A PHP Error was encountered

Severity: Warning

Message: file_get_contents(https://...@pubfacts.com&api_key=b8daa3ad693db53b1410957c26c9a51b4908&a=1): Failed to open stream: HTTP request failed! HTTP/1.1 429 Too Many Requests

Filename: helpers/my_audit_helper.php

Line Number: 176

Backtrace:

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 176
Function: file_get_contents

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 250
Function: simplexml_load_file_from_url

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3122
Function: getPubMedXML

File: /var/www/html/application/controllers/Detail.php
Line: 575
Function: pubMedSearch_Global

File: /var/www/html/application/controllers/Detail.php
Line: 489
Function: pubMedGetRelatedKeyword

File: /var/www/html/index.php
Line: 316
Function: require_once

Nonlinear ultrasonic standing waves: two-dimensional simulations in bubbly liquids. | LitMetric

Nonlinear ultrasonic standing waves: two-dimensional simulations in bubbly liquids.

Ultrason Sonochem

ESCET, Universidad Rey Juan Carlos, Madrid, Spain.

Published: March 2011

We present the results of numerical predictions for analyzing the behavior of nonlinear ultrasonic standing waves in two-dimensional cavities filled with bubbly liquids. The model we solve accounts for nonlinearity, dissipation, and dispersion of the two-dimensional media due to the bubbles. The numerical simulations are based on a finite-difference scheme. They consider the bubbles evenly distributed in the liquid. Results are shown for high-amplitude signals. They make it possible to observe how the linear modes turn into multi-frequency nonlinear fields.

Download full-text PDF

Source
http://dx.doi.org/10.1016/j.ultsonch.2010.09.002DOI Listing

Publication Analysis

Top Keywords

nonlinear ultrasonic
8
ultrasonic standing
8
standing waves
8
waves two-dimensional
8
bubbly liquids
8
two-dimensional simulations
4
simulations bubbly
4
liquids numerical
4
numerical predictions
4
predictions analyzing
4

Similar Publications

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!