A Pseudo-Stokes Mesh Motion Algorithm

This work presents a moving mesh methodology based on the solution of a pseudo flow problem. The mesh motion is modeled as a pseudo Stokes problem solved by an explicit finite element projection method. The mesh quality requirements are satisfied by employing a null divergent velocity condition. This methodology is applied to triangular unstructured meshes and compared to well known approaches such as the ones based on diffusion and pseudo structural problems. One of the test cases is an airfoil with a fully meshed domain. A specific rotation velocity is imposed as the airfoil boundary condition. The other test is a set of two cylinders that move toward each other. A mesh quality criterion is employed to identify critically distorted elements and to evaluate the performance of each mesh motion approach. The results obtained for each test case show that the pseudo-flow methodology produces satisfactory meshes during the moving process.     

Non-local order in Mott insulators,duality and Wilson loops

It is shown that the Mott insulating and superfluid phases of bosons in an optical lattice may be distinguished by a non-local ‘parity order parameter’ which is directly accessible via single site resolution imaging. In one dimension, the lattice Bose model is dual to a classical interface roughening problem. We use known exact results from the latter to prove that the parity order parameter exhibits long range order in the Mott insulating phase, consistent with recent experiments by Endres et al. [M. Endres, M. Cheneau, T. Fukuhara, C. Weitenberg, P. Schauß, C. Gross, L. Mazza, M.C. Bañuls, L. Pollet, I. Bloch, et al., Science 334 (2011) 200]. In two spatial dimensions, the parity order parameter can be expressed in terms of an equal time Wilson loop of a non-trivial U(1)$U\left(1\right)$ gauge theory in 2+1$2+1$ dimensions which exhibits a transition between a Coulomb and a confining phase. The negative logarithm of the parity order parameter obeys a perimeter law in the Mott insulator and is enhanced by a logarithmic factor in the superfluid.     

The heroic age,the creation of quantum mechanics, 1925–1940

A number of important physics curriculum projects have produced course materials, or are in the process of doing so, for different levels of science education in the United States of America. This article surveys the scene under such headings as the Origins, the Aims, the Patterns of Construction, the Teaching Methods, the Teacher Training and the Evaluation Techniques pertaining to each of ten selected projects. An attempt is then made to draw inferences, from the American work, that are relevant to the present and future position of physics education in Britain. It is observed that action on many of these inferences would be consistent with the recommendations of the ‘Deinton Report’.

No attempt is made to give detailed surveys, or criticism, of the American projects since much of the work is only at trial stage.     

Remanent quantum correlations in dissipative qubits

Starting from the exact evolution of a Markovian dissipative quantum walk, a non-Markovian decoherence of two qubits interacting with a phonon thermal bath has been investigated analytically using quantum information tools. Concurrence and quantum discord are affected in a complex way, showing that entanglement decreases with dissipation. At the limit where dissipation dominates, quantum correlations survive in time as ∝t^−1/2$\propto t^{-1/2}$. Thus, even under the influence of dissipation, two qubits retain their quantumness for a long time. Quantum correlations could be therefore observed for a long time in related photonic experiments.     

Understanding the enhanced synchronization of delay-coupled networks with fluctuating topology

We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the coupling delay along the network links and time scale at which the topology changes. Concentrating on a linearized model, we develop an analytical theory for the stability of a synchronized solution. In two limit cases, the system can be reduced to an “effective” topology: in the fast switching approximation, when the network fluctuations are much faster than the internal time scale and the coupling delay, the effective network topology is the arithmetic mean over the different topologies. In the slow network limit, when the network fluctuation time scale is equal to the coupling delay, the effective adjacency matrix is the geometric mean over the adjacency matrices of the different topologies. In the intermediate regime, the system shows a sensitive dependence on the ratio of time scales, and on the specific topologies, reproduced as well by numerical simulations. Our results are shown to describe the synchronization properties of fluctuating networks of delay-coupled chaotic maps.     

An independent component analysis-based approach on ballistocardiogram artifact removing

Interest about simultaneous electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data acquisition has rapidly increased during the last years because of the possibility that the combined method offers to join temporal and spatial resolution, providing in this way a powerful tool to investigate spontaneous and evoked brain activities. However, several intrinsic features of MRI scanning become sources of artifacts on EEG data. Noise sources of a highly predictable nature such as those related to the pulse MRI sequence and those determined by magnetic gradient switching during scanning do not represent a major problem and can be easily removed. On the contrary, the ballistocardiogram (BCG) artifact, a large signal visible on all EEG traces and related to cardiac activity inside the magnetic field, is determined by sources that are not fully stereotyped and causing important limitations in the use of artifact-removing strategies. Recently, it has been proposed to use independent component analysis (ICA) to remove BCG artifact from EEG signals. ICA is a statistical algorithm that allows blind separation of statistically independent sources when the only available information is represented by their linear combination. An important drawback with most ICA algorithms is that they exhibit a stochastic behavior: each run yields slightly different results such that the reliability of the estimated sources is difficult to assess. In this preliminary report, we present a method based on running the FastICA algorithm many times with slightly different initial conditions. Clustering structure in the signal space of the obtained components provides us with a new way to assess the reliability of the estimated sources.