17,778 research outputs found
Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations
Several recent methods used to analyze asymptotic stability of
delay-differential equations (DDEs) involve determining the eigenvalues of a
matrix, a matrix pencil or a matrix polynomial constructed by Kronecker
products. Despite some similarities between the different types of these
so-called matrix pencil methods, the general ideas used as well as the proofs
differ considerably. Moreover, the available theory hardly reveals the
relations between the different methods.
In this work, a different derivation of various matrix pencil methods is
presented using a unifying framework of a new type of eigenvalue problem: the
polynomial two-parameter eigenvalue problem, of which the quadratic
two-parameter eigenvalue problem is a special case. This framework makes it
possible to establish relations between various seemingly different methods and
provides further insight in the theory of matrix pencil methods.
We also recognize a few new matrix pencil variants to determine DDE
stability.
Finally, the recognition of the new types of eigenvalue problem opens a door
to efficient computation of DDE stability
Towards Fractional Gradient Elasticity
An extension of gradient elasticity through the inclusion of spatial
derivatives of fractional order to describe power-law type of non-locality is
discussed. Two phenomenological possibilities are explored. The first is based
on the Caputo fractional derivatives in one-dimension. The second involves the
Riesz fractional derivative in three-dimensions. Explicit solutions of the
corresponding fractional differential equations are obtained in both cases. In
the first case it is shown that stress equilibrium in a Caputo elastic bar
requires the existence of a non-zero internal body force to equilibrate it. In
the second case, it is shown that in a Riesz type gradient elastic continuum
under the action of a point load, the displacement may or may not be singular
depending on the order of the fractional derivative assumed.Comment: 10 pages, LaTe
Entomopathogenic nematodes for biological control of codling moth
Entomopathogenic nematodes are often found naturally infecting codling moth larvae. The
effect of an autumn treatment with S. feltiae on the fruit damage in the following summer
was evaluated by treating 4 different apple orchards in October 2004 and 2005 at
application rates of 3.75; 2 and 1.5 billion nematodes in 4000 l / ha. In three of the treated
orchards, one treated with 3.75x109 nematodes/ha the other two treated with 2e9
nematode/ha, reduction in fruit damage was around 50%. In the most heavily infested
orchard, which was treated with 1.5x109 nematode/ha only 33% reduction in fruit damage
was achieved. Compared to previous studies, this was the first assessing the effect on the
fruit damage in the summer following the treatment rather than assessing the mortality of
sentinel larvae fixed to the treated tree trunks
- …