# Difference between revisions of "Applied/ACMS/absS13"

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=== Andrej Zlatoš (UW) === | === Andrej Zlatoš (UW) === | ||

− | + | We study fine details of spreading of reactive processes (e.g., combustion) in multi-dimensional inhomogeneous media. One often observes a transition from one stable state (e.g., unburned fuel) to another (e.g., burned fuel) to happen on short spatial as well as temporal scales. We demonstrate that this phenomenon also occurs in the simplest model for reactive processes, reaction-diffusion equations with ignition-type reaction functions, under very general assumptions. | |

+ | |||

+ | Specifically, we show that in up to three spatial dimensions, the width (both in space and time) of the zone where reaction occurs stays uniformly bounded in time for some fairly general classes of initial data, and this bound even becomes independent of the initial datum after an initial time interval. Such results have recently been obtained in one spatial dimension but were unknown in higher dimensions. As one indication of the added difficulties, we also show that three dimensions is indeed the borderline case, and the result is false for general inhomogeneous media in four and more dimensions. | ||

=== Matthew Johnston (UW) === | === Matthew Johnston (UW) === |

## Revision as of 22:12, 4 March 2013

## Contents

# ACMS Abstracts: Spring 2013

### Arnd Scheel (Minnesota)

Motivated by precipitation patterns such as Liesegang rings, we discuss patterns formed in the wake of moving fronts. It turns out that strikingly simple kinetic mechanisms can lead to a plethora of patterns, from simple bands and stripes to spirals and helices. We'll discuss a number of mathematical problems that arise when one tries to predict which wavenumbers and what type of pattern would arise in the wake of fronts. Applications include elementary chemistry, patterns in bacteria colonies, and self-assembly of nano-scale textures.

### Kourosh Shoele (RE Vision Consulting)

Studying the interaction between fluid and structure is a fundamental step in understanding the underpinnings of many engineering and physical phenomena, from energy harvesting to biolocomotion of insects, birds and fishes. The complex nature of these interactions makes the design of computational, experimental, and analytical techniques for modeling such problems challenging. Here I discuss new procedures, both in potential flow and viscous flow, for studying the interactions of a flexible structure with a flow. In particular, I will focus on two particular phenomena, the flow interaction with skeleton-reinforced fish fins and the extraction of ocean energy through oscillating systems.

### Andrej Zlatoš (UW)

We study fine details of spreading of reactive processes (e.g., combustion) in multi-dimensional inhomogeneous media. One often observes a transition from one stable state (e.g., unburned fuel) to another (e.g., burned fuel) to happen on short spatial as well as temporal scales. We demonstrate that this phenomenon also occurs in the simplest model for reactive processes, reaction-diffusion equations with ignition-type reaction functions, under very general assumptions.

Specifically, we show that in up to three spatial dimensions, the width (both in space and time) of the zone where reaction occurs stays uniformly bounded in time for some fairly general classes of initial data, and this bound even becomes independent of the initial datum after an initial time interval. Such results have recently been obtained in one spatial dimension but were unknown in higher dimensions. As one indication of the added difficulties, we also show that three dimensions is indeed the borderline case, and the result is false for general inhomogeneous media in four and more dimensions.

### Matthew Johnston (UW)

TBA

### Nigel Boston (UW)

TBA

### Cary Forest (UW)

*Stirring Magnetized Plasma*

Recently, a new concept for stirring a hot (T=100000 C), unmagnetized plasma has been demonstrated, making it possible to study the Dynamos and the Magnetorotational Instability (MRI) for the first time in a laboratory plasma. In the Plasma Couette Experiment, plasma is conﬁned by a cylindrical, axisymmetric multicusp magnetic field. The field vanishes rapidly away from the boundaries, leaving a large, unmagnetized plasma in the bulk. Azimuthal flows (6 km/s) are driven with JxB torque using biased, heated filaments located at a single toroidal position at the boundary. Measurements show that momentum couples viscously from the magnetized edge to the unmagnetized core, and that the flow is axisymmetric. In order for the toroidal velocity to couple inward, the collisional ion viscosity must overcome the drag due to ion-neutral collisions. Flow speeds can be adjusted by simply increasing the bias voltage of the electrodes. When flow is driven only from the outer boundary, the plasma rotates as a solid-body and the MRI is stable. However, the addition of electrodes at the inner boundary enables us to drive the sheared flow necessary for destabilizing the MRI. This experiment has already achieved magnetic Reynolds numbers of Rm~50 and magnetic Prandtl numbers of Pm ~0.3–6, which are approaching regimes shown to excite the MRI in local linear analysis and global Hall-MHD numerical simulations. Experiments characterizing the MRI will compare the onset threshold to theoretical and numerical predictions, look for altered velocity profiles due to momentum transport during nonlinear saturation, and identify two fluid effects expected to arise from the Hall term and plasma-neutral interactions (important in protoplanetary accretion disks).

While these experiments have been carried out, have also been constructing a much larger (3 m diameter) dynamo experiment based on a Von Kármán like flow in a sphere that should be capable of generating plasmas with Rm~1500. Several different scenarios have been investigated numerically to show that the experiment has a very good chance of being a dynamo, including steady von Kármán flow that generates an equatorial dipole, and a new Galloway-Proctor like flow that uses time dependent boundary conditions to generate smooth, but chaotic flows that give a fast dynamo. The experiment is now constructed and will be described in this talk. Initial results on plasma formation will be presented.

### Shanan Peters (UW)

TBA

### Shreyas Mandre (Brown)

TBA

### Ben Recht (UW)

TBA

### Silas Alben (Michigan)

TBA