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Vortex states in high-$T_{\rm c}$ superconductors with point defects are studied by large-scale Monte Carlo simulations of the three-dimensional frustrated XY model. A critical point is observed on the first-order phase boundary between the…

We suggest a rigorous definition of the pathwise flux across the boundary of a bounded open set for transient finite energy diffusion processes. The expectation of such a flux has the property of depending only on the current velocity $v$,…

Diffusion-driven flow is a boundary layer flow arising from the interplay of gravity and diffusion in density-stratified fluids when a gravitational field is non-parallel to an impermeable solid boundary. This study investigates…

Nonlinear convection structures are investigated in quantitative detail as a function of Rayleigh number for several negative and positive Soret coupling strengths (separation ratios) and different Lewis and Prandtl numbers characterizing…

A better understanding of the ice-ocean couplings is required to better characterise the hydrosphere of the icy moons. Using global numerical simulations in spherical geometry, we have investigated here the interplay between rotating…

We describe ideal incompressible hydrodynamics on the hyperbolic plane which is an infinite surface of constant negative curvature. We derive equations of motion, general symmetries and conservation laws, and then consider turbulence with…

In a domain of the Euclidean space, we estimate from below the distance to the boundary of global maximum points of solutions of elliptic and parabolic equations with homogeneous Dirichlet boundary values. As reference cases, we first…

Superconductors like other solids cannot relax instantaneously from thermally excited (disturbed) states to thermodynamic equilibrium. In this paper, relaxation of a multi-filamentary and of a thin film superconductor from thermal…

It is understood in a general sense that turbulent fluid motion below the shock front in a core-collapse supernova stiffens the effective equation of state of the fluid and aids in the revival of the explosion. However, when one wishes to…

The asymptotic suction boundary layer (ASBL) is a parallel shear flow that becomes turbulent in a bypass transition in parameter regions where the laminar profile is stable. We here add a temperature gradient perpendicular to the plate and…

Continued progress in observational stellar astrophysics requires a deep understanding of the underlying convection dynamics. We present results of realistic 3D radiative hydrodynamic simulations of the outer layers of a moderate mass star…

We study Rayleigh-Benard convection in the high-Rayleigh-number and high-Prandtl-number regime, i.e., we consider a fluid in a container that is exposed to strong heating of the bottom and cooling of the top plate in the absence of inertia…

We consider a classical problem of linear stability of convective rolls in a plane layer with stress-free horizontal boundaries near the onset of convection. The problem has been studied by a number of authors, who have shown that rolls of…

We investigate a novel bursting state in inclined layer thermal convection in which convection rolls exhibit intermittent, localized, transverse bursts. With increasing temperature difference, the bursts increase in duration and number…

Heated pipe flow is widely used in thermal engineering applications, but the presence of buoyancy force can cause intermittency, or multiple flow states at the same parameter values. Such changes in the flow lead to substantial changes in…

The previous investigation on Rayleigh-B\'enard convection of a dilute classical gas [T. Kita: J. Phys. Soc. Jpn. {\bf 75} (2006) 124005] is extended to calculate entropy change of the convective transition with the rigid boundaries. We…

The natural convection of incompressible fluid in a porous medium causes for some boundary conditions a strong non-uniqueness in the form of a continuous family of steady states. We are interested in the situation when these boundary…

We describe how a convectively unstable active field in an open flow configuration becomes absolutely unstable due to local mixing. A representation of the mixing region as those with locally enhanced effective diffusion allows us to find…

We study convection in a volumetrically heated fluid which is cooled from both plates and is under rotation through the use of direct numerical simulations. The onset of convection matches similar systems and predictions from asymptotic…

The theory describing the evolution of inhomogeneous vortex tangle at zero temperature is developed on the bases of kinetics of merging and splitting vortex loops. Vortex loops composing the vortex tangle can move as a whole with some drift…