259 research outputs found
Random attractors for stochastic evolution equations driven by fractional Brownian motion
The main goal of this article is to prove the existence of a random attractor
for a stochastic evolution equation driven by a fractional Brownian motion with
. We would like to emphasize that we do not use the usual
cohomology method, consisting of transforming the stochastic equation into a
random one, but we deal directly with the stochastic equation. In particular,
in order to get adequate a priori estimates of the solution needed for the
existence of an absorbing ball, we will introduce stopping times to control the
size of the noise. In a first part of this article we shall obtain the
existence of a pullback attractor for the non-autonomous dynamical system
generated by the pathwise mild solution of an nonlinear infinite-dimensional
evolution equation with non--trivial H\"older continuous driving function. In a
second part, we shall consider the random setup: stochastic equations having as
driving process a fractional Brownian motion with . Under a
smallness condition for that noise we will show the existence and uniqueness of
a random attractor for the stochastic evolution equation
Mikrochemische Zinkbestimmung im Serum und Urin
Peer Reviewe
The random case of Conley's theorem
The well-known Conley's theorem states that the complement of chain recurrent
set equals the union of all connecting orbits of the flow on the compact
metric space , i.e. , where
denotes the chain recurrent set of , stands for
an attractor and is the basin determined by . In this paper we show
that by appropriately selecting the definition of random attractor, in fact we
define a random local attractor to be the -limit set of some random
pre-attractor surrounding it, and by considering appropriate measurability, in
fact we also consider the universal -algebra -measurability besides -measurability, we are able to obtain
the random case of Conley's theorem.Comment: 15 page
Calcite distribution and orientation in the tergite exocuticle of the isopods porcellio scaber and armadillidium vulgare (Oniscidea, Crustacea) - A combined FE-SEM, polarized SCm-RSI and EBSD study
The crustacean cuticle is a bio-composite consisting of hierarchically organized chitin-protein fibres, reinforced with calcite, amorphous calcium carbonate and phosphates. Comparative studies revealed that the structure and composition of tergite cuticle of terrestrial isopods is adapted to the habitat of the animals, and to their behavioural patterns to avoid predation. In this contribution we use FE-SEM, polarized SCm-RSI and EBSD to investigate micro- and nano-patterns of mineral phase distribution and crystal orientation within the tergite cuticle of the two terrestrial isopod species Armadillidium vulgare and Porcellio scaber. The results show that the proximal regions of the exocuticle contain both calcite and ACC, with ACC located within the pore canals. Calcite forms hierarchically organised mesocrystalline aggregates of similar crystallographic orientation. Surprisingly, c-axis orientation preference is horizontal in regard to the local cuticle surface for both species, in contrast to mollusc and brachiopod shell structures in which the c-axis is always perpendicular to the shell surface. The overall sharpness of calcite crystal orientation is weak compared to that of mollusc shells. However, there are considerable differences in texture sharpness between the two isopod species. In the thick cuticle of the slow-walking A. vulgare calcite is more randomly oriented resulting in more isotropic mechanical properties of the cuticle. In contrast, the rather thin and more flexible cuticle of the fast- running P. scaber texture sharpness is stronger with a preference of c-axis orientation being parallel to the bilateral symmetry-plane of the animal, leading to more anisotropic mechanical properties of the cuticle. These differences may represent adaptations to different external and/or internal mechanical loads the cuticle has to resist during predatory attempts
Smooth stable and unstable manifolds for stochastic partial differential equations
Invariant manifolds are fundamental tools for describing and understanding
nonlinear dynamics. In this paper, we present a theory of stable and unstable
manifolds for infinite dimensional random dynamical systems generated by a
class of stochastic partial differential equations. We first show the existence
of Lipschitz continuous stable and unstable manifolds by the Lyapunov-Perron's
method. Then, we prove the smoothness of these invariant manifolds
Random attractors for degenerate stochastic partial differential equations
We prove the existence of random attractors for a large class of degenerate
stochastic partial differential equations (SPDE) perturbed by joint additive
Wiener noise and real, linear multiplicative Brownian noise, assuming only the
standard assumptions of the variational approach to SPDE with compact
embeddings in the associated Gelfand triple. This allows spatially much rougher
noise than in known results. The approach is based on a construction of
strictly stationary solutions to related strongly monotone SPDE. Applications
include stochastic generalized porous media equations, stochastic generalized
degenerate p-Laplace equations and stochastic reaction diffusion equations. For
perturbed, degenerate p-Laplace equations we prove that the deterministic,
infinite dimensional attractor collapses to a single random point if enough
noise is added.Comment: 34 pages; The final publication is available at
http://link.springer.com/article/10.1007%2Fs10884-013-9294-
The random case of Conley's theorem: III. Random semiflow case and Morse decomposition
In the first part of this paper, we generalize the results of the author
\cite{Liu,Liu2} from the random flow case to the random semiflow case, i.e. we
obtain Conley decomposition theorem for infinite dimensional random dynamical
systems. In the second part, by introducing the backward orbit for random
semiflow, we are able to decompose invariant random compact set (e.g. global
random attractor) into random Morse sets and connecting orbits between them,
which generalizes the Morse decomposition of invariant sets originated from
Conley \cite{Con} to the random semiflow setting and gives the positive answer
to an open problem put forward by Caraballo and Langa \cite{CL}.Comment: 21 pages, no figur
Sea-land transitions in isopods: pattern of symbiont distribution in two species of intertidal isopods Ligia pallasii and Ligia occidentalis in the Eastern Pacific
Studies of microbial associations of intertidal isopods in the primitive genus Ligia (Oniscidea, Isopoda) can help our understanding of the formation of symbioses during sea-land transitions, as terrestrial Oniscidean isopods have previously been found to house symbionts in their hepatopancreas. Ligia pallasii and Ligia occidentalis co-occur in the high intertidal zone along the Eastern Pacific with a large zone of range overlap and both species showing patchy distributions. In 16S rRNA clone libraries mycoplasma-like bacteria (Firmicutes), related to symbionts described from terrestrial isopods, were the most common bacteria present in both host species. There was greater overall microbial diversity in Ligia pallasii compared with L. occidentalis. Populations of both Ligia species along an extensive area of the eastern Pacific coastline were screened for the presence of mycoplasma-like symbionts with symbiont-specific primers. Symbionts were present in all host populations from both species but not in all individuals. Phylogenetically, symbionts of intertidal isopods cluster together. Host habitat, in addition to host phylogeny appears to influence the phylogenetic relation of symbionts
- …