7,078 research outputs found
Deterministic Brownian motion generated from differential delay equations
This paper addresses the question of how Brownian-like motion can arise from
the solution of a deterministic differential delay equation. To study this we
analytically study the bifurcation properties of an apparently simple
differential delay equation and then numerically investigate the probabilistic
properties of chaotic solutions of the same equation. Our results show that
solutions of the deterministic equation with randomly selected initial
conditions display a Gaussian-like density for long time, but the densities are
supported on an interval of finite measure. Using these chaotic solutions as
velocities, we are able to produce Brownian-like motions, which show
statistical properties akin to those of a classical Brownian motion over both
short and long time scales. Several conjectures are formulated for the
probabilistic properties of the solution of the differential delay equation.
Numerical studies suggest that these conjectures could be "universal" for
similar types of "chaotic" dynamics, but we have been unable to prove this.Comment: 15 pages, 13 figure
Growth and characterization of ZnTe films grown on GaAs, InAs, GaSb, and ZnTe
We report the successful growth of ZnTe on nearly lattice-matched III-V buffer layers of InAs (0.75%), GaSb (0.15%), and on GaAs and ZnTe by molecular beam epitaxy. In situ reflection high-energy electron diffraction measurements showed the characteristic streak patterns indicative of two-dimensional growth. Photoluminescence measurements on these films show strong and sharp features near the band edge with no detectable luminescence at longer wavelengths. The integrated photoluminescence intensity from the ZnTe layers increased with better lattice match to the buffer layer. The ZnTe epilayers grown on high-purity ZnTe substrates exhibited stronger luminescence than the substrates. We observe narrow luminescence linewidths (full width at half maximum ~ 1–2 Å) indicative of uniform high quality growth. Secondary-ion mass spectroscopy and electron microprobe measurements, however, reveal substantial outdiffusion of Ga and In for growths on the III-V buffer layers
Electrical determination of the valence-band discontinuity in HgTe-CdTe heterojunctions
Current-voltage behavior is studied experimentally in a Hg0.78Cd0.22Te-CdTe-Hg0.78Cd0.22Te heterostructure grown by molecular beam epitaxy. At temperatures above 160 K, energy-band diagrams suggest that the dominant low-bias current is thermionic hole emission across the CdTe barrier layer. This interpretation yields a direct determination of 390±75 meV for the HgTe-CdTe valence-band discontinuity at 300 K. Similar analyses of current-voltage data taken at 190–300 K suggest that the valence-band offset decreases at low temperatures in this heterojunction
Accommodation of lattice mismatch in Ge_(x)Si_(1−x)/Si superlattices
We present evidence that the critical thickness for the appearance of misfit defects in a given material and heteroepitaxial structure is not simply a function of lattice mismatch. We report substantial differences in the relaxation of mismatch stress in Ge_(0.5)Si_(0.5)/Si superlattices grown at different temperatures on (100) Si substrates. Samples have been analyzed by x‐ray diffraction, channeled Rutherford backscattering, and transmission electron microscopy. While a superlattice grown at 365 °C demonstrates a high degree of elastic strain, with a dislocation density <10^5 cm^(−2) , structures grown at higher temperatures show increasing numbers of structural defects, with densities reaching 2×10^(10) cm^(−2) at a growth temperature of 530 °C. Our results suggest that it is possible to freeze a lattice‐mismatched structure in a highly strained metastable state. Thus it is not surprising that experimentally observed critical thicknesses are rarely in agreement with those predicted by equilibrium theories
Testing Identifiable Kernel P Systems Using an X-machine Approach
This paper presents a testing approach for kernel P systems (kP systems),
based on the X-machine testing framework and the concept of cover automaton. The
testing methodology ensures that the implementation conforms the speci cations, under
certain conditions, such as the identi ably concept in the context of kernel P systems
Low-Energy Charge-Density Excitations in MgB: Striking Interplay between Single-Particle and Collective Behavior for Large Momenta
A sharp feature in the charge-density excitation spectra of single-crystal
MgB, displaying a remarkable cosine-like, periodic energy dispersion with
momentum transfer () along the -axis, has been observed for the first
time by high-resolution non-resonant inelastic x-ray scattering (NIXS).
Time-dependent density-functional theory calculations show that the physics
underlying the NIXS data is strong coupling between single-particle and
collective degrees of freedom, mediated by large crystal local-field effects.
As a result, the small- collective mode residing in the single-particle
excitation gap of the B bands reappears periodically in higher Brillouin
zones. The NIXS data thus embody a novel signature of the layered electronic
structure of MgB.Comment: 5 pages, 4 figures, submitted to PR
Robust Dropping Criteria for F-norm Minimization Based Sparse Approximate Inverse Preconditioning
Dropping tolerance criteria play a central role in Sparse Approximate Inverse
preconditioning. Such criteria have received, however, little attention and
have been treated heuristically in the following manner: If the size of an
entry is below some empirically small positive quantity, then it is set to
zero. The meaning of "small" is vague and has not been considered rigorously.
It has not been clear how dropping tolerances affect the quality and
effectiveness of a preconditioner . In this paper, we focus on the adaptive
Power Sparse Approximate Inverse algorithm and establish a mathematical theory
on robust selection criteria for dropping tolerances. Using the theory, we
derive an adaptive dropping criterion that is used to drop entries of small
magnitude dynamically during the setup process of . The proposed criterion
enables us to make both as sparse as possible as well as to be of
comparable quality to the potentially denser matrix which is obtained without
dropping. As a byproduct, the theory applies to static F-norm minimization
based preconditioning procedures, and a similar dropping criterion is given
that can be used to sparsify a matrix after it has been computed by a static
sparse approximate inverse procedure. In contrast to the adaptive procedure,
dropping in the static procedure does not reduce the setup time of the matrix
but makes the application of the sparser for Krylov iterations cheaper.
Numerical experiments reported confirm the theory and illustrate the robustness
and effectiveness of the dropping criteria.Comment: 27 pages, 2 figure
On q-Gaussians and Exchangeability
The q-Gaussians are discussed from the point of view of variance mixtures of
normals and exchangeability. For each q< 3, there is a q-Gaussian distribution
that maximizes the Tsallis entropy under suitable constraints. This paper shows
that q-Gaussian random variables can be represented as variance mixtures of
normals. These variance mixtures of normals are the attractors in central limit
theorems for sequences of exchangeable random variables; thereby, providing a
possible model that has been extensively studied in probability theory. The
formulation provided has the additional advantage of yielding process versions
which are naturally q-Brownian motions. Explicit mixing distributions for
q-Gaussians should facilitate applications to areas such as option pricing. The
model might provide insight into the study of superstatistics.Comment: 14 page
Numerical studies of the Lagrangian approach for reconstruction of the conductivity in a waveguide
We consider an inverse problem of reconstructing the conductivity function in
a hyperbolic equation using single space-time domain noisy observations of the
solution on the backscattering boundary of the computational domain. We
formulate our inverse problem as an optimization problem and use Lagrangian
approach to minimize the corresponding Tikhonov functional. We present a
theorem of a local strong convexity of our functional and derive error
estimates between computed and regularized as well as exact solutions of this
functional, correspondingly. In numerical simulations we apply domain
decomposition finite element-finite difference method for minimization of the
Lagrangian. Our computational study shows efficiency of the proposed method in
the reconstruction of the conductivity function in three dimensions
Genetic Control of Circuit Function: Vsx1 and Irx5 Transcription Factors Regulate Contrast Adaptation in the Mouse Retina
Transcriptional programs guide the specification of neural cell types in the developing nervous system. However, it is unclear whether such programs also control specific aspects of neural circuit function at maturity. In the mammalian retina, Vsx1 and Irx5 transcription factors are present in a subset of bipolar interneurons that convey signals from photoreceptors to ganglion cells. The biased expression of Vsx1 and Irx5 in hyperpolarizing OFF compared with depolarizing ON bipolar cells suggests that these transcription factors may selectively regulate signal processing in OFF circuits. To test this hypothesis, we generated mice lacking both Vsx1 and Irx5. Bipolar cells in these mice were morphologically normal, but the expression of cell-specific markers in some OFF but not ON bipolar cells was reduced or absent. To assess visual function in Vsx1/Irx5/ retinas, we recorded light responses from ensembles of retinal ganglion cells (RGCs). We first identified functional RGC types in control mice and describe their response properties and adaptation to temporal contrast using a simple linearnonlinear model. We found that spacetime receptive fields of RGCs are unchanged in Vsx1/Irx5/ mice compared with control retinas. In contrast, response threshold, gain, and range were lowered in a cell-type-specific manner in OFF but not ON RGCs in Vsx1/Irx5/ retinas. Finally, we discovered that the ability to adapt to temporal contrast is greatly reduced in OFF RGCs in the double mutant, suggesting that Vsx1 and Irx5 control specific aspects of visual function in circuits of the mammalian retina
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