## 10 Citations

### Transitions and bifurcations of darcy-brinkman-marangoni convection

- PhysicsDiscrete & Continuous Dynamical Systems - B
- 2021

This study examines dynamic transitions of Brinkman equation coupled with the thermal diffusion equation modeling the surface tension driven convection in porous media. First, we show that the…

### Dynamical transition theory of hexagonal pattern formations

- MathematicsCommunications in Nonlinear Science and Numerical Simulation
- 2020

### Complex bifurcations in Bénard–Marangoni convection

- Physics
- 2015

We study the dynamics of a system defined by the Navier–Stokes equations for a non-compressible fluid with Marangoni boundary conditions in the two-dimensional case. We show that more complicated…

### Navier-Stokes equations under Marangoni boundary conditions generate all hyperbolic dynamics

- Mathematics, Physics
- 2015

The dynamics defined by the Navier-Stokes equations under the Marangoni boundary conditions in a two dimensional domain is considered. This model of fluid dynamics involve fundamental physical…

### Dynamic transitions of generalized Kuramoto-Sivashinsky equation

- Mathematics
- 2016

In this article, we study the dynamic transition for the one dimensional generalized Kuramoto-Sivashinsky equation with periodic condition. It is shown that if the value of the dispersive parameter…

### Dynamic Transition Theory

- Physics
- 2014

This chapter introduces the dynamic transition theory for nonlinear dissipative systems developed recently by the authors. The main focus is the derivation of a general principle, Principle 1, on…

### Geophysical Fluid Dynamics and Climate Dynamics

- Geology, Environmental SciencePhase Transition Dynamics
- 2019

Our Earth’s atmosphere and oceans are rotating geophysical fluids that are two important components of the planet’s climate system. The atmosphere and the oceans are extremely rich in their…

## References

SHOWING 1-10 OF 20 REFERENCES

### Nonlinear dynamics of surface-tension-driven instabilities

- Physics
- 2001

A century after Henri Benard discovered cellular convective structures, thermal convection in fluid layers still remains a central subject in nonlinear physics. Within this framework,…

### Pattern Selection in Surface Tension Driven Flows

- Physics
- 1998

When a motionless liquid layer is heated from below, spontaneous convection appears when the vertical temperature gradient exceeds a critical value. Under slightly supercritical conditions, the…

### HEXAGONAL MARANGONI CONVECTION IN A RECTANGULAR BOX WITH SLIPPERY WALLS

- Physics
- 1993

A linear and nonlinear study of surface-tension-driven instability in a rectangular box with slippery lateral walls is presented. Particular attention is devoted to steady convection with hexagonal…

### Rayleigh Bénard convection: dynamics and structure in the physical space

- Physics, Mathematics
- 2006

The main objective of this article is part of a research program to link the dynamics of fluid flows with the structure and its transitions in the physical spaces. As a prototype of problem and to…

### Nonlinear Marangoni convection in bounded layers. Part 1. Circular cylindrical containers

- PhysicsJournal of Fluid Mechanics
- 1982

We consider liquid in a circular cylinder that undergoes nonlinear Marangoni insta- bility. The upper free surface of the liquid is taken to have large-enough surface tension that surface deflections…

### On convection cells induced by surface tension

- PhysicsJournal of Fluid Mechanics
- 1958

A mechanism is proposed by which cellular convective motion of the type observed by H. Bénard, which hitherto has been attributed to the action of buoyancy forces, can also be induced by surface…

### Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag

- Mathematics
- 1988

Contents: General results and concepts on invariant sets and attractors.- Elements of functional analysis.- Attractors of the dissipative evolution equation of the first order in time:…

### An introduction to semiflows

- Mathematics
- 2004

DYNAMICAL PROCESSES Introduction Ordinary Differential Equations Attracting Sets Iterated Sequences Lorenz' Equations Duffing's Equation Summary ATTRACTORS OF SEMIFLOWS Distance and Semidistance…