The Non-Linear Growth of the Magnetic Rayleigh-Taylor Instability

This work examines the effect of the embedded magnetic field strength on the non-linear development of the magnetic Rayleigh-Taylor Instability (RTI) (with a field-aligned interface) in an ideal gas close to the incompressible limit in three dimensions. Numerical experiments are conducted in a domain sufficiently large so as to allow the predicted critical modes to develop in a physically realistic manner. The ratio between gravity, which drives the instability in this case (as well as in several of the corresponding observations), and magnetic field strength is taken up to a ratio which accurately reflects that of observed astrophysical plasma, in order to allow comparison between the results of the simulations and the observational data which served as inspiration for this work. This study finds reduced non-linear growth of the rising bubbles of the RTI for stronger magnetic fields, and that this is directly due to the change in magnetic field strength, rather than the indirect effect of altering characteristic length scales with respect to domain size. By examining the growth of the falling spikes, the growth rate appears to be enhanced for the strongest magnetic field strengths, suggesting that rather than affecting the development of the system as a whole, increased magnetic field strengths in fact introduce an asymmetry to the system. Further investigation of this effect also revealed that the greater this asymmetry, the less efficiently the gravitational energy is released. By better understanding the under-studied regime of such a major phenomenon in astrophysics, deeper explanations for observations may be sought, and this work illustrates that the strength of magnetic fields in astrophysical plasmas influences observed RTI in subtle and complex ways.Comment: Accepted for publication by A&A. 10 pages, 9 figure

Investigating the Dynamics and Density Evolution of Returning Plasma Blobs from the 2011 June 7 Eruption

This work examines infalling matter following an enormous Coronal Mass Ejection (CME) on 2011 June 7. The material formed discrete concentrations, or blobs, in the corona and fell back to the surface, appearing as dark clouds against the bright corona. In this work we examined the density and dynamic evolution of these blobs in order to formally assess the intriguing morphology displayed throughout their descent. The blobs were studied in five wavelengths (94, 131, 171, 193 and 211 \AA) using the Solar Dynamics Observatory Atmospheric Imaging Assembly (SDO/AIA), comparing background emission to attenuated emission as a function of wavelength to calculate column densities across the descent of four separate blobs. We found the material to have a column density of hydrogen of approximately 2 $\times$ 10$^{19}$ cm$^{-2}$, which is comparable with typical pre-eruption filament column densities. Repeated splitting of the returning material is seen in a manner consistent with the Rayleigh-Taylor instability. Furthermore, the observed distribution of density and its evolution are also a signature of this instability. By approximating the three-dimensional geometry (with data from STEREO-A), volumetric densities were found to be approximately 2 $\times$ 10$^{-14}$ g cm$^{-3}$, and this, along with observed dominant length-scales of the instability, was used to infer a magnetic field of the order 1 G associated with the descending blobs.Comment: 9 pages, 13 figures, accepted for publication in Ap

2nd Annual Computer & Technology Law Institute

Materials from the 2nd Annual Computer & Technology Law Institute held by UK/CLE in March 2000

The roots of romantic cognitivism:(post) Kantian intellectual intuition and the unity of creation and discovery

During the romantic period, various authors expressed the belief that through creativity, we can directly access truth. To modern ears, this claim sounds strange. In this paper, I attempt to render the position comprehensible, and to show how it came to seem plausible to the romantics. I begin by offering examples of this position as found in the work of the British romantics. Each thinks that the deepest knowledge can only be gained by an act of creativity. I suggest the belief should be seen in the context of the post-Kantian embrace of “intellectual intuition.” Unresolved tensions in Kant's philosophy had encouraged a belief that creation and discovery were not distinct categories. The post-Kantians held that in certain cases of knowledge (for Fichte, knowledge of self and world; for Schelling, knowledge of the Absolute) the distinction between discovering a truth and creating that truth dissolves. In this context, the cognitive role assigned to acts of creativity is not without its own appeal

7 june 2011 eruption/fallback

<p>304 Å</p

Blobs

<p>171 Å images of the blob analysed and background frame used; calculated column densities and G values of blob.</p

Chaotic Evolution via Generalized Probabilistic Automata (Probabilistic Arrays)

briefly the conventional probabilistic model in automata theory; the main objective is to observe that the corresponding distributional transformations are linear and have simple asymptotics under iteration. For a time-sequential finite-state probabilistic machine which is autonomous (free of inputs, or with only a constant clocked-time input), the only significant quantities are the states, the state-to-state (conditional) transition probabilities, and the (unconditional) state-occupancy probabilities. In this setting, a machine with n states is defined by specifying its one-step transition probabilities a ij , i, j = 1, 2, . . . , n; the interpretation is that a ij is the numerical label on the directed edge from state #i to state #j in the state graph, or the ij entry 1 The contribution of the first author was sup

A Mathematical Model of Cardiac Action Potential: Application to Wave Propagation

of the Dissertation A Mathematical Model of Cardiac Action Potential: Application to Wave Propagation by Mikhail Karpoukhin Doctor of Philosophy in Computer Science University of California, Los Angeles, 1996 Professor Walter J. Karplus, Co-Chair Professor Boris Y. Kogan, Co-Chair Heart fibrillation, the main reason for sudden cardiac death, can be studied on the computer using mathematical models of action potential propagation. Full physiological models are difficult to use due to their complexity. Existing simplified models suffer from a number of drawbacks. In this research existing simplified models are studied to find out their advantages and disadvantages. This is accomplished by comparative analysis, using a developed common approach, of the three most popular simplified models: FitzHugh-Nagumo, Van Capelle and Karma. As a result, a new method of simplified model synthesis is developed, and a new third-order model is proposed which correctly reproduces the shape of action pot..