Related papers: The edge as a Lagrangian Coherent Structure in a h…

Dynamical-systems approaches to spatiotemporal chaos have been developed primarily for single-phase flows, where the system state is defined by bulk velocity fields. Extending these ideas to two-phase flows remains challenging because the…

In the past two decades, our understanding of the transition to turbulence in shear flows with linearly stable laminar solutions has greatly improved. Regarding the susceptibility of the laminar flow, two concepts have been particularly…

The laminar-turbulent boundary S is the set separating initial conditions which relaminarise uneventfully from those which become turbulent. Phase space trajectories on this hypersurface in cylindrical pipe flow look to be chaotic and show…

Large-eddy simulations (LES) are widely-used for computing high Reynolds number turbulent flows. Spatial filtering theory for LES is not without its shortcomings, including how to define filtering for wall-bounded flows, commutation errors…

Topological phases are often characterized by special edge states confined near the boundaries by an energy gap in the bulk. On raising temperature, these edge states are lost in a clean system due to mobile thermal excitations. Recently…

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and…

A characteristic feature of topological systems is the presence of robust gapless edge states. In this work the effect of time-dependent perturbations on the edge states is considered. Specifically we consider perturbations that can be…

Understanding how biomechanical reorganization governs key biological processes, such as morphogenesis and development, requires predictive insights into stress distributions and cellular behavior. While traditional approaches focused on…

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…

We study the effect of turbulence on a sedimenting layer of particles by means of direct numerical simulations. A Lagrangian model in which particles are considered as tracers with an additional downward settling velocity is integrated…

Concepts and tools from network theory, the so-called Lagrangian Flow Network framework, have been successfully used to obtain a coarse-grained description of transport by closed fluid flows. Here we explore the application of this…

Experiments and simulations lend mounting evidence for the edge state hypothesis on subcritical transition to turbulence, which asserts that simple states of fluid motion mediate between laminar and turbulent shear flow as their stable…

Lagrangian descriptors reveal the dynamical skeleton governing transport mechanisms of a generic flow. In doing so, they unveil geometrical structures in the phase space that separate regions with different qualitative behavior. This work…

Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures…

Phase space structures such as dividing surfaces, normally hyperbolic invariant manifolds, their stable and unstable manifolds have been an integral part of computing quantitative results such as transition fraction, stability erosion in…

Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of…

We present a framework for the scale-invariance characterization of stochastic processes in reconstructed finite-dimensional phase spaces. This framework analyses the structural and dynamical properties of the phase space and is based on a…

We numerically investigate the orbital dynamics of a two-dimensional galactic model, emphasizing the influence of stable and unstable manifolds on the evolution of orbits. In our analysis we use evaluations of the system's Lagrangian…

Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of…

A driven system of three species of particle diffusing on a ring is studied in detail. The dynamics is local and conserves the three densities. A simple argument suggesting that the model should phase separate and break the translational…