Wave transmission coefficient

Fig. 12.23. Wave transmission coefficient for conventional breakwater and geocore breakwater. 12.3.5.4. Wave runup performance...

T. Wamsley and J. Ahrens, Computation of wave transmission coefficients at detached breakwaters for shoreline response modelling. Coasted Structures 03, Portland, USA (2003). 

An important performance parameter for artificial reefs and submerged breakwaters is the wave transmission coefficient AT, which is the ratio of the approaching wave height to the transmitted wave height, (Fig. 20.32). Values of Kt range between 0 (no waves... 

The transmission coefficient Cl (Qj,t), considering transient (broadband) sources, is time-dependent and therefore accounts for the possible pulse deformation in the refraction process. It also takes account of the quantity actually computed in the solid (displacement, velocity potential,...) and the possible mode-conversion into shear waves and is given by... 

The use of air-bome ultrasound for the excitation and reception of surface or bulk waves introduces a number of problems. The acoustic impedance mismatch which exists at the transducer/air and the air/sample interfaces is the dominant factor to be overcome in this system. Typical values for these three media are about 35 MRayls for a piezo-ceramic (PZT) element and 45 MRayls for steel, compared with just 0.0004 MRayls for air. The transmission coefficient T for energy from a medium 1 into a medium 2 is given by... 

Thus, overcoming the activation barrier is performed here by fluctuation of the solvent polarization to the transitional configuration P, whereas electron-proton transmission coefficient is determined by the overlap of the electron-proton wave-functions of the initial and final states. 

The term exp[iax] in equations (2.47) indicates travel in the positive x-direction, while exp[—iax] refers to travel in the opposite direction. The coefficient A is, then, the amplitude of the incident wave, B is the amplitude of the reflected wave, and F is the amplitude of the transmitted wave. In region III, the particle moves in the positive x-direction, so that G is zero. The relative probability of tunneling is given by the transmission coefficient T... 

Effect of diagonal-off-diagonal dynamic disorder (D-off-DDD). The polarization fluctuations and the local vibrations give rise to variation of the electron densities in the donor and the acceptor, i.e., they lead to a modulation of the electron wave functions A and B. This leads to a modulation of the overlapping of the electron clouds of the donor and the acceptor and hence to a different transmission coefficient from that calculated in the approximation of constant electron density (ACED). This modulation may change the path of transition on the potential energy surfaces. 

Larger values of the transmission coefficient, k, due to improved overlapping of the wave functions of quantum particles (electrons, protons, etc.). 

The material for an acoustic lens should have a low attenuation, and a high velocity to minimize aberrations. Sapphire is an excellent material in both these respects. But the high velocity has a less desirable consequence. An acoustic impedance can be defined, which is equal to the product of the velocity and the density. The impedance of sapphire for longitudinal waves travelling parallel to the c-axis is thus 44.3 Mrayl, compared with the impedance of water which at room temperature is about 1.5 Mrayl, rising to 1.525 Mrayl at 60°C. When sound is transmitted across an interface between two materials of different impedance, the stress amplitude transmission coefficient is ( 6.4.1 Auld 1973 Brekhovskikh and Godin 1990)... 

These reflection and transmission coefficients relate the pressure amplitude in the reflected wave, and the amplitude of the appropriate stress component in each transmitted wave, to the pressure amplitude in the incident wave. The pressure amplitude in the incident wave is a natural parameter to work with, because it is a scalar quantity, whereas the displacement amplitude is a vector. The displacement amplitude reflection coefficient has the opposite sign to (6.90) or (6.94) the displacement amplitude transmission coefficients can be obtained from (6.91) and (6.92) by dividing by the appropriate longitudinal or shear impedance in the solid and multiplying by the impedance in the fluid. The impedances actually relate force per unit area to displacement velocity, but displacement velocity is related to displacement by a factor to which is the same for each of the incident, reflected, and transmitted waves, and so it all comes to the same thing in the end. In some mathematical texts the reflection... 

Dong, R. and Adler, L. (1984). Measurements of reflection and transmission coefficients of Rayleigh waves from cracks. /. Acoust. Soc. Am. 76,1761-3. [264]... 

The density of the probability flow in the falling wave is proportional to k , in the reflected wave to k1 B 2, and in the transmitted wave to k2 A 2. The transmission coefficient, D, is equal to the ratio of the density of the probability flow in the transmitted wave to the density in the falling wave... 

We employ matrix methods in order to obtain the reflection and transmission coefficient of the electromagnetic field within the device. Stratified structures with isotropic and homogeneous media and parallel-plane interfaces can be described by 2 x 2 matrices because the equations governing the propagation of the electric field are linear and the tangential component of the electric field is continuous [15,16], We consider a plane wave incident from the... 

When light is incident from the ambient side in the positive x direction, there is no wave propagating in the negative x direction inside the substrate. This means that Em+1 = 0. For the whole layered structure, the resulting complex reflection and transmission coefficients can be expressed by using the matrix elements of the total system transfer matrix of (6.8) ... 

In addition to the tensor element dependence of the sum-frequency intensity, there is also a dependence on the geometry of the experiment that manifests itself in the linear and non-linear Fresnel factors that describe the behaviour of the three light beams at the interface. Fresnel factors are the reflection and transmission coefficients for electromagnetic radiation at a boundary and depend on the frequency, polarization and incident angle of the electromagnetic waves and the indices of refraction for the media at the boundary [16,21]. 

When the sound is incident obliquely on a plane interface (as shown in Fig.2a), and if both media support only one type of wave (a longitudinal wave if the medium is air or water), then Eg.15 can still be used to calculate the reflection and transmission coefficient. However, the expressions for Z and Z are modified as follows [2,7],... 

If the coating material is solid, such as a viscoelastic polymer, then an incident longitudinal wave may generate both longitudinal and shear waves in the coating. The expressions for the reflection and transmission coefficients are then more complicated than Eqs.l6 and 17 [8]. 

When an uitrasonic compressionai wave impinges normaiiy on a boundary between two materiais of different acoustic impedances, it is partly reflected and partly transmitted. The ratio of the ampiitude of the refiected wave A ) to that of the incident wave A is called the reflection coefficient (R), and the ratio of the amplitude of the transmitted wave At) to that of the incident wave the transmission coefficient (T). The appropriate coefficients when particie velocity amplitudes are used are [41]... 

These theoretical considerations also gave a basis for the consideration of the optimal distance of discharge, which is a result of competition between the activation energy AG and the overlap of electronic wave functions of the initial and final states. The reaction site for outer-sphere electrochemical reactions is presumed to be separated from the electrode surface by a layer of solvent molecules (see, for instance, [129]). In consequence, the influence of imaging interactions on AGJ predicted by the Marcus equation is small, which explains why such interactions are neglected in many calculations. However, considerations of metal field penetration show that the reaction sites close to the electrode are not favored [128], though contributions to ks from more distant reaction sites will be diminished by a smaller transmission coefficient. If the reaction is strongly nonadiabatic, then the closest approach to the electrode is favorable. 

We consider two metallic free-electron systems, with atomically flat surfaces separated by vacuum over a distance Ax (Figure 20). In fact, the model system is an extension of the metal surface considered in Section 4.5. The complex potential energy barrier at a metal surface, discussed in Section 4.5 is simplified here to a rectangular barrier. We look for the quantum-mechanical probability that an electron in phase A is also present in phase B. This probability is given by the ratio of squared amplitudes, and A, of the free-electron wave function in phase B and A, respectively. It is quantified by the transmission coefficient ... 

We now turn to a quantitative examination of the feasibility of conditional Fock state generation using our preparation and retrieval technique. For applications in long-distance quantum communication, the quality of the atomic state preparation is the most important quantity. Assuming perfect atom-photon correlations in the write Raman processes, we can find the density matrix p for the number of atomic spin-wave excitations conditioned on the detection of ns Stokes photons. Here we consider only the spin-wave modes correlated with our detection mode. For example, in the absence of losses and background, the conditional atomic density matrix is simply p(ns) = ns)(ns. Loss on the Stokes channel (characterized by transmission coefficient a.s) leads to a statistical mixture of spin-wave excitations,... 

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