At present, fast waveform digitizing circuit is more and more employed in modern physics experiments for processing the signals from an array detector. A new fast waveform sampling digitizing circuit developed by us is presented in this paper. Differ
ent with the traditional waveform digitizing circuit constructed with analog to digital converter(ADC) or time to digital converter(TDC), it is developed based on domino ring sampler(DRS), a switched capacitor array(SCA) chip. A DRS4 chip is used as a core device in our circuit, which has a fast sampling rate up to five gigabit samples per second (GSPS). The circuit has advantages of high resolution, low cost, low power dissipation, high channel density and small size. The quite satisfactory results are acquired by the preliminary performance test of this circuit board. Eight channels can be provided by one board, which has a 1-volt input dynamic range for each channel. The circuit linearity is better than 0.1%, the noise is less than 0.5 mV (root mean square, RMS), and its time resolution is about 50ps. The several boards can be cascaded to construct a multi-board system. The good performances make the circuit board to be used not only for physics experiments, but also for other applications.
We construct model wavefunctions for the collective modes of fractional quantum Hall systems. The wavefunctions are expressed in terms of symmetric polynomials characterized by a root partition and a squeezed basis, and show excellent agreement with
exact diagonalization results for finite systems. In the long wavelength limit, the model wavefunctions reduce to those predicted by the single-mode approximation, and remain accurate at energies above the continuum of roton pairs.
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it represents a n
atural route to understand the dynamics, as well as to synthesize or optimize the functions, of networks. A broad spectrum of network structural patterns have been respectively reported in the past decade, such as communities, multipartites, hubs, authorities, outliers, bow ties, and others. Here, we show that most individual real-world networks demonstrate multiplex structures. That is, a multitude of known or even unknown (hidden) patterns can simultaneously situate in the same network, and moreover they may be overlapped and nested with each other to collaboratively form a heterogeneous, nested or hierarchical organization, in which different connective phenomena can be observed at different granular levels. In addition, we show that the multiplex structures hidden in exploratory networks can be well defined as well as effectively recognized within an unified framework consisting of a set of proposed concepts, models, and algorithms. Our findings provide a strong evidence that most real-world complex systems are driven by a combination of heterogeneous mechanisms that may collaboratively shape their ubiquitous multiplex structures as we observe currently. This work also contributes a mathematical tool for analyzing different sources of networks from a new perspective of unveiling multiplex structures, which will be beneficial to multiple disciplines including sociology, economics and computer science.
By extending Koisos examples to the non-compact case, we construct complete gradient Kahler-Ricci solitons of various types on certain holomorphic line bundles over compact Kahler-Einstein manifolds. Moreover, a uniformization result on steady gradie
nt Kahler-Ricci solitons with non-negative Ricci curvature is obtained under additional assumptions.
