Localized gap soliton trains of Bose-Einstein condensates in an optical lattice

We develop a systematic analytical approach to study the linear and nonlinear solitary excitations of quasi-one-dimensional Bose-Einstein condensates trapped in an optical lattice. For the linear case, the Bloch wave in the $nth$ energy band is a linear superposition of Mathieu's functions $ce_{n-1}$ and $se_n$; and the Bloch wave in the $nth$ band gap is a linear superposition of $ce_n$ and $se_n$. For the nonlinear case, only solitons inside the band gaps are likely to be generated and there are two types of solitons -- fundamental solitons (which is a localized and stable state) and sub-fundamental solitons (which is a lacalized but unstable state). In addition, we find that the pinning position and the amplitude of the fundamental soliton in the lattice can be controlled by adjusting both the lattice depth and spacing. Our numerical results on fundamental solitons are in quantitative agreement with those of the experimental observation [Phys. Rev. Lett. {\bf92}, 230401 (2004)]. Furthermore, we predict that a localized gap soliton train consisting of several fundamental solitons can be realized by increasing the length of the condensate in currently experimental conditions.Comment: 9 pages, 6 figures, accepted for publicaiton in PR

Mining Frequent Graph Patterns with Differential Privacy

Discovering frequent graph patterns in a graph database offers valuable information in a variety of applications. However, if the graph dataset contains sensitive data of individuals such as mobile phone-call graphs and web-click graphs, releasing discovered frequent patterns may present a threat to the privacy of individuals. {\em Differential privacy} has recently emerged as the {\em de facto} standard for private data analysis due to its provable privacy guarantee. In this paper we propose the first differentially private algorithm for mining frequent graph patterns. We first show that previous techniques on differentially private discovery of frequent {\em itemsets} cannot apply in mining frequent graph patterns due to the inherent complexity of handling structural information in graphs. We then address this challenge by proposing a Markov Chain Monte Carlo (MCMC) sampling based algorithm. Unlike previous work on frequent itemset mining, our techniques do not rely on the output of a non-private mining algorithm. Instead, we observe that both frequent graph pattern mining and the guarantee of differential privacy can be unified into an MCMC sampling framework. In addition, we establish the privacy and utility guarantee of our algorithm and propose an efficient neighboring pattern counting technique as well. Experimental results show that the proposed algorithm is able to output frequent patterns with good precision

Transmutation prospect of long-lived nuclear waste induced by high-charge electron beam from laser plasma accelerator

Photo-transmutation of long-lived nuclear waste induced by high-charge relativistic electron beam (e-beam) from laser plasma accelerator is demonstrated. Collimated relativistic e-beam with a high charge of approximately 100 nC is produced from high-intensity laser interaction with near-critical-density (NCD) plasma. Such e-beam impinges on a high-Z convertor and then radiates energetic bremsstrahlung photons with flux approaching 10^{11} per laser shot. Taking long-lived radionuclide ^{126}Sn as an example, the resulting transmutation reaction yield is the order of 10^{9} per laser shot, which is two orders of magnitude higher than obtained from previous studies. It is found that at lower densities, tightly focused laser irradiating relatively longer NCD plasmas can effectively enhance the transmutation efficiency. Furthermore, the photo-transmutation is generalized by considering mixed-nuclide waste samples, which suggests that the laser-accelerated high-charge e-beam could be an efficient tool to transmute long-lived nuclear waste.Comment: 13 pages, 8 figures, it has been submitted to Physics of Plasm

Domain wall propagation through spin wave emission

We theoretically study field-induced domain wall (DW) motion in an electrically insulating ferromagnet with hard- and easy-axis anisotropies. DWs can propagate along a dissipationless wire through spin wave emission locked into the known soliton velocity at low fields. In the presence of damping, the mode appears before the Walker breakdown field for strong out-of-plane magnetic anisotropy, and the usual Walker rigid-body propagation mode becomes unstable when the field is between the maximal-DW-speed field and Walker breakdown field.Comment: 4 pages, 4 figure

Optimal time-dependent polarized current pattern for fast domain wall propagation in nanowires: Exact solutions for biaxial and uniaxial anisotropies

One of the important issues in nanomagnetism is to lower the current needed for a technologically useful domain wall (DW) propagation speed. Based on the modified Landau-Lifshitz-Gilbert (LLG) equation with both Slonczewski spin-transfer torque and the field-like torque, we derive the optimal spin current pattern for fast DW propagation along nanowires. Under such conditions, the DW velocity in biaxial wires can be enhanced as much as ten times compared to the velocities achieved in experiments so far. Moreover, the fast variation of spin polarization can help DW depinning. Possible experimental realizations are discussed.Comment: 4 pages, 1 figur