4,020 research outputs found
Time-Dependent 2-D Vector Field Topology: An Approach Inspired by Lagrangian Coherent Structures
This paper presents an approach to a time-dependent variant of the concept of
vector field topology for 2-D vector fields. Vector field topology is defined
for steady vector fields and aims at discriminating the domain of a vector
field into regions of qualitatively different behaviour. The presented approach
represents a generalization for saddle-type critical points and their
separatrices to unsteady vector fields based on generalized streak lines, with
the classical vector field topology as its special case for steady vector
fields. The concept is closely related to that of Lagrangian coherent
structures obtained as ridges in the finite-time Lyapunov exponent field. The
proposed approach is evaluated on both 2-D time-dependent synthetic and vector
fields from computational fluid dynamics
Visualizing Spacetime Curvature via Gradient Flows I: Introduction
Traditional approaches to the study of the dynamics of spacetime curvature in
a very real sense hide the intricacies of the nonlinear regime. Whether it be
huge formulae, or mountains of numerical data, standard methods of presentation
make little use of our remarkable skill, as humans, at pattern recognition.
Here we introduce a new approach to the visualization of spacetime curvature.
We examine the flows associated with the gradient fields of invariants derived
from the spacetime. These flows reveal a remarkably rich structure, and offer
fresh insights even for well known analytical solutions to Einstein's
equations. This paper serves as an overview and as an introduction to this
approach.Comment: 10 pages twocolumn revtex 4-1 two figures. Final form to appear in
Phys Rev
A Method for Data-Driven Simulations of Evolving Solar Active Regions
We present a method for performing data-driven simulations of solar active
region formation and evolution. The approach is based on magnetofriction, which
evolves the induction equation assuming the plasma velocity is proportional to
the Lorentz force. The simulations of active region coronal field are driven by
temporal sequences of photospheric magnetograms from the Helioseismic Magnetic
Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO). Under
certain conditions, the data-driven simulations produce flux ropes that are
ejected from the modeled active region due to loss of equilibrium. Following
the ejection of flux ropes, we find an enhancement of the photospheric
horizontal field near the polarity inversion line. We also present a method for
the synthesis of mock coronal images based on a proxy emissivity calculated
from the current density distribution in the model. This method yields mock
coronal images that are somewhat reminiscent of images of active regions taken
by instruments such as SDO's Atmospheric Imaging Assembly (AIA) at extreme
ultraviolet wavelengths.Comment: Accepted to ApJ; comments/questions related to this article are
welcome via e-mail, even after publicatio
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