A parallel and adaptive multigrid solver for the solutions of the optimal control of geometric evolution laws in two and three dimensions

We present a problem concerning the optimal control of geometric evolution laws. This is a minimisation problem that aims to find a control η which minimises the objective functional J subject to some imposed constraints. We apply this methodology to an application of whole cell tracking. Given two sets of data of cell morphologies, we may solve the optimal control problem to dynamically reconstruct the cell movements between the time frame of these two sets of data. This problem is solved in two and three space dimensions, using a state-of-the-art numerical method, namely multigrid, with adaptivity and parallelism

Zirconium carbide as an electrocatalyst for the chromous-chromic redox couple

Zirconium carbide is used as a catalyst in a REDOX cell for the oxidation of chromous ions to chromic ions and for the reduction of chromic ions to chromous ions. The zirconium carbide is coated on an inert electronically conductive electrode which is present in the anode fluid of the cell

D^0-D^0bar mixing in \Upsilon(1S) \to D^0 D^0bar decay at Super-B

\Dz-\Dzb mixing and significant CP violation in the charm system may indicate the signature of new physics. In this study, we suggest that the coherent \DzDzb events from the decay of \Upsilon(1S) \to \Dz \Dzb can be used to measure both mixing parameters and CP violation in charm decays. The neutral $D$ mesons from $\Upsilon(1S)$ decay are strongly boosted, so that it will offer the possibility to measure the proper-time interval, $\Delta t$, between the fully-reconstructed \Dz and \Dzb. Both coherent and time-dependent information can be used to extract \Dz-\Dzb mixing parameters. The sensitivity of the measurement should be improved at B factories or super-B.Comment: 6 pages, 1 figure, this is the last version to appear in Phys. Rev.

Dispersive Cylindrical Cloaks under Non-Monochromatic Illumination

Transformation-based cylindrical cloaks and concentrators are illuminated with non-monochromatic waves and unusual effects are observed with interesting potential applications. The transient responses of the devices are studied numerically with the Finite-Difference Time-Domain method and the results are verified with analytical formulas. We compute the effective bandwidth of several cloaking schemes as well as the effect of losses on the performance of the structures. We also find that narrowband behavior, frequency shift effects, time delays and spatial disturbances of the incoming waves are dominant due to the inherently dispersive nature of the devices. These effects are important and should be taken into account when designing metamaterial-based devices.Comment: 12 pages, 9 figure

Rashba spin splitting in biased semiconductor quantum wells

Rashba spin splitting (RSS) in biased semiconductor quantum wells is investigated theoretically based on the eight-band envelope function model. We find that at large wave vectors, RSS is both nonmonotonic and anisotropic as a function of in-plane wave vector, in contrast to the widely used linear and isotropic model. We derive an analytical expression for RSS, which can correctly reproduce such nonmonotonic behavior at large wave vectors. We also investigate numerically the dependence of RSS on the various band parameters and find that RSS increases with decreasing band gap and subband index, increasing valence band offset, external electric field, and well width. Our analytical expression for RSS provides a satisfactory explanation to all these features.Comment: 5 pages, 4 figures, author names corrected, submitted to Phys. Rev.

Noncommutativity as a Possible Origin of the Ultrahigh Energy Cosmic Ray and the TeV-photon Paradoxes

In this paper, we present a general modified dispersion relation derived from q-deformed noncommutative theory and apply it to the ultrahigh energy cosmic ray and the TeV-photon paradoxes--threshold anomalies. Our purpose is not only trying to solve these puzzles by noncommutative theory but also to support noncommutative theory through the coincidence of the region in the parameter space for resolving the threshold anomalies with the one from the q-deformed noncommutative theory.Comment: 9 pages, 1 figur

Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice

We show that the spin liquid phase of the half-filled Hubbard model on the triangular lattice can be described by a pure spin model. This is based on a high-order strong coupling expansion (up to order 12) using perturbative continuous unitary transformations. The resulting spin model is consistent with a transition from three-sublattice long-range magnetic order to an insulating spin liquid phase, and with a jump of the double occupancy at the transition. Exact diagonalizations of both models show that the effective spin model is quantitatively accurate well into the spin liquid phase, and a comparison with the Gutzwiller projected Fermi sea suggests a gapless spectrum and a spinon Fermi surface.Comment: 4 pages, 4 figures, published versions with additional dat