12,821 research outputs found
Moduli spaces of vector bundles on a singular rational ruled surface
We study moduli spaces parametrizing slope semistable vector
bundles of rank and fixed Chern classes 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 is rational as a variety defined over .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
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