Existence Of The Magnetorotational Instability

By posing and solving a global axisymmetric eigenvalue problem on an infinite domain with modes vanishing at zero and infinity for a differentially rotating MHD plasma, the conditions for the occurrence of a purely growing low-frequency mode known as the magnetorotational instability (MRI) are mapped. It is shown that the MRI criterion drawn from the "local dispersion relation" is at best inadequate and may even be misleading. The physics of the MRI is rather nuanced. It is dictated by the details of the radial profile of the rotation velocity Omega(r) and not just by the sign and the magnitude of its gradient, Omega'. The salient features of the class of profiles for which the MRI-like eigenmodes may occur are given along with the eigenspectrum. For a variety of other profiles, it is shown that an unstable magnetorotational mode is not a valid eigensolution.Institute for Fusion Studie

Asymmetry-Driven Structure Formation in Pair Plasmas

The nonlinear propagation of electromagnetic waves in pair plasmas, in which the electrostatic potential plays a very important but subdominant role of a "binding glue" is investigated. Several mechanisms for structure formation are investigated, in particular, the "asymmetry" in the initial temperatures of the constituent species. It is shown that the temperature asymmetry leads to a (localizing) nonlinearity that is new and qualitatively different from the ones originating in ambient mass or density difference. The temperature asymmetry driven focusing-defocusing nonlinearity supports stable localized wave structures in 1-3 dimensions, which, for certain parameters, may have flat-top shapes.Comment: 23 pages, 6 figures, introduction revised, edited typos, accepted for publication in Phys. Rev.

Acceleration of Plasma Flows Due to Reverse Dynamo Mechanism

The "reverse-dynamo" mechanism - the amplification/generation of fast plasma flows by micro scale (turbulent) magnetic fields via magneto-fluid coupling is recognized and explored. It is shown that macro-scale magnetic fields and flows are generated simultaneously and proportionately from micro scale fields and flows. The stronger the micro-scale driver, the stronger are the macro-scale products. Stellar and astrophysical applications are suggested.Comment: 16 pages including 3 figures. The Astrophys. J. (accepted); additional material is given for clarification; terminology is change

Modeling of short scale turbulence in the solar wind

The solar wind serves as a laboratory for investigating magnetohydrodynamic turbulence under conditions irreproducible on the terra firma. Here we show that the frame work of Hall magnetohydrodynamics (HMHD), which can support three quadratic invariants and allows nonlinear states to depart fundamentally from the Alfv&#233;nic, is capable of reproducing in the inertial range the three branches of the observed solar wind magnetic fluctuation spectrum - the Kolmogorov branch <i>f</i>^-5/3 steepening to <i>f</i>^-&alpha;₁ with <!-- MATH $alpha_1{simeq}3{-}4$ --> <IMG WIDTH='61' HEIGHT='29' ALIGN='MIDDLE' BORDER='0' src='http://www.nonlin-processes-geophys.net/12/75/2005/npg-12-75-img3.gif' ALT='$alpha_1{simeq}3{-}4$'> on the high frequency side and flattening to <i>f</i>^-1 on the low frequency side. These fluctuations are found to be associated with the nonlinear Hall-MHD Shear Alfv&#233;n waves. The spectrum of the concomitant whistler type fluctuations is very different from the observed one. Perhaps the relatively stronger damping of the whistler fluctuations may cause their unobservability. The issue of equipartition of energy through the so called Alfv&#233;n ratio acquires a new status through its dependence, now, on the spatial scale

Vortex Bubble Formation in Pair Plasmas

It is shown that delocalized vortex solitons in relativistic pair plasmas with small temperature asymmetries can be unstable for intermediate intensities of the background electromagnetic field. Instability leads to the generation of ever-expanding cavitating bubbles in which the electromagnetic fields are zero. The existence of such electromagnetic bubbles is demonstrated by qualitative arguments based on a hydrodynamic analogy, and by numerical solutions of the appropriate Nonlinear Schr\"odinger equation with a saturating nonlinearity.Comment: 4 pages of two-column text, 2 figure

Balancing Bounded Treewidth Circuits

Algorithmic tools for graphs of small treewidth are used to address questions in complexity theory. For both arithmetic and Boolean circuits, it is shown that any circuit of size $n^{O(1)}$ and treewidth $O(\log^i n)$ can be simulated by a circuit of width $O(\log^{i+1} n)$ and size $n^c$, where $c = O(1)$, if $i=0$, and $c=O(\log \log n)$ otherwise. For our main construction, we prove that multiplicatively disjoint arithmetic circuits of size $n^{O(1)}$ and treewidth $k$ can be simulated by bounded fan-in arithmetic formulas of depth $O(k^2\log n)$. From this we derive the analogous statement for syntactically multilinear arithmetic circuits, which strengthens a theorem of Mahajan and Rao. As another application, we derive that constant width arithmetic circuits of size $n^{O(1)}$ can be balanced to depth $O(\log n)$, provided certain restrictions are made on the use of iterated multiplication. Also from our main construction, we derive that Boolean bounded fan-in circuits of size $n^{O(1)}$ and treewidth $k$ can be simulated by bounded fan-in formulas of depth $O(k^2\log n)$. This strengthens in the non-uniform setting the known inclusion that $SC^0 \subseteq NC^1$. Finally, we apply our construction to show that {\sc reachability} for directed graphs of bounded treewidth is in $LogDCFL$