Long-time behavior of three-dimensional gravity-capillary solitary waves on deep water generated by a moving air-blowing forcing: Numerical study

2018 ◽  
Vol 98 (3) ◽  
Author(s):  
Yeunwoo Cho
Keyword(s):  
Solitary Waves ◽  
Deep Water ◽  
Numerical Study ◽  
Three Dimensional ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Air Blowing ◽  
Long Time ◽  
Dimensional Gravity

scholarly journals EXTREME LONG-TIME DYNAMIC MONTE CARLO SIMULATIONS FOR METASTABLE DECAY IN THE d=3 ISING FERROMAGNET

2003 ◽  
Vol 14 (01) ◽  
pp. 121-131 ◽  
Author(s):  
MIROSLAV KOLESIK ◽  
M. A. NOVOTNY ◽  
PER ARNE RIKVOLD
Keyword(s):  
Metastable Phase ◽  
Three Dimensional ◽  
Glauber Dynamics ◽  
Simulation Method ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Time Dynamic ◽  
Dynamic Monte Carlo ◽  
Long Time ◽  
Good Agreement

We study the extreme long-time behavior of the metastable phase of the three-dimensional Ising model with Glauber dynamics in an applied magnetic field and at a temperature below the critical temperature. For these simulations, we use the advanced simulation method of projective dynamics. The algorithm is described in detail, together with its application to the escape from the metastable state. Our results for the field dependence of the metastable lifetime are in good agreement with theoretical expectations and span more than 50 decades in time.

scholarly journals Oscillation of three-dimensional time scale systems with fixed point theorems

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1915-1925
Author(s):  
Özkan Öztürk ◽  
Raegan Higgins ◽  
Georgia Kittou
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Three Dimensional ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Nonoscillatory Solutions ◽  
Long Time ◽  
Oscillation And Nonoscillation

Oscillation and nonoscillation theories play very important roles in gaining information about the long-time behavior of solutions of a system. Therefore, we investigate the asymptotic behavior of nonoscillatory solutions as well as the existence of such solutions so that one can determine the limit behavior. For the existence, we use some fixed point theorems such as Schauder?s fixed point theorem and the Knaster fixed point theorem.

A Three-Dimensional Autowave Turbulence

1998 ◽  
Vol 08 (04) ◽  
pp. 677-684 ◽  
Author(s):  
V. N. Biktashev
Keyword(s):  
Three Dimensional ◽  
Topological Defects ◽  
Self Organization ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Vortex Filaments ◽  
Principal Role ◽  
Cardiac Fibrillation ◽  
Internal Instability ◽  
Long Time

Autowave vortices are topological defects in autowave fields in nonlinear active media of various natures and serve as centers of self-organization in the medium. In three-dimensional media, the topological defects are lines, called vortex filaments. Evolution of three-dimensional vortices, in certain conditions, can be described in terms of evolution of their filaments, analogously to that of hydrodynamical vortices in LIA approximation. In the motion equation for the filament, a coefficient called filament tension, plays a principal role, and determines qualitative long-time behavior. While vortices with positive tension tend to shrink and so either collapse or stabilize to a straight shape, depending on boundary conditions, vortices with negative tension show internal instability of shape. This is an essentially three-dimensional effect, as two-dimensional media with the same parameters do not possess any peculiar properties. In large volumes, the instability of filaments can lead to propagating, nondecremental activity composed of curved vortex filaments that multiply and annihilate in an apparently chaotic manner. This may be related to a mechanism of cardiac fibrillation.

Experimental observation of gravity–capillary solitary waves generated by a moving air suction

2016 ◽  
Vol 808 ◽  
pp. 168-188 ◽  
Author(s):  
Beomchan Park ◽  
Yeunwoo Cho
Keyword(s):  
Experimental Observation ◽  
Solitary Waves ◽  
Deep Water ◽  
Small Amplitude ◽  
Three Dimensional ◽  
Phase Speed ◽  
Linear Phase ◽  
Wave Patterns ◽  
Air Blowing ◽  
Linear And Nonlinear

Gravity–capillary solitary waves are generated by a moving ‘air-suction’ forcing instead of a moving ‘air-blowing’ forcing. The air-suction forcing moves horizontally over the surface of deep water with speeds close to the minimum linear phase speed $c_{min}=23~\text{cm}~\text{s}^{-1}$. Three different states are observed according to forcing speeds below $c_{min}$. At relatively low speeds below $c_{min}$, small-amplitude linear circular depressions are observed, and they move steadily ahead of and along with the moving forcing. As the forcing speed increases close to $c_{min}$, however, nonlinear three-dimensional (3-D) gravity–capillary solitary waves are observed, and they move steadily ahead of and along with the moving forcing. Finally, when the forcing speed is very close to $c_{min}$, oblique shedding phenomena of 3-D gravity–capillary solitary waves are observed ahead of the moving forcing. We found that all the linear and nonlinear wave patterns generated by the air-suction forcing correspond to those generated by the air-blowing forcing. The main difference is that 3-D gravity–capillary solitary waves are observed ‘ahead of’ the air-suction forcing whereas the same waves are observed ‘behind’ the air-blowing forcing.

Dynamics of a 3D Benjamin–Bona–Mahony equations with sublinear operator

2020 ◽  
Vol 121 (1) ◽  
pp. 75-100
Author(s):  
Mingxia Zhao ◽  
Xin-Guang Yang ◽  
Xingjie Yan ◽  
Xiaona Cui
Keyword(s):  
Shallow Water ◽  
Energy Equation ◽  
Three Dimensional ◽  
Solution Process ◽  
Sublinear Operator ◽  
Sufficient Condition ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Pullback Attractors ◽  
Long Time

This paper is concerned with the tempered pullback dynamics for a three dimensional Benjamin–Bona–Mahony equations with sublinear operator on bounded domain, which describes the long time behavior for long waves model in shallow water with friction. By virtue of a new retarded Gronwall inequality, and using the energy equation method from J.M. Ball (Disc. Cont. Dyn. Syst. 10 (2004) 31–52) to achieve asymptotic compactness for solution process, the minimal family of pullback attractors has been obtained, which reduces a single trajectory under a sufficient condition.

Two-dimensional gravity–capillary solitary waves on deep water: generation and transverse instability

2017 ◽  
Vol 834 ◽  
pp. 92-124 ◽  
Author(s):  
Beomchan Park ◽  
Yeunwoo Cho
Keyword(s):  
Solitary Waves ◽  
Deep Water ◽  
Three Dimensional ◽  
Phase Speed ◽  
Narrow Slit ◽  
Two Dimensional ◽  
Transverse Instability ◽  
High Speeds ◽  
Linear Waves ◽  
Dimensional Gravity

Two-dimensional (2-D) gravity–capillary solitary waves are generated using a moving pressure jet from a 2-D narrow slit as a forcing onto the surface of deep water. The forcing moves horizontally over the surface of the deep water at speeds close to the minimum phase speed $c_{min}=23~\text{cm}~\text{s}^{-1}$. Four different states are observed according to the forcing speed. At relatively low speeds below $c_{min}$, small-amplitude depressions are observed and they move steadily just below the moving forcing. As the forcing speed increases towards $c_{min}$, nonlinear 2-D gravity–capillary solitary waves are observed, and they move steadily behind the moving forcing. When the forcing speed is very close to $c_{min}$, periodic shedding of a 2-D local depression is observed behind the moving forcing. Finally, at relatively high speeds above $c_{min}$, a pair of short and long linear waves is observed, respectively ahead of and behind the moving forcing. In addition, we observe the transverse instability of free 2-D gravity–capillary solitary waves and, further, the resultant formation of three-dimensional gravity–capillary solitary waves. These experimental observations are compared with numerical results based on a model equation that admits gravity–capillary solitary wave solutions near $c_{min}$. They agree with each other very well. In particular, based on a linear stability analysis, we give a theoretical proof for the transverse instability of the 2-D gravity–capillary solitary waves on deep water.

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