6,767 research outputs found
Blister patterns and energy minimization in compressed thin films on compliant substrates
This paper is motivated by the complex blister patterns sometimes seen in
thin elastic films on thick, compliant substrates. These patterns are often
induced by an elastic misfit which compresses the film. Blistering permits the
film to expand locally, reducing the elastic energy of the system. It is
natural to ask: what is the minimum elastic energy achievable by blistering on
a fixed area fraction of the substrate? This is a variational problem involving
both the {\it elastic deformation} of the film and substrate and the {\it
geometry} of the blistered region. It involves three small parameters: the {\it
nondimensionalized thickness} of the film, the {\it compliance ratio} of the
film/substrate pair and the {\it mismatch strain}. In formulating the problem,
we use a small-slope (F\"oppl-von K\'arm\'an) approximation for the elastic
energy of the film, and a local approximation for the elastic energy of the
substrate.
For a 1D version of the problem, we obtain "matching" upper and lower bounds
on the minimum energy, in the sense that both bounds have the same scaling
behavior with respect to the small parameters. For a 2D version of the problem,
our results are less complete. Our upper and lower bounds only "match" in their
scaling with respect to the nondimensionalized thickness, not in the dependence
on the compliance ratio and the mismatch strain. The upper bound considers a 2D
lattice of blisters, and uses ideas from the literature on the folding or
"crumpling" of a confined elastic sheet. Our main 2D result is that in a
certain parameter regime, the elastic energy of this lattice is significantly
lower than that of a few large blisters
The coarsening of folds in hanging drapes
We consider the elastic energy of a hanging drape -- a thin elastic sheet,
pulled down by the force of gravity, with fine-scale folding at the top that
achieves approximately uniform confinement. This example of energy-driven
pattern formation in a thin elastic sheet is of particular interest because the
length scale of folding varies with height. We focus on how the minimum elastic
energy depends on the physical parameters. As the sheet thickness vanishes, the
limiting energy is due to the gravitational force and is relatively easy to
understand. Our main accomplishment is to identify the "scaling law" of the
correction due to positive thickness. We do this by (i) proving an upper bound,
by considering the energies of several constructions and taking the best; (ii)
proving an ansatz-free lower bound, which agrees with the upper bound up to a
parameter-independent prefactor. The coarsening of folds in hanging drapes has
also been considered in the recent physics literature, using a self-similar
construction whose basic cell has been called a "wrinklon." Our results
complement and extend that work, by showing that self-similar coarsening
achieves the optimal scaling law in a certain parameter regime, and by showing
that other constructions (involving lateral spreading of the sheet) do better
in other regions of parameter space. Our analysis uses a geometrically linear
F\"{o}ppl-von K\'{a}rm\'{a}n model for the elastic energy, and is restricted to
the case when Poisson's ratio is zero.Comment: 34 page
Quantal Density Functional Theory of Degenerate States
The treatment of degenerate states within Kohn-Sham density functional theory
(KS-DFT) is a problem of longstanding interest. We propose a solution to this
mapping from the interacting degenerate system to that of the noninteracting
fermion model whereby the equivalent density and energy are obtained via the
unifying physical framework of quantal density functional theory (Q-DFT). We
describe the Q-DFT of \textit{both} ground and excited degenerate states, and
for the cases of \textit{both} pure state and ensemble v-representable
densities. This then further provides a rigorous physical interpretation of the
density and bidensity energy functionals, and of their functional derivatives,
of the corresponding KS-DFT. We conclude with examples of the mappings within
Q-DFT.Comment: 10 pages. minor changes made. to appear in PR
Spectrometer for Hard X-Ray Free Electron Laser Based on Diffraction Focusing
X-ray free electron lasers (XFELs) generate sequences of ultra-short,
spatially coherent pulses of x-ray radiation. We propose the diffraction
focusing spectrometer (DFS), which is able to measure the whole energy spectrum
of the radiation of a single XFEL pulse with an energy resolution of . This is much better than for most modern x-ray
spectrometers. Such resolution allows one to resolve the fine spectral
structure of the XFEL pulse. The effect of diffraction focusing occurs in a
single crystal plate due to dynamical scattering, and is similar to focusing in
a Pendry lens made from the metamaterial with a negative refraction index. Such
a spectrometer is easier to operate than those based on bent crystals. We show
that the DFS can be used in a wide energy range from 5 keV to 20 keV.Comment: 9 pages, 8 figures, 2 table
Lattice deformations at martensite-martensite interfaces in Ni-Al
The atomic configurations at macrotwin interfaces between microtwinned martensite plates in material are investigated using high resolution transmission electron microscopy (HRTEM). The observed structures are interpreted in view of possible formation mechanisms of these interfaces. A distinction is made between cases in which the microtwins, originating from mutually perpendicular \{110\} austenite planes, enclose a final angle larger or smaller than , measured over the boundary. Two different configurations, one with crossing microtwins and the other with ending microtwins producing a step configuration are described. The latter is related with the existence of microtwin sequences with changing variant widths. Although both features appear irrespective of the material’s preparation technique, rapid solidification seems to prefer the step configuration. Depending on the actual case, tapering, bending and tip splitting of the small microtwin variants is observed. Sever lattice deformations and reorientations occur in a region of 5 – 10 nm around the interface while sequences of single plane ledges gradually bending the microtwins are found up to 50 nm away form the interface. These structures and deformations are interpreted in view of the need to accommodate any remaining stresses
A measure of conductivity for lattice fermions at finite density
We study the linear response to an external electric field of a system of
fermions in a lattice at zero temperature. This allows to measure numerically
the Euclidean conductivity which turns out to be compatible with an analytical
calculation for free fermions. The numerical method is generalizable to systems
with dynamical interactions where no analytical approach is possible.Comment: version to be published in Physics Letters
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