A study of the high-inclination population in the Kuiper belt - II. The Twotinos

As the second part of our study, in this paper we proceed to explore the dynamics of the high-inclination Twotinos in the 1:2 Neptune mean motion resonance (NMMR). Depending on the inclination $i$, we show the existence of two critical eccentricities $e_a(i)$ and $e_c(i)$, which are lower limits of the eccentricity $e$ for the resonant angle $\sigma$ to exhibit libration and asymmetric libration, respectively. Accordingly, we have determined the libration centres $\sigma_0$ for inclined orbits, which are strongly dependent on $i$. With initial $\sigma=\sigma_0$ on a fine grid of $(e, i)$, the stability of orbits in the 1:2 NMMR is probed by 4-Gyr integrations. It is shown that symmetric librators are totally unstable for $i\ge30^{\circ}$; while stable asymmetric librators exist for $i$ up to $90^{\circ}$. We further investigate the 1:2 NMMR capture and retention of planetesimals with initial inclinations $i_0\le90^{\circ}$ in the planet migration model using a time-scale of $2\times10^7$ yr. We find that: (1) the capture efficiency of the 1:2 NMMR decreases drastically with the increase of $i_0$, and it goes to 0 when $i_0\ge60^{\circ}$; (2) the probability of discovering Twotinos with $i>25^{\circ}$, beyond observed values, is roughly estimated to be $\le0.1$ per cent; (3) more particles are captured into the leading rather than the trailing asymmetric resonance for $i_0\le10^{\circ}$, but this number difference appears to be the opposite at $i_0=20^{\circ}$ and is continuously varying for even larger $i_0$; (4) captured Twotinos residing in the trailing resonance or having $i>15^{\circ}$ are practically outside the Kozai mechanism, like currently observed samples.Comment: 13 pages, 10 figures, Accepted by MNRAS. Comments welcome

A survey of sparse representation: algorithms and applications

Sparse representation has attracted much attention from researchers in fields of signal processing, image processing, computer vision and pattern recognition. Sparse representation also has a good reputation in both theoretical research and practical applications. Many different algorithms have been proposed for sparse representation. The main purpose of this article is to provide a comprehensive study and an updated review on sparse representation and to supply a guidance for researchers. The taxonomy of sparse representation methods can be studied from various viewpoints. For example, in terms of different norm minimizations used in sparsity constraints, the methods can be roughly categorized into five groups: sparse representation with $l_0$-norm minimization, sparse representation with $l_p$-norm (0$<$p$<$1) minimization, sparse representation with $l_1$-norm minimization and sparse representation with $l_{2,1}$-norm minimization. In this paper, a comprehensive overview of sparse representation is provided. The available sparse representation algorithms can also be empirically categorized into four groups: greedy strategy approximation, constrained optimization, proximity algorithm-based optimization, and homotopy algorithm-based sparse representation. The rationales of different algorithms in each category are analyzed and a wide range of sparse representation applications are summarized, which could sufficiently reveal the potential nature of the sparse representation theory. Specifically, an experimentally comparative study of these sparse representation algorithms was presented. The Matlab code used in this paper can be available at: http://www.yongxu.org/lunwen.html.Comment: Published on IEEE Access, Vol. 3, pp. 490-530, 201

Metascreen-Based Acoustic Passive Phased Array

Conventional phased arrays require a large number of sources in forming a complex wave front, resulting in complexity and a high cost to operate the individual sources. We present a passive phased array using an acoustic metascreen that transmits sound energy from a single source and steers the transmitted wave front to form the desired fields. The metascreen is composed of elements that have a discrete resolution along the screen at an order smaller than the wavelength, allowing for fine wave-front shaping beyond the paraxial approximation. The performance is verified in experiment by forming a self-bending beam. Our metascreen-based passive array with its simplicity and capability has applications in places where conventional active arrays are complex and have limitations.Acoustical Society of AmericaNational Basic Research Program of China (973 Program) 2010CB327803 2012CB921504National Natural Science Foundation of China 11174138 11174139 11222442 81127901 11274168Physic