Related papers: Finite-Time Braiding Exponents
We review the behavior of the entropy per particle in various two-dimensional electronic systems. The entropy per particle is an important characteristic of any many body system that tells how the entropy of the ensemble of electrons…
A numerical code is described for constructing Doppler maps from the orbital variation of line profiles of (mass transfering) binaries. It uses an algorithm related to Richardson-Lucy iteration, and is much faster than the standard…
In the first half of the paper we construct a Morse-type theory on certain spaces of braid diagrams. We define a topological invariant of closed positive braids which is correlated with the existence of invariant sets of parabolic flows…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
Two finite element approximations of the Oldroyd-B model for dilute polymeric fluids are considered, in bounded 2- and 3-dimensional domains, under no flow boundary conditions. The pressure and the symmetric conformation tensor are…
In this paper, we propose an approach for solving PDEs on evolving surfaces using a combination of the trace finite element method and a fast marching method. The numerical approach is based on the Eulerian description of the surface…
We study dynamically crowded solutions of stiff fibers deep in the semidilute regime, where the motion of a single constituent becomes increasingly confined to a narrow tube. The spatiotemporal dynamics for wave numbers resolving the motion…
Final version. To appear in Discrete and Continuous Dynamical Systems - A.
Cell blebs are protrusions of the cell membrane and can be instrumental for cell migration. We derive a continuum model for the mechanical and geometrical aspects of the onset of blebbing in terms of a force balance. It is abstract and…
We report recent results from a high resolution numerical study of fluid particles transported by a fully developed turbulent flow. Single particle trajectories were followed for a time range spanning more than three decades, from less than…
Topology optimization methods face serious challenges when applied to structural design with fluid-structure interaction (FSI) loads, specially for high Reynolds fluid flow. This paper devises an explicit boundary method that employs…
Entropy production (EP) is a key quantity in thermodynamics, and yet measuring EP has remained a challenging task. Here we introduce an EP estimator, called multidimensional entropic bound (MEB), utilizing an ensemble of trajectories…
Localized magnetic reconnection at the dayside magnetopause leads to the production of Flux Transfer Events (FTEs). The magnetic field within the FTEs exhibit complex helical flux-rope topologies. Leveraging the Adaptive Mesh Refinement…
We demonstrate the accurate calculation of entropies and free energies for a variety of liquid metals using an extension of the two phase thermodynamic (2PT) model based on a decomposition of the velocity autocorrelation function into…
We introduce a method of time series analysis for two-dimensional transient flow patterns based on Topological Flow Data Analysis (TFDA), a new approach to topological data analysis. TFDA identifies local topological flow structures from an…
Using the maximum-entropy method, we calculate the end-to-end distance distribution of the force stretched chain from the moments of the distribution, which can be obtained from the extension-force curves recorded in single-molecule…
We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.
Whether the system under study is a shoal of fish, a collection of neurons, or a set of interacting atmospheric and oceanic processes, transfer entropy measures the flow of information between time series and can detect possible causal…
The detection of coherent structures is an important problem in fluid dynamics, particularly in geophysical applications. For instance, knowledge of how regions of fluid are isolated from each other allows prediction of the ultimate fate of…
Monge-Kantorovich optimal mass transport (OMT) provides a blueprint for geometries in the space of positive densities -- it quantifies the cost of transporting a mass distribution into another. In particular, it provides natural options for…