Transit passenger origin-destination estimation in congested transit networks with elastic line frequencies

This paper deals with the transit passenger origin-destination (O-D) estimation problem by using updated passenger counts in congested transit networks and outdated prior O-D matrix. A bilevel programming approach is extended for the transit passenger O-D updating problem where the upper-level problem seeks to minimize the sum of error measurements in passenger counts and O-D matrices, while the lower level is the stochastic user equilibrium assignment problem for congested transit networks. The transit assignment framework is based on a frequency-adaptive transit network model in this paper, which can help determine transit line frequencies and the network flow pattern simultaneously in congested transit networks. A heuristic solution algorithm is adapted for solving the transit passenger O-D estimation problem. Finally, a numerical example is used to illustrate the applications of the proposed model and solution algorithm. The work described in this paper was mainly supported by two research grants from the Research Grants Council of the Hong Kong Special Administrative Region (Project No. PolyU 5143/03E and PolyU 5040/02E).     

Resonant frequencies for a narrow strip grating

This paper deals with the existence and the distribution of the resonances associated with the Maxwell system in a periodic infinite structure, obtained by loading a substrate with a periodic perturbation. We give an integral formulation of the homogeneous diffraction problem. By boundary integral operators method, the existence and distribution of resonances is reduced to the determination of the characteristic values of two meromorphic operator valued functions. We give existence results on complex resonances close to the resonances of the substrate and also on real resonances. Copyright © 1999 John Wiley & Sons, Ltd.     

Numerical analysis for a locally damped wave equation

We consider a semi-discrete finite element formulation with artificial viscosity for the numerical approximation of a problem that models the damped vibrations of a string with fixed ends. The damping coefficient depends on the spatial variable and is effective only in a sub-interval of the domain. For this scheme, the energy of semi-discrete solutions decays exponentially and uniformly with respect to the mesh parameter to zero. We also introduce an implicit in time discretization. Error estimates for the semi-discrete and fully discrete schemes in the energy norm are provided and numerical experiments performed.     

Resonant response of a strong electromagnetic wave beam to a gravitational wave in a static magnetic field

Concrete forms of resonant response (ER) for a strong electromagnetic (EM) wave beam (photon flux) propagating in a static magnetic field to a standing gravitational wave (gravitons) are given, and the corresponding perturbation solutions and resonant conditions are obtained. It is found that perturbed EM fields (PEMFs) contain three new components with frequencies Io,* w,l and ωP_g respectively. In the case of ω_e⋙ω_g, the PEMFs are manifested as the EM wave beams with frequency ω_e and a standing EM wave with ω_g. The former and the background EM wave beam (BE-MWB) have the same propagating direction, while in the case of ω_g⋙ω_e, all PEMFs are expressed as the standing EM waves with frequency ω_g. The resonant response occurs in two cases of ω_e = 1/2 ω_g andω_e, = ω_g only. Then not only the first order perturbed energy fluxes (PEFs) propagating in the same and opposite directions of the BEMWB can be generated, but also radial and tangential PEFs which are perpendicular to the above directions can be produced. This effect might provide a new way for the EM detection of the gravitational waves (GWs). Moreover, the possible schemes of displaying perturbed effects induced by the standing GW withh = 10^-33 - 10^-35 and λ_g = 0.1 m at the level of the single photon avalanche and in a typicla laboratory dimension are reviewed.     

On the behavior of resonant frequencies in the presence of small anisotropic imperfections

In this paper we provide a rigorous derivation of an asymptotic formulae for perturbations in the resonant frequencies of the two-(or three-) dimensional Laplacian operator under geometric variation of the domain. The asymptotic expansion is developed in the presence and with respect to size of the (anisotropic) imperfections of small shapes having constitutive parameters different from the background conductivity. The main feature of the method is to yield a robust procedure making it possible to recover information about the location, shape, and material properties of the anisotropic imperfections.     

一个曲面波方程的精确解

Abstract. Some exact travelling wave solutions and rational travelling wave solutions of a sur-face wave equation in a convecting fluid are given in this paper.     

Exterior dirichlet problem for the reduced wave equation: asymptotic analysis of low frequencies

The order of convergence for the low frequency asymptotics of the exterior Dirichlet problem for the Helmholtz equation with variable, possibly non-smooth coefficients is shown to be Ω², the square of the frequency, except of some singular cases. In these cases the asymptotics are characterized completely by some lower order terms in the spherical harmonics expansion of the solution to the static problem.     

Resonant wave motion in a non-homogeneous system

A nonlinear theory of resonant wave motion in an inhomogeneous system (arising from different mechanical applications) is considered. Depending on the magnitude of the influence of inhomogeneity two different situations are encountered. The system may behave either as a nonlinear one-degree-of-freedom oscillator exhibiting a response curve with either soft or hard spring behaviour or for a sufficiently small influence of inhomogeneity, there are periodic shock waves in a certain frequency band about the linear resonance frequency, a phenomenon that is familiar from homogeneous systems like a gas filled tube being excited close to resonance.     

Notes on exact travelling wave solutions for a long wave-short wave model

This paper considers a long wave-short wave model. It shows that under three different parameter conditions, this system has three types of exact explicit travelling wave solutions. Their parametric representations have been given.     

A blow-up theorem for a discrete semilinear wave equation

In this paper, a discretization of a semilinear wave equation whose nonlinear term is a power function is investigated. It is shown that, when a condition on the initial value problem, similar to that governing the existence of blow-up solutions for the original continuous equation is met, the newly introduced difference equation has blow-up solutions with characteristics corresponding to those of the blow-up solutions for the original equation.     

Global solutions for a nonlinear wave equation

In this work the existence of a global solution for the mixed problem associated to the nonlinear equation

is proved in a Hilbert space framework by using Galerkin method.     

Planar bifurcation method of dynamical system for investigating different kinds of bounded travelling wave solutions of a generalized Camassa-Holm equation

In this study, by using planar bifurcation method of dynamical system, we study a generalized Camassa-Holm (gCH) equation. As results, under different parameter conditions, many bounded travelling wave solutions such as periodic waves, periodic cusp waves, solitary waves, peakons, loops and kink waves are given. The dynamic properties of these exact solutions are investigated.     

Solitary wave solutions and kink wave solutions for a generalized KDV-mKDV equation

Bifurcation method of dynamical systems is employed to investigate solitary wave solutions and kink wave solutions of the generalized KDV-mKDV equation. Under some parameter conditions, their explicit expressions are obtained.     

New travelling wave solutions for a nonlinearly dispersive wave equation of Camassa-Holm equation type

In this paper, the integral bifurcation method is used to study a nonlinearly dispersive wave equation of Camassa-Holm equation type. Loop soliton solution and periodic loop soliton solution, solitary wave solution and solitary cusp wave solution, smooth periodic wave solution and non-smooth periodic wave solution of this equation are obtained, their dynamic characters are discussed. Some solutions have an interesting phenomenon that one solution admits multi-waves when parameters vary.     

Global nonlinear stability of longitudinal wave for the planar motion of elastic string with linear Hooke's law

In this paper, we consider the global nonlinear stability of longitudinal wave for the planar motion of elastic string with linear Hooke's law. First, we will give the representation of the traveling wave solution to the recast hyperbolic system. Then, by using the weighted function method, we obtain the global stability of longitudinal wave solution for nonlinear elastic string equation.     

A numerical method for reconstructing the coefficient in a wave equation

We present a numerical method for reconstructing the coefficient in a wave equation from a single measurement of partial Dirichlet boundary data. The original inverse problem is converted to a nonlinear integral differential equation, which is solved by an iterative method. At each iteration, one linear second‐order elliptic problem is solved to update the reconstruction of the coefficient, then the reconstructed coefficient is used to solve the forward problem to obtain the new data for the next iteration. The initial guess of the iterative method is provided by an approximate model. This model extends the approximate globally convergent method proposed by Beilina and Klibanov, which has been well developed for the determination of the coefficient in a special wave equation. Numerical experiments are presented to demonstrate the stability and robustness of the proposed method with noisy data.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 289–307, 2015     

Exponential energy decay of solutions for a system of viscoelastic wave equations of Kirchhoff type with strong damping

The initial boundary value problem for a system of viscoelastic wave equations of Kirchhoff type with strong damping is considered. We prove that, under suitable assumptions on relaxation functions and certain initial data, the decay rate of the solutions energy is exponential.     

Exact traveling wave solutions for a modified Camassa-Holm equation

In this paper, the bifurcation method of planar dynamical systems is utilized to investigate a modified Camassa-Holm equation. After dividing the parametric space, some explicit parametric conditions are derived for the existence of traveling wave solutions. Several exact traveling solutions are also obtained.     

Estimates for wave and Klein-Gordon equations on modulation spaces

We prove that the fundamental semi-group eit(m 2I+|Δ|)1/2(m = 0) of the Klein-Gordon equation is bounded on the modulation space M ps,q(Rn) for all 0 < p,q ∞ and s ∈ R.Similarly,we prove that the wave semi-group eit|Δ|1/2 is bounded on the Hardy type modulation spaces μsp,q(Rn) for all 0 < p,q ∞,and s ∈ R.All the bounds have an asymptotic factor tn|1/p 1/2| as t goes to the infinity.These results extend some known results for the case of p 1.Also,some applications for the Cauchy problems related to the semi-group eit(m2I+|Δ|)1/2 are obtained.Finally we discuss the optimum of the factor tn|1/p 1/2| and raise some unsolved problems.