Bivariate spline interpolation with optimal approximation order

Let be a triangulation of some polygonal domain f c R2 and let S9 (A) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermite-type interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181

Effective Hamiltonian study of excitations in a boson- fermion mixture with attraction between components

An effective Hamiltonian for the Bose subsystem in the mixture of ultracold atomic clouds of bosons and fermions with mutual attractive interaction is used for investigating collective excitation spectrum. The ground state and mode frequencies of the $^{87}$Rb and $^{40}$K mixture are analyzed quantitatively at zero temperature. We find analytically solutions of the hydrodynamics equations in the Thomas- Fermi approximation. We discuss the relation between the onset of collapse and collective modes softening and the dependence of collective oscillations on scattering length and number of boson atoms.Comment: 9 pages, 5 figure

Fractional Quantum Hall States in Narrow Channels

A model system is considered where two dimensional electrons are confined by a harmonic potential in one direction, and are free in the other direction. Ground state in strong magnetic fields is investigated through numerical diagonalization of the Hamiltonian. It is shown that the fractional quantum Hall states are realized even in the presence of the external potential under suitable conditions, and a phase diagram is obtained.Comment: 8 pages, 2 figures (not included

A Bias-Aware EnKF Estimator for Aerodynamic Flows

Ensemble methods can integrate measurement data and CFD-based models to estimate the state of fluid systems in a robust and cost-efficient way. However, discretization errors can render numerical solutions a biased representation of reality. Left unaccounted for, biased forecast and observation models can lead to poor estimator performance. In this work, we propose a low-rank representation for the bias whose dynamics is represented by a colorednoise process. System state and bias parameters are simultaneously corrected on-line with the Ensemble Kalman Filter (EnKF) algorithm. The proposed methodology is demonstrated to achieve a 70% error reduction for the problem of estimating the state of the two-dimensional low-Re flow past a flat plate at high angle of attack using an ensemble of coarse-mesh simulations and pressure measurements at the surface of the body, compared to a bias-blind estimator. Strategies to determine the bias statistics and to deal with nonlinear observation functions in the context of ensemble methods are discussed

A time frequency analysis of wave packet fractional revivals

We show that the time frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time domain analysis. This advantage is crucial in reconstructing the initial state of the wave packet when its coherent structure is short-lived and decays before it is fully revived. Our calculations are based on the model example of fractional revivals in a Rydberg wave packet of circular states. We end by providing an analytical investigation which fully agrees with our numerical observations on the utility of time-frequency analysis in the study of wave packet fractional revivals.Comment: 9 pages, 4 figure

Co-ordination between Rashba spin-orbital interaction and space charge effect and enhanced spin injection into semiconductors

We consider the effect of the Rashba spin-orbital interaction and space charge in a ferromagnet-insulator/semiconductor/insulator-ferromagnet junction where the spin current is severely affected by the doping, band structure and charge screening in the semiconductor. In diffusion region, if the the resistance of the tunneling barriers is comparable to the semiconductor resistance, the magnetoresistance of this junction can be greatly enhanced under appropriate doping by the co-ordination between the Rashba effect and screened Coulomb interaction in the nonequilibrium transport processes within Hartree approximation.Comment: 4 pages, 3 figure

Third Order Renormalization Group applied to the attractive one-dimensional Fermi Gas

We consider a Callan-Symanzik and a Wilson Renormalization Group approach to the infrared problem for interacting fermions in one dimension with backscattering. We compute the third order (two-loop) approximation of the beta function using both methods and compare it with the well known multiplicative Gell-Mann Low approach. We point out a previously unnoticed qualitative dependence of the third order fixed point on an arbitrary dimensionless parameter, which strongly suggest the spurious nature of the fixed point.Comment: 16 pages, Revised version, added comment

Classification of Human Retinal Microaneurysms Using Adaptive Optics Scanning Light Ophthalmoscope Fluorescein Angiography

Purpose. Microaneurysms (MAs) are considered a hallmark of retinal vascular disease, yet what little is known about them is mostly based upon histology, not clinical observation. Here, we use the recently developed adaptive optics scanning light ophthalmoscope (AOSLO) fluorescein angiography (FA) to image human MAs in vivo and to expand on previously described MA morphologic classification schemes. Methods. Patients with vascular retinopathies (diabetic, hypertensive, and branch and central retinal vein occlusion) were imaged with reflectance AOSLO and AOSLO FA. Ninety-three MAs, from 14 eyes, were imaged and classified according to appearance into six morphologic groups: focal bulge, saccular, fusiform, mixed, pedunculated, and irregular. The MA perimeter, area, and feret maximum and minimum were correlated to morphology and retinal pathology. Select MAs were imaged longitudinally in two eyes. Results. Adaptive optics scanning light ophthalmoscope fluorescein angiography imaging revealed microscopic features of MAs not appreciated on conventional images. Saccular MAs were most prevalent (47%). No association was found between the type of retinal pathology and MA morphology (P = 0.44). Pedunculated and irregular MAs were among the largest MAs with average areas of 4188 and 4116 μm2, respectively. Focal hypofluorescent regions were noted in 30% of MAs and were more likely to be associated with larger MAs (3086 vs. 1448 μm2, P = 0.0001). Conclusions. Retinal MAs can be classified in vivo into six different morphologic types, according to the geometry of their two-dimensional (2D) en face view. Adaptive optics scanning light ophthalmoscope fluorescein angiography imaging of MAs offers the possibility of studying microvascular change on a histologic scale, which may help our understanding of disease progression and treatment response

Continuous melting of compact polymers

The competition between chain entropy and bending rigidity in compact polymers can be addressed within a lattice model introduced by P.J. Flory in 1956. It exhibits a transition between an entropy dominated disordered phase and an energetically favored crystalline phase. The nature of this order-disorder transition has been debated ever since the introduction of the model. Here we present exact results for the Flory model in two dimensions relevant for polymers on surfaces, such as DNA adsorbed on a lipid bilayer. We predict a continuous melting transition, and compute exact values of critical exponents at the transition point.Comment: 5 pages, 1 figur