Moduli spaces of vector bundles on a singular rational ruled surface

We study moduli spaces $M_X(r,c_1,c_2)$ parametrizing slope semistable vector bundles of rank $r$ and fixed Chern classes $c_1, c_2$ on a ruled surface whose base is a rational nodal curve. We show that under certain conditions, these moduli spaces are irreducible, smooth and rational (when non-empty). We also prove that they are non-empty in some cases. We show that for a rational ruled surface defined over real numbers, the moduli space $M_X(r,c_1,c_2)$ is rational as a variety defined over $\mathbb R$.Comment: Final versio

Chirped dissipative solitons of the complex cubic-quintic nonlinear Ginzburg-Landau equation

Approximate analytical chirped solitary pulse (chirped dissipative soliton) solutions of the one-dimensional complex cubic-quintic nonlinear Ginzburg-Landau equation are obtained. These solutions are stable and highly-accurate under condition of domination of a normal dispersion over a spectral dissipation. The parametric space of the solitons is three-dimensional, that makes theirs to be easily traceable within a whole range of the equation parameters. Scaling properties of the chirped dissipative solitons are highly interesting for applications in the field of high-energy ultrafast laser physics.Comment: 20 pages, 12 figures, the mathematical apparatus is presented in detail in http://info.tuwien.ac.at/kalashnikov/NCGLE2.htm

The Effect of Configurational Entropy of Mixing on the Design and Development of Novel Materials

The configurational entropy of mixing (∆Smix) has a profound influence on the stability of various phases in different materials at intermediate and high temperatures. Recently, it has been observed that ∆Smix can be used as an important tool to design novel multicomponent materials with fascinating properties. ∆Smix affects ∆Gmix and tends to stabilize the FCC/ BCC/HCP multicomponent solid solutions over brittle phases including compounds. This opens up vistas to design novel solid solution-based materials with improved mechanical, functional properties. Accordingly, multicomponent and multiprinciple alloys were developed in 2004, and subsequently, novel ceramics and polymers have been designed. The present paper is intended to provide an insight into the role of ∆Smix to design novel metallic, ceramic as well as polymeric materials

The Complex Time WKB Approximation And Particle Production

The complex time WKB (CWKB) approximation has been an effective technique to understand particle production in curved as well as in flat spacetime. Earlier we obtained the standard results on particle production in time dependent gauge in various curved spacetime. In the present work we generalize the technique of CWKB to the equivalent problems in space dependent gauge. Using CWKB, we first obtain the gauge invariant result for particle production in Minkowski spacetime in strong electric field. We then carry out particle production in de-Sitter spacetime in space dependent gauge and obtain the same result that we obtained earlier in time dependent gauge. The results obtained for de-Sitter spacetime has a obvious extension to particle production in black hole spacetime. It is found that the origin of Planckian spectrum is due to repeated reflections between the turning points. As mentioned earlier, it is now explicitly shown that particle production is accompanied by rotation of currents.Comment: 12 pages, Revte