917 research outputs found
Ellipsoidal bounds on state trajectories for discrete-time systems with linear fractional uncertainties
Computation of exact ellipsoidal bounds on the state trajectories of discrete-time linear systems that have time-varying or time-invariant linear fractional parameter uncertainties and ellipsoidal uncertainty in the initial state is known to be NP-hard. This paper proposes three algorithms to compute ellipsoidal bounds on such a state trajectory set and discusses the tradeoffs between computational complexity and conservatism of the algorithms. The approach employs linear matrix inequalities to determine an initial estimate of the ellipsoid that is refined by the subsequent application of the skewed structured singular value ν. Numerical examples are used to illustrate the application of the proposed algorithms and to compare the differences between them, where small conservatism for the tightest bounds is observed.Institute for Advanced Computing Applications and Technologie
Nonlinear Optical Response of Spin Density Wave Insulators
We calculate the third order nonlinear optical response in the Hubbard model
within the spin density wave (SDW) mean field ansatz in which the gap is due to
onsite Coulomb repulsion. We obtain closed-form analytical results in one
dimension (1D) and two dimension (2D), which show that nonlinear optical
response in SDW insulators in 2D is stronger than both 3D and 1D. We also
calculate the two photon absorption (TPA) arising from the stress tensor term.
We show that in the SDW, the contribution from stress tensor term to the
low-energy peak corresponding to two photon absorption becomes identically zero
if we consider the gauge invariant current properly.Comment: we use \psfrag in figur
Shear bands in granular flow through a mixing length model
We discuss the advantages and results of using a mixing-length, compressible
model to account for shear banding behaviour in granular flow. We formulate a
general approach based on two function of the solid fraction to be determined.
Studying the vertical chute flow, we show that shear band thickness is always
independent from flowrate in the quasistatic limit, for Coulomb wall boundary
conditions. The effect of bin width is addressed using the functions developed
by Pouliquen and coworkers, predicting a linear dependence of shear band
thickness by channel width, while literature reports contrasting data. We also
discuss the influence of wall roughness on shear bands. Through a Coulomb wall
friction criterion we show that our model correctly predicts the effect of
increasing wall roughness on the thickness of shear bands. Then a simple
mixing-length approach to steady granular flows can be useful and
representative of a number of original features of granular flow.Comment: submitted to EP
Bioengineering the ameloblastoma tumour to study its effect on bone nodule formation
Ameloblastoma is a benign, epithelial cancer of the jawbone, which causes bone resorption and disfigurement to patients affected. The interaction of ameloblastoma with its tumour stroma drives invasion and progression. We used stiff collagen matrices to engineer active bone forming stroma, to probe the interaction of ameloblastoma with its native tumour bone microenvironment. This bone-stroma was assessed by nano-CT, transmission electron microscopy (TEM), Raman spectroscopy and gene analysis. Furthermore, we investigated gene correlation between bone forming 3D bone stroma and ameloblastoma introduced 3D bone stroma. Ameloblastoma cells increased expression of MMP-2 and -9 and RANK temporally in 3D compared to 2D. Our 3D biomimetic model formed bone nodules of an average surface area of 0.1 mm2 and average height of 92.37 ± 7.96 μm over 21 days. We demonstrate a woven bone phenotype with distinct mineral and matrix components and increased expression of bone formation genes in our engineered bone. Introducing ameloblastoma to the bone stroma, completely inhibited bone formation, in a spatially specific manner. Multivariate gene analysis showed that ameloblastoma cells downregulate bone formation genes such as RUNX2. Through the development of a comprehensive bone stroma, we show that an ameloblastoma tumour mass prevents osteoblasts from forming new bone nodules and severely restricted the growth of existing bone nodules. We have identified potential pathways for this inhibition. More critically, we present novel findings on the interaction of stromal osteoblasts with ameloblastoma
Nonlinear Optical Response Functions of Mott Insulators Based on Dynamical Mean Field Approximation
We investigate the nonlinear optical susceptibilities of Mott insulators with
the dynamical mean field approximation. The two-photon absorption (TPA) and the
third-harmonic generation (THG) spectra are calculated, and the classification
by the types of coupling to external fields shows different behavior from
conventional semiconductors. The direct transition terms are predominant both
in the TPA and THG spectra, and the importance of taking all types of
interaction with the external field into account is illustrated in connection
with the THG spectrum and dcKerr effect. The dependence of the TPA and THG
spectra on the Coulomb interaction indicate a scaling relation. We apply this
relation to the quantitative evaluation and obtain results comparable to those
of experiments.Comment: 14 pages, 12 figure
Nonlinear optical response and spin-charge separation in one-dimensional Mott insulators
We theoretically study the nonlinear optical response and photoexcited states
of the Mott insulators. The nonlinear optical susceptibility \chi^(3) is
calculated by using the exact diagonalization technique on small clusters. From
the systematic study of the dependence of \chi^(3) on dimensionality, we find
that the spin-charge separation plays a crucial role in enhancing \chi^(3) in
the one-dimensional (1D) Mott insulators. Based on this result, we propose a
holon-doublon model, which describes the nonlinear response in the 1D Mott
insulators. These findings show that the spin-charge separation will become a
key concept of optoelectronic devices.Comment: 5 pages with 3 figures, to appear in PRB RC, 15 August 200
Parity forbidden excitations of Sr2CuO2Cl2 revealed by optical third-harmonic spectroscopy
We present the first study of nonlinear optical third harmonic generation in
the strongly correlated charge-transfer insulator Sr2CuO2Cl2. For fundamental
excitation in the near-infrared, the THG spectrum reveals a strongly resonant
response for photon energies near 0.7 eV. Polarization analysis reveals this
novel resonance to be only partially accounted for by three-photon excitation
to the optical charge-transfer exciton, and indicates that an even-parity
excitation at 2 eV, with a_1g symmetry, participates in the third harmonic
susceptibility.Comment: Requires RevTeX v4.0beta
Local shell-to-shell energy transfer via nonlocal Interactions in fluid turbulence
In this paper we analytically compute the strength of nonlinear interactions
in a triad, and the energy exchanges between wavenumber shells in
incompressible fluid turbulence. The computation has been done using
first-order perturbative field theory. In three dimension, magnitude of triad
interactions is large for nonlocal triads, and small for local triads. However,
the shell-to-shell energy transfer rate is found to be local and forward. This
result is due to the fact that the nonlocal triads occupy much less Fourier
space volume than the local ones. The analytical results on three-dimensional
shell-to-shell energy transfer match with their numerical counterparts. In
two-dimensional turbulence, the energy transfer rates to the near-by shells are
forward, but to the distant shells are backward; the cumulative effect is an
inverse cascade of energy.Comment: 10 pages, Revtex
Optical excitations in a one-dimensional Mott insulator
The density-matrix renormalization-group (DMRG) method is used to investigate
optical excitations in the Mott insulating phase of a one-dimensional extended
Hubbard model. The linear optical conductivity is calculated using the
dynamical DMRG method and the nature of the lowest optically excited states is
investigated using a symmetrized DMRG approach. The numerical calculations
agree perfectly with field-theoretical predictions for a small Mott gap and
analytical results for a large Mott gap obtained with a strong-coupling
analysis. Is is shown that four types of optical excitations exist in this Mott
insulator: pairs of unbound charge excitations, excitons, excitonic strings,
and charge-density-wave (CDW) droplets. Each type of excitations dominates the
low-energy optical spectrum in some region of the interaction parameter space
and corresponds to distinct spectral features: a continuum starting at the Mott
gap (unbound charge excitations), a single peak or several isolated peaks below
the Mott gap (excitons and excitonic strings, respectively), and a continuum
below the Mott gap (CDW droplets).Comment: 12 pages (REVTEX 4), 12 figures (in 14 eps files), 1 tabl
Band structure and optical properties of germanium sheet polymers
The band structure of H-terminated Ge sheet polymers is calculated using density-functional theory in the local density approximation and compared to the optical properties of epitaxial polygermyne layers as determined from reflection, photoluminescence, and photoluminescence excitation measurements. A direct band gap of 1.7 eV is predicted and a near resonant excitation of the photoluminescence is observed experimentally close to this energy
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