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