A priori and a posteriori W1,∞W^{1,\infty} error analysis of a QC method for complex lattices

In this paper we prove a priori and a posteriori error estimates for a multiscale numerical method for computing equilibria of multilattices under an external force. The error estimates are derived in a $W^{1,\infty}$ norm in one space dimension. One of the features of our analysis is that we establish an equivalent way of formulating the coarse-grained problem which greatly simplifies derivation of the error bounds (both, a priori and a posteriori). We illustrate our error estimates with numerical experiments.Comment: 23 page

Electron interferometry in quantum Hall regime: Aharonov-Bohm effect of interacting electrons

An apparent h/fe Aharonov-Bohm flux period, where f is an integer, has been reported in coherent quantum Hall devices. Such sub-period is not expected for non-interacting electrons and thus is thought to result from interelectron Coulomb interaction. Here we report experiments in a Fabry-Perot interferometer comprised of two wide constrictions enclosing an electron island. By carefully tuning the constriction front gates, we find a regime where interference oscillations with period h/2e persist throughout the transition between the integer quantum Hall plateaus 2 and 3, including half-filling. In a large quantum Hall sample, a transition between integer plateaus occurs near half-filling, where the bulk of the sample becomes delocalized and thus dissipative bulk current flows between the counterpropagating edges ("backscattering"). In a quantum Hall constriction, where conductance is due to electron tunneling, a transition between forward- and back-scattering is expected near the half-filling. In our experiment, neither period nor amplitude of the oscillations show a discontinuity at half-filling, indicating that only one interference path exists throughout the transition. We also present experiments and an analysis of the front-gate dependence of the phase of the oscillations. The results point to a single physical mechanism of the observed conductance oscillations: Aharonov-Bohm interference of interacting electrons in quantum Hall regime.Comment: 10 pages, 4 Fig

An asymptotic fitting finite element method with exponential mesh refinement for accurate computation of corner eddies in viscous flows

It is well known that any viscous fluid flow near a corner consists of infinite series of eddies with decreasing size and intensity, unless the angle is larger than a certain critical angle[28]. The objective of the current work is to simulate such infinite series of eddies occurring in steady flows in domains with corners. The problem is approached by high-order finite element method with exponential mesh refinement near the corners, coupled with analytical asymptotics of the flow near the corners. Such approach allows one to compute position and intensity of the eddies near the corners in addition to the other main features of the flow. The method was tested on the problem of the lid-driven cavity flow as well as on the problem of the backward-facing step flow. The results of computations of the lid-driven cavity problem show that the proposed method computes the central eddy with accuracy comparable to the best of existing methods and is more accurate for computing the corner eddies than the existing methods. The results also indicate that the relative error of finding the eddies’ intensity and position decreases uniformly for all the eddies as the mes

Numerical Methods for Multilattices

Among the efficient numerical methods based on atomistic models, the quasicontinuum (QC) method has attracted growing interest in recent years. The QC method was first developed for crystalline materials with Bravais lattice and was later extended to multilattices (Tadmor et al, 1999). Another existing numerical approach to modeling multilattices is homogenization. In the present paper we review the existing numerical methods for multilattices and propose another concurrent macro-to-micro method in the numerical homogenization framework. We give a unified mathematical formulation of the new and the existing methods and show their equivalence. We then consider extensions of the proposed method to time-dependent problems and to random materials.Comment: 31 page

A Necessary And Sufficient Condition of Distillability with unite fidelity from Finite Copies of a Mixed State: The Most Efficient Purification Protocol

It is well known that any entangled mixed state in $2\otimes 2$ systems can be purified via infinite copies of the mixed state. But can one distill a pure maximally entangled state from finite copies of a mixed state in any bipartite system by local operation and classical communication? This is more meaningful in practical application. We give a necessary and sufficient condition of this distillability. This condition can be expressed as: there exists distillable-subspaces. According to this condition, one can judge whether a mixed state is distillable or not easily. We also analyze some properties of distillable-subspaces, and discuss the most efficient purification protocols. Finally, we discuss the distillable enanglement of two-quibt system for the case of finite copies.Comment: a revised versio

W Boson Inclusive Decays to Quarkonium at the LHC

In this paper, the production rates of quarkonia eta_c, J/psi, eta_b, Upsilon, B_c and B_c^* through W boson decay at the LHC are calculated, at the leading order in both the QCD coupling constant and in v, the typical velocity of the heavy quark inside of mesons. It shows that a sizable number of quarkonia from W boson decay will be produced at the LHC. Comparison with the predictions by using quark fragmentation mechanism is also discussed. Results show that, for the charmonium production through W decay, the difference between predictions by the fragmentation mechanism and complete leading order calculation is around 3%, and it is insensitive to the uncertainties of theoretical parameters; however, for the bottomonium and B_c^(*) productions, the difference cannot be ignored as the fragmentation mechanism is less applicable here due to the relatively large ratio mb/mw.Comment: Updated to match the published version in EPJ