It is known that Fourier’s heat equation, which is parabolic, implies an infinite velocity propagation, or, in other words, that the mechanism of heat conduction is established instantaneously under all conditions. T...It is known that Fourier’s heat equation, which is parabolic, implies an infinite velocity propagation, or, in other words, that the mechanism of heat conduction is established instantaneously under all conditions. This is unacceptable on physical grounds in spite of the fact that Fourier’s law agrees well with experiment. However, discrepancies are likely to occur when extremely short distances or extremely short time intervals are considered, as they must in some modern problems of aero-thermodynamics. Cattaneo and independently Vernotte proved that such process can be described by Heaviside’s telegraph equation. This paper shows that this fact can be derived using calculus of variations, by application of the Euler-Lagrange equation. So, we proved that the equation of heat conduction with finite velocity propagation of the thermal disturbance can be obtained as a solution to one variational problem.展开更多
This paper is devoted to studying the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation. The asymptotic theory and validity of formal approximations are constructed on long time...This paper is devoted to studying the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation. The asymptotic theory and validity of formal approximations are constructed on long timescale O(\epsilon\(-1)). As an application of the asymptotic theory, the initial value problems for a special telegraph equation are studied and two asymptotic solutions of order O(\epsilon\(-)1) are presented.展开更多
A new numerical algorithm for telegraph equations with homogeneous boundary con- ditions is proposed. Due to the damping terms in telegraph equations, there is no royal conservation law according to Noether＇s theorem...A new numerical algorithm for telegraph equations with homogeneous boundary con- ditions is proposed. Due to the damping terms in telegraph equations, there is no royal conservation law according to Noether＇s theorem. The algorithm origins from the discovery of a transform applied to a telegraph equation, which transforms the telegraph equation to a Klein-Gordon equation. The Symplectic method is then brought in this algorithm to solve the Klein-Gordon equation, which is based on the fact that the Klein-Gordon equation with the homogeneous boundary condition is a perfect Hamiltonian system and the symplectic method works very well for Hamiltonian systems. The transformation itself and the inverse transformation theoretically bring no error to the numerical computation. Therefore the error only comes from the symplectic scheme chosen. The telegraph equation is finally explicitly computed when an explicit symplectic scheme is utilized. A relatively long time result can be expected due to the application of the symplectic method. Mean- while, we present order analysis for both one-dimensional and multi-dimensional cases in the paper. The efficiency of this approach is demonstrated with numerical examples.展开更多
Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a ...Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.展开更多
Using the adoption and expansion of wired telegraph in China during the late 19^(th) century,this paper investigates the effect of cost reductions for knowledge exchange on China’s industrial growth before the outbre...Using the adoption and expansion of wired telegraph in China during the late 19^(th) century,this paper investigates the effect of cost reductions for knowledge exchange on China’s industrial growth before the outbreak of the War of Resistance Against Japanese Aggression(1931-1945),thus testing Baldwin’s theory of“the Great Convergence”in which developing countries are empowered by information and communication technologies.Based on panel data of 1858-1937,we found that wired telegraph access had a significantly positive effect,as well as a long-term growth effect,on the entry of industrial enterprises.Our mechanism analysis indicates that wired telegraph access accelerated early-stage industrialization in localities by encouraging market integration,human capital accumulation,and auxiliary commercial organizations.Only a few countries firmly asserted their telegraph sovereignty and set up their own workforce educational system during telegraph adoption.This explains why the Great Convergence arising from technology importation only occurred in a small number of countries.Our findings contribute to understanding the source of China’s modern industrial progress,as well as why global inequities remain.展开更多
The space-fractional telegraph equation is analyzed and the Fourier transform of its funda-mental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satis...The space-fractional telegraph equation is analyzed and the Fourier transform of its funda-mental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satisfies thespace-fractional telegraph equation, is presented. Its limiting behaviour and the connectionwith symmetric stable processes is also examined.展开更多
The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random t...The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random telegraph signal noise in the pixel source follower based on the binomial distribution is set up. The number of electrons captured or released by the oxide traps in the unit time is described as the random variables which obey the binomial distribution. As a result,the output states and the corresponding probabilities of the first and the second samples of the correlated double sampling circuit are acquired. The standard deviation of the output states after the correlated double sampling circuit can be obtained accordingly. In the simulation section, one hundred thousand samples of the source follower MOSFET have been simulated,and the simulation results show that the proposed model has the similar statistical characteristics with the existing models under the effect of the channel length and the density of the oxide trap. Moreover, the noise histogram of the proposed model has been evaluated at different environmental temperatures.展开更多
Magnetohydrodynamics couples the Navier-Stokes and Maxwell’s equations to describe the flow of electrically conducting fluids in magnetic fields.Maxwell’s equations require the divergence of the magnetic field to va...Magnetohydrodynamics couples the Navier-Stokes and Maxwell’s equations to describe the flow of electrically conducting fluids in magnetic fields.Maxwell’s equations require the divergence of the magnetic field to vanish,but this condition is typically not preserved exactly by numerical algorithms.Solutions can develop artifacts because structural properties of the magnetohydrodynamic equations then fail to hold.Magnetohydrodynamics with hyperbolic divergence cleaning permits a nonzero divergence that evolves under a telegraph equation,designed to both damp the divergence,and propagate it away from any sources,such as poorly resolved regions with large spatial gradients,without significantly increasing the computational cost.We show that existing lattice Boltzmann algorithms for magnetohydrodynamics already incorporate hyperbolic divergence cleaning,though they typically use parameter values for which it reduces to parabolic divergence cleaning under a slowly-varying approximation.We recover hyperbolic divergence cleaning by adjusting the relaxation rate for the trace of the tensor that represents the electric field,and absorb the contribution from the symmetric-traceless part of this tensor using a change of variables.Numerical experiments confirm that the qualitative behaviour changes from parabolic to hyperbolic when the relaxation time for the trace of the electric field tensor is increased.展开更多
In this paper,we develop a lattice Boltzmann model for a class ofone-dimensional nonlinear wave equations,including the second-order hyperbolictelegraph equation,the nonlinear Klein-Gordon equation,the damped and unda...In this paper,we develop a lattice Boltzmann model for a class ofone-dimensional nonlinear wave equations,including the second-order hyperbolictelegraph equation,the nonlinear Klein-Gordon equation,the damped and undampedsine-Gordon equation and double sine-Gordon equation.By choosing properly theconservation condition between the macroscopic quantity u,and the distributionfunctions and applying the Chapman-Enskog expansion,the governing equation isrecovered correctly from the lattice Boltzmann equation.Moreover,the local equilib-rium distribution function is obtained.The results of numerical examples have beencompared with the analytical solutions to confirm the good accuracy and the applica-bility of our scheme.展开更多
This study of the introduction of telegraphy to China in the late-nineteenth century tells three interrelated stories： China＇s pursuit of telegraphic sovereignty with its strategic networking of the empire in the pe...This study of the introduction of telegraphy to China in the late-nineteenth century tells three interrelated stories： China＇s pursuit of telegraphic sovereignty with its strategic networking of the empire in the period 1881-99; the functioning of China＇s hybrid express courier-telegraphic communications infrastructure; and the international communications crisis during the Boxer Uprising and the ＂Siege of the Legations＂ in 1900. The material reality of two inter-connected networks--the privately owned Imperial Telegraph Administration network and the government-run telegraph network--allowed Qing-era Beijing and its provincial governors to communicate with much greater speed. The materiality of these networks--how this new communications technology affected the practical realities of government communications, including the ease of lateral communications between provincial governors--is explored in the context of the communications crisis of 1900. In May and June of 1900 all telegraph lines to Beijing, and throughout much of North China, were cut or otherwise destroyed. While these blinded Western governments are no longer able to exchange telegrams with their Beijing-based envoys, the Qing express courier system continued to operate. Moreover, both the court and provincial officials quickly improvised ad hoc telegraphic communication protocols through the use of ＂transfer telegrams＂ （zhuandian） that relied on mounted express couriers between Beijing and those North China telegraph stations with working network connections. This assessment of real-time secret imperial communications between the Qing court and the provinces is based on the documentary register Suishou dengji （Records of [documents] at hand） maintained by communications managers in the Grand Council. China lost its telegraphic sovereignty in the capital region when Allied troops occupied the Beijing-Tianjin line of communications in the summer and fall of 1900. Moreover, Western dreams of laying, landing, and controlling subm展开更多
文摘It is known that Fourier’s heat equation, which is parabolic, implies an infinite velocity propagation, or, in other words, that the mechanism of heat conduction is established instantaneously under all conditions. This is unacceptable on physical grounds in spite of the fact that Fourier’s law agrees well with experiment. However, discrepancies are likely to occur when extremely short distances or extremely short time intervals are considered, as they must in some modern problems of aero-thermodynamics. Cattaneo and independently Vernotte proved that such process can be described by Heaviside’s telegraph equation. This paper shows that this fact can be derived using calculus of variations, by application of the Euler-Lagrange equation. So, we proved that the equation of heat conduction with finite velocity propagation of the thermal disturbance can be obtained as a solution to one variational problem.
文摘This paper is devoted to studying the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation. The asymptotic theory and validity of formal approximations are constructed on long timescale O(\epsilon\(-1)). As an application of the asymptotic theory, the initial value problems for a special telegraph equation are studied and two asymptotic solutions of order O(\epsilon\(-)1) are presented.
基金Acknowledgments. This work is supported by the Natural Science Foundation of China （NSFC） under grant 11371287 and the International Science and Technology Cooperation Program of China under grant 2010DFA14700.
文摘A new numerical algorithm for telegraph equations with homogeneous boundary con- ditions is proposed. Due to the damping terms in telegraph equations, there is no royal conservation law according to Noether＇s theorem. The algorithm origins from the discovery of a transform applied to a telegraph equation, which transforms the telegraph equation to a Klein-Gordon equation. The Symplectic method is then brought in this algorithm to solve the Klein-Gordon equation, which is based on the fact that the Klein-Gordon equation with the homogeneous boundary condition is a perfect Hamiltonian system and the symplectic method works very well for Hamiltonian systems. The transformation itself and the inverse transformation theoretically bring no error to the numerical computation. Therefore the error only comes from the symplectic scheme chosen. The telegraph equation is finally explicitly computed when an explicit symplectic scheme is utilized. A relatively long time result can be expected due to the application of the symplectic method. Mean- while, we present order analysis for both one-dimensional and multi-dimensional cases in the paper. The efficiency of this approach is demonstrated with numerical examples.
文摘Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.
基金supported by the General Project of the National Social Science Fund of China(Grant No.NSSFC)“Research on the Changes of Modern East Asian Order”(Grant No.18BSS028).
文摘Using the adoption and expansion of wired telegraph in China during the late 19^(th) century,this paper investigates the effect of cost reductions for knowledge exchange on China’s industrial growth before the outbreak of the War of Resistance Against Japanese Aggression(1931-1945),thus testing Baldwin’s theory of“the Great Convergence”in which developing countries are empowered by information and communication technologies.Based on panel data of 1858-1937,we found that wired telegraph access had a significantly positive effect,as well as a long-term growth effect,on the entry of industrial enterprises.Our mechanism analysis indicates that wired telegraph access accelerated early-stage industrialization in localities by encouraging market integration,human capital accumulation,and auxiliary commercial organizations.Only a few countries firmly asserted their telegraph sovereignty and set up their own workforce educational system during telegraph adoption.This explains why the Great Convergence arising from technology importation only occurred in a small number of countries.Our findings contribute to understanding the source of China’s modern industrial progress,as well as why global inequities remain.
基金Project supported by the National Natural Science Foundation of China (No. 10071014).
文摘The space-fractional telegraph equation is analyzed and the Fourier transform of its funda-mental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satisfies thespace-fractional telegraph equation, is presented. Its limiting behaviour and the connectionwith symmetric stable processes is also examined.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61372156 and 61405053)the Natural Science Foundation of Zhejiang Province of China(Grant No.LZ13F04001)
文摘The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random telegraph signal noise in the pixel source follower based on the binomial distribution is set up. The number of electrons captured or released by the oxide traps in the unit time is described as the random variables which obey the binomial distribution. As a result,the output states and the corresponding probabilities of the first and the second samples of the correlated double sampling circuit are acquired. The standard deviation of the output states after the correlated double sampling circuit can be obtained accordingly. In the simulation section, one hundred thousand samples of the source follower MOSFET have been simulated,and the simulation results show that the proposed model has the similar statistical characteristics with the existing models under the effect of the channel length and the density of the oxide trap. Moreover, the noise histogram of the proposed model has been evaluated at different environmental temperatures.
文摘Magnetohydrodynamics couples the Navier-Stokes and Maxwell’s equations to describe the flow of electrically conducting fluids in magnetic fields.Maxwell’s equations require the divergence of the magnetic field to vanish,but this condition is typically not preserved exactly by numerical algorithms.Solutions can develop artifacts because structural properties of the magnetohydrodynamic equations then fail to hold.Magnetohydrodynamics with hyperbolic divergence cleaning permits a nonzero divergence that evolves under a telegraph equation,designed to both damp the divergence,and propagate it away from any sources,such as poorly resolved regions with large spatial gradients,without significantly increasing the computational cost.We show that existing lattice Boltzmann algorithms for magnetohydrodynamics already incorporate hyperbolic divergence cleaning,though they typically use parameter values for which it reduces to parabolic divergence cleaning under a slowly-varying approximation.We recover hyperbolic divergence cleaning by adjusting the relaxation rate for the trace of the tensor that represents the electric field,and absorb the contribution from the symmetric-traceless part of this tensor using a change of variables.Numerical experiments confirm that the qualitative behaviour changes from parabolic to hyperbolic when the relaxation time for the trace of the electric field tensor is increased.
基金The authors are very thankful to the reviewers for their valuable suggestions toimprove the quality of the paper.This work is supported by National Natural Science Foundation of China(Nos.11101399,11271171,11301234)the Provincial Natural Science Foundation of Jiangxi(Nos.20161ACB20006,20142BCB23009,20151BAB201012).
文摘In this paper,we develop a lattice Boltzmann model for a class ofone-dimensional nonlinear wave equations,including the second-order hyperbolictelegraph equation,the nonlinear Klein-Gordon equation,the damped and undampedsine-Gordon equation and double sine-Gordon equation.By choosing properly theconservation condition between the macroscopic quantity u,and the distributionfunctions and applying the Chapman-Enskog expansion,the governing equation isrecovered correctly from the lattice Boltzmann equation.Moreover,the local equilib-rium distribution function is obtained.The results of numerical examples have beencompared with the analytical solutions to confirm the good accuracy and the applica-bility of our scheme.
文摘This study of the introduction of telegraphy to China in the late-nineteenth century tells three interrelated stories： China＇s pursuit of telegraphic sovereignty with its strategic networking of the empire in the period 1881-99; the functioning of China＇s hybrid express courier-telegraphic communications infrastructure; and the international communications crisis during the Boxer Uprising and the ＂Siege of the Legations＂ in 1900. The material reality of two inter-connected networks--the privately owned Imperial Telegraph Administration network and the government-run telegraph network--allowed Qing-era Beijing and its provincial governors to communicate with much greater speed. The materiality of these networks--how this new communications technology affected the practical realities of government communications, including the ease of lateral communications between provincial governors--is explored in the context of the communications crisis of 1900. In May and June of 1900 all telegraph lines to Beijing, and throughout much of North China, were cut or otherwise destroyed. While these blinded Western governments are no longer able to exchange telegrams with their Beijing-based envoys, the Qing express courier system continued to operate. Moreover, both the court and provincial officials quickly improvised ad hoc telegraphic communication protocols through the use of ＂transfer telegrams＂ （zhuandian） that relied on mounted express couriers between Beijing and those North China telegraph stations with working network connections. This assessment of real-time secret imperial communications between the Qing court and the provinces is based on the documentary register Suishou dengji （Records of [documents] at hand） maintained by communications managers in the Grand Council. China lost its telegraphic sovereignty in the capital region when Allied troops occupied the Beijing-Tianjin line of communications in the summer and fall of 1900. Moreover, Western dreams of laying, landing, and controlling subm
