相关论文: A Determining Form for the 2D Rayleigh-B\'enard Pr…
We investigate the dynamics of a fluid layer subject to an imposed bottom heat flux and a top monotonically-increasing temperature profile driving horizontal convection. We use direct numerical simulations and consider a large range of…
In this article we derive the explicit solution of 2-D Stokes system in exterior of the disc with no-slip condition on inner boundary and given velocity $\mathbf{v}_\infty$ at infinity. It turned out it is the first application of the…
When the classical Rayleigh-B\'enard (RB) system is rotated about its vertical axis roughly three regimes can be identified. In regime I (weak rotation) the large scale circulation (LSC) is the dominant feature of the flow. In regime II…
We analyzed the performance of Convolutional Autoencoders in generating reduced-order representations the temperature field of 2D Rayleigh-B\'enard flows at $Pr=1$ and Rayleigh numbers extending from $10^6$ to $10^8$, capturing the range…
The self-consistency equations for the independent order parameters as well as the free energy expression for the mean-field RVB model of the spin-1/2 Heisenberg Hamiltonian on the anisotropic triangular lattice is considered in the…
This paper investigates the global structures of periodic orbits that appear in Rayleigh-B\'enard convection, which is modeled by a two-dimensional perturbed Hamiltonian model, by focusing upon resonance, symmetry and bifurcation of the…
We reformulate in Lagrangian coordinates the two-phase free boundary problem for the equations of Magnetohydrodynamics in a infinite slab, which is incompressible, viscous and of zero resistivity, as one for the Navier-Stokes equations with…
We perform a bifurcation analysis of a two-dimensional magnetic Rayleigh--B\'enard problem using a numerical technique called deflated continuation. Our aim is to study the influence of the magnetic field on the bifurcation diagram as the…
In most results concerning bounds on the heat transport in the Rayleigh-B\'{e}nard convection problem no-slip boundary conditions for the velocity field are assumed. Nevertheless it is debatable, whether these boundary conditions reflect…
In this work, we investigate the presence and impact of stable eigenmodes in Rayleigh-B\'{e}nard convection that arises due to a temperature gradient within a fluid system. The nonlinear evolution of the canonical convection system is cast…
A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of…
In this work, we propose an adjoint-based optimization procedure to control the onset of the Rayleigh-B\'enard instability with a melting front. A novel cut cell method is used to solve the Navier-Stokes equations in the Boussinesq…
In this paper, we investigate both deterministic and stochastic 2D Navier Stokes equations with anisotropic viscosity. For the deterministic case, we prove the global well-posedness of the system with initial data in the anisotropic Sobolev…
We study the long-time behaviour of the temperature-driven compressible flows. We show that numerical solutions of a structure-preserving finite volume method generate a discrete attractor that consists of entire discrete trajectories.…
In this paper we investigate two-dimensional (2D) Rayleigh-B\'enard convection using direct numerical simulation in Boussinesq fluids of Prandtl number $P = 6.8$ confined between thermally conducting plates. We show through the simulation…
The exact solution of the two-dimensional (2D) Ising model at an external magnetic field is derived by a modified Clifford algebraic approach. At first, the transfer matrices are analyzed in three representations, i.e., Clifford algebraic…
We study the influence of thermal boundary conditions on large aspect ratio Rayleigh-B\'enard convection by a joint analysis of experimental and numerical data sets for a Prandl number $\mathrm{Pr = 7}$ and Rayleigh numbers $\mathrm{Ra =…
The effects of a dispersed particulate phase on the onset of Rayleigh-B\'enard convection in a fluid layer is studied theoretically by means of a two-fluid Eulerian modelization. The particles are non-Brownian, spherical, with inertia and…
Our understanding of the material organization of complex fluid flows has recently benefited from mathematical developments in the theory of objective coherent structures. These methods have provided a wealth of approaches that identify…
In this article, we study the long time behavior of solutions of a variant of the Boussinesq system in which the equation for the velocity is parabolic while the equation for the temperature is hyperbolic. We prove that the system has a…