Probabilistic programming models for traffic incident management operations planning

This paper proposes mathematical programming models with probabilistic constraints in order to address incident response and resource allocation problems for the planning of traffic incident management operations. For the incident response planning, we use the concept of quality of service during a potential incident to give the decision-maker the flexibility to determine the optimal policy in response to various possible situations. An integer programming model with probabilistic constraints is also proposed to address the incident response problem with stochastic resource requirements at the sites of incidents. For the resource allocation planning, we introduce a mathematical model to determine the number of service vehicles allocated to each depot to meet the resource requirements of the incidents by taking into account the stochastic nature of the resource requirement and incident occurrence probabilities. A detailed case study for the incident resource allocation problem is included to demonstrate the use of proposed model in a real-world context. The paper concludes with a summary of results and recommendations for future research.     

Note on a Uniqueness Theorem of Schiffer

AMS (MOS): 35R30, 76Q05

The uniqueness of the inverse scattering problem is examined. It is shown that the boundary conditions must be suitably restricted to secure uniqueness. For one class the far-field pattern for one incident field is sufficient for uniqueness and, for a wider class, information from a finite number of distinct incident waves suffices. In either case, the far-field also dictates the boundary condition on the scatterer.     

On over-reflection of acoustic-gravity waves incident upon a magnetic shear layer in a compressible fluid

A study is made of over-reflection of acoustic-gravity waves incident upon a magnetic shear layer in an isothermal compressible electrically conducting fluid in the presence of an external magnetic field. The reflection and transmission coefficients of hydromagnetic acoustic-gravity waves incident upon magnetic shear layer are calculated. The invariance of wave-action flux is used to investigate the properties of reflection, transmission and absorption of the waves incident upon the shear layer, and then to discuss how these properties depend on the wavelength, length scale of the shear layers, and the ratio of the flow speed and phase speed of the waves. Special attention is given to the relationship between the wave-amplification and critical-level behaviour. It is shown that there exists a critical level within the shear layer and the wave incident upon the shear layer is over-reflected, that is, more energy is reflected back towards the source than was originally emitted. The mechanism of the over-reflection (or wave amplification) is due to the fact that the excess reflected energy is extracted by the wave from the external magnetic field. It is also found that the absence of critical level within the shear layer leads to non-amplification of waves. For the case of very large vertical wavelength of waves, the coefficients of incident, reflected and transmitted energy are calculated. In this limiting situation, the wave is neither amplified nor absorbed by the shear layer. Finally, it is shown that resonance occurs at a particular value of the phase velocity of the wave.     

Computation of paraxial wave fields using transparent boundary conditions

The parabolic wave equation is solved numerically by applying transparent conditions used to confine the computational domain. A numerical implementation of the boundary conditions is proposed based on representing the incident wave as a superposition of Gaussian beams. A modification of the transparent conditions in the case of dielectric objects extending beyond the computational domain is described. Numerical examples are presented.     

Reflection of magneto-thermoelastic waves with two relaxation times and temperature dependent elastic moduli

The model of the equations of generalized magneto-thermoelasticity with two relaxation times in an isotropic elastic medium under the effect of reference temperature on the modulus of elasticity is established. The modulus of elasticity is taken as a linear function of reference temperature. Reflection of magneto-thermoelastic waves under generalized thermoelasticity theory is employed to study the reflection of plane harmonic waves from a semi-infinite elastic solid in a vacuum. The expressions for the reflection coefficients, which are the relations of the amplitudes of the reflected waves to the amplitude of the incident waves, are obtained. Similarly, the reflection coefficients ratios variations with the angle of incident under different conditions are shown graphically. A comparison is made with the results predicted by the coupled theory and with the case where the modulus of elasticity is independent of temperature.     

Dynamical theory of spectroscopy with femtosecond pulse excitation

The dynamical theory of spectroscopy with femtosecond pulse excitation is applied to a direct dissociation process. In the ultrashort pulse case, the fluorescence-like emission peak occurs in Raman scattering as the incident frequency is tuned near resonance. All properties of the spectroscopy can be explained by the correlation function.     

The Sommerfeld half-plane problem revisited,IV: Variations on a theme of Carlson and Heins

A plane wave is incident upon an infinite set of equally spaced, semi-infinite parallel and staggered plates. The boundary conditions on the plates alternate between the Dirichlet and Neumann ones. This problem is formulated as a pair of coupled Wiener-Hopf integral equations and solved by a method proposed by A. E. Heins in 1950. For the case of specular reflection, that is, a single reflected plane wave, the magnitudes of the reflection coefficient and the transmission coefficients are determined.     

各向异性压电介质摩擦接触界面波动特性分析

应用Fourier(傅立叶)分析及奇异积分方程技术研究了弹性波与一般压电介质单侧接触界面的相互作用问题.以界面只产生滑移不分离的情况为例,分析了问题的求解思路和过程,给出了弹性波引起界面滑移或分离的条件.以六角晶系极化碳酸钡陶瓷材料和三角晶系石英材料为例,分析了不同材料摩擦接触界面对弹性波入射的不同反应,给出了不同的入射角及不同的外加压力和电场对界面的影响特性.界面产生滑移和分离时,问题的边界条件具有非线性,导致高频谐波出现,以石英材料为例分析了高频成分随外加条件的变化特性.     

On Impulse Distortion in Dispersive Media

Pulse distortion is due to nonlinear wave number functions of the frequency. For the case of smooth nonlinear wave numbers, a sequence of approximations to the propagation operator which carries the incident pulse to the distorted output pulse is set forth. When applied to the actual incident pulse, they allow the study of the development of the distortion with (a) increasing travel length in the propagation medium and (b) also with respect to the properties of the propagation medium. Of special interest are Gaussian incident pulses for which the distorted pulse form is more concisely representable. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Diffraction of a sinusoidal impulse by a rigid strip

The diffraction of a sinusoidal impulse by an absolutely rigid strip is considered. Approximate formulas are obtained for the field measured at large distances from the strip in the direction of the incident impulse (the case of location). The results are expressed in terms of Fresnel integrals. The possibility of determining the width of the strip and the angle between it and the direction of the incident impulse or the basis of the envelope of the location field is discussed. Graphs of the envelopes for certain specific cases are presented.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 62, pp. 39–47, 1976.The author is grateful to D. P. Kouzov for his attention to the work.     

Generalization of the optical theorem to a singular source in the presence of a half-space

The scattering of the field of an electric dipole by a local penetrable body in the presence of a transparent half-space is considered. A relation is obtained that is similar to the optical theorem in the case of an incident plane wave. With this generalization, the fluorescence enhancement factor or the efficiency of an optical antenna can be calculated without computing the absorbed energy, which considerably reduces the computational costs.     

Experimental study on the non- specularly reflected ultrasonic beam on a liquid- solid interface

The reflected fields of a slightly divergent ultrasonic beam on a liquid-solid interface are recorded by a Schlieren system, and the lateral beam displacements on the interface are measured. The range of the incident angle_i is around the Rayleigh angle_c. The displacements are found to decrease as the incident angle increases. Theoretical calculation reveals that the displacements decrease with the increase in the incident angle for a divergent incident beam, but increase with that for a convergent one. The calculated curve of- _i are in agreement with the experimental results.     

Reflection of Shock Fronts in a van der Waals Fluid

In this paper, the reflection phenomenon of a vapor shock front （both sides of the front are in the vapor phase） in a van der Waals fluid is considered. Both the 1-dimensional case and the multidimensional case are investigated. The authors find that under certain conditions, the reflected wave can be a single shock, or a single subsonic phase boundary, or one weak shock together with one subsonic phase boundary, which depends on the strength of the incident shock. This is different from the known result for the reflection of shock fronts in a gas dynamical system due to Chen in 1989.     

On the complexity of the planar edge-disjoint paths problem with terminals on the outer boundary

It is shown that both the undirected and the directed edge-disjoint paths problem are NP-complete, if the supply graph is planar and all edges of the demand graph are incident with vertices lying on the outer boundary of the supply graph. In the directed case, the problem remains NP-complete, if in addition the supply graph is acyclic. The undirected case solves open problem no. 56 of A. Schrijver’s book Combinatorial Optimization.     

Fastest mixing Markov chain problem for the union of two cliques

A symmetric, random walk on a graph G can be defined by prescribing weights to the edges in such a way that for each vertex the sum of the weights of the edges incident to the vertex is at most one. The fastest mixing, Markov chain (FMMC) problem for G is to determine the weighting that yields the fastest mixing random walk. We solve the FMMC problem in the case that G is the union of two complete graphs.     

The linear sampling method for anisotropic media

We consider the inverse scattering problem of determining the support of an anisotropic inhomogeneous medium from a knowledge of the incident and scattered time harmonic acoustic wave at fixed frequency. To this end, we extend the linear sampling method from the isotropic case to the case of anisotropic medium. In the case when the coefficients are real we also show that the set of transmission eigenvalues forms a discrete set.     

Change of Polarity for Periodic Waves in the Variable‐Coefficient Korteweg‐de Vries Equation

We examine the variable‐coefficient Kortweg‐de Vries equation for the situation when the coefficient of the quadratic nonlinear term changes sign at a certain critical point. This case has been widely studied for a solitary wave, which is extinguished at the critical point and replaced by a train of solitary waves of the opposite polarity to the incident wave, riding on a pedestal of the original polarity. Here, we examine the same case but for a modulated periodic wave train. Using an asymptotic analysis, we show that in contrast a periodic wave is preserved with a finite amplitude as it passes through the critical point, but a phase change is generated causing the wave to reverse its polarity.     

Inverse nonstationary problem of scattering for a hyperbolic system of n equations of the first order on a semiaxis

In connection with a joint study of n-1 problems with diverse boundary conditions we construct a scattering operator for a hyperbolic system on a semiaxis for the case of n-1 incident and one scattered wave. The possibility of the unique recovery of the coefficients of the system with respect to the scattering operator is shown.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 12, pp. 1638–1646, December, 1991.     

Uniqueness results in the inverse scattering problem for periodic structures

This paper is concerned with the inverse electromagnetic scattering by a 2D (impenetrable or penetrable) smooth periodic curve. Precisely, we establish global uniqueness results on the inverse problem of determining the grating profile from the scattered fields corresponding to a countably infinite number of quasiperiodic incident waves. For the case of an impenetrable and partially coated perfectly reflecting grating, we prove that the grating profile and its physical property can be uniquely determined from the scattered field measured above the periodic structure. For the case of a penetrable grating, we show that the periodic interface can be uniquely recovered by the scattered field measured only above the interface. A key ingredient in our proofs is a novel mixed reciprocity relation that is derived in this paper for the periodic structures and seems to be new. Copyright © 2012 John Wiley & Sons, Ltd.