227 research outputs found
On the equality of Hausdorff and box counting dimensions
By viewing the covers of a fractal as a statistical mechanical system, the
exact capacity of a multifractal is computed. The procedure can be extended to
any multifractal described by a scaling function to show why the capacity and
Hausdorff dimension are expected to be equal.Comment: CYCLER Paper 93mar001 Latex file with 3 PostScript figures (needs
psfig.sty
Full oxide heterostructure combining a high-Tc diluted ferromagnet with a high-mobility conductor
We report on the growth of heterostructures composed of layers of the
high-Curie temperature ferromagnet Co-doped (La,Sr)TiO3 (Co-LSTO) with
high-mobility SrTiO3 (STO) substrates processed at low oxygen pressure. While
perpendicular spin-dependent transport measurements in STO//Co-LSTO/LAO/Co
tunnel junctions demonstrate the existence of a large spin polarization in
Co-LSTO, planar magnetotransport experiments on STO//Co-LSTO samples evidence
electronic mobilities as high as 10000 cm2/Vs at T = 10 K. At high enough
applied fields and low enough temperatures (H < 60 kOe, T < 4 K) Shubnikov-de
Haas oscillations are also observed. We present an extensive analysis of these
quantum oscillations and relate them with the electronic properties of STO, for
which we find large scattering rates up to ~ 10 ps. Thus, this work opens up
the possibility to inject a spin-polarized current from a high-Curie
temperature diluted oxide into an isostructural system with high-mobility and a
large spin diffusion length.Comment: to appear in Phys. Rev.
Expanding direction of the period doubling operator
We prove that the period doubling operator has an expanding direction at the
fixed point. We use the induced operator, a ``Perron-Frobenius type operator'',
to study the linearization of the period doubling operator at its fixed point.
We then use a sequence of linear operators with finite ranks to study this
induced operator. The proof is constructive. One can calculate the expanding
direction and the rate of expansion of the period doubling operator at the
fixed point
On the Hyperbolicity of Lorenz Renormalization
We consider infinitely renormalizable Lorenz maps with real critical exponent
and combinatorial type which is monotone and satisfies a long return
condition. For these combinatorial types we prove the existence of periodic
points of the renormalization operator, and that each map in the limit set of
renormalization has an associated unstable manifold. An unstable manifold
defines a family of Lorenz maps and we prove that each infinitely
renormalizable combinatorial type (satisfying the above conditions) has a
unique representative within such a family. We also prove that each infinitely
renormalizable map has no wandering intervals and that the closure of the
forward orbits of its critical values is a Cantor attractor of measure zero.Comment: 63 pages; 10 figure
Cyclotron resonance of the quasi-two-dimensional electron gas at Hg1-xCdxTe grain boundaries
The magnetotransmission of a p-type Hg0.766Cd0.234Te bicrystal containing a single grain boundary with an inversion layer has been investigated in the submillimetre wavelength range. For the first time the cyclotron resonance lines belonging to the various electric subbands of a quasi-two-dimensional carrier system at a grain boundary could be detected. The measured cyclotron masses and the subband densities determined from Shubnikov-de Haas experiments are compared with theoretical predictions and it is found that the data can be explained very well within the framework of a triangular well approximation model which allows for non-parabolic effects
Nucleation in Systems with Elastic Forces
Systems with long-range interactions when quenced into a metastable state
near the pseudo-spinodal exhibit nucleation processes that are quite different
from the classical nucleation seen near the coexistence curve. In systems with
long-range elastic forces the description of the nucleation process can be
quite subtle due to the presence of bulk/interface elastic compatibility
constraints. We analyze the nucleation process in a simple 2d model with
elastic forces and show that the nucleation process generates critical droplets
with a different structure than the stable phase. This has implications for
nucleation in many crystal-crystal transitions and the structure of the final
state
Piecewise Linear Models for the Quasiperiodic Transition to Chaos
We formulate and study analytically and computationally two families of
piecewise linear degree one circle maps. These families offer the rare
advantage of being non-trivial but essentially solvable models for the
phenomenon of mode-locking and the quasi-periodic transition to chaos. For
instance, for these families, we obtain complete solutions to several questions
still largely unanswered for families of smooth circle maps. Our main results
describe (1) the sets of maps in these families having some prescribed rotation
interval; (2) the boundaries between zero and positive topological entropy and
between zero length and non-zero length rotation interval; and (3) the
structure and bifurcations of the attractors in one of these families. We
discuss the interpretation of these maps as low-order spline approximations to
the classic ``sine-circle'' map and examine more generally the implications of
our results for the case of smooth circle maps. We also mention a possible
connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request
Electron-phonon interaction in a local region
The paper reports on a study of electron-phonon interaction within a limited
nanosized region. We invoked the modified Fr\"{o}hlich's Hamiltonian to
calculate the electron self-energy, as well as the elastic and inelastic
scattering cross sections. New effects have been revealed, more specifically: a
bound state forms within the limited nanosized region, electrons undergo
resonant elastic scattering, with strong inelastic scattering being possible
from this state even at low electron energies. The effect of scattering on the
magnetic-field-independent dephasing time, in particular, in a
diamond-decorated carbon nanotube, has been determined. The effect of strong
inelastic electron scattering on thermal resistance at the metal-insulator
interface is discussed.Comment: 13 pages, 2 figure
Evidence for semiconducting behavior with a narrow band gap of Bernal graphite
We have studied the resistivity of a large number of highly oriented graphite
samples with areas ranging from several mm to a few m and
thickness from nm to several tens of micrometers. The measured
resistance can be explained by the parallel contribution of semiconducting
graphene layers with low carrier density cm and the one from
metallic-like internal interfaces. The results indicate that ideal graphite
with Bernal stacking structure is a narrow-gap semiconductor with an energy gap
meV.Comment: 14 pages, 4 Figures, to be published in New Journal of Physics (in
press, 2012
Neural Correlates of Visual Aesthetics – Beauty as the Coalescence of Stimulus and Internal State
How do external stimuli and our internal state coalesce to create the distinctive aesthetic pleasures that give vibrance to human experience? Neuroaesthetics has so far focused on the neural correlates of observing beautiful stimuli compared to neutral or ugly stimuli, or on neural correlates of judging for beauty as opposed to other judgments. Our group questioned whether this approach is sufficient. In our view, a brain region that assesses beauty should show beauty-level-dependent activation during the beauty judgment task, but not during other, unrelated tasks. We therefore performed an fMRI experiment in which subjects judged visual textures for beauty, naturalness and roughness. Our focus was on finding brain activation related to the rated beauty level of the stimuli, which would take place exclusively during the beauty judgment. An initial whole-brain analysis did not reveal such interactions, yet a number of the regions showing main effects of the judgment task or the beauty level of stimuli were selectively sensitive to beauty level during the beauty task. Of the regions that were more active during beauty judgments than roughness judgments, the frontomedian cortex and the amygdala demonstrated the hypothesized interaction effect, while the posterior cingulate cortex did not. The latter region, which only showed a task effect, may play a supporting role in beauty assessments, such as attending to one's internal state rather than the external world. Most of the regions showing interaction effects of judgment and beauty level correspond to regions that have previously been implicated in aesthetics using different stimulus classes, but based on either task or beauty effects alone. The fact that we have now shown that task-stimulus interactions are also present during the aesthetic judgment of visual textures implies that these areas form a network that is specifically devoted to aesthetic assessment, irrespective of the stimulus type
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