Quadrupole Instabilities of Relativistic Rotating Membranes

We generalize recent study of the stability of isotropic (spherical) rotating membranes to the anisotropic ellipsoidal membrane. We find that while the stability persists for deformations of spin $l=1$, the quadrupole and higher spin deformations ($l\geq 2$) lead to instabilities. We find the relevant instability modes and the corresponding eigenvalues. These indicate that the ellipsoidal rotating membranes generically decay into finger-like configurations.Comment: 5 pages, 1 figur

Rotating Toroidal Branes in Supermembrane and Matrix Theory

In the lightcone frame, where the supermembrane theory and the Matrix model are strikingly similar, the equations of motion admit an elegant complexification in even dimensional spaces. Although the explicit rotational symmetry of the target space is lost, the remaining unitary symmetries apart from providing a simple and unifying description of all known solutions suggest new ones for rotating spherical and toroidal membranes. In this framework the angular momentum is represented by U(1) charges which balance the nonlinear attractive forces of the membrane. We examine in detail a six dimensional rotating toroidal membrane solution which lives in a 3-torus, $T^3$ and admits stable radial modes. In Matrix Theory it corresponds to a toroidal N-$D_{0}$ brane bound state. We demonstrate its existence and discuss its radial stability.Comment: 7 pages, revte

Production of large volume discharges in water and their industrial applications

Plasmas with a large volume have been produced in low pressure gases using the diffusion and flow of plasmas. In liquid, arc discharge plasmas have been produced for the basic researches and some applications. The volume of the arc plasma is limited. Here, the production of large volume discharge plasmas in water and their industrial applications are described