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The main aim of this paper is to describe the dynamic transitions in flows described by the two-dimensional, barotropic vorticity equation in a periodic zonal channel. In \cite{CGSW03}, the existence of a Hopf bifurcation in this model as…
We consider the Mode Coupling Theory (MCT) of Glass transition for a Binary fluid. The Equations of Nonlinear Fluctuating Hydrodynamics are obtained with a proper choice of the slow variables corresponding to the conservation laws. The…
We analyze rate-dependent tipping in a fast/slow system with an equilibrium near the fold of a critical manifiold. We find a Hopf bifurcation as the rate parameter increases in the reduced co-moving system. This implies the growth of a…
This study presents a first-principles model to predict the two-phase pressure drop in gas-liquid intermittent flow through round capillaries, which serve as the simplest analogous of a porous medium. Building upon the classical capillary…
We analyse three codimension-two bifurcations occurring in nonsmooth systems, when a non-hyperbolic cycle (fold, flip, and Neimark-Sacker cases, both in continuous- and discrete-time) interacts with one of the discontinuity boundaries…
The aim of this paper is to investigate the asymptotic behavior of a biphase tumor fluid flow derived by 2-scale homogenisation techniques in recent works. This biphase fluid flow model accounts for the capillary wall permeability, and the…
We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a…
Many physical situations are characterized by interfaces with a non trivial shape so that relevant geometric features, such as interfacial area, curvature or unit normal vector, can be used as main indicators of the topology of the…
The problem of two-phase flow in straight capillaries of polygonal cross section displays many of the dynamic characteristics of rapid interfacial motions associated with pore-scale displacements in porous media. Fluid inertia is known to…
We perform a geometric study of the equilibrium locus of the flow that models the diffusion process over a circular network of cells. We prove that when considering the set of all possible values of the parameters, the equilibrium locus is…
We discuss the sharp interface limit of a diffuse interface model for a two-phase flow of two partly miscible viscous Newtonian fluids of different densities, when a certain parameter \epsilon>0 related to the interface thickness tends to…
We analyse the topological (knot-theoretic) features of a certain codimension-one bifurcation of a partially hyperbolic fixed point in a flow on $\real^3$ originally described by Shil'nikov. By modifying how the invariant manifolds wrap…
In the optimal velocity model with a time lag, we show that there appear multiple exact solutions in some ranges of car density, describing a uniform flow, a stable and an unstable congested flows. This establishes the presence of…
We revisit the bifurcation theory of the Lotka-Volterra quadratic system \begin{eqnarray} X_0 :\left\{\begin{aligned} \dot{x}=& - y -x^2+y^2 ,\\ \dot{y}= &\;\;\;\;x - 2xy \end{aligned} \right. \end{eqnarray} with respect to arbitrary…
A liquid-liquid two-phase Taylor-Couette flow is of fundamental and practical importance in multiphase flow systems. This study investigates the flow transitions in such a system with constant axial flow and gradually increased rotation of…
We study the drift induced by the passage of two cylinders through an unbounded extent of inviscid incompressible fluid under the assumption that the flow is two-dimensional and steady in the moving frame of reference. The goal is to assess…
We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a…
We examine the fluid flow forced by precession of a rotating cylindrical container using numerical simulations and experimental flow measurements with ultrasonic Doppler velocimetry (UDV). The analysis is based on the decomposition of the…
In this contribution, we derive a gas-liquid two-scale multi-fluid model with capillarity effects to enable a novelinterface regularization approach for multi-fluid models. As this unified modelling is capable of switching from theinterface…
Optical systems that combine nonlinearity with coupling between various subsystems offer a flexible platform for observing a diverse range of nonlinear dynamics. Furthermore, engineering tolerances are such that the subsystems can be…