EIGENFUNCTION EXPANSION FOR STURM-LIOUVILLE PROBLEMS WITH TRANSMISSION CONDITIONS AT ONE INTERIOR POINT

The purpose of this article is to extend some spectral properties of regular Sturm- Liouville problems to the special type discontinuous boundary-value problem, which consists of a Sturm-Liouville equation together with eigenparameter-dependent boundary conditions and two supplementary transmission conditions. We construct the resolvent operator and Green＇s function and prove theorems about expansions in terms of eigenfunctions in modified Hilbert space L2[a, b].

CONVERGENCE RESULTS FOR NON-OVERLAP SCHWARZ WAVEFORM RELAXATION ALGORITHM WITH CHANGING TRANSMISSION CONDITIONS

In this paper,we establish a new algorithm to the non-overlapping Schwarz domain decomposition methods with changing transmission conditions for solving one dimensional advection reaction diffusion problem.More precisely,we first describe the new algorithm and prove the convergence results under several natural assumptions on the sequences of parameters which determine the transmission conditions.Then we give a simple method to estimate the new value of parameters in each iteration.The interesting advantage of our method is that one may update the better parameters in each iteration to save the computational cost for optimizing the parameters after many steps.Finally some numerical experiments are performed to show the behavior of the convergence rate for the new method.

STURM-LIOUVILLE PROBLEMS WITH EIGENDEPENDENT BOUNDARY AND TRANSMISSIONS CONDITIONS

The purpose of this paper is to extend some fundamental spectral properties of regular Sturm-Liouville problems to special kind discontinuous boundary value problem, which consist of a Sturm-Liouville equation with piecewise continuous potential together with eigenvalue parameter on the boundary and transmission conditions. The authors suggest their own approach for finding asymptotic approximations formulas for eigenvalues and eigenfunctions of such discontinuous problems.

Green Function of Fourth-order Differential Operator with Eigenparameter-dependent Boundary and Transmission Conditions

We investigate a class of fourth-order regular differential operator with transmission conditions at an interior discontinuous point and the eigenparameter appears not only in the differential equation but also in the boundary conditions. We prove that the operator is symmetric, construct basic solutions of differential equation, and give the corresponding Green function of the operator is given.

J-selfadjointness of a class of high-order differential operators with transmission conditions

This paper is to investigate the J-selfadjointness of a class of high-order complex coefficients differential operators with transmission conditions.Using the Lagrange bilinear form of J-symmetric differential equations,the definition of J-selfadjoint differential operators and the method of matrix representation,we prove that the operator is J-selfadjoint operator,and the eigenvectors and eigen-subspaces corresponding to different eigenvalues are C-orthogonal.

Cell transmission model based traffic signal timing in oversaturated conditions

In order to investigate enhancements to cell transmission model (CTM) as a tool for traffic signal timing in oversaturated conditions, randomly distributed saturation flow rates and arrival rates were used instead of constant values to simulate traffic flow movement, estimate the average delay of the network and search for an optimal traffic signal timing plan. A case study was given to demonstrate that the proposed methodology can capture unique phenomena in oversaturated conditions such as forward wave, spillback and lane entrance blockage. The results show that CTM underestimates travel time by 25% when compared to Simtraffic, while the enhanced CTM underestimates by only 3%. A second case study shows that a dynamic signal timing plan is superior to a fixed signal timing plan in the term of average delay.

A novel conditional cell transmission model for oversaturated arterials

The objective of this work is to develop a novel feature for traffic flow models, when traffic queues on two-way arterials periodically extend until then they block an upstream signal in oversaturated conditions. The new model, proposed as conditional cell transmission model （CCTM） has been developed with two improvements. First, cell transmission model （CTM） is expanded for two-way arterials by taking account of all diverging and merging activities at intersections. Second, a conditional cell is added to simulate periodic spillback and blockages at an intersection. The results of experiments for a multilane, two-way, three-signal sample network demonstrate that CCTM can accommodate various traffic demands and accurate representation of blockages at intersections. The delay of left turns is underestimated by 40 % in moderate conditions and by 58% in oversamrated condition when using the CTM rather than CCTM. Finally, the consistency between HCS 2000 and CCTM shows that CCTM is a reliable methodology of modeling traffic flow in oversaturated condition.

Sensitivity analysis of key input parameters in conditional cell transmission model for oversaturated arterials

A novel conditional cell transmission model （CCTM） is a potential simulation tool because it accommodates all traffic conditions from light condition to oversaturated condition. To test the performance of the CCTM, a series of experiments for sensitivity analysis were designed and performed for a multilane, two-way, three-signal sample network. Experiment 1 shows that the model is performed in a logical and expected manner with variations in traffic demand with time and direction. Experiment 2 shows when the possibility of the occurrence of a useful gap increases to 60% and 100%, the delays in left rams decrease by 5% and 15%, respectively. In Experiment 3, comparing the possibility of a conditional cell of 0 with 100%, delay of left turn and delay of the entire network were underestimated by 58% and 11%, respectively. Hence, sensitivity analysis demonstrates that by reflecting local drivers＇ behaviors properly, the CCTM provides an accurate representation of traffic flow in simulating oversaturated traffic conditions.

A NEW INTEGRAL EQUATION FORMULATION FOR SCATTERING BY PENETRABLE DIFFRACTION GRATINGS

This paper is concerned with the problem of scattering of time-harmonic electromag- netic waves from penetrable diffraction gratings in the 2D polarization case. We propose a new, weakly singular, integral equation formulation for the scattering problem which is proved to be uniquely solvable. A main feature of the new integral equation formula- tion is that it avoids the computation of the normal derivative of double-layer potentials which is difficult and time consuming. A fast numerical algorithm is also developed for the scattering problem, based on the NystrSm method for the new integral equation. Nu- merical examples are also shown to illustrate the applicability of the new integral equation formulation.