Wave Function and Pair Distribution Function of a Dilute Bose Gas

The wave function of a dilute hard sphere Bose gas at low temperatures is discussed, emphasizing the formation of pairs. The pair distribution function is calculated for two values of $\sqrt{\rho a^3}$.Comment: 2 pages, 1 figur

General rogue waves and their dynamics in several reverse time integrable nonlocal nonlinear equations

A study of general rogue waves in some integrable reverse time nonlocal nonlinear equations is presented. Specifically, the reverse time nonlocal nonlinear Schr\"odinger (NLS) and nonlocal Davey-Stewartson (DS) equations are investigated, which are nonlocal reductions from the AKNS hierarchy. By using Darboux transformation (DT) method, several types of rogue waves are constructed. Especially, a unified binary DT is found for this nonlocal DS system, thus the solution formulas for nonlocal DSI and DSII equation can be written in an uniform expression. Dynamics of these rogue waves is separately explored. It is shown that the (1+1)-dimensional rogue waves in nonlocal NLS equation can be bounded for both x and t, or develop collapsing singularities. It is also shown that the (1+2)-dimensional line rogue waves in the nonlocal DS equations can be bounded for all space and time, or have finite-time blowing-ups. All these types depend on the values of free parameters introduced in the solution. In addition, the dynamics patterns in the multi- and higher-order rogue waves exhibits more richer structures, most of which have no counterparts in the corresponding local nonlinear equations.Comment: 22 pages, 12 figure

Dynamics of Rogue Waves in the Partially PT-symmetric Nonlocal Davey-Stewartson Systems

In this work, we study the dynamics of rogue waves in the partially $\cal{PT}$-symmetric nonlocal Davey-Stewartson(DS) systems. Using the Darboux transformation method, general rogue waves in the partially $\cal{PT}$-symmetric nonlocal DS equations are derived. For the partially $\cal{PT}$-symmetric nonlocal DS-I equation, the solutions are obtained and expressed in term of determinants. For the partially $\cal{PT}$-symmetric DS-II equation, the solutions are represented as quasi-Gram determinants. It is shown that the fundamental rogue waves in these two systems are rational solutions which arises from a constant background at $t\rightarrow -\infty$, and develops finite-time singularity on an entire hyperbola in the spatial plane at the critical time. It is also shown that the interaction of several fundamental rogue waves is described by the multi rogue waves. And the interaction of fundamental rogue waves with dark and anti-dark rational travelling waves generates the novel hybrid-pattern waves. However, no high-order rogue waves are found in this partially $\cal{PT}$-symmetric nonlocal DS systems. Instead, it can produce some high-order travelling waves from the high-order rational solutions.Comment: 22 pages, 26 figure

All-optical controlled phase gate in quantum dot molecules

We propose a two-qubit optically controlled phase gate in quantum dot molecules via adiabatic passage and hole tunneling. Our proposal combines the merits of the current generation of vertically stacked self-assembled InAs quantum dots and adiabatic passage. The simulation shows an implementation of the gate with a fidelity exceeding 0.98

Development of Krylov and AMG linear solvers for large-scale sparse matrices on GPUs

This research introduce our work on developing Krylov subspace and AMG solvers on NVIDIA GPUs. As SpMV is a crucial part for these iterative methods, SpMV algorithms for single GPU and multiple GPUs are implemented. A HEC matrix format and a communication mechanism are established. And also, a set of specific algorithms for solving preconditioned systems in parallel environments are designed, including ILU(k), RAS and parallel triangular solvers. Based on these work, several Krylov solvers and AMG solvers are developed. According to numerical experiments, favorable acceleration performance is acquired from our Krylov solver and AMG solver under various parameter conditions

How Much Frequency Can Be Reused in 5G Cellular Networks---A Matrix Graph Model

The 5th Generation cellular network may have the key feature of smaller cell size and denser resource employment, resulted from diminishing resource and increasing communication demands. However, small cell may result in high interference between cells. Moreover, the random geographic patterns of small cell networks make them hard to analyze, at least excluding schemes in the well-accepted hexagonal grid model. In this paper, a new model---the matrix graph is proposed which takes advantage of the small cell size and high inter-cell interference to reduce computation complexity. This model can simulate real world networks accurately and offers convenience in frequency allocation problems which are usually NP-complete. An algorithm dealing with this model is also given, which asymptotically achieves the theoretical limit of frequency allocation, and has a complexity which decreases with cell size and grows linearly with the network size. This new model is specifically proposed to characterize the next-generation cellular networks.Comment: 12 page

Parallel Triangular Solvers on GPU

In this paper, we investigate GPU based parallel triangular solvers systematically. The parallel triangular solvers are fundamental to incomplete LU factorization family preconditioners and algebraic multigrid solvers. We develop a new matrix format suitable for GPU devices. Parallel lower triangular solvers and upper triangular solvers are developed for this new data structure. With these solvers, ILU preconditioners and domain decomposition preconditioners are developed. Numerical results show that we can speed triangular solvers around seven times faster

Observation of a reversal of breakout reconnection preceding a jet: evidence of oscillatory magnetic reconnection?

Recent studies have revealed that solar jets involving minifilament eruptions may be initiated under the well-known magnetic-breakout mechanism. Before or just at the onset of those jets, there should be a current sheet, where breakout magnetic reconnection takes place, between open fields and the outside of the jet-base arcade carrying minifilament in its core. In this paper we present a jet produced by eruption of two minifilaments lying at the jet base. A current sheet is directly detected near the jet base before the onset of the eruption, suggesting the magnetic-breakout mechanism. However, we further find that the current sheet undergoes a transition. The current sheet first shortens to zero in length, but then lengthens towards an orthogonal direction relative to its initial orientation. The change of the current sheet gives rise to a reversal of the breakout reconnection, as the inflow and outflow regions before the transition become the outflow and inflow regions after the transition, respectively. We therefore propose that this observation provides evidence for the so-called oscillatory reconnection which is defined by a series of reconnection reversals but not yet proved to exist in real plasma environment of the solar atmosphere.Comment: 13 pages, 5 figures, accepted for publication in Ap

The Formation of a Small-scale Filament after Flux Emergence on the Quiet Sun

We present observations of the formation process of a small-scale filament on the quiet Sun during 5-6 February 2016 and investigate its formation cause. Initially, a small dipole emerged and its associated arch filament system was found to reconnect with overlying coronal fields accompanied by numerous EUV bright points. When bright points faded out, many elongated dark threads formed bridging the positive magnetic element of dipole and external negative network fields. Interestingly, an anti-clockwise photospheric rotational motion (PRM) set in within the positive endpoint region of newborn dark threads following the flux emergence and lasted for more than 10 hours. Under the drive of the PRM, these dispersive dark threads gradually aligned along the north-south direction and finally coalesced into an inverse S-shaped filament. Consistent with the dextral chirality of the filament, magnetic helicity calculations show that an amount of negative helicity was persistently injected from the rotational positive magnetic element and accumulated during the formation of the filament. These observations suggest that twisted emerging fields may lead to the formation of the filament via reconnection with pre-existing fields and release of its inner magnetic twist. The persistent PRM might trace a covert twist relaxation from below photosphere to the low corona.Comment: 9 figure

Witnessing tether-cutting reconnection at the onset of a partial eruption

In this paper, we study the onset process of a solar eruption on 21 February 2015, focusing on its unambiguous precursor phase. With multi-wavelength imaging observations from the Atmospheric Imaging Assembly (AIA), definitive tether-cutting (TC) reconnection signatures, i.e., flux convergence and cancellation, bidirectional jets, as well as topology change of hot loops, were clearly observed below the pre-eruption filament. As TC reconnection progressed between the sheared arcades that enveloped the filament, a channel-like magnetic flux rope (MFR) arose in multi-wavelength AIA passbands wrapping around the main axis of the filament. With the subsequent ascent of the newborn MFR, the filament surprisingly split into three branches. After a 7-hour slow rise phase, the high-lying branch containing by the MFR abruptly accelerated causing a two-ribbon flare; while the two low-lying branches remained stable forming a partial eruption. Complemented by kinematic analysis and decay index calculation, we conclude that TC reconnection played a key role in building up the eruptive MFR and triggering its slow rise. The onset of the torus instability may have led the high-lying branch into the standard eruption scenario in the fashion of a catastrophe.Comment: 9 figure