A shallow-water sloshing model for wave breaking in rectangular tanks

2014 ◽  
Vol 746 ◽  
pp. 437-465 ◽  
Author(s):  
Matteo Antuono ◽  
Andrea Bardazzi ◽  
Claudio Lugni ◽  
Maurizio Brocchini
Keyword(s):  
Shallow Water ◽  
Wave Breaking ◽  
Analytic Solution ◽  
Turbulent Viscosity ◽  
Approximate Analytic Solution ◽  
Experimental Campaign ◽  
Proposed Model ◽  
Water Conditions ◽  
Reliability And Robustness ◽  
Good Agreement

AbstractWe propose a simple, robust and efficient sloshing model that accounts for breaking phenomena evolving in rectangular tanks and in shallow-water conditions. The model has been obtained by applying Fourier analysis to Boussinesq-type equations and using an approximate analytic solution for the vorticity generated by wave breaking. The toe of the breaker and the intensity of the vorticity injected at the free surface are computed on the basis of literature results for coastal-type breakers. A first experimental campaign has been used to calibrate the turbulent viscosity of the sloshing model, while a second campaign has been run as final validation. The overall good agreement between the numerical outputs and the experimental data confirms the reliability and robustness of the proposed model.

scholarly journals On the Analytical Approximation of the Nonlinear Cubic Oscillator by an Iteration Method

2019 ◽  
pp. 1-9
Author(s):  
B. M. Ikramul Haque ◽  
A. K. M. Selim Reza ◽  
Md. Mominur Rahman
Keyword(s):  
Nonlinear Oscillator ◽  
Analytic Solution ◽  
Analytical Approximation ◽  
Approximate Analytic Solution ◽  
Rapid Convergence ◽  
Modified Technique ◽  
Validity Range ◽  
Approximate Frequency ◽  
Truncated Fourier Series ◽  
Good Agreement

A modified approximate analytic solution of the cubic nonlinear oscillator “ ” has been obtained based on an iteration procedure. Here we have used the truncated Fourier series in each iterative step. The approximate frequencies obtained by this technique show a good agreement with the exact frequency. The percentage of error between exact frequency and our fifth approximate frequency is as low as 0.009%. The calculation with this technique is very easy. This easily-calculated modified technique accelerates the rapid convergence, reduces the error and increases the validity range of the solution.

scholarly journals A Modified Solution of the Nonlinear Singular Oscillator by Extended Iteration Procedure

2019 ◽  
pp. 1-9
Author(s):  
B. M. Ikramul Haque ◽  
M. M. Ayub Hossain
Keyword(s):  
Fourier Series ◽  
Analytic Solution ◽  
Rate Of Change ◽  
Iteration Procedure ◽  
Approximate Analytic Solution ◽  
Modified Technique ◽  
The Third ◽  
Present Technique ◽  
Approximate Frequency ◽  
Good Agreement

A modified solution of the nonlinear singular oscillator has been obtained based on the extended iteration procedure. We have used an appropriate truncation of the obtained Fourier series in each step of iterations to determine the approximate analytic solution of the oscillator. The third approximate frequency of the nonlinear singular oscillator shows a good agreement with its exact values. Earlier different authors presented the analytic solution of the oscillator by using various types of methods. We have compared the results obtained by the modified technique with some of the existing results. We see that some of their techniques deviate from higher-order approximations and the present technique performs comparatively better.  The rate of change of percentage of error of the presented modified solution shows the validity of convergence.

scholarly journals Compact Modelling of Electrical, Optical and Thermal Properties of Multi-Colour Power LEDs Operating on a Common PCB

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1286
Author(s):  
Krzysztof Górecki ◽  
Przemysław Ptak
Keyword(s):  
Integrated Circuits ◽  
Optical Model ◽  
Printed Circuit Board ◽  
Circuit Board ◽  
Junction Temperature ◽  
Optical Parameters ◽  
Spice Simulation ◽  
Light Emitting ◽  
Proposed Model ◽  
Good Agreement

This paper concerns the problem of modelling electrical, thermal and optical properties of multi-colour power light-emitting diodes (LEDs) situated on a common PCB (Printed Circuit Board). A new form of electro-thermo-optical model of such power LEDs is proposed in the form of a subcircuit for SPICE (Simulation Program with Integrated Circuits Emphasis). With the use of this model, the currents and voltages of the considered devices, their junction temperature and selected radiometric parameters can be calculated, taking into account self-heating phenomena in each LED and mutual thermal couplings between each pair of the considered devices. The form of the formulated model is described, and a manner of parameter estimation is also proposed. The correctness and usefulness of the proposed model are verified experimentally for six power LEDs emitting light of different colours and mounted on an experimental PCB prepared by the producer of the investigated devices. Verification was performed for the investigated diodes operating alone and together. Good agreement between the results of measurements and computations was obtained. It was also proved that the main thermal and optical parameters of the investigated LEDs depend on a dominant wavelength of the emitted light.

Static and Dynamic Structure of Molecular Monomers and Dimers of the Rare-earth Fluorides

2001 ◽  
Vol 56 (5) ◽  
pp. 381-385
Author(s):  
Z. Akdeniz ◽  
M . Gaune-Escard ◽  
M. P. Tosi
Keyword(s):  
Rare Earth ◽  
Bond Length ◽  
Geometrical Structure ◽  
Vibrational Mode ◽  
Dynamic Structure ◽  
Molecular Shape ◽  
Proposed Model ◽  
Infrared Studies ◽  
Charged Clusters ◽  
Good Agreement

Abstract We determine a model of the ionic interactions in RF3 compounds, where R is a rare-earth element in the series from La to Lu, by an analysis of data on the bond length and the vibrational mode frequencies of the PrF3, GdF3 and HoF3 molecular monomers. All RF3 monomers are predicted to have a pyramidal shape, displaying a progressive flattening of the molecular shape in parallel with the lanthanide contraction of the bond length. The vibrational frequencies of all monomers are calculated, the results being in good agreement with the data from infrared studies of matrix-isolated molecules. We also evaluate the geometrical structure and the vibrational spectrum of the La2F6 and Ce2F6 dimers, as a further test of the proposed model. -PACS 36.40.Wa (Charged clusters)

scholarly journals An approximate analytic solution of a particular boundary value problem

2001 ◽  
Vol 27 (8) ◽  
pp. 513-520
Author(s):  
Ugur Tanriver ◽  
Aravinda Kar
Keyword(s):  
Boundary Value Problem ◽  
Heat Conduction Equation ◽  
Analytic Solution ◽  
Boundary Value ◽  
Three Dimensional ◽  
Welding Process ◽  
Approximate Analytic Solution ◽  
Analytic Expression ◽  
Steady State Heat ◽  
Laser Welding Process

This note is concerned with the three-dimensional quasi-steady-state heat conduction equation subject to certain boundary conditions in the wholex′y′-plane and finite inz′-direction. This type of boundary value problem arises in laser welding process. The solution to this problem can be represented by an integral using Fourier analysis. This integral is approximated to obtain a simple analytic expression for the temperature distribution.

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