scholarly journals REMARKS ON THE CALCULATION OF AMPLITUDES OF THE LINEAR WAVE PRODUCED BY A WAVE MACHINE

2011 ◽  
Vol 1 (5) ◽  
pp. 5
Author(s):  
J. Kravtchenko
Keyword(s):  
Wave Amplitude ◽  
Differential Operators ◽  
Salient Feature ◽  
Theoretical Explanation ◽  
Physical Significance ◽  
Linear Wave ◽  
Sinusoidal Movement ◽  
Mathematical Difficulties ◽  
Series Of Functions ◽  
Made In

We are indebted to Havelock and to Biesel for their theoretical explanation of the mechanics of generation of the Stokes plane wave produced by a wave machine operating with a simple sinusoidal movement. The calculation of the wave amplitude, produced in this way, is the most salient feature of this theory. We add nothing new to this research. But in view of its importance it seems fitting to pay special attention to a few mathematical difficulties that remain in the exposition of the above-mentioned authors, to indicate ways in which they may be solved in part, to simplify a few theoretical demonstrations and to make some comments on the physical significance of a theory which depends on very simplifying hypotheses. More accurately speaking, we investigate a series of functions of one variable, introduced by Havelock and Biesel to present the solution of the problem. A gap in the theory is closed by showing that the series is complete; in fact, to establish this point, it is sufficient to employ a few results of the spectrum theory of certain differential operators. We complement then the indications of Biesel on the legitimacy of the term by term derivation of the series developments he has formed. Finally an elementary re-examination is made of the nature of singularities found in this solution and whose study has been made in a less direct manner in the works mentioned above. It would appear that all the above remarks can be of assistance to technicians in the study of many analogous questions.

scholarly journals Wave Propagation on Microstate Geometries

2019 ◽  
Vol 21 (3) ◽  
pp. 705-760 ◽  
Author(s):  
Joe Keir
Keyword(s):  
Wave Equation ◽  
Decay Rates ◽  
Mathematical Treatment ◽  
Linear Wave ◽  
Local Energy ◽  
Linear Wave Equation ◽  
Uniform Decay ◽  
Uniformly Bounded ◽  
Kaluza Klein ◽  
Made In

AbstractSupersymmetric microstate geometries were recently conjectured (Eperon et al. in JHEP 10:031, 2016. 10.1007/JHEP10(2016)031) to be nonlinearly unstable due to numerical and heuristic evidence, based on the existence of very slowly decaying solutions to the linear wave equation on these backgrounds. In this paper, we give a thorough mathematical treatment of the linear wave equation on both two- and three-charge supersymmetric microstate geometries, finding a number of surprising results. In both cases, we prove that solutions to the wave equation have uniformly bounded local energy, despite the fact that three-charge microstates possess an ergoregion; these geometries therefore avoid Friedman’s “ergosphere instability” (Friedman in Commun Math Phys 63(3):243–255, 1978). In fact, in the three-charge case we are able to construct solutions to the wave equation with local energy that neither grows nor decays, although these data must have non-trivial dependence on the Kaluza–Klein coordinate. In the two-charge case, we construct quasimodes and use these to bound the uniform decay rate, showing that the only possible uniform decay statements on these backgrounds have very slow decay rates. We find that these decay rates are sublogarithmic, verifying the numerical results of Eperon et al. (2016). The same construction can be made in the three-charge case, and in both cases the data for the quasimodes can be chosen to have trivial dependence on the Kaluza–Klein coordinates.

scholarly journals XIII.—The Plant Remains in the Scottish Peat Mosses

1907 ◽  
Vol 45 (2) ◽  
pp. 335-360 ◽  
Author(s):  
Francis J. Lewis
Keyword(s):  
Salient Feature ◽  
The South ◽  
Scottish Highlands ◽  
Arctic Vegetation ◽  
Arctic Plants ◽  
Plant Remains ◽  
Low Levels ◽  
Made In

An investigation of the peat mosses in some districts of the Scottish Highlands was made in 1905, with a view of comparing the features found there with those already recorded from the Southern Uplands in 1904. The salient feature met with in the Southern districts was the existence in all the older mosses of an upper and lower forest-bed, with a zone of Arctic plants intercalated between. The existence of this Arctic plant bed, stretching at the same horizon through the peat in districts widely separated, indicates a lowering of temperature which must have obtained over much greater areas; for the conditions implied by the presence of an Arctic vegetation at low levels in the South of Scotland would suffice—precipitation being great enough—to produce glaciation in the Highlands.

scholarly journals Characterization of Complex Image Spatial Structures Based on Symmetrical Weibull Distribution Model for Texture Pattern Classification

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-23
Author(s):  
Jinping Liu ◽  
Jiezhou He ◽  
Zhaohui Tang ◽  
Pengfei Xu ◽  
Wuxia Zhang ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Pattern Classification ◽  
Differential Operators ◽  
Theoretical Explanation ◽  
Human Vision ◽  
Distribution Model ◽  
Human Beings ◽  
Gaussian Derivative ◽  
Texture Pattern ◽  
Perception System

Texture pattern classification has long been an essential issue in computer vision (CV). However, texture is a kind of perceptual concept of human beings in scene observation or content understanding, which cannot be defined or described clearly in CV. Visually, the visual appearance of the complex spatial structure (CSS) of texture pattern (TP) generally depends on the random organization (or layout) of local homogeneous fragments (LHFs) in the imaged surface. Hence, it is essential to investigate the latent statistical distribution (LSD) behavior of LHFs for distinctive CSS feature characterization to achieve good classification performance. This work presents an image statistical modeling-based TP identification (ISM-TPI) method. It firstly makes a theoretical explanation of the Weibull distribution (WD) behavior of the LHFs of the imaged surface in the imaging process based on the sequential fragmentation theory (SFT), which consequently derives a symmetrical WD model (SWDM) to characterize the LSD of the TP’s SS. Multidirectional and multiscale TP features are then characterized by the SWDM parameters based on the oriented differential operators; in other words, texture images are convolved with multiscale and multidirectional Gaussian derivative filters (GDFs), including the steerable isotropic GDFs (SIGDFs) and the oriented anisotropic GDFs (OAGDFs), for the omnidirectional and multiscale SS detail exhibition with low computational complexity. Finally, SWDM-based TP feature parameters, demonstrated to be directly related to the human vision perception system with significant physical perception meaning, are extracted and used to TP classification with a partial least squares-discriminant analysis- (PLS-DA-) based classifier. The effectiveness of the proposed ISM-TPI method is verified by extensive experiments on three texture image databases. The classification results demonstrate the superiority of the proposed methods over several state-of-the-art TP classification methods.

Rayleigh waves from a moving thrust fault

1972 ◽  
Vol 62 (3) ◽  
pp. 751-762
Author(s):  
A. K. Mal
Keyword(s):  
Free Surface ◽  
Earthquake Engineering ◽  
Amplitude Modulation ◽  
Rayleigh Waves ◽  
Wave Amplitude ◽  
Thrust Fault ◽  
Arbitrary Orientation ◽  
Period Range ◽  
Epicentral Region ◽  
Made In

Abstract The amplitude of the Rayleigh waves produced by a finite, propagating dip-slip fault of arbitrary orientation in a homogeneous, isotropic half-space is obtained. The fault is assumed to initiate suddenly at depth and to spread unilaterally to the free surface with constant speed. The Rayleigh-wave amplitude ahead of the fault break is shown to be considerably higher than that behind the initial epicenter. There is severe amplitude modulation in the epicentral region caused by the interference of waves traveling in opposite directions. The numerical results indicate that for Rayleigh waves in the period range of interest in earthquake engineering, a number of simplifications can be made in modeling an earthquake source of this type.

Preferential orientation of spheroidal particles in wavy flow

2018 ◽  
Vol 856 ◽  
pp. 850-869 ◽  
Author(s):  
Michelle H. DiBenedetto ◽  
Nicholas T. Ouellette
Keyword(s):  
Wave Field ◽  
Water Column ◽  
Particle Shape ◽  
Wave Amplitude ◽  
Theoretical Study ◽  
Stable Limit Cycle ◽  
Stokes Drift ◽  
Linear Wave ◽  
Stable Limit ◽  
Wave Parameters

We report a theoretical study of the angular dynamics of small, non-inertial spheroidal particles in a linear wave field. We recover the observation recently reported by DiBenedetto et al. (J. Fluid Mech., vol. 837, 2018, pp. 320–340) that the orientation of these spheroids tends to a stable limit cycle consisting of a preferred value with a superimposed oscillation. We show that this behaviour is a consequence of finite wave amplitude and is the angular analogue of Stokes drift. We derive expressions for both the preferred orientation of the particles, which depends only on particle shape, and the amplitude of the oscillation about this preferred value, which additionally depends on the wave parameters and the depth of the particle in the water column.

scholarly journals Common-Sense Rejected by Physicists:

2021 ◽  
Vol 19 ◽  
pp. 233-280
Author(s):  
Jeffrey Boyd
Keyword(s):  
Cell Phone ◽  
Smart Phone ◽  
Linear Wave ◽  
Zero Energy ◽  
Inertial Frames ◽  
Elementary Waves ◽  
First Time ◽  
Time Continuum ◽  
Decisive Advantage ◽  
Made In

We propose a new integration of relativity and quantum mechanics (QM). Your cell phone or smart phone is a rich source of empirical information about relativity. It tells time based on a system called Coordinated Universal Time (UTC) which assumes absolute simultaneity: all observers in all inertial frames observe the same sequence of all events. You must choose whether to trust the time on your cell phone, or trust Einstein’s incompatible ideas about a space-time continuum. As concerns QM, the existence of “weirdness” means a mistake was made in QM’s starting assumptions. This article finds and corrects that mistake and presents for the first time, a quantum world free of all weirdness. There is another half to nature, previously unrecognized. It is devoid of energy and matter, namely zero-energy Elementary Waves which move within the medium of aether. We derive the linear wave PDE’s. There is evidence that Elementary Waves are in control of nature, despite their lack of energy. The existence of UFO’s (Unidentified Flying Objects) suggests that someone has learned how to control Elementary Waves. If we could learn from the UFO’s, we might acquire a decisive advantage in our battle against climate change.

scholarly journals Variation in Magnetic Field Strength During a Specific Anisotropic Gravitational Collapse

1976 ◽  
Vol 29 (5) ◽  
pp. 461 ◽  
Author(s):  
DP Mason
Keyword(s):  
Magnetic Field ◽  
General Relativity ◽  
Energy Density ◽  
Field Strength ◽  
Gravitational Collapse ◽  
Mass Density ◽  
Rest Mass ◽  
Physical Significance ◽  
The Magnetic Field ◽  
Made In

The MHD approximation has been made in general relativity to derive expressions in terms of the fluid's total proper energy density and rest-mass density for the variation in the strength of the magnetic field during the anisotropic gravitational collapse in which the condition ?ab HaHb = 0 holds throughout the collapse, where ?ab is the expansion tensor. The physical significance of this condition is also examined.

scholarly journals Rapid Flow Model with Lateral Inflow

1992 ◽  
Vol 23 (2) ◽  
pp. 57-72 ◽  
Author(s):  
W. G. Strupczewski ◽  
Z. W. Kundzewicz
Keyword(s):  
Impulse Response ◽  
Flow Model ◽  
Physical Significance ◽  
Flood Routing ◽  
Conflicting Demands ◽  
Lateral Inflow ◽  
Rapid Flow ◽  
Analytical Series ◽  
The Cost ◽  
Made In

The rapid flow model (equivalent to the distributed delayed Muskingum model) is an attractive linear flood routing model meeting the conflicting demands of physical significance and simplicity. After having relaxed the assumption of negligible lateral inflow, made in former studies, the impulse response of the above model with lateral inflow is derived in the analytical (series) form. The cumulants of the impulse response of the model are developed. Although the results presented were obtained for the spatially uniform distribution of lateral inflow, it is possible to solve it also for non-uniform lateral inflows, at the cost of additional algebra.

Mode conversion, corner singularities and matrix Wiener—Hopf factorization in diffraction theory

1995 ◽  
Vol 451 (1942) ◽  
pp. 399-423 ◽  
Keyword(s):  
Mode Conversion ◽  
Stress Singularity ◽  
Diffraction Theory ◽  
Linear Wave ◽  
Corner Singularities ◽  
Matrix Kernel ◽  
Vast Number ◽  
Linear Wave Propagation ◽  
Physical Importance ◽  
Mathematical Difficulties

The diffraction of acoustic, electromagnetic and elastic waves by an edge is a subject of continuing mathematical and physical importance. The physical motivation for research is the vast number of technological and geophysical applications of the fundamental models of linear wave propagation in continuous media, while the mathematical drive is to understand and devise new analytical and numerical techniques for their quantification. This paper is concerned with certain physical aspects of diffraction which have proven to give the most troublesome of mathematical difficulties. These are mode conversion, that is when the incident wave is scattered among different modes supported by the propagating medium, and edge or corner singularities, when the diffracting obstacle creates a ‘stress singularity’. It is shown, by way of a particular example, that the exact solution of diffraction problems involving these phenomena will in general give rise to a vector Wiener-Hopf equation with a matrix kernel whose factorization is non-commutative. The main result of this paper is a new procedure, motivated by a precise treatment of both the corner singularity and mode conversion, for determining the factors in this case.

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