Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani et al. (Automatica 46(10), 1616-1625, 2010 ). Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE's. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully discrete approximations derived using finite elements in space and an implicit Euler method in time. The analysis is carried out for abstract Schrödinger and wave conservative systems with bounded observation (locally distributed)

A Robust and Reliable Test to Measure Stereopsis in the Clinic

yesPurpose: The purpose of this study was to develop a convenient test of stereopsis in the clinic that is both robust and reliable and capable of providing a measure of variability necessary to make valid comparisons between measurements obtained at different occasions or under different conditions. Methods: Stereo acuity was measured based on principles derived from the laboratory measurement of stereopsis (i.e., staircase method). Potential premeasurement compensations are described if there is a significant degree of ocular misalignment, reduced visual acuity, or aniseikonia. Forty-six adults at McGill University, 44 adults at Auckland University, and 51 adults from the University of Bradford, with an age range of 20 to 65 years old and normal or corrected-to-normal vision participated in this study. Results: Stereo acuity within this normal population was widely distributed, with a significant percentage (28%) of the population with only coarse stereo (>300 arc seconds). Across subjects, the SD was approximately 25% of the mean. Measurements at two different times were strongly (r = 0.79) and significantly (P < 0.001) correlated, with little to no significant (P = 0.79) bias (0.01) between test and retest measures of stereopsis. Conclusions: The application enables measurements over the wide disparity range and not just at the finest disparities. In addition, it allows changes in stereopsis of the order of 1.9 to be statistically distinguished

Disentanglement and Inseparability correlation : in two-qubit system

Started from local universal isotropic disentanglement, a threshold inequality on reduction factors is proposed, which is necessary and sufficient for this type of disentanglement processes. Furthermore, we give the conditions realizing ideal disentanglement processes provided that some information on quantum states is known. In addition, based on fully entangled fraction, a concept called inseparability correlation is presented. Some properties on inseparability correlation coefficient are studied.Comment: 10 Pages, 2 Figures, REVTeX; to appear in PR

Elastic and electronic properties of fluorite RuO₂ from first principle

The elastic, thermodynamic, and electronic properties of fluorite RuO₂ under high pressure are investigated by plane-wave pseudopotential density functional theory. The optimized lattice parameters, elastic constants, bulk modulus, and shear modulus are consistent with other theoretical values. The phase transition from modified fluorite-type to fluorite is 88 GPa (by localized density approximation, LDA) or 115.5 GPa (by generalized gradient approximation, GGA). The Young's modulus and Lamé's coefficients are also studied under high pressure. The structure turned out to be stable for the pressure up to 120 GPa by calculating elastic constants. In addition, the thermodynamic properties, including the Debye temperature, heat capacity, thermal expansion coefficient, Grüneisen parameter, and Poisson's ratio, are investigated. A small band gap is found in the electronic structure of fluorite RuO₂ and the bandwidth increases with the pressure. Also, the present mechanical and electronic properties demonstrate that the bonding nature is a combination of covalent, ionic, and metallic contributions.Пружнi, термодинамiчнi та електричнi властивостi флюориту RuO₂ при високому тиску дослiджуються за допомогою теорiї функцiоналу густини з плоскохвильовим псевдопотенцiалом. Оптимiзованi параметри гратки, пружнi сталi, об’ємний модуль i модуль зсуву узгоджуються з iншими теоретичними значеннями. Фазовий перехiд з модифiкованого флюориту до флюориту є при 88 GPa (наближення локальної густини, LDA), чи при 115.5 GPa (узагальнене градiєнтне наближення, GGA). Також дослiджено модуль Юнга i коефiцiєнти Ламе при високих тисках. Структура є стабiльною для тискiв до 120 GPa, якщо обчислювати пружнi сталi. Крiм того, дослiджено термодинамiчнi властивостi, включаючи температуру Дебая, теплоємнiсть, коефiцiєнт теплового розширення, параметр Грюнайзена i коефiцiєнт Пуассона. В електроннiй структурi флюориту RuO₂ знайдено малу зонну щiлину i ширина зони зростає iз тиском. Також, представленi механiчнi та електроннi властивостi демонструють, що природа зв’язування є комбiнацiєю ковалентного, iонного i металiчного вкладiв

Scheme for the implementation of a universal quantum cloning machine via cavity-assisted atomic collisions in cavity QED

We propose a scheme to implement the $1\to2$ universal quantum cloning machine of Buzek et.al [Phys. Rev.A 54, 1844(1996)] in the context of cavity QED. The scheme requires cavity-assisted collision processes between atoms, which cross through nonresonant cavity fields in the vacuum states. The cavity fields are only virtually excited to face the decoherence problem. That's why the requirements on the cavity quality factor can be loosened.Comment: to appear in PR

Experimental preparation of Werner state via spontaneous parametric down-conversion

We present an experiment of preparing Werner state via spontaneous parametric down-conversion and controlled decoherence of photons in this paper. In this experiment two independent BBO (beta-barium borate) crystals are used to produce down-conversion light beams, which are mixed to prepare Werner state.Comment: 6 pages, 4 figures and 2 table

Entanglement Sudden Death in Band Gaps

Using the pseudomode method, we evaluate exactly time-dependent entanglement for two independent qubits, each coupled to a non-Markovian structured environment. Our results suggest a possible way to control entanglement sudden death by modifying the qubit-pseudomode detuning and the spectrum of the reservoirs. Particularly, in environments structured by a model of a density-of-states gap which has two poles, entanglement trapping and prevention of entanglement sudden death occur in the weak-coupling regime