Narrow Results

In the recent years, various geo-synthetic components find an extensive application in civil and coastal engineering practice. Commonly, geo-synthetics have a wide application for secondary or tertiary purposes, such as filtration, separation, barrier, reinforcement, whereas, they can be potentially exploited for various other applications in the coastal engineering practice. A sustainable seawall cross-section comprising different geo-synthetic products was proposed to be erected along the Pallana Beach ($19^{\circ }17^{\prime }55.19^{\prime \prime }$ N and $76^{\circ }23^{\prime }18.55^{\prime \prime }$ E), located in Alleppey district of Kerala along the south-west Indian coastline. Since the subsoil at the location is poorly graded, it was decided to replace the conventional materials like rock boulders and concrete armour units with geo-synthetic products. A comprehensive physical model study was conducted to assess the hydrodynamic performance (i.e. reflection, run-up, and pressure distribution) of the geo-synthetic seawall cross-section for a wide range of random wave characteristics and two water depth conditions. The relative overtopping rates for the seawall at varying water levels are computed conservatively from the guidelines prescribed by the EurOtop Manual and XGB Overtopping model.

Teacher professional development is important in order for teachers to effectively address changing contextual realities. Effective professional development builds on teachers’ experience and relates to their practice. The paper presents guiding ideas and lessons learnt from teacher development component of a research project that aimed at improving numeracy performance of pupils by focusing on teachers’ assessment practices. Based on conclusions, recommendations are made for possible approaches to future PD especially in similar contexts.

In this paper, we discussed the longitudinal harmonic waves reflection from a solid elastic half-space with electromagnetic and gravity fields influence, considering a fractional order via fractional exponential function method. The clarifications are required for the reflection amplitudes ratios (i.e. the ratios between the reflected waves amplitude and the incident waves amplitude). The results obtained were calculated analytically and displayed by graphs to show the physical meaning of the phenomenon. A comparison has been made between the fractional and integer derivatives. The results of this paper demonstrate the rigor and effectiveness of the considered fractional technique.

The method of Lin and Huang [Lin and Huang [2004] “Decomposition of incident and reflected higher harmonic waves using four wave gauges,” Coast. Eng.51(5), 395–406.] (LH) is improved for resolution of incident and reflected strongly nonlinear regular waves in shallow waters with measurements of four stationary wave gauges. For first harmonics, wavenumbers, amplitudes and initial phases are obtained by using a nonlinear least squares method. For higher harmonics, wavenumbers of free and bound modes are determined from linear dispersion relation and multiple of first-harmonic wavenumbers, respectively, and the other unknowns are solved by using a linear least squares method. Auto-correlation function is used to determine fundamental wave period for gaining a good performance of Fourier transform. The efficiency and accuracy of the present method are demonstrated by using artificial data and numerical flume data. It is also demonstrated that the present method is less sensitive to signal noise and gauge spacings. Comparison between the present method and the LH method indicates the necessity of employing nonlinear method in determining fundamental wavenumbers of nonlinear shallow-water waves. Finally, the present method is extended to account for obliquely-incident waves. Sensitivity tests indicate the robustness of the extended method with respect to incident angles. Relative position of gauges in the array for avoiding singularity is suggested.

In this paper, we establish the existence and uniqueness of solutions of reflected stochastic partial differential equations (SPDEs) driven both by Brownian motion and by Poisson random measure in a convex domain. Penalization method plays a crucial role.

A systematic analysis of matched layers is undertaken with special attention to better understand the remarkable method of Bérenger. We prove that the Bérenger and closely related layers define well-posed transmission problems in great generality. When the Bérenger method or one of its close relatives is well-posed, perfect matching is proved. The proofs use the energy method, Fourier–Laplace transform, and real coordinate changes for Laplace transformed equations. It is proved that the loss of derivatives associated with the Bérenger method does not occur for elliptic generators. More generally, an essentially necessary and sufficient condition for loss of derivatives in Bérenger's method is proved. The sufficiency relies on the energy method with pseudodifferential multiplier. Amplifying and nonamplifying layers are identified by a geometric optics computation. Among the various flavors of Bérenger's algorithm for Maxwell's equations, our favorite choice leads to a strongly well-posed augmented system and is both perfect and nonamplifying in great generality. We construct by an extrapolation argument an alternative matched layer method which preserves the strong hyperbolicity of the original problem and though not perfectly matched has leading reflection coefficient equal to zero at all angles of incidence. Open problems are indicated throughout.

This chapter discusses how a lesson closure, which should be present in every Mathematics lesson, can be carried out effectively to promote offline metacognition. According to the theory of constructivism, learning is achieved through making connection between the new concept and a learner’s prior knowledge, or schema. Lesson closure is crucial to provide a time and space for students to consolidate their learning and acquire the mathematical concepts. We will introduce a strategy to close a lesson in which the teacher uses students’ reflection of their learning to create a visual representation, known as a closure diagram. This activity provides a structure that allows students to either integrate the knowledge into their schema or identify gaps in their learning. Both situations involve students regulating their thinking, which is metacognitive in nature. Variations of the closure strategy for different purposes will also be discussed and illustrated with artefacts from classroom lessons.

In this note we will discuss a new reflection principle which follows from the Proper Forcing Axiom. The immediate purpose will be to prove that the bounded form of the Proper Forcing Axiom implies both that 2^ω = ω₂ and that satisfies the Axiom of Choice. It will also be demonstrated that this reflection principle implies that □(κ) fails for all regular κ > ω₁.

In this paper, we explore the application of nonlocal theory to analyze the phenomenon of coupled thermoelastic wave reflection in a semiconducting diffusive medium, considering its temperature rate dependence. The governing equations are deconstructed using the Helmholtz vector rule, allowing us to delve into the behavior of the system. By calculating the dispersion relation in terms of propagation speed, we investigate four coupled longitudinal waves alongside an independent nondispersive transverse wave within the local medium. The cut-off frequencies for each wave are discussed, shedding light on their characteristics. Furthermore, we delve into the phenomenon of coupled longitudinal displacement waves at the medium’s boundary. Analytical derivations of amplitude ratios are presented, accompanied by graphical representations of their behavior, focusing on a semiconductor material such as copper. We examine the effects of physical parameters, including the nonlocal and diffusive parameters, on the obtained results. It is important to note that the existing literature primarily lacks consideration of diffusivity and plasma transportation. Lastly, we validate our findings by investigating the conservation of energy within the system.

Using the method of Girsanov’s transformation, we investigate Talagrand’s quadratic transportation cost inequalities for the laws of the solutions of stochastic partial differential equations (SPDEs) with two reflection walls under the uniform norm on the continuous functions space. These equations are driven by fractional noises.

We propose a reflective acoustic metasurface by taking advantage of the synergetic coupling of two kinds of widely used elements, the resonant cavity and the labyrinthine beam. A full 2$\pi$ phase shift range can be obtained by varying the neck width. The structure manipulates the reflective waves on a very deep subwavelength scale with the thickness being only 1/50 of the wavelength, which eliminates the enormous obstacle in low frequency applications. The synergetic coupling of the resonant cavity and the inner labyrinthine beams provide a useful guide for the design of acoustic metasurfaces.

This paper aimed at studying the effect of initial stress and impedance boundary surface on the elastic waves propagation in transversely isotropic materials. The governing equations of transversely isotropic materials with initial stress are treated in the $xy$-plane to obtain the phase velocities of two waves, quasi-longitudinal ($qP$) and quasi-transverse ($qS$) waves. The normal mode operation is employed to obtain the expression of the displacement components and stress components. The problem of reflection of incident waves at the impedance boundary of transversely isotropic material is also investigated in the presence of initial stress to obtain the amplitude ratios of reflected waves. The variations of displacement and force stress are illustrated with respect to the axis of propagation by employing amplitude ratio expression. The effect of initial stress and impedance parameters on the expression of displacement and force stress as well as amplitude ratios of transversely isotropic materials are illustrated graphically for a particular model.

This article briefly reflects some of my interactions with Dr. Britton Chance (BC), from a perspective of his graduate student.

In this paper, we study a large deviation principle for a reflected stochastic partial differential equation on infinite spatial domain. A new sufficient condition for the weak convergence criterion proposed by Matoussi, Sabbagh and Zhang [A. Matoussi, W. Sabbagh and T.-S. Zhang, Large deviation principles of obstacle problems for quasilinear stochastic PDEs, Appl. Math. Optim. 83(2) (2021) 849–879] plays an important role in the proof.

Recent designs of dielectric-metamaterial composites have some advantages in improving the coupling effect of light in the visible region. The refractive index of the designed metal mesh or fishnet metamaterial structure consists of metals such as Ag, Cu and Al with MgF₂ dielectric material as the substrate which is calculated theoretically using Bruggeman equation. It has been established recently that the dielectric-metamaterial reflector coating (DMMRC) produces outstanding results. It drastically increases the internal reflection and enhances absorption in the visible region. DMMRC is designed by two slabs with exclusive thickness and contrary refractive indices. One is dielectric material and the other is negative refractive index material (NIM). This theoretical model can be treated as a photonic crystal and hence novel light trapping mechanism can be revealed. The transmission spectrum is analyzed using the transverse matrix method (TMM). This system may also be analyzed for various incident angles and for various substrates which are used to improve the efficiency of the solar cell.

A complete and fully developed theory of all optical phenomena (refraction, reflection, absorption, and transparency) and the corresponding optical properties of ultrathin crystalline films (optical indices) are presented in this paper, especially along the direction in which the structure is spatially limited (perpendicular to surfaces). While these indices depend on the position of the crystallographic plane (where the mentioned optical phenomena occur) with respect to the two interfaces, these values can be measured/ determined in experiments only for the film as a whole. For these reasons, it is important to answer the question of how to define these optical indices precisely.

This study indicates that the removal of reflections from T-ray signals can be carried out in the frequency domain without prior knowledge of material parameters or sample thickness. By fitting polynomials to the logarithm and the argument of the sample's transfer function, the Fabry-Pérot reflection term is canceled out, leading to disappearance of the reflections in spatial domain. The method successfully removes the reflections for optically thick samples under the condition of noise or amplitude fluctuations. The application to optically thin samples is possible when the samples are subjected to broadband terahertz measurements. The Fabry-Pérot free signal, when used as input to the parameter estimation method, results in correct material parameters with low variance.

We extend the results of Laver on using inverse limits to reflect large cardinals of the form, there exists an elementary embedding L_α(V_λ+1) → L_α(V_λ+1). Using these inverse limit reflection embeddings directly and by broadening the collection of U(j)-representable sets, we prove structural results of L(V_λ+1) under the assumption that there exists an elementary embedding j : L(V_λ+1) → L(V_λ+1). As a consequence we show the impossibility of a generalized inverse limit X-reflection result for X ⊆ V_λ+1, thus focusing the study of L(ℝ) generalizations on L(V_λ+1).

We report a graphene-based tunable ultra-narrowband mid-infrared filter which can be tuned from 4.45122 $\mu$m to 4.44675 $\mu$m by tuning the Fermi level from 0.2 eV to 0.6 eV. Furthermore, the reflection bandwidth is less than 0.2 nm and the reflection rate is more than 0.55. The ultra-narrowband filter is designed based on the guided-mode resonance (GMR) effect. The shift of reflection peak is mainly caused by the change of the real part of the graphene’s permittivity. This tunable ultra-narrowband mid-infrared filter can be applied in the mid-infrared microscopy.

In this paper, the transmission and reflection of acoustic waves into and from an underground tunnel are investigated by producing an impact load on the ground and measuring the acoustic pressure levels at different time intervals. For this purpose, a sound detector is placed on the ground and then from an arbitrary location on the surface, acoustic waves are transmitted into the ground from an acoustic source. The pressure levels of acoustic waves transmitted into the tunnel space and reflected back to the ground surface are measured, and the effects of several parameters on the attenuation of acoustic pressure levels of transmitted and reflected sound waves are evaluated. Moreover, the effects of parameters such as soil type, concrete type and thickness, buried depth of the underground structure and also the effect of acoustic absorbers on the transmission, propagation and reflection of acoustic waves into and from the tunnel are investigated. The results obtained indicate that the two parameters of soil type and buried depth have the greatest effect on the transmission of acoustic waves, whereas all the parameters considered are important with regard to the reflection of acoustic waves. In addition, it was observed that the use of acoustic absorbers in tunnel structures has a significant effect on the attenuation of transmitted and reflected acoustic waves.