Correcting the polarization effect in low frequency Dielectric Spectroscopy

We demonstrate a simple and robust methodology for measuring and analyzing the polarization impedance appearing at interface between electrodes and ionic solutions, in the frequency range from 1 to $10^6$ Hz. The method assumes no particular behavior of the electrode polarization impedance and it only makes use of the fact that the polarization effect dies out with frequency. The method allows a direct and un-biased measurement of the polarization impedance, whose behavior with the applied voltages and ionic concentration is methodically investigated. Furthermore, based on the previous findings, we propose a protocol for correcting the polarization effect in low frequency Dielectric Spectroscopy measurements of colloids. This could potentially lead to the quantitative resolution of the $\alpha$-dispersion regime of live cells in suspension

Gutzwiller density functional theory for correlated electron systems

We develop a new density functional theory (DFT) and formalism for correlated electron systems by taking as reference an interacting electron system that has a ground state wavefunction which obeys exactly the Gutzwiller approximation for all one particle operators. The solution of the many electron problem is mapped onto the self-consistent solution of a set of single particle Schroedinger equations analogous to standard DFT-LDA calculations.Comment: 4 page

Trajectory Optimization and NMPC Tracking for a Fixed Wing UAV in Deep Stall with Perch Landing

This paper presents a novel recovery technique for a fixed-wing UAV (Unmanned Aerial Vehicle) based on constrained optimization: i) we propose a trajectory generation for landing the UAV where it first reduces its altitude by deep stalling, then perches on a recovery net, ii) we design an NMPC (Nonlinear Model Predictive Control) tracking controller with terminal constraints for the optimal generated trajectory under disturbances. Compared to nominal net recovery procedures, this technique greatly reduces the landing time and the final airspeed of the UAV. Simulation results for various wind conditions demonstrate the feasibility of the idea.Comment: 8 pages, 13 figure

A Stabilizing NMPC Strategy for a Class of Nonholonomic Systems with Drift

In this paper, we present a stabilizing Nonlinear Model Predictive Control (NMPC) scheme tailored for a class of nonholonomic systems with drift, where the acceleration is laterally restrained. Examples include a mobile robot with drifting wheels on a planar surface or a spacecraft maneuvering in a vacuum. The novelty lies in the formulation of the terminal set, reachable from a significant distance from the equilibrium, and the terminal cost, represented as the integration of the stage cost. The proposed approach establishes essential steps for ensuring stability and feasibility guarantees. Simulation results substantiate the viability and effectiveness of the NMPC scheme.Comment: Submitted to an international conferenc

Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms

In this paper we study the problem of uniqueness of solutions to the Hartree and Hartree-Fock equations of atoms. We show, for example, that the Hartree-Fock ground state of a closed shell atom is unique provided the atomic number $Z$ is sufficiently large compared to the number $N$ of electrons. More specifically, a two-electron atom with atomic number $Z\geq 35$ has a unique Hartree-Fock ground state given by two orbitals with opposite spins and identical spatial wave functions. This statement is wrong for some $Z>1$, which exhibits a phase segregation.Comment: 18 page

Evolutions of helical edge states in disordered HgTe/CdTe quantum wells

We study the evolutions of the nonmagnetic disorder-induced edge states with the disorder strength in the HgTe/CdTe quantum wells. From the supercell band structures and wave-functions, it is clearly shown that the conducting helical edge states, which are responsible for the reported quantized conductance plateau, appear above a critical disorder strength after a gap-closing phase transition. These edge states are then found to decline with the increase of disorder strength in a stepwise pattern due to the finite-width effect, where the opposite edges couple with each other through the localized states in the bulk. This is in sharp contrast with the localization of the edge states themselves if magnetic disorders are doped which breaks the time-reversal symmetry. The size-independent boundary of the topological phase is obtained by scaling analysis, and an Anderson transition to an Anderson insulator at even stronger disorder is identified, in-between of which, a metallic phase is found to separate the two topologically distinct phases.Comment: 7 pages, 5 figure

Dielectric Behavior of Nonspherical Cell Suspensions

Recent experiments revealed that the dielectric dispersion spectrum of fission yeast cells in a suspension was mainly composed of two sub-dispersions. The low-frequency sub-dispersion depended on the cell length, whereas the high-frequency one was independent of it. The cell shape effect was qualitatively simulated by an ellipsoidal cell model. However, the comparison between theory and experiment was far from being satisfactory. In an attempt to close up the gap between theory and experiment, we considered the more realistic cells of spherocylinders, i.e., circular cylinders with two hemispherical caps at both ends. We have formulated a Green function formalism for calculating the spectral representation of cells of finite length. The Green function can be reduced because of the azimuthal symmetry of the cell. This simplification enables us to calculate the dispersion spectrum and hence access the effect of cell structure on the dielectric behavior of cell suspensions.Comment: Preliminary results have been reported in the 2001 March Meeting of the American Physical Society. Accepted for publications in J. Phys.: Condens. Matte