over interval(0,a)and joint occupation times over semi-infinite intervals(-∞,a)and(b,∞)for a time-homogeneous diffusion process up to an independent exponential time e_(q)for 0<a<b.The results are expressed in terms of solutions to the differential equations associated with the diffusion generator.Applying these results,we obtain explicit expressions on the Laplace transform of occupation time and joint occupation time for Brownian motion with drift.
文摘A semi-analytical solution is presented using method of Laplace transform for the transient pulse electroosmotic flow (EOF) of Maxwell fluid in a circular micro-channel. The driving mode of pulse EOF here is considered as an ideal rectangle pulse. The solution involves solving the linearized Poisson-Boltzmann (P-B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. The results show that the profiles of pulse EOF velocity vary rapidly and gradually stabilize as the increase of time <img src="Edit_440fb0f5-5539-4a78-8311-93b2664c8117.png" alt="" /> within a half period. The velocity profiles at the center of the micro-channel increase significantly with relaxation time <img src="Edit_ffb813ed-0046-40bc-95e6-76057f46ce32.png" alt="" />, especially for the smaller pulse width <em>a</em>. However, as the pulse width <em>a </em>increases, this change will be less obvious. At the same time, the different change frequency of velocity profiles will slow down, which means a long cycle time. Additionally, the time needed to attain the steady status becomes longer with the increase of relaxation time <img src="Edit_d1b31535-84c1-417e-b987-6ca53ab1616b.png" alt="" /> and pulse width <em>a</em>.
基金Project supported by the Key Program of the National Natural Science Foundation of China （Grant No. 51134018）.
文摘The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models with fractional derivatives are investigated analytically, and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order.
基金Project(51576213)supported by the National Natural Science Foundation of ChinaProject(2015RS4015)supported by the Hunan Scientific Program,ChinaProject(2016zzts323)supported by the Innovation Project of Central South University,China
文摘Gas–liquid two-phase flow abounds in industrial processes and facilities. Identification of its flow pattern plays an essential role in the field of multiphase flow measurement. A bluff body was introduced in this study to recognize gas–liquid flow patterns by inducing fluid oscillation that enlarged differences between each flow pattern. Experiments with air–water mixtures were carried out in horizontal pipelines at ambient temperature and atmospheric pressure. Differential pressure signals from the bluff-body wake were obtained in bubble, bubble/plug transitional, plug, slug, and annular flows. Utilizing the adaptive ensemble empirical mode decomposition method and the Hilbert transform, the time–frequency entropy S of the differential pressure signals was obtained. By combining S and other flow parameters, such as the volumetric void fraction β, the dryness x, the ratio of density φ and the modified fluid coefficient ψ, a new flow pattern map was constructed which adopted S（1–x）φ and （1–β）ψ as the vertical and horizontal coordinates, respectively. The overall rate of classification of the map was verified to be 92.9% by the experimental data. It provides an effective and simple solution to the gas–liquid flow pattern identification problems.
文摘The Fourier transformations are used mainly with respect to the space variables. In certain circumstances, however, for reasons of expedience or necessity, it is desirable to eliminate time as a variable in the problem. This is achieved by means of the Laplace transformation. We specify the particular concepts of the q-Laplace transform. The convolution for these transforms is considered in some detail.
文摘On the basis of Terzaghi's one-dimensional consolidation theory, the variation of effective stress ratio in layered saturated soils with impeded boundaries under time-dependent loading was studied. By the method of Laplace transform, the solution was presented. Influences of different kinds of cyclic loadings and impeded boundaries conditions were discussed. Through numerical inversion of Laplace transform, useful illustrations were given considering several common time-dependent loadings. Pervious or impervious boundary condition is just the special case of the problem considered here. Compared with average index method,the results from the method illustrated are more accurate.
基金This workwas supported in part by the Air Force Office of Scientific Research.
文摘A hybrid finite element-Laplace transform method is implemented to analyze the time domain electromagnetic scattering induced by a 2-D overfilled cavity embedded in the infinite ground plane.The algorithm divides the whole scattering domain into two,interior and exterior,sub-domains.In the interior sub-domain which covers the cavity,the problem is solved via the finite element method.The problem is solved analytically in the exterior sub-domain which slightly overlaps the interior subdomain and extends to the rest of the upper half plane.The use of the Laplace transform leads to an analytical link condition between the overlapping sub-domains.The analytical link guides the selection of the overlapping zone and eliminates the need to use the conventional Schwartz iteration.This dramatically improves the efficiency for solving transient scattering problems.Numerical solutions are tested favorably against analytical ones for a canonical geometry.The perfect link over the artificial boundary between the finite element approximation in the interior and analytical solution in the exterior further indicates the reliability of the method.An error analysis is also performed.
基金Supported by NSFC(Grant Nos.11171101,11171044,11571052 and 11671132)Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP)+2 种基金Education Ministry of China,Hu’nan Normal UniversityNatural Science Foundation of Hu’nan Province(Grant No.2016JJ4061)Scientific Research Pro ject of Hu’nan University of Arts and Science(Grant No.15ZD05)
文摘For a < r < b, the approach of Li and Zhou(2014) is adopted to find joint Laplace transforms of occupation times over intervals(a, r) and(r, b) for a time homogeneous diffusion process before it first exits from either a or b. The results are expressed in terms of solutions to the differential equations associated with the diffusions generator. Applying these results, we obtain more explicit expressions on the joint Laplace transforms of occupation times for Brownian motion with drift, Brownian motion with alternating drift and skew Brownian motion, respectively.
文摘The forces on rigid particles moving in relation to fluid having been studied and the equation of modifications of their expressions under different flow conditions discussed, a general form of equation for discrete particles' motion in arbitrary flow field is obtained. The mathematical features of the linear form of the equation are clarified and analytical solution of the linearized equation is gotten by means of Laplace transform. According to above theoretical results, the effects of particles' properties on its motion in several typical flow field are studied, with some meaningful conclusions being reached.
基金The paper was financially supported by the National Natural Science Foundation of China (No. 19802008)Excellent Doctoral Dissertation Grant of the Ministry of Education of China (No. 199927)
文摘Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.
