4,874 research outputs found
Covariant Poisson equation with compact Lie algebras
The covariant Poisson equation for Lie algebra-valued mappings defined in
3-dimensional Euclidean space is studied using functional analytic methods.
Weighted covariant Sobolev spaces are defined and used to derive sufficient
conditions for the existence and smoothness of solutions to the covariant
Poisson equation. These conditions require, apart from suitable continuity,
appropriate local integrability of the gauge potentials and global weighted
integrability of the curvature form and the source. The possibility of
nontrivial asymptotic behaviour of a solution is also considered. As a
by-product, weighted covariant generalisations of Sobolev embeddings are
established.Comment: 31 pages, LaTeX2
Paschen\u27s Law for a Hollow Cathode Discharge
An expression for the breakdown voltage of a one‐dimensional hollow cathode discharge has been derived. The breakdown condition which corresponds to Paschen’s law contains, in addition to the first Townsend coefficient, and the secondary electron emission coefficient two parameters which characterize the reflecting action of the electric field and the lifetime of the electrons in the discharge. The breakdown voltage for a hollow cathode discharge in helium was calculated and compared to that of a glow discharge operating under similar conditions
Contribution to the laser welding of wrought and spray-compacted aluminum alloys and the impact of the alloy composition on the welding microstructure
Critical behavior of colloid-polymer mixtures in random porous media
We show that the critical behavior of a colloid-polymer mixture inside a
random porous matrix of quenched hard spheres belongs to the universality class
of the random-field Ising model. We also demonstrate that random-field effects
in colloid-polymer mixtures are surprisingly strong. This makes these systems
attractive candidates to study random-field behavior experimentally.Comment: 4 pages, 3 figures, to appear in Phys. Rev. Let
Amplification of different marker sequences for identification of Agrobacterium vitis strains
Research Not
Structural and Magnetic Dynamics in the Magnetic Shape Memory Alloy NiMnGa
Magnetic shape memory Heusler alloys are multiferroics stabilized by the
correlations between electronic, magnetic and structural order. To study these
correlations we use time resolved x-ray diffraction and magneto-optical Kerr
effect experiments to measure the laser induced dynamics in a Heusler alloy
NiMnGa film and reveal a set of timescales intrinsic to the system. We
observe a coherent phonon which we identify as the amplitudon of the modulated
structure and an ultrafast phase transition leading to a quenching of the
incommensurate modulation within 300~fs with a recovery time of a few ps. The
thermally driven martensitic transition to the high temperature cubic phase
proceeds via nucleation within a few ps and domain growth limited by the speed
of sound. The demagnetization time is 320~fs, which is comparable to the
quenching of the structural modulation.Comment: 5 pages, 3 figures. Supplementary materials 5 pages, 5 figure
Asymptotically free scalar curvature-ghost coupling in Quantum Einstein Gravity
We consider the asymptotic-safety scenario for quantum gravity which
constructs a non-perturbatively renormalisable quantum gravity theory with the
help of the functional renormalisation group. We verify the existence of a
non-Gaussian fixed point and include a running curvature-ghost coupling as a
first step towards the flow of the ghost sector of the theory. We find that the
scalar curvature-ghost coupling is asymptotically free and RG relevant in the
ultraviolet. Most importantly, the property of asymptotic safety discovered so
far within the Einstein-Hilbert truncation and beyond remains stable under the
inclusion of the ghost flow.Comment: 8 pages, 3 figures, RevTe
Evolutionary multi-stage financial scenario tree generation
Multi-stage financial decision optimization under uncertainty depends on a
careful numerical approximation of the underlying stochastic process, which
describes the future returns of the selected assets or asset categories.
Various approaches towards an optimal generation of discrete-time,
discrete-state approximations (represented as scenario trees) have been
suggested in the literature. In this paper, a new evolutionary algorithm to
create scenario trees for multi-stage financial optimization models will be
presented. Numerical results and implementation details conclude the paper
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