33,825 research outputs found
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 energy
band is a linear superposition of Mathieu's functions and ;
and the Bloch wave in the band gap is a linear superposition of
and . 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
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