Mitigation of railway-induced vibrations by using periodic wave impeding barriers

2022 ◽  
Author(s):  
Chao He ◽  
Shunhua Zhou ◽  
Peijun Guo
Keyword(s):  
Periodic Wave

Entrainment and Annihilation of Reentrant Excitation in a Periodically Stimulated Ring of Excitable Media

1997 ◽  
Vol 36 (04/05) ◽  
pp. 290-293
Author(s):  
L. Glass ◽  
T. Nomura
Keyword(s):  
Cardiac Arrhythmias ◽  
Initial Phase ◽  
Human Heart ◽  
Periodic Wave ◽  
Excitable Media ◽  
One Dimensional ◽  
Clinical Observations ◽  
Periodic Stimulation ◽  
Reentrant Excitation ◽  
Stimulation Of

Abstract:Excitable media, such as nerve, heart and the Belousov-Zhabo- tinsky reaction, exhibit a large excursion from equilibrium in response to a small but finite perturbation. Assuming a one-dimensional ring geometry of sufficient length, excitable media support a periodic wave of circulation. As in the periodic stimulation of oscillations in ordinary differential equations, the effects of periodic stimuli of the periodically circulating wave can be described by a one-dimensional Poincaré map. Depending on the period and intensity of the stimulus as well as its initial phase, either entrainment or termination of the original circulating wave is observed. These phenomena are directly related to clinical observations concerning periodic stimulation of a class of cardiac arrhythmias caused by reentrant wave propagation in the human heart.

Inverse design of layered periodic wave barriers based on deep learning

2021 ◽  
pp. 146442072110168
Author(s):  
Chen-Xu Liu ◽  
Gui-Lan Yu
Keyword(s):  
Deep Learning ◽  
Activation Function ◽  
Periodic Wave ◽  
P Wave ◽  
Soil Parameters ◽  
S Wave ◽  
Output Frequency ◽  
Great Generality ◽  
Typical Range ◽  
Deep Learning Model

This study presents an approach based on deep learning to design layered periodic wave barriers with consideration of typical range of soil parameters. Three cases are considered where P wave and S wave exist separately or simultaneously. The deep learning model is composed of an autoencoder with a pretrained decoder which has three branches to output frequency attenuation domains for three different cases. A periodic activation function is used to improve the design accuracy, and condition variables are applied in the code layer of the autoencoder to meet the requirements of practical multi working conditions. Forty thousand sets of data are generated to train, validate, and test the model, and the designed results are highly consistent with the targets. The presented approach has great generality, feasibility, rapidity, and accuracy on designing layered periodic wave barriers which exhibit good performance in wave suppression in targeted frequency range.

Traveling Wave Solutions of a Two-Component Dullin–Gottwald–Holm System

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Jiyu Zhong ◽  
Shengfu Deng
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Phase Portraits ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Two Component ◽  
Planar Systems

In this paper, we investigate the traveling wave solutions of a two-component Dullin–Gottwald–Holm (DGH) system. By qualitative analysis methods of planar systems, we investigate completely the topological behavior of the solutions of the traveling wave system, which is derived from the two-component Dullin–Gottwald–Holm system, and show the corresponding phase portraits. We prove the topological types of degenerate equilibria by the technique of desingularization. According to the dynamical behaviors of the solutions, we give all the bounded exact traveling wave solutions of the system, including solitary wave solutions, periodic wave solutions, cusp solitary wave solutions, periodic cusp wave solutions, compactonlike wave solutions, and kinklike and antikinklike wave solutions. Furthermore, to verify the correctness of our results, we simulate these bounded wave solutions using the software maple version 18.

ANALYTICAL STUDY ON NONLINEAR DIFFERENTIAL–DIFFERENCE EQUATIONS VIA A NEW METHOD

2010 ◽  
Vol 24 (08) ◽  
pp. 761-773
Author(s):  
HONG ZHAO
Keyword(s):  
Difference Equations ◽  
Elliptic Function ◽  
Analytical Study ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Jacobian Elliptic Function ◽  
Jacobian Elliptic Functions ◽  
Periodic Wave Solutions ◽  
Trigonometric Function Solutions

Based on the computerized symbolic computation, a new rational expansion method using the Jacobian elliptic function was presented by means of a new general ansätz and the relations among the Jacobian elliptic functions. The results demonstrated an effective direction in terms of a uniformed construction of the new exact periodic solutions for nonlinear differential–difference equations, where two representative examples were chosen to illustrate the applications. Various periodic wave solutions, including Jacobian elliptic sine function, Jacobian elliptic cosine function and the third elliptic function solutions, were obtained. Furthermore, the solitonic solutions and trigonometric function solutions were also obtained within the limit conditions in this paper.

Periodic wave solution of the Kundu-Mukherjee-Naskar equation in birefringent fibers via the Hamiltonian-based algorithm

2021 ◽  
Author(s):  
Kang-Jia Wang ◽  
Hong-Wei Zhu
Keyword(s):  
Wave Solution ◽  
Bright Light ◽  
Periodic Wave ◽  
Optical Soliton ◽  
Numerical Results ◽  
Periodic Wave Solution ◽  
Soliton Dynamics ◽  
Good Agreement

Abstract The Kundu-Mukherjee-Naskar equation can be used to address certain optical soliton dynamics in the (2+1) dimensions. In this paper, we aim to find its periodic wave solution by the Hamiltonian-based algorithm. Compared with the existing results, they have a good agreement, which strongly proves the correctness of the proposed method. Finally, the numerical results are presented in the form of 3-D and 2-D plots. The results in this work are expected to shed a bright light on the study of the periodic wave solution in physics.

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