A Numerical Realization of the Wiener–Hopf Method for the Kolmogorov Backward Equation

2019 ◽  
pp. 399-426
Author(s):  
Oleg Kudryavtsev ◽  
Vasily Rodochenko
Keyword(s):  
Numerical Realization ◽  
Backward Equation ◽  
Hopf Method

SH-Wave Scattering From the Interface Defect

2017 ◽  
Vol 5 (1) ◽  
pp. 45-50
Author(s):  
Myron Voytko ◽  
◽  
Yaroslav Kulynych ◽  
Dozyslav Kuryliak
Keyword(s):  
Half Space ◽  
Wave Diffraction ◽  
Scattered Field ◽  
Wave Scattering ◽  
Elastic Layer ◽  
Analytical Form ◽  
Structure Parameters ◽  
Sh Wave ◽  
Interface Defect ◽  
Hopf Method

The problem of the elastic SH-wave diffraction from the semi-infinite interface defect in the rigid junction of the elastic layer and the half-space is solved. The defect is modeled by the impedance surface. The solution is obtained by the Wiener- Hopf method. The dependences of the scattered field on the structure parameters are presented in analytical form. Verifica¬tion of the obtained solution is presented.

Embedding non-linear filtering in autonomous underwater vehicle dynamics via the Kolmogorov backward equation

2021 ◽  
pp. 014233122110196
Author(s):  
Ravish H. Hirpara ◽  
Shambhu N. Sharma
Keyword(s):  
State Vector ◽  
Autonomous Underwater Vehicle ◽  
Underwater Vehicle ◽  
Linear Filtering ◽  
Homogeneous Markov Process ◽  
Non Linear ◽  
Backward Equation ◽  
Noise Correction ◽  
Ito Process ◽  
Correction Terms

This paper revisits the state vector of an autonomous underwater vehicle (AUV) dynamics coupled with the underwater Markovian stochasticity in the ‘non-linear filtering’ context. The underwater stochasticity is attributed to atmospheric turbulence, planetary interactions, sea surface conditions and astronomical phenomena. In this paper, we adopt the Itô process, a homogeneous Markov process, to describe the AUV state vector evolution equation. This paper accounts for the process noise as well as observation noise correction terms by considering the underwater filtering model. The non-linear filtering of the paper is achieved using the Kolmogorov backward equation and the evolution of the conditional characteristic function. The non-linear filtering equation is the cornerstone formalism of stochastic optimal control systems. Most notably, this paper introduces the non-linear filtering theory into an underwater vehicle stochastic system by constructing a lemma and a theorem for the underwater vehicle stochastic differential equation that were not available in the literature.

scholarly journals Deep neural networks for waves assisted by the Wiener–Hopf method

2020 ◽  
Vol 476 (2235) ◽  
pp. 20190846 ◽  
Author(s):  
Xun Huang
Keyword(s):  
Neural Networks ◽  
Wave Equations ◽  
Deep Neural Networks ◽  
Research Strategy ◽  
Propagation Model ◽  
Physical Constraints ◽  
Aerospace Applications ◽  
Feed Forward Network ◽  
New Perspective ◽  
Hopf Method

In this work, the classical Wiener–Hopf method is incorporated into the emerging deep neural networks for the study of certain wave problems. The essential idea is to use the first-principle-based analytical method to efficiently produce a large volume of datasets that would supervise the learning of data-hungry deep neural networks, and to further explain the working mechanisms on underneath. To demonstrate such a combinational research strategy, a deep feed-forward network is first used to approximate the forward propagation model of a duct acoustic problem, which can find important aerospace applications in aeroengine noise tests. Next, a convolutional type U-net is developed to learn spatial derivatives in wave equations, which could help to promote computational paradigm in mathematical physics and engineering applications. A couple of extensions of the U-net architecture are proposed to further impose possible physical constraints. Finally, after giving the implementation details, the performance of the neural networks are studied by comparing with analytical solutions from the Wiener–Hopf method. Overall, the Wiener–Hopf method is used here from a totally new perspective and such a combinational research strategy shall represent the key achievement of this work.

Numerical realization and structure characterization on random close packings of cuboid particles with different aspect ratios

2019 ◽  
Vol 344 ◽  
pp. 514-524 ◽  
Author(s):  
Zhouzun Xie ◽  
Xizhong An ◽  
Xiaohong Yang ◽  
Changxing Li ◽  
Yansong Shen
Keyword(s):  
Numerical Realization ◽  
Structure Characterization ◽  
Aspect Ratios

Temperature Distribution in a Cylindrical Rod Moving From a Chamber at One Temperature to a Chamber at Another Temperature

1964 ◽  
Vol 86 (2) ◽  
pp. 265-270 ◽  
Author(s):  
G. Horvay ◽  
M. Dacosta
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Arbitrary Constant ◽  
Families Of Curves ◽  
Special Cases ◽  
Method Of Solution ◽  
Lower Chamber ◽  
Higher Temperature ◽  
Hopf Method ◽  
The Heat Transfer Coefficient

When an infinitely long cylindrical rod travels from a chamber at one temperature ϑa to a chamber (insulated from the first) at a higher temperature ϑf, then heat will leak out along the rod from the second chamber to the first, whose amount decreases as the speed of the rod increases. Using the Wiener-Hopf method of solution, we determine the temperature distribution in the rod for the case where in the second chamber the heat-transfer coefficient h+ is infinite, while in the first chamber it has an arbitrary constant value h. Families of curves illustrate the temperature distribution in the two special cases where h = ∞ (isothermal boundary conditions in lower chamber) and where h = 0 (rod is insulated in lower chamber).

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