Locality preserving projection （LPP） is a typical and popular dimensionality reduction （DR） method,and it can potentially find discriminative projection directions by preserving the local geometric structure in da...Locality preserving projection （LPP） is a typical and popular dimensionality reduction （DR） method,and it can potentially find discriminative projection directions by preserving the local geometric structure in data. However,LPP is based on the neighborhood graph artificially constructed from the original data,and the performance of LPP relies on how well the nearest neighbor criterion work in the original space. To address this issue,a novel DR algorithm,called the self-dependent LPP （sdLPP） is proposed. And it is based on the fact that the nearest neighbor criterion usually achieves better performance in LPP transformed space than that in the original space. Firstly,LPP is performed based on the typical neighborhood graph; then,a new neighborhood graph is constructed in LPP transformed space and repeats LPP. Furthermore,a new criterion,called the improved Laplacian score,is developed as an empirical reference for the discriminative power and the iterative termination. Finally,the feasibility and the effectiveness of the method are verified by several publicly available UCI and face data sets with promising results.展开更多
The matrix expression for the 3 D transient dynamic boundary integral equation in Laplace transform space is obtained and the degenerative element method has been implemented to treat the kernel function over the sin...The matrix expression for the 3 D transient dynamic boundary integral equation in Laplace transform space is obtained and the degenerative element method has been implemented to treat the kernel function over the singular element. In the computer program BEMTDY the Koizumi′s numerical inversion method is used and three examples of the 3 D vibrated foundation under harmonic forces and the influence with both adjacent foundations are studied.展开更多
A new approach is proposed to analyze the settlement behavior for single pile embedded in layered soils. Firstly, soil layers surrounding pile shaft are simulated by using distributed Voigt model, and finite soil laye...A new approach is proposed to analyze the settlement behavior for single pile embedded in layered soils. Firstly, soil layers surrounding pile shaft are simulated by using distributed Voigt model, and finite soil layers under the pile end are assumed to be virtual soil-pile whose cross-section area is the same as that of the pile shaft. Then, by means of Laplace transform and impedance function transfer method to solve the static equilibrium equation of pile, the analytical solution of the displacement impedance fimction at the pile head is derived. Furthermore, the analytical solution of the settlement at the head of single pile is theoretically derived by virtue of convolution theorem. Based on these solutions, the influences of parameters of soil-pile system on the settlement behavior for single pile are analyzed. Also, comparison of the load-settlement response for two well-instrumented field tests in multilayered soils is given to demonstrate the effectiveness and accuracy of the proposed approach. It can be noted that the presented solution can be used to calculate the settlement of single pile for the preliminary design of pile foundation.展开更多
Taking the effect of finite soil layers below pile end into account,the longitudinal dynamic response of pile undergoing dynamic loading in layered soil was theoretically investigated.Firstly,finite soil layers below ...Taking the effect of finite soil layers below pile end into account,the longitudinal dynamic response of pile undergoing dynamic loading in layered soil was theoretically investigated.Firstly,finite soil layers below pile end are modeled as virtual soil pile whose cross-section area is the same as that of the pile and the soil layers surrounding the pile are described by the plane strain model.Then,by virtue of Laplace transform and impedance function transfer method,the analytical solution of longitudinal dynamic response at the pile head in frequency domain is yielded.Also,the semi-analytical solution in time domain undergoing half-cycle sine pulse at the pile head is obtained by means of inverse Laplace transform.Based on these solutions,a parametric study is conducted to analyze emphatically the effects of parameters of soil below pile end on velocity admittance and reflected wave signals at the pile head.Additionally,a comparison with other models with different supporting conditions from soil below pile end is performed to verify the model presented.展开更多
One-dimensional consolidation of visco-elastic aquitard due to withdrawal of deep-groundwater was studied.Merchant model was used to simulate visco-elastic characteristic of aquitard.General solutions of the governing...One-dimensional consolidation of visco-elastic aquitard due to withdrawal of deep-groundwater was studied.Merchant model was used to simulate visco-elastic characteristic of aquitard.General solutions of the governing equation were obtained by applying Laplace transform with respect to time,and then the pore-pressure,strain and deformation of the aquitard could be calculated by Laplace inversion.A case was analyzed to validate the correctness of the present method.Finally,some consolidation properties of the problem were analyzed.Comparison of the average degree of consolidation defined by pore pressure with that defined by settlement shows that they are different and the maximum difference is 22.8%.The influences of parameters of Merchant model and the rate of the water level on the consolidation are great.The smaller the viscosity coefficient is,the later the rate of consolidation decreases.The rate of consolidation is decreased with the decrease of the rate of the water level fall.Therefore,the lagged effect of land subsidence should be considered in the actual project.展开更多
The transient response of an unlimited cylindrical cavity buried in the infinite elastic soil subjected to an anti-plane impact load along the cavern axis direction was studied.Using Laplace transform combining with c...The transient response of an unlimited cylindrical cavity buried in the infinite elastic soil subjected to an anti-plane impact load along the cavern axis direction was studied.Using Laplace transform combining with contour integral of the Laplace inverse transform specifically,the general analytical expressions of the soil displacement and stress are obtained in the time domain,respectively.And the numerical solutions of the problem computed by analytical expressions are presented.In the time domain,the dynamic responses of the infinite elastic soil are analyzed,and the calculation results are compared with those from numerical inversion proposed by Durbin and the static results.One observes good agreement between analytical and numerical inversion results,lending the further support to the method presented.Finally,some valuable shear wave propagation laws are gained: the displacement of the soil remains zero before the wave arrival,and after the shear wave arrival,the stress and the displacement at this point increase abruptly,then reduce and tend to the static value gradually at last.The wave attenuates along the radial,therefore the farther the wave is from the source,the smaller the stress and the displacement are,and the stress and the displacement are just functions of the radial distance from the axis.展开更多
In order to study temperature field distribution in burnt surrounding rock and to determine ranges of burnt surrounding rock, coal-wall coking cycle and heat influence in the underground coal gasification(UCG) stope, ...In order to study temperature field distribution in burnt surrounding rock and to determine ranges of burnt surrounding rock, coal-wall coking cycle and heat influence in the underground coal gasification(UCG) stope, based on the Laplace transform and inversion formula, we studied the temperature analytical solution of one-dimensional unsteady heat conduction for multi-layer overlying strata under the first and the forth kinds of boundary conditions, and we also carried out a numerical simulation of twodimensional unsteady heat conduction by the COMSOL multiphysics. The results show that when the boundary temperature of surrounding rock has a linear decrease because of a directional movement of heat source in the UCG flame working face, the temperature in surrounding rock increases first and then decreases with time, the peak of temperature curve decreases gradually and its position moves inside surrounding rock from the boundary. In the surrounding rock of UCG stope, there is an envelope curve of temperature curve clusters. We analyzed the influence of thermophysical parameters on envelope curves and put forward to take envelope curve as the calculation basis for ranges of burnt surrounding rock, coal-wall coking cycle and heat influence. Finally, the concrete numerical values are given by determining those judgement standards and temperature thresholds, which basically tally with the field geophysical prospecting results.展开更多
An analytical solution was presented to the unsaturated soil with a finite thickness under confinement in the lateral direction and sinusoidal cyclic loading in the vertical direction based on Fredlund's one-dimen...An analytical solution was presented to the unsaturated soil with a finite thickness under confinement in the lateral direction and sinusoidal cyclic loading in the vertical direction based on Fredlund's one-dimensional consolidation equation for unsaturated soil. The transfer relationship between the state vectors at the top surface and any depth was gained by applying the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy's law and Fick's law. The excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain were obtained by using the Laplace transform with the initial and boundary conditions. The analytical solutions of the excess pore-air and pore-water pressures at any depth and settlement were obtained in the time domain by performing the inverse Laplace transforms. A typical example illustrates the consolidation characteristics of unsaturated soil under sinusoidal loading from analytical results. Finally, comparisons between the analytical solutions and results of the numerical method indicate that the analytical solution is correct.展开更多
This paper presented a new convenient method for viscoelastic problems which are generally solved through complex Laplace transform. State space equation is derived from the differential form of constitutive equation ...This paper presented a new convenient method for viscoelastic problems which are generally solved through complex Laplace transform. State space equation is derived from the differential form of constitutive equation of linear viscoelastic solid that can be solved by a precise integration method which is used in many fields with the advantages of high precision and convenience. For linear viscoelastic solids and crack, the finite elements program of the precise integration method is developed, which appears to be efficient and precise.展开更多
Sound propagation and the initial value problems in gas mixtures of two components are investigated. By using the eigen theory of linearized Boltzmann equations, a model equations is formed, with the use of the Fourie...Sound propagation and the initial value problems in gas mixtures of two components are investigated. By using the eigen theory of linearized Boltzmann equations, a model equations is formed, with the use of the Fourier-Laplace transform for model equations derived, the dispersion relations for both components are obtained.展开更多
An alternate non-Fourier heat conduction equation is derived from consideration of translation motion of spinless electron under a driving force due to an applied temperature gradient. This equation is a eapite ad cal...An alternate non-Fourier heat conduction equation is derived from consideration of translation motion of spinless electron under a driving force due to an applied temperature gradient. This equation is a eapite ad calcem,temperature. Elimination of the rate of change of velocity with respect to time leads to a non-Fourier heat conduction equation with a accumulation of temperature or ballistic term in it. The new constitutive heat conduction equation is combined with the energy balance equation in one dimension. The governing equation for transient temperature a partial differential equation （Eq. （23）） is solved for by the method of Laplace transforms. The problem considered is the semi-infinite medium with constant thermo physical properties with constant wall temperature boundary condition. A closed form analyticalexpression for the transient temperature was obtained （Eq. （36）） after truncation of higher order terms in the infinite binomial series and use of convolution and lag properties. This solution is compared with that obtained using the parabolic Fourier model and the damped wave model as presented in an earlier study. The predictions of Eq. （36） are closer to the Fourier model. The convex nature of the temperature curve is present.展开更多
The new inversion formula of the Laplace transform is considered. In the formula we use only the positive values ofx SiCoLT（x） = c S（x）, L（S（x）） = T（x）, c = const., x 〉 O,from the real axis. Si is the sinus...The new inversion formula of the Laplace transform is considered. In the formula we use only the positive values ofx SiCoLT（x） = c S（x）, L（S（x）） = T（x）, c = const., x 〉 O,from the real axis. Si is the sinus transform, Co is the cosines transform of Fourier and L is the Laplace transform.展开更多
The influence of parameters pertaining to the confinant structure on water hammer had been less studied than those relative to the fluid. One of them is the inner pipe-diameter, a basic structural-parameter that makes...The influence of parameters pertaining to the confinant structure on water hammer had been less studied than those relative to the fluid. One of them is the inner pipe-diameter, a basic structural-parameter that makes its influence in essential hydraulic topics such as head loss, in pipelines. In this paper, the objective is to analyze the inner-diameter influence on water hammer phenomenon. An analytical algorithm for solving the unsteady-one-dimensional water hammer model had been applied. It had allowed estimating the instantaneous head at any point of a single pipeline. The model was solved by mean of the Laplace＇s Transformed application and the anti-transforming procedure into the complex field. To determinate the influence of internal-diameter conduit on the pressure oscillation, four distinct inside-diameter values were introduced into the solution, successively. The first overpressure-peak at each case was tabulated along with the corresponding inner^liameter and a mathematical relation had been founded. The obtained results show a close dependence between both, over-pressure peaks and internal-pipe diameter. It was founded that this dependence is given in terms of a non-linear relation between them. It was further founded that the wave frequency is sensitive to the variation of the pipe-diameter.展开更多
Here is introduced some novel algorithms which made use of polygarnma functions to get the exact limits of a broad class of infinite series. Moreover, Laplace transform is used to find the sum of many convergent infin...Here is introduced some novel algorithms which made use of polygarnma functions to get the exact limits of a broad class of infinite series. Moreover, Laplace transform is used to find the sum of many convergent infinite series. These exact limits are found in different branches of physics for some special cases series and are in complete agreement with the values found by other authors. Moreover, the methods presented here are generalized and applied to other wide variety of sums, including alternating series. Finally, these methods are simple and quite powerful to calculate the limits of many convergent series as you can see from the examples included.展开更多
This study proposes a general imperfect thermal contact model to predict the thermal contact resistance at the interface among multi-layered composite structures.Based on the Green-Lindsay(GL)thermoelastic theory,semi...This study proposes a general imperfect thermal contact model to predict the thermal contact resistance at the interface among multi-layered composite structures.Based on the Green-Lindsay(GL)thermoelastic theory,semi analytical solutions of temperature increment and displacement of multi-layered composite structures are obtained by using the Laplace transform method,upon which the effects of thermal resistance coefficient,partition coefficient,thermal conductivity ratio and heat capacity ratio on the responses are studied.The results show that the generalized imperfect thermal contact model can realistically describe the imperfect thermal contact problem.Accordingly,it may degenerate into other thermal contact models by adjusting the thermal resistance coefficient and partition coefficient.展开更多
A further development of exclusively inverse frequency domain method for leak detection in pipelines is presented and validated.The location and leakage can be determined by analyzing the difference of transient water...A further development of exclusively inverse frequency domain method for leak detection in pipelines is presented and validated.The location and leakage can be determined by analyzing the difference of transient water head response between the simulated and measured data in frequency domain.The transient signals are generated by portion sharp closure of a valve from the small constant opening and it needs only a few meters of water.The discrete boundary conditions and observation data are both transformed in frequency domain by Laplace transform.Example in numerical simulation is studied for demonstration of this approach.The application of the method to an experimental pipeline confirms the analysis and illustrates successful detection of the single pipeline leak.The precalibration approach is presented to minimize the effect of data and model error and it splits the method into two parts.One uses data from a known state to fit the parameters of the model and the other uses data from the current state for the fitting of leak parameters using the now calibrated model.Some important practical parameters such as wave speed,friction in steady and unsteady state and the adaptability of the method are discussed.It was found that the nonlinearity errors associated with valve boundary condition could be prevented by consideration of the induced flow perturbation curve shape.展开更多
The sloshing of inviscid liquid of stratified density in a rectangular tank is analyzed.As the flow is no longer irrotional,the governing equation is found to be quite different from the Laplace equation used for the ...The sloshing of inviscid liquid of stratified density in a rectangular tank is analyzed.As the flow is no longer irrotional,the governing equation is found to be quite different from the Laplace equation used for the liquid of constant density.In particular it contains terms of mixed temporal and spatial derivatives.The problem is solved based on the variable separation method and Laplace transform for the constant Vaisala-Brunt frequency.It is found that the stratification of density may have small effects on those natural frequencies associated with the constant density,but many new natural frequencies have appeared as a result of its effect.展开更多
This paper proposes a minimum contrast methodology to estimate the drift parameter for the Ornstein-Uhlenbeck process driven by fractional Brownian motion of Hurst index, which is greater than one half. Both the stron...This paper proposes a minimum contrast methodology to estimate the drift parameter for the Ornstein-Uhlenbeck process driven by fractional Brownian motion of Hurst index, which is greater than one half. Both the strong consistency and the asymptotic normality of this minimum contrast estimator are studied based on the Laplace transform. The numerical simulation results confirm the theoretical analysis and show that the minimum contrast technique is effective and efficient.展开更多
基金Supported by the National Natural Science Foundation of China (60973097)the Scientific Research Foundation of Liaocheng University(X0810029)~~
文摘Locality preserving projection （LPP） is a typical and popular dimensionality reduction （DR） method,and it can potentially find discriminative projection directions by preserving the local geometric structure in data. However,LPP is based on the neighborhood graph artificially constructed from the original data,and the performance of LPP relies on how well the nearest neighbor criterion work in the original space. To address this issue,a novel DR algorithm,called the self-dependent LPP （sdLPP） is proposed. And it is based on the fact that the nearest neighbor criterion usually achieves better performance in LPP transformed space than that in the original space. Firstly,LPP is performed based on the typical neighborhood graph; then,a new neighborhood graph is constructed in LPP transformed space and repeats LPP. Furthermore,a new criterion,called the improved Laplacian score,is developed as an empirical reference for the discriminative power and the iterative termination. Finally,the feasibility and the effectiveness of the method are verified by several publicly available UCI and face data sets with promising results.
文摘The matrix expression for the 3 D transient dynamic boundary integral equation in Laplace transform space is obtained and the degenerative element method has been implemented to treat the kernel function over the singular element. In the computer program BEMTDY the Koizumi′s numerical inversion method is used and three examples of the 3 D vibrated foundation under harmonic forces and the influence with both adjacent foundations are studied.
基金Project(50879077) supported by the National Natural Science Foundation of China
文摘A new approach is proposed to analyze the settlement behavior for single pile embedded in layered soils. Firstly, soil layers surrounding pile shaft are simulated by using distributed Voigt model, and finite soil layers under the pile end are assumed to be virtual soil-pile whose cross-section area is the same as that of the pile shaft. Then, by means of Laplace transform and impedance function transfer method to solve the static equilibrium equation of pile, the analytical solution of the displacement impedance fimction at the pile head is derived. Furthermore, the analytical solution of the settlement at the head of single pile is theoretically derived by virtue of convolution theorem. Based on these solutions, the influences of parameters of soil-pile system on the settlement behavior for single pile are analyzed. Also, comparison of the load-settlement response for two well-instrumented field tests in multilayered soils is given to demonstrate the effectiveness and accuracy of the proposed approach. It can be noted that the presented solution can be used to calculate the settlement of single pile for the preliminary design of pile foundation.
基金Project(50879077) supported by the National Natural Science Foundation of China
文摘Taking the effect of finite soil layers below pile end into account,the longitudinal dynamic response of pile undergoing dynamic loading in layered soil was theoretically investigated.Firstly,finite soil layers below pile end are modeled as virtual soil pile whose cross-section area is the same as that of the pile and the soil layers surrounding the pile are described by the plane strain model.Then,by virtue of Laplace transform and impedance function transfer method,the analytical solution of longitudinal dynamic response at the pile head in frequency domain is yielded.Also,the semi-analytical solution in time domain undergoing half-cycle sine pulse at the pile head is obtained by means of inverse Laplace transform.Based on these solutions,a parametric study is conducted to analyze emphatically the effects of parameters of soil below pile end on velocity admittance and reflected wave signals at the pile head.Additionally,a comparison with other models with different supporting conditions from soil below pile end is performed to verify the model presented.
基金Project(50608038/E0806) supported by the National Natural Science Foundation of China
文摘One-dimensional consolidation of visco-elastic aquitard due to withdrawal of deep-groundwater was studied.Merchant model was used to simulate visco-elastic characteristic of aquitard.General solutions of the governing equation were obtained by applying Laplace transform with respect to time,and then the pore-pressure,strain and deformation of the aquitard could be calculated by Laplace inversion.A case was analyzed to validate the correctness of the present method.Finally,some consolidation properties of the problem were analyzed.Comparison of the average degree of consolidation defined by pore pressure with that defined by settlement shows that they are different and the maximum difference is 22.8%.The influences of parameters of Merchant model and the rate of the water level on the consolidation are great.The smaller the viscosity coefficient is,the later the rate of consolidation decreases.The rate of consolidation is decreased with the decrease of the rate of the water level fall.Therefore,the lagged effect of land subsidence should be considered in the actual project.
文摘The transient response of an unlimited cylindrical cavity buried in the infinite elastic soil subjected to an anti-plane impact load along the cavern axis direction was studied.Using Laplace transform combining with contour integral of the Laplace inverse transform specifically,the general analytical expressions of the soil displacement and stress are obtained in the time domain,respectively.And the numerical solutions of the problem computed by analytical expressions are presented.In the time domain,the dynamic responses of the infinite elastic soil are analyzed,and the calculation results are compared with those from numerical inversion proposed by Durbin and the static results.One observes good agreement between analytical and numerical inversion results,lending the further support to the method presented.Finally,some valuable shear wave propagation laws are gained: the displacement of the soil remains zero before the wave arrival,and after the shear wave arrival,the stress and the displacement at this point increase abruptly,then reduce and tend to the static value gradually at last.The wave attenuates along the radial,therefore the farther the wave is from the source,the smaller the stress and the displacement are,and the stress and the displacement are just functions of the radial distance from the axis.
基金supported by the State Key Laboratory of Coal Resources and Safe Mining (No. SKLCRSM10X04)the National Natural Science Foundation of China ((No. 21243006)+1 种基金the Foundation of Ministry of Education of China ((No. 02019)the Priority Academic Program Development of Jiangsu Higher Education Institutions (No.SZBF2011-6-B35)
文摘In order to study temperature field distribution in burnt surrounding rock and to determine ranges of burnt surrounding rock, coal-wall coking cycle and heat influence in the underground coal gasification(UCG) stope, based on the Laplace transform and inversion formula, we studied the temperature analytical solution of one-dimensional unsteady heat conduction for multi-layer overlying strata under the first and the forth kinds of boundary conditions, and we also carried out a numerical simulation of twodimensional unsteady heat conduction by the COMSOL multiphysics. The results show that when the boundary temperature of surrounding rock has a linear decrease because of a directional movement of heat source in the UCG flame working face, the temperature in surrounding rock increases first and then decreases with time, the peak of temperature curve decreases gradually and its position moves inside surrounding rock from the boundary. In the surrounding rock of UCG stope, there is an envelope curve of temperature curve clusters. We analyzed the influence of thermophysical parameters on envelope curves and put forward to take envelope curve as the calculation basis for ranges of burnt surrounding rock, coal-wall coking cycle and heat influence. Finally, the concrete numerical values are given by determining those judgement standards and temperature thresholds, which basically tally with the field geophysical prospecting results.
基金Project(2010G016-B)supported by Science and Technology Research and Development of China
文摘An analytical solution was presented to the unsaturated soil with a finite thickness under confinement in the lateral direction and sinusoidal cyclic loading in the vertical direction based on Fredlund's one-dimensional consolidation equation for unsaturated soil. The transfer relationship between the state vectors at the top surface and any depth was gained by applying the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy's law and Fick's law. The excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain were obtained by using the Laplace transform with the initial and boundary conditions. The analytical solutions of the excess pore-air and pore-water pressures at any depth and settlement were obtained in the time domain by performing the inverse Laplace transforms. A typical example illustrates the consolidation characteristics of unsaturated soil under sinusoidal loading from analytical results. Finally, comparisons between the analytical solutions and results of the numerical method indicate that the analytical solution is correct.
基金National Natural Science Foundation ofChina(No.10 172 0 78)
文摘This paper presented a new convenient method for viscoelastic problems which are generally solved through complex Laplace transform. State space equation is derived from the differential form of constitutive equation of linear viscoelastic solid that can be solved by a precise integration method which is used in many fields with the advantages of high precision and convenience. For linear viscoelastic solids and crack, the finite elements program of the precise integration method is developed, which appears to be efficient and precise.
基金Supported by National Natural Science Foundation of China under Grant No.10861008the "211 Project" Innovative Talents Training Program of Inner Mongolia University and Grant-in-Aid for Scientific Research from Inner Mongolia University of Technology under Grant No.ZS201032
文摘Sound propagation and the initial value problems in gas mixtures of two components are investigated. By using the eigen theory of linearized Boltzmann equations, a model equations is formed, with the use of the Fourier-Laplace transform for model equations derived, the dispersion relations for both components are obtained.
文摘An alternate non-Fourier heat conduction equation is derived from consideration of translation motion of spinless electron under a driving force due to an applied temperature gradient. This equation is a eapite ad calcem,temperature. Elimination of the rate of change of velocity with respect to time leads to a non-Fourier heat conduction equation with a accumulation of temperature or ballistic term in it. The new constitutive heat conduction equation is combined with the energy balance equation in one dimension. The governing equation for transient temperature a partial differential equation （Eq. （23）） is solved for by the method of Laplace transforms. The problem considered is the semi-infinite medium with constant thermo physical properties with constant wall temperature boundary condition. A closed form analyticalexpression for the transient temperature was obtained （Eq. （36）） after truncation of higher order terms in the infinite binomial series and use of convolution and lag properties. This solution is compared with that obtained using the parabolic Fourier model and the damped wave model as presented in an earlier study. The predictions of Eq. （36） are closer to the Fourier model. The convex nature of the temperature curve is present.
文摘The new inversion formula of the Laplace transform is considered. In the formula we use only the positive values ofx SiCoLT（x） = c S（x）, L（S（x）） = T（x）, c = const., x 〉 O,from the real axis. Si is the sinus transform, Co is the cosines transform of Fourier and L is the Laplace transform.
文摘The influence of parameters pertaining to the confinant structure on water hammer had been less studied than those relative to the fluid. One of them is the inner pipe-diameter, a basic structural-parameter that makes its influence in essential hydraulic topics such as head loss, in pipelines. In this paper, the objective is to analyze the inner-diameter influence on water hammer phenomenon. An analytical algorithm for solving the unsteady-one-dimensional water hammer model had been applied. It had allowed estimating the instantaneous head at any point of a single pipeline. The model was solved by mean of the Laplace＇s Transformed application and the anti-transforming procedure into the complex field. To determinate the influence of internal-diameter conduit on the pressure oscillation, four distinct inside-diameter values were introduced into the solution, successively. The first overpressure-peak at each case was tabulated along with the corresponding inner^liameter and a mathematical relation had been founded. The obtained results show a close dependence between both, over-pressure peaks and internal-pipe diameter. It was founded that this dependence is given in terms of a non-linear relation between them. It was further founded that the wave frequency is sensitive to the variation of the pipe-diameter.
文摘Here is introduced some novel algorithms which made use of polygarnma functions to get the exact limits of a broad class of infinite series. Moreover, Laplace transform is used to find the sum of many convergent infinite series. These exact limits are found in different branches of physics for some special cases series and are in complete agreement with the values found by other authors. Moreover, the methods presented here are generalized and applied to other wide variety of sums, including alternating series. Finally, these methods are simple and quite powerful to calculate the limits of many convergent series as you can see from the examples included.
基金Projects(42477162,52108347,52178371,52168046,52178321,52308383)supported by the National Natural Science Foundation of ChinaProjects(2023C03143,2022C01099,2024C01219,2022C03151)supported by the Zhejiang Key Research and Development Plan,China+6 种基金Project(LQ22E080010)supported by the Exploring Youth Project of Zhejiang Natural Science Foundation,ChinaProject(LR21E080005)supported by the Outstanding Youth Project of Natural Science Foundation of Zhejiang Province,ChinaProject(2022M712964)supported by the Postdoctoral Science Foundation of ChinaProject(2023AFB008)supported by the Natural Science Foundation of Hubei Province for Youth,ChinaProject(202203)supported by Engineering Research Centre of Rock-Soil Drilling&Excavation and Protection,Ministry of Education,ChinaProject(202305-2)supported by the Science and Technology Project of Zhejiang Provincial Communication Department,ChinaProject(2021K256)supported by the Construction Research Founds of Department of Housing and Urban-Rural Development of Zhejiang Province,China。
文摘This study proposes a general imperfect thermal contact model to predict the thermal contact resistance at the interface among multi-layered composite structures.Based on the Green-Lindsay(GL)thermoelastic theory,semi analytical solutions of temperature increment and displacement of multi-layered composite structures are obtained by using the Laplace transform method,upon which the effects of thermal resistance coefficient,partition coefficient,thermal conductivity ratio and heat capacity ratio on the responses are studied.The results show that the generalized imperfect thermal contact model can realistically describe the imperfect thermal contact problem.Accordingly,it may degenerate into other thermal contact models by adjusting the thermal resistance coefficient and partition coefficient.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51109230, 50679085)the Special Funds of IWHR (Grant No. 0912)
文摘A further development of exclusively inverse frequency domain method for leak detection in pipelines is presented and validated.The location and leakage can be determined by analyzing the difference of transient water head response between the simulated and measured data in frequency domain.The transient signals are generated by portion sharp closure of a valve from the small constant opening and it needs only a few meters of water.The discrete boundary conditions and observation data are both transformed in frequency domain by Laplace transform.Example in numerical simulation is studied for demonstration of this approach.The application of the method to an experimental pipeline confirms the analysis and illustrates successful detection of the single pipeline leak.The precalibration approach is presented to minimize the effect of data and model error and it splits the method into two parts.One uses data from a known state to fit the parameters of the model and the other uses data from the current state for the fitting of leak parameters using the now calibrated model.Some important practical parameters such as wave speed,friction in steady and unsteady state and the adaptability of the method are discussed.It was found that the nonlinearity errors associated with valve boundary condition could be prevented by consideration of the induced flow perturbation curve shape.
基金the State Key Laboratory of Ocean Engineering for its support (Grant No. GP010818)
文摘The sloshing of inviscid liquid of stratified density in a rectangular tank is analyzed.As the flow is no longer irrotional,the governing equation is found to be quite different from the Laplace equation used for the liquid of constant density.In particular it contains terms of mixed temporal and spatial derivatives.The problem is solved based on the variable separation method and Laplace transform for the constant Vaisala-Brunt frequency.It is found that the stratification of density may have small effects on those natural frequencies associated with the constant density,but many new natural frequencies have appeared as a result of its effect.
基金National Science Fund for Distinguished Young Scholars of China (Grant No. 70825005)National Natural Science Foundation of China (Grant No. 71171086)+2 种基金Natural Science Foundation of Guangdong Province of China (Grant No. S2011040005723)the Fundamental Research Funds for the Central Universities, SCUT (2012ZM0029)supported by GDUPS(2010)
文摘This paper proposes a minimum contrast methodology to estimate the drift parameter for the Ornstein-Uhlenbeck process driven by fractional Brownian motion of Hurst index, which is greater than one half. Both the strong consistency and the asymptotic normality of this minimum contrast estimator are studied based on the Laplace transform. The numerical simulation results confirm the theoretical analysis and show that the minimum contrast technique is effective and efficient.
