Related papers: A self-similar dynamics in viscous spheres
We confirm numerically that the Johnson-Segalman model is able to reproduce the continual oscillations of the falling sphere observed in some viscoelastic models. The empirical choice of parameters used in the Johnson-Segalman model is from…
In this paper, the dynamics of spontaneous shape fluctuations of a single, giant quasi-spherical vesicle formed of a single lipid species is revisited theoretically. A coherent physical theory for the dynamics is developed based on a number…
We investigate the evolution of self-gravitating either dissipative or non--dissipative systems satisfying the condition of minimal complexity, and whose areal radius velocity is proportional to the areal radius (quasi-homologous…
We review a recently proposed definition of complexity of the structure of self--gravitating fluids \cite{ch1}, and the criterium to define the simplest mode of their evolution. We analyze the origin of these concepts and their possible…
Robust empirical constitutive laws for granular materials in air or in a viscous fluid have been expressed in terms of timescales based on the dynamics of a single particle. However, some behaviours such as viscosity bifurcation or shear…
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…
We investigate the anisotropic evolution of spacetime driven by perfect fluid with off-diagonal shear-viscosity components. We consider the simplest form of the equation of state for fluid, for which the pressure and the shear stress are…
We study in this work the dynamics of a collection of identical hollow spheres (ping-pong balls) that rest on a horizontal metallic grid. Fluidization is achieved by means of a turbulent air current coming from below. The upflow is adjusted…
It is shown that a new type of the self-similar spherical ionization waves may exist in gases. All spatial scales and the propagation velocity of such waves increase exponentially in time. Conditions for existence of these waves are…
A classical model of fluid dynamics is considered which describes the shape evolution of a viscous liquid droplet on a homogeneous substrate. All equilibria are characterized and their stability is analyzed by a geometric reduction…
We summarize the general formalism describing surface flows in three-dimensional space in a form which is suitable for various astrophysical applications. We then apply the formalism to the analysis of non-radial perturbations of…
The self-similar equilibrium models of self-gravitating, rotating, isothermal systems are investigated analytically. In these models the rotation velocity is constant and the density varies as $\frac{f(\theta, \phi)}{r^2}$, where $r$ and…
Self-propelled particles can navigate complex environments, including viscous fluid interfaces with curved geometries. In this work, we study the emergent dynamics of a suspension of self-propelled particles confined to a stationary curved…
By linearly scaling the initial data set (mass and kinetic energy functions) together with the initial area radius of a collapsing dust sphere, we find a symmetry of the collapse dynamics. That is, the linear transformation defines an…
We study the dynamics of spatially homogeneous and isotropic spacetimes containing a fluid undergoing microscopic velocity diffusion in a cosmological scalar field. After deriving a few exact solutions of the equations, we continue by…
The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier-Stokes equations. The mean swimming velocity and the mean rate of dissipation…
A new one-dimensional, dynamical model is proposed for geometrically thin, self-gravitating viscous accretion discs. The vertically integrated equations are simplified using the slow accretion limit and the monopole approximation with a…
This series of works revisits the geometry, dynamics, and covariant phase space of spherically symmetric spacetimes with the aim of exploring the thermodynamics of spacetime from their dynamical properties. In this first paper, we examine…
We model the gravitational behaviour of a radiating star when the exterior geometry is the generalised Vaidya spacetime. The interior matter distribution is shear-free and undergoing radial heat flow. The exterior energy momentum tensor is…
We have investigated spherically symmetric spacetimes which contain a perfect fluid obeying the polytropic equation of state and admit a kinematic self-similar vector of the second kind which is neither parallel nor orthogonal to the fluid…