Related papers: Irreversible and dissipative systems
The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by…
Locally broken symmetries are used across fields to transport matter, particles and information in preferential directions. Beyond local mechanisms, spatially distributed nonlinearities in crystalline media have enabled non-reciprocal…
Global aspects of the motion of passive scalars in time-dependent incompressible fluid flows are well described by volume-preserving (Liouvillian) three-dimensional maps. In this paper the possible invariant structures in Liouvillian maps…
Dynamical systems whose symplectic structure degenerates, becoming noninvertible at some points along the orbits are analyzed. It is shown that for systems with a finite number of degrees of freedom, like in classical mechanics, the…
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…
This paper investigates the nonlinear dynamics of Newton's problem of minimal resistance in radial fields. We move beyond classical translational symmetry to analyze two non-equilibrium scenarios: a scale-invariant free expansion and an…
We present the formal derivation of a new unidirectional model for unsteady mixed flows in non uniform closed water pipe. In the case of free surface incompressible flows, the \FS-model is formally obtained, using formal asymptotic…
A new discrete time-reversible map of a unit square onto itself is proposed. The map comprises of piecewise linear two-dimensional operations, and is able to represent the macroscopic features of both equilibrium and nonequilibrium…
We construct small-amplitude steady periodic gravity water waves arising as the free surface of water flows that contain stagnation points and possess a discontinuous distribution of vorticity in the sense that the flows consist of two…
Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather…
We present the general properties of dynamic dissipative fluid distribution endowed with hyperbolical symmetry. All the equations required for its analysis are exhibited and used to contrast the behavior of the system with the spherically…
In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid…
We present an extension of the Piecewise Parabolic Method to special relativistic fluid dynamics in multidimensions. The scheme is conservative, dimensionally unsplit, and suitable for a general equation of state. Temporal evolution is…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
We study the rheology of a suspension of soft deformable droplets subjected to a pressure-driven flow. Through computer simulations, we measure the apparent viscosity as a function of droplet concentration and pressure gradient, and provide…
Discontinuous time derivatives are used to model threshold-dependent switching in such diverse applications as dry friction, electronic control, and biological growth. In a continuous flow, a discon- tinuous derivative can generate multiple…
Osmotically driven flow across a semi-permeable membrane under a constant static pressure difference is revisited with referring to the previous reports for reverse osmosis. A few mathematical techniques for obtaining the approximate…
Based on non-equilibrium thermodynamics we derive a set of general equations relating the partial volumetric flow rates to each other and to the total volumetric flow rate in immiscible two-phase flow in porous media. These equations…
Incompressible flows are modeled by a coupled system of partial differential equations for velocity and pressure, Starting from a divergence-free mixed method proposed in [John, Li, Merdon and Rui, Math. Models Methods Appl. Sci.…
Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of…