Differential quadrature method for space-fractional diffusion equations on 2D irregular domains

In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by L\'{e}vy processes, which are sometimes called super-diffusion equations. In this article, we develop the differential quadrature (DQ) methods for solving the 2D space-fractional diffusion equations on irregular domains. The methods in presence reduce the original equation into a set of ordinary differential equations (ODEs) by introducing valid DQ formulations to fractional directional derivatives based on the functional values at scattered nodal points on problem domain. The required weighted coefficients are calculated by using radial basis functions (RBFs) as trial functions, and the resultant ODEs are discretized by the Crank-Nicolson scheme. The main advantages of our methods lie in their flexibility and applicability to arbitrary domains. A series of illustrated examples are finally provided to support these points.Comment: 25 pages, 25 figures, 7 table

Laser Mode Bifurcations Induced by PT\mathcal{PT}-Breaking Exceptional Points

A laser consisting of two independently-pumped resonators can exhibit mode bifurcations that evolve out of the exceptional points (EPs) of the linear system at threshold. The EPs are non-Hermitian degeneracies occurring at the parity/time-reversal ($\mathcal{PT}$) symmetry breaking points of the threshold system. Above threshold, the EPs become bifurcations of the nonlinear zero-detuned laser modes, which can be most easily observed by making the gain saturation intensities in the two resonators substantially different. Small pump variations can then switch abruptly between different laser behaviors, e.g. between below-threshold and $\mathcal{PT}$-broken single-mode operation.Comment: 4 pages, 3 figure

Transport in gapped bilayer graphene: the role of potential fluctuations

We employ a dual-gated geometry to control the band gap \Delta in bilayer graphene and study the temperature dependence of the resistance at the charge neutrality point, RNP(T), from 220 to 1.5 K. Above 5 K, RNP(T) is dominated by two thermally activated processes in different temperature regimes and exhibits exp(T3/T)^{1/3} below 5 K. We develop a simple model to account for the experimental observations, which highlights the crucial role of localized states produced by potential fluctuations. The high temperature conduction is attributed to thermal activation to the mobility edge. The activation energy approaches \Delta /2 at large band gap. At intermediate and low temperatures, the dominant conduction mechanisms are nearest neighbor hopping and variable-range hopping through localized states. Our systematic study provides a coherent understanding of transport in gapped bilayer graphene.Comment: to appear in Physical Review B: Rapid Com

Bloch Oscillation under a Bichromatic Laser: Quasi-Miniband Formation, Collapse, and Dynamical Delocalization and Localization

A novel DC and AC driving configuration is proposed for semiconductor superlattices, in which the THz AC driving is provided by an intense bichromatic cw laser. The two components of the laser, usually in the visible light range, are near but not exactly resonant with interband Wannier-Stark transitions, and their frequency difference equals the Wannier-Stark ladder spacing. Multi-photon processes with the intermediate states in the conduction (valence) band cause dynamical delocalization and localization of valence (conduction) electrons, and the corresponding formation and collapse of the quasi-minibands.Comment: 4 pages, 3 figure

Electron-phonon bound states in graphene in a perpendicular magnetic field

The spectrum of electron-phonon complexes in a monolayer graphene is investigated in the presence of a perpendicular quantizing magnetic field. Despite the small electron-phonon coupling, usual perturbation theory is inapplicable for calculation of the scattering amplitude near the threshold of the optical phonon emission. Our findings beyond perturbation theory show that the true spectrum near the phonon emission threshold is completely governed by new branches, corresponding to bound states of an electron and an optical phonon with a binding energy of the order of $\alpha \omega_{0}$ where $\alpha$ is the electron-phonon coupling and $\omega_{0}$ the phonon energy.Comment: To be published in Phys. Rev. Lett., 5 pages, 3 figures, 1 tabl

Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid

We propose an experiment to directly probe the non-Abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana bound states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark state subspace.Comment: 4 pages; Add detailed discussion of feasibility of the scheme;add ref

A distinct sortase SrtB anchors and processes a streptococcal adhesin AbpA with a novel structural property.

Surface display of proteins by sortases in Gram-positive bacteria is crucial for bacterial fitness and virulence. We found a unique gene locus encoding an amylase-binding adhesin AbpA and a sortase B in oral streptococci. AbpA possesses a new distinct C-terminal cell wall sorting signal. We demonstrated that this C-terminal motif is required for anchoring AbpA to cell wall. In vitro and in vivo studies revealed that SrtB has dual functions, anchoring AbpA to the cell wall and processing AbpA into a ladder profile. Solution structure of AbpA determined by NMR reveals a novel structure comprising a small globular α/β domain and an extended coiled-coil heliacal domain. Structural and biochemical studies identified key residues that are crucial for amylase binding. Taken together, our studies document a unique sortase/adhesion substrate system in streptococci adapted to the oral environment rich in salivary amylase

Neutron scattering study of commensurate magnetic ordering in single crystal CeSb2_2

Temperature and field-dependent magnetization $M(H,T)$ measurements and neutron scattering study of a single crystal CeSb$_2$ are presented. Several anomalies in the magnetization curves have been confirmed at low magnetic field, i.e., 15.6 K, 12 K, and 9.8 K. These three transitions are all metamagnetic transitions (MMT), which shift to lower temperatures as the magnetic field increases. The anomaly at 15.6 K has been suggested as paramagnetic (PM) to ferromagnetic (FM) phase transition. The anomaly located at around 12 K is antiferromagnetic-like transition, and this turning point will clearly split into two when the magnetic field $H\geq0.2$ T. Neutron scattering study reveals that the low temperature ground state of CeSb$_2$ orders antiferromagnetically with commensurate propagation wave vectors $\textbf{k}=(-1,\pm1/6,0)$ and $\textbf{k}=(\pm1/6,-1,0)$, with N\'eel temperature $T_N\sim9.8$ K. This transition is of first-order, as shown in the hysteresis loop observed by the field cooled cooling (FCC) and field cooled warming (FCW) processes.Comment: 7 pages,9 figure

Long-term Evolution of Protostellar and Protoplanetary Disks. I. Outbursts

As an initial investigation into the long-term evolution of protostellar disks, we explore the conditions required to explain the large outbursts of disk accretion seen in some young stellar objects. We use one-dimensional time-dependent disk models with a phenomenological treatment of the magnetorotational instability (MRI) and gravitational torques to follow disk evolution over long timescales. Comparison with our previous two-dimensional disk model calculations (Zhu et al. 2009b, Z2009b) indicates that the neglect of radial effects and two-dimensional disk structure in the one-dimensional case makes only modest differences in the results; this allows us to use the simpler models to explore parameter space efficiently. We find that the mass infall rates typically estimated for low-mass protostars generally result in AU-scale disk accretion outbursts, as predicted by our previous analysis (Zhu et al. 2009a,Z2009a). We also confirm quasi-steady accretion behavior for high mass infall rates if the values of $\alpha$-parameter for the magnetorotational instability is small, while at this high accretion rate convection from the thermal instability may lead to some variations. We further constrain the combinations of the $\alpha$-parameter and the MRI critical temperature, which can reproduce observed outburst behavior. Our results suggest that dust sublimation may be connected with full activation of the MRI. This is consistent with the idea that small dust captures ions and electrons to suppress the MRI. In a later paper we will explore both long-term outburst and disk evolution with this model, allowing for infall from protostellar envelopes with differing angular momenta.Comment: Accepted to publish in Ap