Mathematical Foundations of Propagation Models in Underwater Acoustics

1983 ◽  
Author(s):  
K.E. GILBERT ◽  
M.F. WERBY
Keyword(s):  
Underwater Acoustics ◽  
Propagation Models ◽  
Mathematical Foundations

scholarly journals Improving the Performance of Mode-Based Sound Propagation Models by Using Perturbation Formulae for Eigenvalues and Eigenfunctions

2021 ◽  
Vol 9 (9) ◽  
pp. 934
Author(s):  
Alena Zakharenko ◽  
Mikhail Trofimov ◽  
Pavel Petrov
Keyword(s):  
Sound Propagation ◽  
Underwater Acoustics ◽  
Computational Cost ◽  
Normal Modes ◽  
Sound Field ◽  
Field Calculation ◽  
Combined Model ◽  
Eigenvalues And Eigenfunctions ◽  
Propagation Models ◽  
Area Of Interest

Numerous sound propagation models in underwater acoustics are based on the representation of a sound field in the form of a decomposition over normal modes. In the framework of such models, the calculation of the field in a range-dependent waveguide (as well as in the case of 3D problems) requires the computation of normal modes for every point within the area of interest (that is, for each pair of horizontal coordinates x,y). This procedure is often responsible for the lion’s share of total computational cost of the field simulation. In this study, we present formulae for perturbation of eigenvalues and eigenfunctions of normal modes under the water depth variations in a shallow-water waveguide. These formulae can reduce the total number of mode computation instances required for a field calculation by a factor of 5–10. We also discuss how these formulae can be used in a combination with a wide-angle mode parabolic equation. The accuracy of such combined model is validated in a series of numerical examples.

scholarly journals Use of Underwater Acoustics in Marine Conservation and Policy: Previous Advances, Current Status, and Future Needs

2021 ◽  
Vol 9 (2) ◽  
pp. 173
Author(s):  
Shane Guan ◽  
Tiffini Brookens ◽  
Joseph Vignola
Keyword(s):  
World War Ii ◽  
Sound Propagation ◽  
Underwater Acoustics ◽  
Marine Conservation ◽  
Current Status ◽  
Source Characterization ◽  
Marine Animals ◽  
Significant Information ◽  
Propagation Models ◽  
Interdisciplinary Field

The interdisciplinary field of assessing the impacts of sound on marine life has benefited largely from the advancement of underwater acoustics that occurred after World War II. Acoustic parameters widely used in underwater acoustics were redefined to quantify sound levels relevant to animal audiometric variables, both at the source and receiver. The fundamental approach for assessing the impacts of sound uses a source-pathway-receiver model based on the one-way sonar equation, and most numerical sound propagation models can be used to predict received levels at marine animals that are potentially exposed. However, significant information gaps still exist in terms of sound source characterization and propagation that are strongly coupled with the type and layering of the underlying substrate(s). Additional challenges include the lack of easy-to-use propagation models and animal-specific statistical detection models, as well as a lack of adequate training of regulatory entities in underwater acoustics.

Tasks of computer graphics under conditions of fundamentalization of preparation of an informatics teacher

2020 ◽  
pp. 57-63
Author(s):  
Ye. Yi. Bidaibekov ◽  
V. V. Grinshkun ◽  
S. N. Koneva
Keyword(s):  
Computer Graphics ◽  
Basic Principle ◽  
Fundamental Component ◽  
The Future ◽  
Scope Of Application ◽  
Education Training ◽  
Mathematical Foundations

The article deals with computer graphics tasks related to the activities of the future informatics teacher in conditions of fundamentalization of education. Training of future informatics teachers in the context of the fundamentalization of education requires them to know the range of tasks related to computer graphics and the skills to solve them. In order to enhance the fundamental component of computer graphics, methods are proposed that rely on interprandial communications, as well as on in-depth training of computer graphics. In the course of reasoning, the authors come to the conclusion that the content of computer graphics should be enriched with mathematical foundations of computer graphics and as a result update the content of the computer graphics course with machine graphics algorithms. The basic principle of selecting the content of the course offered is the principle of the fundamentalization of education. Since the scope of application of computer graphics is extensive, in our opinion, the system of tasks and tasks on computer graphics is the most interesting. A feature of this system is the orientation towards solving fundamental problems of computer graphics. It was also revealed during the study that it is possible to reduce the tasks of the proposed system to a certain sequence of stages. The application of stages for a certain type of tasks affects the methods of solving them. Thus, the fundamental training of future informatics teachers in computer graphics requires them to know these stages and methods of solving fundamental computer graphics tasks.

Degenerate Diffusion Operators Arising in Population Biology (AM-185)

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Adjoint Operator ◽  
Integral Kernel ◽  
Mathematical Finance ◽  
Elliptic Operators ◽  
Complete Analysis ◽  
Time Behavior ◽  
Degenerate Elliptic Operators ◽  
Regularity Properties ◽  
Degenerate Elliptic ◽  
Mathematical Foundations

This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.

High-Frequency Financial Econometrics

2014 ◽  
Author(s):  
Yacine Aït-Sahalia ◽  
Jean Jacod
Keyword(s):  
High Frequency ◽  
Practical Importance ◽  
Financial Econometrics ◽  
Trading Strategies ◽  
Financial Data ◽  
Jump Processes ◽  
High Frequency Trading ◽  
Microstructure Noise ◽  
Econometric Methods ◽  
Mathematical Foundations

High-frequency trading is an algorithm-based computerized trading practice that allows firms to trade stocks in milliseconds. Over the last fifteen years, the use of statistical and econometric methods for analyzing high-frequency financial data has grown exponentially. This growth has been driven by the increasing availability of such data, the technological advancements that make high-frequency trading strategies possible, and the need of practitioners to analyze these data. This comprehensive book introduces readers to these emerging methods and tools of analysis. The book covers the mathematical foundations of stochastic processes, describes the primary characteristics of high-frequency financial data, and presents the asymptotic concepts that their analysis relies on. It also deals with estimation of the volatility portion of the model, including methods that are robust to market microstructure noise, and address estimation and testing questions involving the jump part of the model. As the book demonstrates, the practical importance and relevance of jumps in financial data are universally recognized, but only recently have econometric methods become available to rigorously analyze jump processes. The book approaches high-frequency econometrics with a distinct focus on the financial side of matters while maintaining technical rigor, which makes this book invaluable to researchers and practitioners alike.

Sign in / Sign up

Export Citation Format

Share Document