scholarly journals Spiral structure in galaxies: large-scale stochastic self-organization of interstellar matter and young stars

1985 ◽  
Vol 106 ◽  
pp. 559-560
Author(s):  
J. V. Feitzinger
Keyword(s):  
Star Formation ◽  
Large Scale ◽  
Spiral Structure ◽  
Reaction Diffusion ◽  
Young Stars ◽  
Reaction Diffusion Equations ◽  
Dissipative Systems ◽  
Interstellar Matter ◽  
Self Organized ◽  
Analytical Work

Galaxies are dissipative systems, and the spatial and time structure of the interstellar medium and young stars is governed by reaction-diffusion equations. The coherent galactic oscillations of star formation self-organized in spiral waves, previously detected by numerical simulations (Seiden, Schulman, Feitzinger, 1982) can be analytically described by the concept of a limit cycle. Analytical work on self-propagating stochastic star formation is also done by Kaufman (1979), Shore (1981, 1982) and Cowie and Rybicki (1982).

A PARALLEL SOLVER FOR REACTION–DIFFUSION SYSTEMS IN COMPUTATIONAL ELECTROCARDIOLOGY

2004 ◽  
Vol 14 (06) ◽  
pp. 883-911 ◽  
Author(s):  
PIERO COLLI FRANZONE ◽  
LUCA F. PAVARINO
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Ionic Currents ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Fiber Direction ◽  
Axially Symmetric ◽  
Reaction Diffusion Systems ◽  
Cardiac Model

In this work, a parallel three-dimensional solver for numerical simulations in computational electrocardiology is introduced and studied. The solver is based on the anisotropic Bidomain cardiac model, consisting of a system of two degenerate parabolic reaction–diffusion equations describing the intra and extracellular potentials of the myocardial tissue. This model includes intramural fiber rotation and anisotropic conductivity coefficients that can be fully orthotropic or axially symmetric around the fiber direction. The solver also includes the simpler anisotropic Monodomain model, consisting of only one reaction–diffusion equation. These cardiac models are coupled with a membrane model for the ionic currents, consisting of a system of ordinary differential equations that can vary from the simple FitzHugh–Nagumo (FHN) model to the more complex phase-I Luo–Rudy model (LR1). The solver employs structured isoparametric Q1finite elements in space and a semi-implicit adaptive method in time. Parallelization and portability are based on the PETSc parallel library. Large-scale computations with up to O(107) unknowns have been run on parallel computers, simulating excitation and repolarization phenomena in three-dimensional domains.

Evidence for Large Scale Cosmic Ray Electron Gradients in the Galaxy

1976 ◽  
Vol 3 (1) ◽  
pp. 1-6 ◽  
Author(s):  
W. R. Webber
Keyword(s):  
Large Scale ◽  
Spiral Structure ◽  
Cosmic Ray ◽  
Point Sources ◽  
Interstellar Matter ◽  
Interstellar Gas ◽  
The Galaxy ◽  
Ray Density ◽  
Γ Rays ◽  
Γ Ray

In recent years observations of γ-ray emission from the disk of the galaxy have provided a new opportunity for research into the structure of the spiral arms of our own galaxy. In Figure 1 we show a map of the structure of the disk of the galaxy as observed for γ-rays of energy > 100 MeV by the SAS-2 satellite (Fichtel et al. 1975). The angular resolution of these measurements is ~ 3°, and besides two point sources at l = 190° and 265° several features related to the spiral structure of the galaxy are evident in the data. Most of these γ-rays are believed to arise from the decay of π° mesons produced by the nuclear interactions of cosmic rays (mostly protons) with the ambient interstellar gas. As a result, the γ-ray fluxes represent a measure of the line of sight integral of the product of the cosmic ray density NCR and the interstellar matter density N1

scholarly journals Non-circular motions in the galaxy as exhibited by very young stars

1964 ◽  
Vol 20 ◽  
pp. 92-99
Author(s):  
H. F. Weaver
Keyword(s):  
Large Scale ◽  
Spiral Structure ◽  
Young Stars ◽  
Significant Fraction ◽  
Fundamental Importance ◽  
General Character ◽  
Gaseous Component ◽  
The Galaxy ◽  
Scale Expansion

I. Expansion of the Gaseous and Stellar Components of the GalaxyIf the gaseous component of the Galaxy is expanding as observed by Rougoor and Oort in the centre of the Galaxy and as postulated by Kerr in his early interpretation of spiral structure, the expansion must represent a phenomenon of fundamental importance in the Galaxy which has, in all probability, been operative for a significant fraction of the age of the Galaxy. Presumably, very young stars formed from this gas and having ages less than 1 % of the age of the Galaxy might be expected to retain in their motions the general character of the large-scale expansion of the gas from which they originated.

scholarly journals Large-scale galactic shock phenomena and the implications on star formation

1970 ◽  
Vol 38 ◽  
pp. 415-422
Author(s):  
W. W. Roberts
Keyword(s):  
Star Formation ◽  
Gravitational Collapse ◽  
Large Scale ◽  
Milky Way ◽  
Spiral Structure ◽  
Triggering Mechanism ◽  
Grand Design ◽  
Armed Spiral

The possible existence of a stationary two-armed spiral shock pattern for a disk-shaped galaxy, such as our own Milky Way System, is demonstrated. It is therefore suggested that large-scale galactic shock phenomena may very well form the large-scale triggering mechanism for the gravitational collapse of gas clouds, leading to star formation along narrow spiral arcs within a two-armed grand design of spiral structure.

Fracture pattern formation in frictional, cohesive, granular material

2010 ◽  
Vol 368 (1910) ◽  
pp. 95-118 ◽  
Author(s):  
Alison Ord ◽  
Bruce E. Hobbs
Keyword(s):  
Pattern Formation ◽  
Granular Media ◽  
Large Scale ◽  
High Stress ◽  
Reaction Diffusion ◽  
Fracture Pattern ◽  
Reaction Diffusion Equations ◽  
Three Dimensions ◽  
Localized Deformation

Naturally, deformed rocks commonly contain crack arrays (joints) forming patterns with systematic relationships to the large-scale deformation. Kinematically, joints can be mode-1, -2 or -3 or combinations of these, but there is no overarching theory for the development of the patterns. We develop a model motivated by dislocation pattern formation in metals. The problem is formulated in one dimension in terms of coupled reaction–diffusion equations, based on computer simulations of crack development in deformed granular media with cohesion. The cracks are treated as interacting defects, and the densities of defects diffuse through the rock mass. Of particular importance is the formation of cracks at high stresses associated with force-chain buckling and variants of this configuration; these cracks play the role of ‘inhibitors’ in reaction–diffusion relationships. Cracks forming at lower stresses act as relatively mobile defects. Patterns of localized deformation result from (i) competition between the growth of the density of ‘mobile’ defects and the inhibition of these defects by crack configurations forming at high stress and (ii) the diffusion of damage arising from these two populations each characterized by a different diffusion coefficient. The extension of this work to two and three dimensions is discussed.

scholarly journals Inverse design of microchannel fluid flow networks using Turing pattern dehomogenization

2020 ◽  
Vol 62 (4) ◽  
pp. 2203-2210
Author(s):  
Ercan M. Dede ◽  
Yuqing Zhou ◽  
Tsuyoshi Nomura
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Large Scale ◽  
Fluid Velocity ◽  
Flow Distribution ◽  
Reaction Diffusion ◽  
Optimization Method ◽  
Reaction Diffusion Equations ◽  
Turing Pattern ◽  
Space Filling

Abstract Microchannel reactors are critical in biological plus energy-related applications and require meticulous design of hundreds-to-thousands of fluid flow channels. Such systems commonly comprise intricate space-filling microstructures to control the fluid flow distribution for the reaction process. Traditional flow channel design schemes are intuition-based or utilize analytical rule-based optimization strategies that are oversimplified for large-scale domains of arbitrary geometry. Here, a gradient-based optimization method is proposed, where effective porous media and fluid velocity vector design information is exploited and linked to explicit microchannel parameterizations. Reaction-diffusion equations are then utilized to generate space-filling Turing pattern microchannel flow structures from the porous media field. With this computationally efficient and broadly applicable technique, precise control of fluid flow distribution is demonstrated across large numbers (on the order of hundreds) of microchannels.

The effects of obstacle size on periodic travelling waves in oscillatory reaction–diffusion equations

2007 ◽  
Vol 464 (2090) ◽  
pp. 365-390 ◽  
Author(s):  
Matthew J Smith ◽  
Jonathan A Sherratt ◽  
Nicola J Armstrong
Keyword(s):  
Large Scale ◽  
Order Approximation ◽  
Travelling Waves ◽  
Natural Populations ◽  
Reaction Diffusion ◽  
Field Studies ◽  
Reaction Diffusion Equations ◽  
Infinite Domain ◽  
Predator Prey ◽  
Predator Prey Model

Many natural populations undergo multi-year cycles, and field studies have shown that these can be organized into periodic travelling waves (PTWs). Mathematical studies have shown that large-scale landscape obstacles represent a natural mechanism for wave generation. Here, we investigate how the amplitude and wavelength of the selected waves depend on the obstacle size. We firstly consider a large circular obstacle in an infinite domain for a reaction–diffusion system of ‘ λ – ω ’ type. We use perturbation theory to derive a leading order approximation to the wave generated by the obstacle. This shows the dependence of the wave properties on both parameter values and obstacle size. We find that the limiting values of the amplitude and wavelength are approached algebraically with distance from the obstacle edge, rather than exponentially in the case of a flat boundary. We use our results to predict the properties of waves generated by a large circular obstacle for an oscillatory predator–prey system, via a reduction of the predator–prey model to normal form close to Hopf bifurcation. Our predictions compare well with numerical simulations. We also discuss the implications of these results for wave stability and briefly investigate the effects of obstacles with elliptical geometries.

scholarly journals MULTISCALE MODELING OFPSEUDOMONAS AERUGINOSASWARMING

2011 ◽  
Vol 21 (supp01) ◽  
pp. 939-954 ◽  
Author(s):  
HUIJING DU ◽  
ZHILIANG XU ◽  
JOSHUA D. SHROUT ◽  
MARK ALBER
Keyword(s):  
Thin Film ◽  
Reaction Diffusion ◽  
Multiscale Model ◽  
Liquid Extraction ◽  
Reaction Diffusion Equations ◽  
Wild Type ◽  
Biological Mechanisms ◽  
Self Organized ◽  
Thin Film Equation ◽  
A Cell

Experiments have shown that wild type P. aeruginosa swarms much faster than rhlAB mutants on 0.4% agar concentration surface. These observations imply that development of a liquid thin film is an important component of the self-organized swarming process. A multiscale model is presented in this paper for studying interplay of key hydrodynamical and biological mechanisms involved in the swarming process of P. aeruginosa. This model combines a liquid thin film equation, convection–reaction–diffusion equations and a cell-based stochastic discrete model. Simulations demonstrate how self-organized swarming process based on the microscopic individual bacterial behavior results in complicated fractal type patterns at macroscopic level. It is also shown that quorum sensing mechanism causing rhamnolipid synthesis and resulting liquid extraction from the substrate lead to the fast swarm expansion. Simulations also demonstrate formation of fingers (tendrils) at the edge of a swarm which have been earlier observed in experiments.

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