scholarly journals Mathematical Fundamentals of a Diagnostic Method by Long Nonlinear Waves for the Structured Media

2020 ◽  
Author(s):  
Vyacheslav Vakhnenko ◽  
Dmitri Vengrovich ◽  
Alexandre Michtchenko
Keyword(s):  
Inverse Problem ◽  
Wave Field ◽  
Nonlinear Waves ◽  
Diagnostic Method ◽  
Heterogeneous Medium ◽  
Homogeneous Medium ◽  
Finite Amplitude ◽  
Long Waves ◽  
Sufficient Information ◽  
Structured Media

We have proven that the long wave with finite amplitude responds to the structure of the medium. The heterogeneity in a medium structure always introduces additional nonlinearity in comparison with the homogeneous medium. At the same time, a question appears on the inverse problem, namely, is there sufficient information in the wave field to reconstruct the structure of the medium? It turns out that the knowledge on the evolution of nonlinear waves enables us to form the theoretical fundamentals of the diagnostic method to define the characteristics of a heterogeneous medium using the long waves of finite amplitudes (inverse problem). The mass contents of the particular components can be denoted with specified accuracy by this diagnostic method.

scholarly journals Reconstruction of Initial Wave Field of a Nonsteady-State Wave Propagation from Limited Measurements at a Specific Spatial Point Based on Stochastic Inversion

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
S. L. Han ◽  
Takeshi Kinoshita
Keyword(s):  
Inverse Problem ◽  
Wave Propagation ◽  
Wave Field ◽  
Simulated Data ◽  
Initial Surface ◽  
Reconstruction Procedure ◽  
Inference Problem ◽  
State Wave ◽  
Initial Wave ◽  
Nonsteady State

This paper studies an inverse problem that can be used for reconstructing initial wave field of a nonsteady-state wave propagation. The inverse problem is ill posed in the sense that small changes in the input data can greatly affect the solution of the problem. To address the difficulty, the problem is formulated in the form of an inference problem in an appropriately constructed stochastic model. It is shown that the stochastic inverse model enables the initial surface disturbance to be reconstructed, including its confidence intervals given the noisy measurements. The reconstruction procedure is illustrated through applications to some simulated data for two- and three-dimensional problem.

Waves of Finite Amplitude in an Infinite Homogeneous Medium.

1954 ◽  
Vol 119 ◽  
pp. 34 ◽  
Author(s):  
H. Lawrence Helfer
Keyword(s):  
Homogeneous Medium ◽  
Finite Amplitude

scholarly journals Nonlinear long waves over a muddy beach

2013 ◽  
Vol 718 ◽  
pp. 371-397 ◽  
Author(s):  
Erell-Isis Garnier ◽  
Zhenhua Huang ◽  
Chiang C. Mei
Keyword(s):  
Boundary Layer ◽  
Thin Layer ◽  
Surface Waves ◽  
Nonlinear Waves ◽  
Water Waves ◽  
Long Waves ◽  
Fluid Mud ◽  
Weakly Nonlinear ◽  
Sea Bottom ◽  
Oscillatory Boundary Layer

AbstractWe analyse theoretically the interaction between water waves and a thin layer of fluid mud on a sloping seabed. Under the assumption of long waves in shallow water, weakly nonlinear and dispersive effects in water are considered. The fluid mud is modelled as a thin layer of viscoelastic continuum. Using the constitutive coefficients of mud samples from two field sites, we examine the interaction of nonlinear waves and the mud motion. The effects of attenuation on harmonic evolution of surface waves are compared for two types of mud with distinct rheological properties. In general mud dissipation is found to damp out surface waves before they reach the shore, as is known in past observations. Similar to the Eulerian current in an oscillatory boundary layer in a Newtonian fluid, a mean displacement in mud is predicted which may lead to local rise of the sea bottom.

Propagation of long waves of finite amplitude at the interface of two viscous fluids

1985 ◽  
Vol 11 (4) ◽  
pp. 481-502 ◽  
Author(s):  
G. Ooms ◽  
A. Segal ◽  
S.Y. Cheung ◽  
R.V.A. Oliemans
Keyword(s):  
Finite Amplitude ◽  
Viscous Fluids ◽  
Long Waves

The initial-value problem for long waves of finite amplitude

1964 ◽  
Vol 20 (1) ◽  
pp. 161-170 ◽  
Author(s):  
Robert R. Long
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Integration ◽  
Initial Value Problem ◽  
Finite Amplitude ◽  
Long Waves ◽  
Initial Value ◽  
Partial Differential ◽  
Long Wave ◽  
Constant Slope

Derived herein is a set of partial differential equations governing the propagation of an arbitrary, long-wave disturbance of small, but finite amplitude. The equations reduce to that of Boussinesq (1872) when the assumption is made that the disturbance is propagating in one direction only. The equations are hyperbolic with characteristic curves of constant slope. The initial-value problem can be solved very readily by numerical integration along characteristics. A few examples are included.

scholarly journals Theoretical DFT study of Cannizzaro reaction mechanism: A mini perspective

2020 ◽  
Vol 11 (2) ◽  
pp. 139-144
Author(s):  
Mohammad Suhail ◽  
Sofi Danish Mukhtar ◽  
Imran Ali ◽  
Ariba Ansari ◽  
Saiyam Arora
Keyword(s):  
Molecular Structure ◽  
Free Radical ◽  
Density Functional ◽  
Heterogeneous Medium ◽  
Homogeneous Medium ◽  
Radical Mechanism ◽  
Ionic Mechanism ◽  
Free Radical Mechanism ◽  
Actual Mechanism ◽  
Cannizzaro Reaction

In regards to the Cannizzaro reaction and its peculiar mechanism, some researchers have presented a free radical mechanism for the Cannizzaro reaction, while others have found that it is feasible through an ionic mechanism, but the actual mechanism has not been finalized yet. The researchers have given the proof of both the mechanisms through their papers published. Actually, Cannizzaro reaction may occur through both mechanisms depending on both molecular structure and different conditions which are yet to be explained. Recently published papers describe that free radical mechanism occurs only in a heterogeneous medium, while an ionic mechanism occurs in a homogeneous medium. We revealed no explanation of the molecular structure-based reason, responsible for a radical or an ionic mechanism. The present paper reviews not only homogeneous/heterogeneous medium conditions but also molecular structure-based facts, which may be responsible for the Cannizzaro reaction to occur through the radical or ionic mechanism, and that may be acceptable to the scientific society. Besides, Density Functional Theory study using Gaussian software was also involved in the explanation of the molecular structure, responsible for one of the two mechanisms. Also, the present paper specifies all points related to future perspectives on which additional studies are required to understand the actual mechanism with a definite molecular structure in the different reaction media.

The Interaction of Nonlinear Waves With the Submerged Caissons of a Gravity Based Structure

2008 ◽  
Author(s):  
Marios Christou ◽  
Jannicke S. Roos ◽  
Chris Swan ◽  
Ove T. Gudmestad
Keyword(s):  
Wave Field ◽  
Incident Wave ◽  
Nonlinear Waves ◽  
Wave Structure ◽  
Boundary Integral ◽  
Numerical Predictions ◽  
Water Region ◽  
Geometric Discontinuities ◽  
The Waves ◽  
Wave Structure Interaction

This paper concerns the numerical description of nonlinear waves propagating over the storage caissons of a gravity based structure. This process produces a steepening of the incident wave-field, which occurs when the waves propagate into the shallower water region above the storage caissons, resulting in the focussing of wave energy. A fully nonlinear Multiple-flux Boundary Element Method (MF-BEM) is applied to simulate this effect. The MF-BEM differs from traditional boundary integral approaches in two important respects: first, a multiple-flux approach is employed to overcome the problem of geometric discontinuities; and, second, no filtering, smoothing, re-gridding or redistribution of the nodes is performed at any stage during the simulations. These two aspects are believed to play an important role in accurately predicting the steepening of the incident wave-field. The numerical predictions are compared to new laboratory observations that examine the extent of this wave-structure interaction and, particularly, the steepening of the incident wave-field.

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