Related papers: Structural stability for a thermal convection mode…
We consider a boundary value problem for the system of equations describing the stationary motion of a viscous nonhomogeneous asymmetric fluid in a bounded planar domain having a $C^2$ boundary. We use a stream-function formulation after…
We consider the spatially inhomogeneous Boltzmann equation for inelastic hard-spheres, with constant restitution coefficient $\alpha\in(0,1)$, under the thermalization induced by a host medium with a fixed Maxwellian distribution and any…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
Recently it was obtained in [Tarzia, Thermal Sci. 21A (2017) 1-11] for the classical two-phase Lam\'e-Clapeyron-Stefan problem an equivalence between the temperature and convective boundary conditions at the fixed face under a certain…
We derive a class of thermodynamically consistent variants of Maxwell/Oldroyd-B type models for viscoelastic fluids. In particular, we study the models that allow one to consider temperature dependent material coefficients. This naturally…
We report and explain a convective phenomenon observed in molecular dynamics simulations that cannot be classified either as a hydrodynamics instability nor as a macroscopically forced convection. Two complementary arguments show that the…
We numerically study thermodynamic and structural properties of the one-component Gaussian core model (GCM) at very high densities. The solid-fluid phase boundary is carefully determined. We find that the density dependence of both the…
We consider a particle dragged through a medium at constant temperature as described by a Langevin equation with a time-dependent potential. The time-dependence is specified by an external protocol. We give conditions on potential and…
The existence of weak solutions to the Navier-Stokes-Fourier system describing the stationary states of a compressible, viscous, and heat conducting fluid in bounded 2D-domains is shown under fairly general and physically relevant…
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is…
When applied to binary solutions, thermal gradients lead to the generation of concentration-gradients and thus to inhomogeneous systems. While being known for more than 150 years, the molecular origins for this phenomenon are still debated,…
We consider the heat equation in a smooth bounded convex domain $\Omega \subset \mathbb{R}^2$ with nonlinear Neumann boundary condition $\partial_\nu u = \lambda (u - u^3)$. Stable non-constant stationary solutions do not exist when…
Bifurcation properties, stability behavior, dynamics, and the heat transfer of convection structures in a horizontal fluid layer that is driven away from thermal equilibrium by imposing a vertical temperature difference are compared with…
Turbulent convection models are thought to be good tools to deal with the convective overshooting in the stellar interior. However, they are too complex to be applied in calculations of stellar structure and evolution. In order to…
This paper reviews results about free convection near a vertical flat plate embedded in some saturated porous medium. We focus on a third order autonomous differential equation that gives a special class of solutions called similarity…
We examine the dependence of a thermodynamic potential of a fluid on the geometry of its container. If motion invariance, continuity, and additivity of the potential are fulfilled, only four morphometric measures are needed to describe…
A system is glassy when the observation time is much smaller than the equilibration time. A unifying thermodynamic picture of the glassy state is presented. Slow configurational modes are in quasi-equilibrium at an effective temperature. It…
The spatial resolution of extensive thermodynamic functions is discussed. A physical definition of the spatial resolution based on a spatial analogy of partial molar quantities is advocated, which is shown to be consistent with how…
Stability of a set of travelling wave solutions to the hyperbolic generalization of the convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.
Motion in the atmosphere or mantle convection are two among phenomena of natural convection induced by internal heat sources. They bifurcate from the conduction state as a result of its loss of stability. In spite of their importance, due…