An asymptotic algorithm is applied to the problem of a finite, thermo-elastic solid containing a surface breaking crack, when the exterior surface is subjected to oscillatory thermal loading. This algorithm involves t...An asymptotic algorithm is applied to the problem of a finite, thermo-elastic solid containing a surface breaking crack, when the exterior surface is subjected to oscillatory thermal loading. This algorithm involves the study of a model problem. An analytical and numerical study of this model problem of a thermo-elastic half space containing a surface breaking crack and subjected to oscillatory thermal loading is presented. The crack surface is traction free. In particular, the amplitude of the stress intensity factor at the crack vertex is found as a function of the crack depth and the frequency of thermal oscillation.展开更多
This paper is concerned with the valuation of single and double barrier knock-out call options in a Markovian regime switching model with specific rebates.The integral formulas of the rebates are derived via matrix Wi...This paper is concerned with the valuation of single and double barrier knock-out call options in a Markovian regime switching model with specific rebates.The integral formulas of the rebates are derived via matrix Wiener-Hopf factorizations and Fourier transform techniques,also,the integral representations of the option prices are constructed.Moreover,the first-passage time density functions in two-state regime model are derived.As applications,several numerical algorithms and numerical examples are presented.展开更多
Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors (DSIFs) for a semi-infinite crack in infinite viscoelastic material subjected to anti-pla...Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors (DSIFs) for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation (ODE). The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.展开更多
In this paper, we obtain sufficient and necessary conditions for local asymptotics for the maximum of a Markov modulated random walk with long-tailed increments and negative drifts, where the local asymptotics means a...In this paper, we obtain sufficient and necessary conditions for local asymptotics for the maximum of a Markov modulated random walk with long-tailed increments and negative drifts, where the local asymptotics means asymptotic behaviour of P( ∈ (x,x + z]) for each z 〉 0, as x→∞ Our results extend and improve the existing ones in the literature.展开更多
Discusses the genuine-optimal circulant preconditioner for finite-section Wiener-Hopf equations. Definition of the genuine-optimal circulant preconditioner; Use of the preconditioned conjugate gradient method; Numeric...Discusses the genuine-optimal circulant preconditioner for finite-section Wiener-Hopf equations. Definition of the genuine-optimal circulant preconditioner; Use of the preconditioned conjugate gradient method; Numerical treatments for high order quadrature rules.展开更多
Based on the dynamic theories of water waves and Mindlin plates, the analytic solution of interaction between smface waves and two-dimensional floating elastic plates with edge-restraint is constructed by use of the W...Based on the dynamic theories of water waves and Mindlin plates, the analytic solution of interaction between smface waves and two-dimensional floating elastic plates with edge-restraint is constructed by use of the Wiener-Hopf technique. Firstly, without regard for elastic edge restraint, the wave-induced responses of elastic floating plate analyzed by the present method are in good agreement with the results from literature and experimental results. Therefore, it can be shown that the present method is valid. Secondly, three end-restraint cases (i.e., the left-end elastic restraints, the both-end elastic restraints, and the right-end elastic restraints) are proposed to reduce the vibration of floating plates, in which the spring is used to connect the sea bottom and the floating plate' s left ( or right ) edge. The relations between the spring stiffness and the parameters of wave-induced responses of floating plates are discussed. Moreover, the effective method to reduce the vibration of floating elastic plates can be obtained through comparison.展开更多
Based on dynamical theories of water waves and dynamics of Mindlin thick plates, the investigation of the wave-induced responses and the vibration reduction of an elastic floating plate are presented using the Wiener-...Based on dynamical theories of water waves and dynamics of Mindlin thick plates, the investigation of the wave-induced responses and the vibration reduction of an elastic floating plate are presented using the Wiener-Hopf technique. Without regard to the case of elastic connector, the calculated results obtained by the present method are in good agreement with those from the literature and the experiment. It can be shown that the present method is valid. Relations between the spring stiffness to be used to connect the sea bottom and the floating plate and the parameters of wave-induced responses of floating plates are investigated using the present method. Therefore, these results can be used as theoretical bases for the design stage of super floating platform systems.展开更多
In the recent thirty years, a great of investigations have been made in the Wiener-Hopf equations and variational inequalities as two mutually independent problems. In this paper, we investigate the equivalenee of the...In the recent thirty years, a great of investigations have been made in the Wiener-Hopf equations and variational inequalities as two mutually independent problems. In this paper, we investigate the equivalenee of the solution of variational inequality and the inversion of the Toeplitz operator when the projection operators P, Q are linear. The solution of general Wiener-Hopf equation is coneluded as the solution of a variational problem. Thus an approximation method of obtaining the maximum value by variational is proposed to obtain the approximation of general Wiener-Hopf equation and apply it to the spaee eontaet problems in the elastieity theory. Espeeially, the solution representation is given in ease that the projection of eontaet surfaee is round. The dosing-form solution is also given when the known displaeement is a polynomial of even power.展开更多
The peridynamic model of a solid is suitable for studying the dynamics of defects in materials.We use the bond-based peridynamic theory to propose a one-dimensional nonlocal continuum model to study a defect in equili...The peridynamic model of a solid is suitable for studying the dynamics of defects in materials.We use the bond-based peridynamic theory to propose a one-dimensional nonlocal continuum model to study a defect in equilibrium and in steady propagation.As the defect propagates,the material particles undergo a transition between two states.By using the Wiener–Hopf method,an explicit analytical solution of the problem is obtained.The relation between the applied force and the propagation speed of the defect is determined;our results show that the defect does not propagate if the applied force is less than a critical value,whereas propagation occurs when the force exceeds that value.The energy properties of the system are investigated.展开更多
For spectrally negative Lévy process (SNLP), we find an expression, in terms of scale functions, for a potential measure involving the maximum and the last time of reaching the maximum up to a draw-down time. As ...For spectrally negative Lévy process (SNLP), we find an expression, in terms of scale functions, for a potential measure involving the maximum and the last time of reaching the maximum up to a draw-down time. As applications, we obtain a potential measure for the reflected SNLP and recover a joint Laplace transform for the Wiener-Hopf factorization for SNLP.展开更多
Modern trends in beam-driven radiation sources include the interaction of Cherenkov wakefields in open-ended circular waveguides with complicated dielectric linings, with a three-layer dielectric capillary recently pr...Modern trends in beam-driven radiation sources include the interaction of Cherenkov wakefields in open-ended circular waveguides with complicated dielectric linings, with a three-layer dielectric capillary recently proposed to reduce radiation divergence being a representative example [Opt. Lett. 45 5416(2020)]. We present a rigorous approach that allows for an analytical description of the electromagnetic processes that occur when the structure is excited by a single waveguide TM mode. In other words, the corresponding canonical waveguide diffraction problem is solved in a rigorous formulation. This is a continuation of our previous papers which considered simpler cases with a homogeneous or two-layer dielectric filling. Here we use the same analytical approach based on the Wiener–Hopf–Fock technique and deal with the more complicated case of a three-layer dielectric lining. Using the obtained rigorous solution, we discuss the possibility of manipulating the far-field radiation pattern using a third layer made of a low permittivity material.展开更多
文摘An asymptotic algorithm is applied to the problem of a finite, thermo-elastic solid containing a surface breaking crack, when the exterior surface is subjected to oscillatory thermal loading. This algorithm involves the study of a model problem. An analytical and numerical study of this model problem of a thermo-elastic half space containing a surface breaking crack and subjected to oscillatory thermal loading is presented. The crack surface is traction free. In particular, the amplitude of the stress intensity factor at the crack vertex is found as a function of the crack depth and the frequency of thermal oscillation.
基金supported by the Key Projects of Statistics Bureau of Zhejiang Province(No.23TJZZ17)the Humanities and Social Sciences Program of Ministry of Education of China(No.21YJA910005)。
文摘This paper is concerned with the valuation of single and double barrier knock-out call options in a Markovian regime switching model with specific rebates.The integral formulas of the rebates are derived via matrix Wiener-Hopf factorizations and Fourier transform techniques,also,the integral representations of the option prices are constructed.Moreover,the first-passage time density functions in two-state regime model are derived.As applications,several numerical algorithms and numerical examples are presented.
基金supported by the National Natural Science Foundation of China(11072060)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors (DSIFs) for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation (ODE). The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10901164 and 10771216) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education We are grateful to Professor Zhenting Hou and the referees for many valuable comments on the draft of this paper. In particular, we wish to thank a referee for pointing out a related new topic stated in Remark 3.9.
文摘In this paper, we obtain sufficient and necessary conditions for local asymptotics for the maximum of a Markov modulated random walk with long-tailed increments and negative drifts, where the local asymptotics means asymptotic behaviour of P( ∈ (x,x + z]) for each z 〉 0, as x→∞ Our results extend and improve the existing ones in the literature.
基金Supported in part by the natural science foundation of China No. 19901017.
文摘Discusses the genuine-optimal circulant preconditioner for finite-section Wiener-Hopf equations. Definition of the genuine-optimal circulant preconditioner; Use of the preconditioned conjugate gradient method; Numerical treatments for high order quadrature rules.
基金This work was supported by the National Natural Science Foundation of China(Grant No.19972018)Distin-guished Young Scholar Science Foundation of Heilongjiang Province of China.
文摘Based on the dynamic theories of water waves and Mindlin plates, the analytic solution of interaction between smface waves and two-dimensional floating elastic plates with edge-restraint is constructed by use of the Wiener-Hopf technique. Firstly, without regard for elastic edge restraint, the wave-induced responses of elastic floating plate analyzed by the present method are in good agreement with the results from literature and experimental results. Therefore, it can be shown that the present method is valid. Secondly, three end-restraint cases (i.e., the left-end elastic restraints, the both-end elastic restraints, and the right-end elastic restraints) are proposed to reduce the vibration of floating plates, in which the spring is used to connect the sea bottom and the floating plate' s left ( or right ) edge. The relations between the spring stiffness and the parameters of wave-induced responses of floating plates are discussed. Moreover, the effective method to reduce the vibration of floating elastic plates can be obtained through comparison.
文摘Based on dynamical theories of water waves and dynamics of Mindlin thick plates, the investigation of the wave-induced responses and the vibration reduction of an elastic floating plate are presented using the Wiener-Hopf technique. Without regard to the case of elastic connector, the calculated results obtained by the present method are in good agreement with those from the literature and the experiment. It can be shown that the present method is valid. Relations between the spring stiffness to be used to connect the sea bottom and the floating plate and the parameters of wave-induced responses of floating plates are investigated using the present method. Therefore, these results can be used as theoretical bases for the design stage of super floating platform systems.
基金National "863" Program Project(2007AA01Z410)the Elitist D Class Project of Beijing(20071D050700175)
文摘In the recent thirty years, a great of investigations have been made in the Wiener-Hopf equations and variational inequalities as two mutually independent problems. In this paper, we investigate the equivalenee of the solution of variational inequality and the inversion of the Toeplitz operator when the projection operators P, Q are linear. The solution of general Wiener-Hopf equation is coneluded as the solution of a variational problem. Thus an approximation method of obtaining the maximum value by variational is proposed to obtain the approximation of general Wiener-Hopf equation and apply it to the spaee eontaet problems in the elastieity theory. Espeeially, the solution representation is given in ease that the projection of eontaet surfaee is round. The dosing-form solution is also given when the known displaeement is a polynomial of even power.
基金the support of the National Natural Science Foundation of China under Grant Nos.12002010 and 11872075.
文摘The peridynamic model of a solid is suitable for studying the dynamics of defects in materials.We use the bond-based peridynamic theory to propose a one-dimensional nonlocal continuum model to study a defect in equilibrium and in steady propagation.As the defect propagates,the material particles undergo a transition between two states.By using the Wiener–Hopf method,an explicit analytical solution of the problem is obtained.The relation between the applied force and the propagation speed of the defect is determined;our results show that the defect does not propagate if the applied force is less than a critical value,whereas propagation occurs when the force exceeds that value.The energy properties of the system are investigated.
基金Man Chen was supported by the China Scholarship Council(No.201908110314)Xianyuan Wu was supported by the National Natural Science Foundation of China(Grant No.11471222)Man Chen and Xianyuan Wu were supported by the Academy for Multidisciplinary Studies,Capital Normal University,and Man Chen and Xiaowen Zhou were supported by RGPIN-2016-06704.
文摘For spectrally negative Lévy process (SNLP), we find an expression, in terms of scale functions, for a potential measure involving the maximum and the last time of reaching the maximum up to a draw-down time. As applications, we obtain a potential measure for the reflected SNLP and recover a joint Laplace transform for the Wiener-Hopf factorization for SNLP.
基金supported by the Russian Science Foundation(Grant No.18-72-10137)。
文摘Modern trends in beam-driven radiation sources include the interaction of Cherenkov wakefields in open-ended circular waveguides with complicated dielectric linings, with a three-layer dielectric capillary recently proposed to reduce radiation divergence being a representative example [Opt. Lett. 45 5416(2020)]. We present a rigorous approach that allows for an analytical description of the electromagnetic processes that occur when the structure is excited by a single waveguide TM mode. In other words, the corresponding canonical waveguide diffraction problem is solved in a rigorous formulation. This is a continuation of our previous papers which considered simpler cases with a homogeneous or two-layer dielectric filling. Here we use the same analytical approach based on the Wiener–Hopf–Fock technique and deal with the more complicated case of a three-layer dielectric lining. Using the obtained rigorous solution, we discuss the possibility of manipulating the far-field radiation pattern using a third layer made of a low permittivity material.