scholarly journals Trajectories of fluid particles in a periodic water wave

2012 ◽  
Vol 370 (1964) ◽  
pp. 1661-1676 ◽  
Author(s):  
Hisashi Okamoto ◽  
Mayumi Shōji
Keyword(s):  
Surface Tension ◽  
Water Wave ◽  
Constant Speed ◽  
New Method ◽  
Stokes Drift ◽  
Numerical Examples ◽  
Fluid Particles ◽  
Constant Shape ◽  
Surface Tension Coefficients

We compute trajectories of fluid particles in a water wave that propagates with a constant shape at a constant speed. The Stokes drift, which asserts that fluid particles are pushed forward by a wave, is proved using a new method. Numerical examples with various gravity and surface tension coefficients are presented.

scholarly journals Barycentric prolate interpolation and pseudospectral differentiation

2021 ◽  
Author(s):  
Yan Tian
Keyword(s):  
Boundary Value Problem ◽  
Convergence Rates ◽  
Boundary Value ◽  
High Accuracy ◽  
Second Order ◽  
New Method ◽  
Numerical Examples ◽  
Helmholtz Problem ◽  
Collocation Scheme

AbstractIn this paper, we provide further illustrations of prolate interpolation and pseudospectral differentiation based on the barycentric perspectives. The convergence rates of the barycentric prolate interpolation and pseudospectral differentiation are derived. Furthermore, we propose the new preconditioner, which leads to the well-conditioned prolate collocation scheme. Numerical examples are included to show the high accuracy of the new method. We apply this approach to solve the second-order boundary value problem and Helmholtz problem.

An Accelerated Iterative Method with Third-Order Convergence

2012 ◽  
Vol 220-223 ◽  
pp. 2658-2661
Author(s):  
Zhong Yong Hu ◽  
Liang Fang ◽  
Lian Zhong Li
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
New Method ◽  
Order Convergence ◽  
Third Order ◽  
Numerical Examples ◽  
Modified Newton’S Method ◽  
Jarratt Method

We present a new modified Newton's method with third-order convergence and compare it with the Jarratt method, which is of fourth-order. Based on this new method, we obtain a family of Newton-type methods, which converge cubically. Numerical examples show that the presented method can compete with Newton's method and other known third-order modifications of Newton's method.

scholarly journals Probability Transform Based on the Ordered Weighted Averaging and Entropy Difference

2020 ◽  
Vol 15 (4) ◽  
Author(s):  
Lipeng Pan ◽  
Yong Deng
Keyword(s):  
Probability Distribution ◽  
Evidence Theory ◽  
Mass Function ◽  
New Method ◽  
Weighted Averaging ◽  
Minimum Entropy ◽  
Transform Method ◽  
Numerical Examples ◽  
Ordered Weighted Averaging ◽  
Open Issue

Dempster-Shafer evidence theory can handle imprecise and unknown information, which has attracted many people. In most cases, the mass function can be translated into the probability, which is useful to expand the applications of the D-S evidence theory. However, how to reasonably transfer the mass function to the probability distribution is still an open issue. Hence, the paper proposed a new probability transform method based on the ordered weighted averaging and entropy difference. The new method calculates weights by ordered weighted averaging, and adds entropy difference as one of the measurement indicators. Then achieved the transformation of the minimum entropy difference by adjusting the parameter r of the weight function. Finally, some numerical examples are given to prove that new method is more reasonable and effective.

scholarly journals A Two-Step Newton-Type Method for Solving System of Absolute Value Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Lei Shi ◽  
Javed Iqbal ◽  
Muhammad Arif ◽  
Alamgir Khan
Keyword(s):  
Newton Method ◽  
New Method ◽  
Generalized Newton Method ◽  
Absolute Value Equations ◽  
Step Method ◽  
Type Method ◽  
Numerical Examples ◽  
Absolute Value ◽  
Generalized Newton

In this paper, we suggest a Newton-type method for solving the system of absolute value equations. This new method is a two-step method with the generalized Newton method as predictor. Convergence of the proposed method is proved under some suitable conditions. At the end, we take several numerical examples to show that the new method is very effective.

Particle paths in nonlinear Schrödinger models in the presence of linear shear currents

2018 ◽  
Vol 855 ◽  
pp. 322-350 ◽  
Author(s):  
C. W. Curtis ◽  
J. D. Carter ◽  
H. Kalisch
Keyword(s):  
Surface Tension ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Stokes Drift ◽  
Carrier Wave ◽  
Nonlinear Schrödinger ◽  
The Mean ◽  
Background Shear

We investigate the effect of constant-vorticity background shear on the properties of wavetrains in deep water. Using the methodology of Fokas (A Unified Approach to Boundary Value Problems, 2008, SIAM), we derive a higher-order nonlinear Schrödinger equation in the presence of shear and surface tension. We show that the presence of shear induces a strong coupling between the carrier wave and the mean-surface displacement. The effects of the background shear on the modulational instability of plane waves is also studied, where it is shown that shear can suppress instability, although not for all carrier wavelengths in the presence of surface tension. These results expand upon the findings of Thomas et al. (Phys. Fluids, vol. 24 (12), 2012, 127102). Using a modification of the generalized Lagrangian mean theory in Andrews & McIntyre (J. Fluid Mech., vol. 89, 1978, pp. 609–646) and approximate formulas for the velocity field in the fluid column, explicit, asymptotic approximations for the Lagrangian and Stokes drift velocities are obtained for plane-wave and Jacobi elliptic function solutions of the nonlinear Schrödinger equation. Numerical approximations to particle trajectories for these solutions are found and the Lagrangian and Stokes drift velocities corresponding to these numerical solutions corroborate the theoretical results. We show that background currents have significant effects on the mean transport properties of waves. In particular, certain combinations of background shear and carrier wave frequency lead to the disappearance of mean-surface mass transport. These results provide a possible explanation for the measurements reported in Smith (J. Phys. Oceanogr., vol. 36, 2006, pp. 1381–1402). Our results also provide further evidence of the viability of the modification of the Stokes drift velocity beyond the standard monochromatic approximation, such as recently proposed in Breivik et al. (J. Phys. Oceanogr., vol. 44, 2014, pp. 2433–2445) in order to obtain a closer match to a range of complex ocean wave spectra.

The NLS and FWI approximation make wrong predictions for the water wave problem in case of small surface tension

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 747-748
Author(s):  
Danish Ali Sunny ◽  
Guido Schneider ◽  
Dominik Zimmermann
Keyword(s):  
Surface Tension ◽  
Water Wave ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Small Surface

New Method and Experimental Study for Fast Evaluating Filling Mould Ability of Al-Si Alloy by Surface Tension

2007 ◽  
Vol 546-549 ◽  
pp. 697-702 ◽  
Author(s):  
De Quan Shi ◽  
Da Yong Li ◽  
Qian Sun ◽  
Gui Li Gao
Keyword(s):  
Experimental Study ◽  
Surface Tension ◽  
Acute Angle ◽  
The Self ◽  
New Method ◽  
Test Surface ◽  
New Apparatus ◽  
The Relationship

On the basis of analyzing the relationship between filling mould ability and surface tension of Al-Si alloy, a new method was put forward that filling mould ability can be fast evaluated by surface tension. To fast test surface tension of Al-Si alloy in front of furnace, a new apparatus had been developed and a new mould had been designed to appraise the ability of filling acute angle of Al-Si alloy by authors. By means of the self-developed new apparatus and new mould, the relationship between surface tension and filling mould ability had also been proved and gotten by many experiments on Al-Si alloys. Depending on the relationship the filling mould ability of Al-Si alloy can be evaluated by surface tension in few seconds before cast.

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