1,157,018 research outputs found
Thick GaN film stress-induced self-separation
Cracking of thick GaN films on sapphire substrates during the cooling down
after the growth was studied. The cracking was suppressed by increasing the
film-to-substrate thickness ratio and by using an intermediate carbon buffer
layer, that reduced the binding energy between the GaN film and the substrate.
Wafer-scale self-separation of thick GaN films has been demonstrated.Comment: Published in Proceedings of the 2019 IEEE Conference of Russian Young
Researchers in Electrical and Electronic Engineering (EIConRus
On the equality of Hausdorff measure and Hausdorff content
We are interested in situations where the Hausdorff measure and Hausdorff
content of a set are equal in the critical dimension. Our main result shows
that this equality holds for any subset of a self-similar set corresponding to
a nontrivial cylinder of an irreducible subshift of finite type, and thus also
for any self-similar or graph-directed self-similar set, regardless of
separation conditions. The main tool in the proof is an exhaustion lemma for
Hausdorff measure based on the Vitali Covering Theorem.
We also give several examples showing that one cannot hope for the equality
to hold in general if one moves in a number of the natural directions away from
`self-similar'. For example, it fails in general for self-conformal sets,
self-affine sets and Julia sets. We also give applications of our results
concerning Ahlfors regularity. Finally we consider an analogous version of the
problem for packing measure. In this case we need the strong separation
condition and can only prove that the packing measure and -approximate
packing pre-measure coincide for sufficiently small .Comment: 21 pages. This version includes applications concerning the weak
separation property and Ahlfors regularity. To appear in Journal of Fractal
Geometr
Hierarchical Self-Assembly of Halogen-Bonded Block Copolymer Complexes into Upright Cylindrical Domains
Self-assembly of block copolymers into well-defined, ordered arrangements of chemically distinct domains is a reliable strategy for preparing tailored nanostructures. Microphase separation results from the system, minimizing repulsive interactions between dissimilar blocks and maximizing attractive interactions between similar blocks. Supramolecular methods have also achieved this separation by introducing small-molecule additives binding specifically to one block by noncovalent interactions. Here, we use halogen bonding as a supramolecular tool that directs the hierarchical self-assembly of low-molecular-weight perfluorinated molecules and diblock copolymers. Microphase separation results in a lamellar-within-cylindrical arrangement and promotes upright cylindrical alignment in films upon rapid casting and without further annealing. Such cylindrical domains with internal lamellar self-assemblies can be cleaved by solvent treatment of bulk films, resulting in separated and segmented cylindrical micelles stabilized by halogen-bond-based supramolecular crosslinks. These features, alongside the reversible nature of halogen bonding, provide a robust modular approach for nanofabricatio
Solution of the local field equations for self-generated glasses
We present a self-consistent local approach to self generated glassiness
which is based on the concept of the dynamical mean field theory to many body
systems. Using a replica approach to self generated glassiness, we map the
problem onto an effective local problem which can be solved exactly. Applying
the approach to the Brazovskii-model, relevant to a large class of systems with
frustrated micro-phase separation, we are able to solve the self-consistent
local theory without using additional approximations. We demonstrate that a
glassy state found earlier in this model is generic and does not arise from the
use of perturbative approximations. In addition we demonstrate that the glassy
state depends strongly on the strength of the frustrated phase separation in
that model.Comment: 11 pages, 3 figure
On the Assouad dimension of self-similar sets with overlaps
It is known that, unlike the Hausdorff dimension, the Assouad dimension of a
self-similar set can exceed the similarity dimension if there are overlaps in
the construction. Our main result is the following precise dichotomy for
self-similar sets in the line: either the \emph{weak separation property} is
satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the
\emph{weak separation property} is not satisfied, in which case the Assouad
dimension is maximal (equal to one).
In the first case we prove that the self-similar set is Ahlfors regular, and
in the second case we use the fact that if the \emph{weak separation property}
is not satisfied, one can approximate the identity arbitrarily well in the
group generated by the similarity mappings, and this allows us to build a
\emph{weak tangent} that contains an interval. We also obtain results in higher
dimensions and provide illustrative examples showing that the
`equality/maximal' dichotomy does not extend to this setting.Comment: 24 pages, 2 figure
- …