scholarly journals Statistical Methods for Property Calculation of Textured Materials

1996 ◽  
Vol 25 (2-4) ◽  
pp. 251-262 ◽  
Author(s):  
T. D. Shermergor
Keyword(s):  
Statistical Methods ◽  
Dynamic Characteristics ◽  
Electromagnetic Waves ◽  
Dielectric Permeability ◽  
Effective Dynamic ◽  
Phase And Group Velocities ◽  
Scattering Factor ◽  
Textured Materials ◽  
Elastic Modules ◽  
Group Velocities

Statistical methods for calculating the effective static and dynamic characteristics of textured microheterogeneous materials such as polycrystals, composites and rocks are considered. Effective static characteristics based on the example of the elastic modules tensor are analyzed. Effective dynamic characteristics based on the example of the dielectric permeability tensor in calculating the scattering factor, phase and group velocities of the propagation of plane electromagnetic waves are presented.

PHASE AND GROUP VELOCITIES OF ELECTROMAGNETIC WAVES IN A MONOCLINIC CRYSTAL

2019 ◽  
Vol 78 (1) ◽  
pp. 1-10 ◽  
Author(s):  
S. K. Tleukenov ◽  
Z. K. Zhalgasbekova ◽  
Yurii Konstantinovich Sirenko
Keyword(s):  
Electromagnetic Waves ◽  
Monoclinic Crystal ◽  
Phase And Group Velocities ◽  
Group Velocities

scholarly journals Two Kinds of Vacuum in Casimir Effect

2021 ◽  
pp. 61-77
Author(s):  
Huang Zhi-Xun
Keyword(s):  
Electromagnetic Waves ◽  
Casimir Effect ◽  
Refraction Index ◽  
Physical Reality ◽  
Negative Energy ◽  
Physical Vacuum ◽  
Quantum Vacuum ◽  
Phase And Group Velocities ◽  
The Difference ◽  
Group Velocities

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

2021 ◽  
pp. 108128652110238
Author(s):  
Barış Erbaş ◽  
Julius Kaplunov ◽  
Isaac Elishakoff
Keyword(s):  
Ad Hoc ◽  
Moving Load ◽  
Low Frequency ◽  
Elastic Beam ◽  
Winkler Foundation ◽  
One Dimensional ◽  
Beam Equations ◽  
Dimensional Equation ◽  
Phase And Group Velocities ◽  
Group Velocities

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.

Compressional‐wave velocities in attenuating media: A laboratory physical model study

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1162-1167 ◽  
Author(s):  
Joseph B. Molyneux ◽  
Douglas R. Schmitt
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Wave Velocity ◽  
Propagation Distance ◽  
Compressional Wave ◽  
Arrival Times ◽  
Wave Velocities ◽  
Amplitude Maximum ◽  
Phase And Group Velocities ◽  
Group Velocities

Elastic‐wave velocities are often determined by picking the time of a certain feature of a propagating pulse, such as the first amplitude maximum. However, attenuation and dispersion conspire to change the shape of a propagating wave, making determination of a physically meaningful velocity problematic. As a consequence, the velocities so determined are not necessarily representative of the material’s intrinsic wave phase and group velocities. These phase and group velocities are found experimentally in a highly attenuating medium consisting of glycerol‐saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from ∼200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepancy but are in poor agreement with the corresponding phase velocity. Wave velocities determined from the time at which the pulse is first detected (signal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high‐frequency limit of the phase velocity in a material where wave velocity increases with frequency. Each method of time picking, however, is self‐consistent, as indicated by the high quality of linear regressions of observed arrival times versus propagation distance.

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

2021 ◽  
Author(s):  
Akash Kharita ◽  
Sagarika Mukhopadhyay
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Love Wave ◽  
Arrival Time ◽  
Epicentral Distance ◽  
Horizontal Distance ◽  
Wave Analysis ◽  
Time Period ◽  
Phase And Group Velocities ◽  
Group Velocities

&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;

Free spheroidal vibrations of the earth at very long periods, Part I— Calculation of periods for several earth models

1963 ◽  
Vol 53 (3) ◽  
pp. 483-501 ◽  
Author(s):  
Leonard E. Alsop
Keyword(s):  
Inner Core ◽  
Computer Programs ◽  
Free Vibrations ◽  
Stoneley Waves ◽  
The Core ◽  
The Earth ◽  
Earth Models ◽  
Shear Modes ◽  
Phase And Group Velocities ◽  
Group Velocities

Abstract Periods of free vibrations of the spheroidal type have been calculated numerically on an IBM 7090 for the fundamental and first two shear modes for periods greater than about two hundred seconds. Calculations were made for four different earth models. Phase and group velocities were also computed and are tabulated herein for the first two shear modes. The behavior of particle motions for different modes is discussed. In particular, particle motions for the two shear modes indicate that they behave in some period ranges like Stoneley waves tied to the core-mantle interface. Calculations have been made also for a model which presumes a solid inner core and will be discussed in Part II. The two computer programs which were made for these calculations are described briefly.

scholarly journals Some aspects of ion-acoustic whistlers in the ionosphere in the presence of negative ions

1989 ◽  
Vol 12 (4) ◽  
pp. 749-772 ◽  
Author(s):  
A. K. Sur ◽  
G. C. Das ◽  
B. Chakraborty ◽  
S. N. Paul ◽  
L. Debnath
Keyword(s):  
Travel Time ◽  
Critical Frequency ◽  
Cyclotron Frequency ◽  
Negative Ions ◽  
Induced Magnetic Field ◽  
Ion Acoustic ◽  
Phase And Group Velocities ◽  
Group Velocities ◽  
Group Travel

A study is made of the propagation of ion-acoustic whistlers in the atmosphere including the effects of negative ions. The dispersion relation, phase and group velocities of whistlers are discussed. It is shown that the presence of negative ions introduces a critical frequency which, for equal ionic masses, is equal to the ion-cyclotron frequency. Special attention is given to the group travel time of whistlers at mid-latitude and equator so that the role of negative ions on the group travel time can be determined. The cyclotron damping of whistlers in the presence of negative ions has been studied. The velocity distribution, total attenuation and the induced magnetic field are calculated from the temporal as well as spatial cyclotron damping. It is suggested that the attenuation of whistlers may cause heating of the ionosphere. It is also indicated that the measurement of the group travel time from its source to the observer at the satellite would help to diagnose the ionospheric parameters. The results of the analysis are presented by several graphical presentations.

Sign in / Sign up

Export Citation Format

Share Document