Vogler  conducted numerical simulations to study the scaling laws in hetero- geneous materials for three types of materials - layeredcomposites, particulate composites and granular materials. In case of layered materials, the simulations agreed with experimental observations of Zhuang  and a second power law scal- ing was recovered. In case of particulate composites, a scaling power of 2 − 3 was recovered. It was pointed out that scattering associated with the particulate nature of the composite played a significant role in the reduction of scaling power. In the case of granular materials, a linear scaling law was observed. A separate model, taking into account the pore collapse, was proposed to explain the linear scaling. Recently, plate impact experiments were conducted by Rauls  on two phase composites. Figure 2.9 shows the schematic of the experimental setup. The target used was a two phase composite made of PMMA matrix with glass beads as inclu- sions. Figure 2.10 shows the cross section of the composite sample. The horizontal markings on the cross section came from polishing the sample for imaging. Par- ticle velocity profiles were measured using Photon Doppler Velocimetry (PDV) at three points on the target surface. Experiments were carried out for different sizes (100 µm, 300 µm, 500 µm, 700 µm and 1000 µm) of glass beads and different bead volume fractions (30% and 40%).
Abstract—The transmission and reﬂection coeﬃcients of electromagnetic waves propagating through the ﬁnite periodicallylayered chiral structure are deﬁned both theoretically (using the propagation matrix method) and experimentally. The coeﬃcients of the propagation matrix of the periodicallylayered chiral medium are obtained. The boundaries of the forbidden bands for a periodic medium, whose unit cell consists of two diﬀerent chiral layers were determined. It is shown that the boundaries of the forbidden bands do not depend on the chirality parameter of the layers. It is found that for certain values of the layers thicknesses, the forbidden band widths tend to zero and that the proposed method for calculation of the reﬂection and transmission coeﬃcients can be used to determine the eﬀective constitutive parameters of artiﬁcial chiral metamaterials. The transmission and reﬂection coeﬃcients of plane electromagnetic waves propagated through the ﬁnite periodicallylayered chiral structure were determined experimentally for 20–40 GHz range. A good agreement between the experimental results and theoretical studies of the forbidden band spectrum for the structure under research has been shown.
A wide spectrum of wave solvers have been developed for modeling wavepropagation in heterogeneous media. An INCS method was developed  to model wavepropagation in heterogeneous media. Liu  proposed a pseudo-spectral time-domain algorithm to solve large- scale problems for acoustic waves in multidimensional, heterogeneous, absorptive media. Varslot and Taraldsen  derived a one-way wave equation which permits smooth variation in all acoustically important variables. Both finite difference and angular spectrum methods are applied for numerical implementation. A second-order wave equation describing nonlinear wavepropagation in heterogeneous, attenuating media is solved numerically with the FDTD method by Pinton et al. . An algorithm for modeling shockwavepropagation in weakly heterogeneous and lossless media was proposed in . A k-space time-domain method for modeling of wavepropagation in heterogeneous media was investigated by Mast et al.  and was later extended to take nonlinear wavepropagation into account , . Clement and Hynynen  combined the ASA with ray theory to describe the propagation of ultrasound through randomly oriented, dissipative, layered media. Vyas and Christensen  modified the traditional ASA for simulating linear wavepropagation in inhomogeneous media. For a more extensive literature review, the readers are referred to chapter 1 or a recent reviewer paper .
of residual stress introduced in the molding process to control interface properties. Composites can be made with strong, perfect transparent interfaces or thermally shocked to produce weaker interfaces. This study will focus on relatively strong interfaces, which are more straightforward to simulate. After trial and error, it was found that mixing PMMA powder and glass beads produces even and random distributions of beads in composites with no evidence of settling or clumping. An even, random distribution mimics the common composites of interest to this study, and is also readily comparable to simulations on geometries with randomly generated particulate location distributions. Molding grade PMMA is slightly different than the PMMA used for windows in typical shockpropagation experiments  . Windows are typically cut from Plexiglas (Atuglas International) or Perspex (Lucite International) sheet for optimal clarity and flatness. PMMA sourced in sheet form is typically cast from high molecular weight monomer. While commercially available sheets can be heated and formed or “welded”, the viscosity of the material is bounded by its underlying chemical structure. At such high molecular weights (1,000,000 MW+) the molding temperature is higher than the autoignition temperature; the material will more readily burn than melt. The extremely long average chain length makes it difficult for the polymer chains to slide past one another to the degree required for compression molding, and thus the cast sheet materials do not depart the rubbery stage, even past 160 ° C . As such, lower molecular weight compositions are chosen. A polymer powder of 75,000 MW (Polysciences, Warrington PA, P/N 04553) with a glass transition temperature, T g , of 105 ° C is used as the matrix for the particulate composites in this study. Due
The Wave Finite Element Method (WFEM) is an e ffi cient tool to study wavepropagation in periodic structures. The WFEM has been applied in numerous previous works such as beam-like structures in its one-dimensional formu- lation [10, 11] and then the method was extended to two-dimensional by  and applied to various type of structures such as cylinders [12, 13], plates [14, 15], thin-walled structures  and curved layered shells . However, to apply the WFEM to textile composites, a fine mesh is needed to describe the geometry precisely, which implies large number of degrees of freedom and therefore large CPU times. Various model order reduction (MOR) strategies have been investigated in order to counteract this issue. One of them is the component mode synthesis (CMS) approach, which has been widely used in the literature [6, 18, 19, 20, 21]. Other techniques exist such as the model reduction strategy introduced in , based on the selection of the contributing waves or the strategy developed in  which relies on frequency interpolation of the transfer matrix eigenvectors.
The purchase of a MASTERPULS® »ultra« provides access to the exclu- sive ICE ShockWave Portal. There you will find up-to-date information from all fields of shockwave therapy. All you need is an Internet con- nection and a corresponding display device such as a smartphone, tab- let or computer.
For simplicity, below we restrict our study to the case of light propagation along the z axis ( β = 0 ) in a nonmagnetic lattice (with µ ˆ = I ˆ being a unit matrix). Like in Ref. , we treat the liquid-crystal layers as optically uniaxial ( ε ij = ε xx δ xi δ jx + ε yy δ yi δ jy + ε zz δ zi δ jz ). It is obvious that zz-components of the tensor ε ˆ will not appear in the final formulae for the case of K || z and, moreover, we have
The ability to quantify and predict the energy absorption/transmission cha- racteristics of multi-layered porous medium is imperative if one is involved in the automotive, launch vehicle, commercial aircraft, architectural acoustics, petroleum exploration, or even in modeling human tissue. A case in point, the first four aforementioned fields rely on effective Noise and Vibration (NV) development for their commercial success. NV development requires the setting of NV targets at different system levels. The targets are then trans- lated to Transmission Loss (TL), Insertion Loss (IL), and absorption (Alpha) performance for the multi-layered porous materials being utilized. Thus, it behooves to have a thorough understanding of the physics behind the energy dissipating mechanism of the material that entails the effects of the fluid meandering through the pores of the material and its interaction with the structural skeleton. In this section of the project the focus is on the thermal interchange that occurs within the porous medium. Via the acoustic model- ing at the micro/macro level it is shown how this thermal exchange affects the acoustic compressibility within the porous material. In order to obtain a comprehensive approach the ensuing acoustic modeling includes the effects due to relaxation process, thus bulk viscosity and instantaneous entropy functions (effects due to vibration of diatomic molecules of air) are incorpo- rated into the equation. The instantaneous entropy functions are explained by means of the Boltzmann’s distribution, partition function, and quantum states. The concept of thermal length and its connection to thermal permea- bility is clarified. Lastly, the results for TL calculations employing the afore- mentioned thermal exchange into the Transfer Matrix Method with finite size How to cite this paper: Teagle-Hernandez,
This MSc project is conducted to assess the influence of sand wave fields on wind waves. The influence on wind waves is made insightful and quantifiable by assessing the spatial variability of amplification factors of the wind wave amplitude and the corresponding near-bed orbital flow velocities inside the domain. Subsequently, a base configuration with certain parameter settings is established. From there a parameter is changed indi- vidually and the change of spatial variability due to this change in parameter is assessed. The base case is chosen based on a high influence situation, which is when the sand wave crests were orientated perpendicular to the wind wave crests. This orientation however causes a symmetric situation and might therefore be a somewhat risky base case. Also, the results may describe very case specific behaviour and therefore the generality of the results may be questioned. To come to more generic conclusions, combinations of param- eters should be assessed for their influence on wind waves and this method of assessment might therefore not be that suitable. From the results in this thesis, it became for ex- ample evident that the orientation angle has a significant influence on the effect of other input parameters (e.g. sand wave height and sand wave length), such that research to the influence of changing combinations of these parameters may result in more in-depth knowledge about the relations of parameters to the effect size. in Section 4.4 however, the influence of various combinations of orientation angles and sand wave lengths were explored, which resulted in local maxima of influence (likely Bragg Resonant cases). As this shows that local maxima exist, it may be required to enhance full exploration of the influence on wind waves by all combinations of parameters: simply assuming linear or exponential behaviour between two parameter values is therefore not sufficient. To prevent extremely numerous of combinations and with that very high computational cost, the parameter space can be reduced from currently 7 to 4 parameters by a scaling procedure of the Mild-Slope Equation to its dimensionless form. The formulation of this dimensionless Mild-Slope Equation is introduced in Appendix D.
This paper presents the numerical investigation of the radar cross section (RCS) versus frequency for diﬀerent conﬁgurations. Comparisons between 2D and 3D solutions in terms of resonant frequencies versus slot width are given. Current distributions and far ﬁeld patterns are plotted at the resonant frequencies for diﬀerent plane wave orientations.
Second, the main interest is in beams focused around the direction of propagation, which makes it possible to work with the paraxial approximation of wave equations. In fact, the paraxial wave equation plays a fundamental role in dealing with electromagnetic and acoustic wavepropagation in dierent media, such as; laser beams in the atmosphere [1-3], optical beams in lenslike wave guides  and in dielectric bers , radiowave propagation in the troposphere 1. Institut Henri Poincare, 86 Bis Route de Croissy, 78110,
Aforementioned invasive methods are being gradually superseded by extracorporeal lithotripsy, available in Pakistan since August 1988, in which externally produced shock waves are focussed onto the stone. Repeated shocks act by alternately compressing the stone as the wave proceeds towards it and expanding it as the wave reflected from the far surface of the stone returns back as a tensile force. The shocks loosen up the texture of the stone, produce cracks in it and chip off minute particles from the surface..
• Multipath is a term used to describe the multiple paths a radio wave may follow between transmitter and receiver. Such propagation paths include the ground wave, ionospheric refraction, reradiation by the ionospheric layers, reflection from the Earth's surface or from more than one ionospheric layer, etc.
Next, the performance of the conformal antenna arrays is investigated. The characteristics of the developed antenna prototypes are validated by the measurements using a probe fed antenna measurement system. The radiation patterns of the antenna can be changed by placing the antenna on objects with different curvature radii. Based on these results, several antenna arrays have been designed together with the switching network. Conformal antenna structures using beam switching technology can be beneficial for high-capacity communication systems. If the line-of-sight (LOS) link is blocked, the main beam direction can be controlled in order to get the highest level of the received signal through a reflection. Future work may contain studies on the antenna packaging and integration of the conformal antennas with the devices, such as smart watches, mobile phones, or radio access points. Conformal antenna design may be improved as well, by characterizing different substrate materials at mm-wave frequencies.
the air-to-water propagation (see Figure 1) and are plot- ted in Figure 4. As expected, due to the reverse varia- tions of the transmission and propagation losses, an op- timum frequency range exists for shallow propagation depths. In this optimum frequency range, there is sig- nificantly smaller power loss. For example, in Figure 4(a), the total loss in 3 - 100 MHz frequency range for a depth of 1 m is 10 dB to 45 dB smaller than the loss at the lowest and highest frequencies of our frequency range. Therefore, according to Figure 4(a) there is a range of optimum frequencies that exhibit minimum losses when a wave propagates from air to shallow fresh water depths. This range of frequencies can improve RF communications with underwater vehicles, or devices. Potential applications that can benefit from operating in the optimum frequency range include the following: 1)
i) Wave theory adopted in this study is based on linear wave theory developed by Airy, which include wave length, wave celerity, group velocity, orbital velocity, wave energy, and wave power. The wave transformations in shallow water included in this study are wave refraction, wave shoaling, and wave breaking.
detection threshold. These time-frequency pairs and corre- sponding singular values are used in the back propagation for the image reconstruction. It is clear from Figure 3 that there are more frequencies used in the image reconstruction of the weld including the larger side drilled hole. The fre- quency spectra of the first singular value, for welds including side drilled holes with radii 0.25 mm, 0.5 mm, 1.25 mm and 2.5 mm, is shown in Figure 4. This figure shows that as the size of the side drilled hole decreases the signature of the fre- quency spectra changes. The resonant peaks move to lower frequencies as one would anticipate from scattering theory . An advantage of the DORT method is that it works in the time-frequency domain and the frequencies which are specific to the inclusion can be used to isolate data to use to create the image.