Two Kinds of Vacuum in Casimir Effect

The Casimir effect is one observable of the existence of the vacuum energy, i.e. the existence of vacuum electromagnetic field. The meaning of this word "vacuum" is physical vacuum, not technology vacuum. Then, we say that the change in the vacuum structure enforced by the plates. There are two kinds of vacuum, one is usual vacua or free vacua (outside the plates). Another is the negative energy vacua (inside the plates), and the refraction index less than 1(n<1). That cause a change in the light speed for electromagnetic waves propagating perpendicular to the plates: △c/c1.6×10-60d-4, and d is the plate distance. When d=10-9m(1nm), △c=10-24c. Then, a two-loop QED effect cause the phase and group velocities of an electromagnetic wave to slightly exceed c. Though the difference are very small, that raise interesting matters of principle. The focus of this paper is to improve the understanding of the nature of quantum vacuum. In the past, to say that "vacuum is not empty" was already a criticism and subversion of classical physics. Now it seems doubly strange to say that there is a negative energy vacuum that is "empty"than the normal physical vacuum. But these theories are rigorously justified; Casimir effect can create an environment with refractive index less than 1(n<1) and lead to the appearance of superluminality, which is one of the representations of "quantum superluminality". These advances in basic science will certainly open up new fields of application, In short, it is not the Casimir structure that creates the quantum vacuum, but the structure that makes the quantum vacuum "emerge"in a clever way as a perceptible physical reality. This is truly a scientific achievement.

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. Asymptotic analysis at a higher order results in a one-dimensional equation of bending motion refining numerous ad hoc developments starting from Timoshenko-type beam equations. Two-term expansions through the foundation stiffness are presented for phase and group velocities, as well as for the critical velocity of a moving load. In addition, the formula for the longitudinal displacements of the beam due to its transverse compression is derived.

Transition from Discrete to Continuous Media: The Impact of Symmetry Changes on Asymptotic Behavior of Waves

This paper is devoted to comparing the asymptotics of a solution, describing the wave motion of a discrete lattice and its continuous approximations. The transition from a discrete medium to a continuous one changes the symmetry of the system. The influence of this change on the asymptotic behavior of waves is of great interest. For the discrete case, Schrödinger’s analytical solution of the initial-value problem for the Lagrange lattice is used. Various continuous approximations are proposed to approximate the lattice. They are based on Debye’s concept of quasicontinuum. The asymptotics of the initial motion and the behavior of the systems in the vicinity of the quasifront and at large times are compared. The approximations of phase and group velocities is analyzed. The merits and limitations of the described approaches are discussed.

Errors Introduced in Estimation of Surface Wave Phase and Group Velocities Due to Wrong Assumptions: An Assessment Using a Simple Model For Love Wave

&lt;p&gt;The surface wave phase and group velocities are estimated by dividing the epicentral distance by phase and group travel times respectively in all the available methods, this is based on the assumptions that (1) surface waves originate at the epicentre and (2) the travel time of the particular group or phase of the surface wave is equal to its arrival time to the station minus the origin time of the causative earthquake; However, both assumptions are wrong since surface waves generate at some horizontal distance away from the epicentre. We calculated the actual horizontal distance from the focus at which they generate and assessed the errors caused in the estimation of group and phase velocities by the aforementioned assumptions in a simple isotropic single layered homogeneous half space crustal model using the example of the fundamental mode Love wave. We took the receiver locations in the epicentral distance range of 100-1000 km, as used in the regional surface wave analysis, varied the source depth from 0 to 35 Km with a step size of 5 km and did the forward modelling to calculate the arrival time of Love wave phases at each receiver location. The phase and group velocities are then estimated using the above assumptions and are compared with the actual values of the velocities given by Love wave dispersion equation. We observed that the velocities are underestimated and the errors are found to be; decreasing linearly with focal depth, decreasing inversely with the epicentral distance and increasing parabolically with the time period. We also derived empirical formulas using MATLAB curve fitting toolbox that will give percentage errors for any realistic combination of epicentral distance, time period and depths of earthquake and thickness of layer in this model. The errors are found to be more than 5% for all epicentral distances lesser than 500 km, for all focal depths and time periods indicating that it is not safe to do regional surface wave analysis for epicentral distances lesser than 500 km without incurring significant errors. To the best of our knowledge, the study is first of its kind in assessing such errors.&lt;/p&gt;

Theoretical model of guided waves in a bone-mimicking plate coupled with soft-tissue layers

Quantitative ultrasound has shown a significant promise in the assessment of bone characteristics in the recent reports. However, our understanding of wave interaction with bone tissues is still far from complete since the propagation of ultrasonic waves in bones is a very challenging topic due to their multilayer nature. The aim of the current study is to develop a theoretical model for guided waves in a bone-mimicking plate coupled with two soft-tissue layers. Here, the bone plate is modeled as an isotropic solid layer while the soft tissues are modeled as fluid layers. Based on the boundary conditions set for the three-layered structure, a characteristic equation is obtained which results in dispersion curves of the phase and group velocities. New expressions for free guided waves propagating in the trilayered plate are introduced. The amplitudes of wave modes generated by time-harmonic loads applied in the plate are theoretically computed by reciprocity consideration. As an example of calculation, the normalized amplitudes of the lowest wave modes are presented. The obtained results and equations discussed in this study could be, in general, useful for further applications in the area of bone quantitative ultrasound.

Wave Dispersion in Multilayered Reinforced Nonlocal Plates under Nonlinearly Varying Initial Stress

This paper deals with the effects of initial stress on wave propagations in small-scale plates with shape memory alloy (SMA) nanoscale wires. The initial stress is exerted on the small-scale plate along both in-plane directions. A scale-dependent model of plates is developed for taking into consideration size influences on the wave propagation. In addition, in order to take into account the effects of SMA nanoscale wires, the one-dimensional Brinson’s model is applied. A set of coupled differential equations is obtained for the non-uniformly prestressed small-scale plate with SMA nanoscale wires. An exact solution is obtained for the phase and group velocities of the prestressed small-scale system. The influences of non-uniformly distributed initial stresses as well as scale and SMA effects on the phase and group velocities are explored and discussed. It is found that initial stresses as well as the orientation and volume fraction of SMA nanoscale wires can be used as a controlling factor for the wave propagation characteristics of small-scale plates.

Frequency derivative of Rayleigh wave phase velocity for fundamental mode dispersion inversion: parametric study and experimental application

SUMMARY Monitoring the small variations of a medium is increasingly important in subsurface geophysics due to climate change. Classical seismic surface wave dispersion methods are limited to quantitative estimations of these small variations when the variation ratio is smaller than 10 per cent, especially in the case of variations in deep media. Based on these findings, we propose to study the contributions of the Rayleigh wave phase velocity derivative with respect to frequency. More precisely, in the first step of assessing its feasibility, we analyse the effects of the phase velocity derivative on the inversion of the fundamental mode in the simple case of a two-layer model. The behaviour of the phase velocity derivative is first analysed qualitatively: the dispersion curves of phase velocity, group velocity and the phase velocity derivative are calculated theoretically for several series of media with small variations. It is shown that the phase velocity derivatives are more sensitive to variations of a medium. The sensitivity curves are then calculated for the phase velocity, the group velocity and the phase velocity derivative to perform quantitative analyses. Compared to the phase and group velocities, the phase velocity derivative is sensitive to variations of the shallow layer and the deep layer shear wave velocity in the same wavelength (frequency) range. Numerical data are used and processed to obtain dispersion curves to test the feasibility of the phase velocity derivative in the inversion. The inversion results of the phase velocity derivative are compared with those of phase and group velocities and show improved estimations for small variations (variation ratio less than 5 per cent) of deep layer shear wave velocities. The study is focused on laboratory experiments using two reduced-scale resin-epoxy models. The differences of these two-layer models are in the deep layer in which the variation ratio is estimated as 16.4 ± 1.1 per cent for the phase velocity inversion and 17.1 ± 0.3 per cent for the phase velocity derivative. The latter is closer to the reference value 17 per cent, with a smaller error.

Application of the total focusing method for quantitative nondestructive testing of anisotropic welds with ultrasound

In this paper, we report on the application of the ultrasonic Total Focusing Method for quantitative imaging of cracks in austenitic welds. Imaging inspection procedures provide more information than punctual measurements. In addition, an image provides more easy access for most human viewers. In ultrasonic testing, array transducers have played an important role in imaging for many years. The Full Matrix Capture technique in combination with Total Focusing is one of the newer methods with decisive advantages. In combination with fast electronics, computer technology and image processing, it now enables tomographic imaging in real time. The functionality of the method and the technical requirements are explained here. Austenitic weld seams are considered as examples for anisotropic materials, which can be examined with this method. An important requirement for quantitative measurement of defect size in anisotropic materials is the knowledge of the ultrasonic phase and group velocities of the inspected volume. The Gradient Elastic Constant Descent Method can deliver unknown parameters, which are needed to calculate these velocities.

Damage detection with the fundamental mode of edge waves

Detection of mechanical damage using Lamb or Rayleigh waves is limited to relatively simple geometries, yet real structures often incorporate features such as free or clamped edges, welds, rivets, ribs and holes. All these features are potential sources of wave reflections and scattering, which make the application of these types of guided waves for damage detection difficult. However, these features can themselves generate so-called ‘feature-guided’ waves. This article details the first application of the fundamental mode of transient edge waves for detection of mechanical damage. The fundamental edge wave mode (ES0) – a natural analogue to Rayleigh waves – is weakly dispersive and may decay with propagation distance. The phase and group velocities of the ES0 wave mode are close to the fundamental shear horizontal (SH0) and symmetric Lamb (S0) wave modes, at low and high frequencies, respectively. It is therefore quite challenging to excite a single ES0 mode and avoid wave coupling. However, it was found experimentally that at medium range frequencies the ES0 mode can be decoupled from SH0 and S0 modes, and its decay is small, allowing for distant detection of defects and damage along free edges of slender structural components. This article provides a brief theory of edge waves, excitation methodology and successful examples of distant detection of crack-like and corrosion damage in I-beam sections, which are widely applied in engineering and construction.