A simple numerical scheme for the 2D shallow-water system

This paper presents a simple numerical scheme for the two dimensional Shallow-Water Equations (SWEs). Inspired by the study of numerical approximation of the one dimensional SWEs Audusse et al. (2015), this paper extends the problem from 1D to 2D with the simplicity of application preserves. The new scheme is implemented into the code TELEMAC-2D [tel2d, 2014] and several tests are made to verify the scheme ability under an equilibrium state at rest and different types of flow regime (i.e., fluvial regime, transcritical flow from fluvial to torrential regime, transcritical flow with a hydraulic jump). The sensitivity analysis is conducted to exam the scheme convergence

Analytical solution for Klein-Gordon equation and action function of the solution for Dirac equation in counter-propagating laser waves

Nonperturbative calculation of QED processes participated by a strong electromagnetic field, especially provided by strong laser facilities at present and in the near future, generally resorts to the Furry picture with the usage of analytical solutions of the particle dynamical equation, such as the Klein-Gordon equation and Dirac equation. However only for limited field configurations such as a plane-wave field could the equations be solved analytically. Studies have shown significant interests in QED processes in a strong field composed of two counter-propagating laser waves, but the exact solutions in such a field is out of reach. In this paper, inspired by the observation of the structure of the solutions in a plane-wave field, we develop a new method and obtain the analytical solution for the Klein-Gordon equation and equivalently the action function of the solution for the Dirac equation in this field, under a largest dynamical parameter condition that there exists an inertial frame in which the particle free momentum is far larger than the other field dynamical parameters. The applicable range of the new solution is demonstrated and its validity is proven clearly. The result has the advantage of Lorentz covariance, clear structure and close similarity to the solution in a plane-wave field, and thus favors convenient application.Comment:

Modified light cone condition via vacuum polarization in a time dependent field

The appearance of unconventional vacuum properties in intense fields has long been an active field of research. In this paper the vacuum polarization effect is investigated via a pump probe scheme of a probe light propagating in the vacuum excited by two counter-propagating laser beams. The modified light cone condition of the probe light is derived analytically for the situation that it passes through the electric/magnetic antinode plane of the pump field. The derivation does not follow the commonly adopted assumption of treating the pump field as a constant field. Differences from the conventional light cone conditions are identified. The implications of the result are discussed with a consideration of the vacuum birefringence measurement.Comment: 7 pages, 0 figure

Trident Pair Production in Colliding Bright X-ray Laser Beams

The magnificent development of strong X-ray lasers motivates the advancement of pair production process studies into higher laser frequency region. In this paper, a resonant electron-positron pair production process with the absorption of two X-ray photons is considered in the impact of an energetic electron at the overlap region of two colliding X-ray laser beams. Laser-dressed QED method is justified to tackle the complexity of the corresponding multiple Feynman diagrams calculation. The dependence of the production rate as well as the positron energy distribution on the relative angles among the directions of the two laser wave vectors and the incoming electron momentum is revealed. It is shown that the non-plane wave laser field configuration arouses novel features in the pair production process compared to the plane-wave case.Comment: 5 pages, 5 figure

Combining RGB and Points to Predict Grasping Region for Robotic Bin-Picking

This paper focuses on a robotic picking tasks in cluttered scenario. Because of the diversity of objects and clutter by placing, it is much difficult to recognize and estimate their pose before grasping. Here, we use U-net, a special Convolution Neural Networks (CNN), to combine RGB images and depth information to predict picking region without recognition and pose estimation. The efficiency of diverse visual input of the network were compared, including RGB, RGB-D and RGB-Points. And we found the RGB-Points input could get a precision of 95.74%.Comment: 5 pages, 6 figure

Three-component topological superfluid in one-dimensional Fermi gases with spin-orbit coupling

We theoretically investigate one-dimensional three-component spin-orbit-coupled Fermi gases in the presence of Zeeman field. By solving the Bogoliubov-de-Gennes equations, we obtain the phase diagram at given chemical potential and order parameter. We show that the system undergoes a phase transition from Bardeen-Cooper-Schrieffer superfluid to topological superfluid as increasing the intensity of Zeeman field. By comparing to the two-component system, we find, besides the topological phase transition from the trivial superfluid to nontrivial topological superfluid, the system can always be in a nontrivial topological superfluid, and there are two Majorana zero energy regions while increasing the magnetic field. We find the three-component spin-orbit-coupled Fermi gases in certain parameter range is more optimizing for experimental realization due to the smaller magnetic field needed. We therefore propose a promising candidate for realizing topological superfluid.Comment: 8 pages, 9 figures, published versio

On Design of Optimal Nonlinear Kernel Potential Function for Protein Folding and Protein Design

Potential functions are critical for computational studies of protein structure prediction, folding, and sequence design. A class of widely used potentials for coarse grained models of proteins are contact potentials in the form of weighted linear sum of pairwise contacts. However, these potentials have been shown to be unsuitable choices because they cannot stabilize native proteins against a large number of decoys generated by gapless threading. We develop an alternative framework for designing protein potential. We describe how finding optimal protein potential can be understood from two geometric viewpoints, and we derive nonlinear potentials using mixture of Gaussian kernel functions for folding and design. The optimization criterion for obtaining parameters of the potential is to minimize bounds on the generalization error of discriminating protein structures and decoys not used in training. In our experiment we use a training set of 440 protein structures repre senting a major portion of all known protein structures, and about 14 million structure decoys and sequence decoys obtained by gapless threading. We succeeded in obtaining nonlinear potential with perfect discrimination of the 440 native structures and native sequences. For the more challenging task of sequence design when decoys are obtained by gapless threading, we show that there is no linear potential with perfect discrimination of all 440 native sequences. Results on an independent test set of 194 proteins also showed that nonlinear kernel potential performs well.Comment: 22 pages, 7 figures, and 5 table

Simplicial edge representation of protein structures and alpha contact potential with confidence measure

Protein representation and potential function are essential ingredients for studying proteins folding and protein prediction. We introduce a novel geometric representation of contact interactions using the edge simplices from alpha shape of protein structure. This representation can eliminate implausible neighbors not in physical contact, and can avoid spurious contact between two residues when a third residue is between them. We develop statistical alpha contact potential. A studentized bootstrap method is then introduced for assessing the 95% confidence intervals for each of the 210 parameters. We found with confidence that there is significant long range propensity (>30 residues apart) for hydrophobic interactions. We test alpha contact potential for native structure discrimination using several decoy sets, and found it often has comparable performance with atom-based potentials requiring more parameters. We also show that alpha contact potential has better performance than potential defined by cut-off distance between geometric centers of side chains. Clustering of alpha contact potentials reveals natural grouping of residues. To explore the relationship between shape representation and physicochemical representation, we test the minimum alphabet size for structure discrimination. We found that there is no significant difference in discrimination when alphabet size varies from 7 to 20, if geometry is represented accurately by alpha simplicial edges. This result suggests that the geometry of packing plays an important role, but the specific residue types are often interchangeable.Comment: 18 pages, 7 figures, and 6 tables. Accepted by Protein

Regularity and rigidity of asymptotically hyperbolic manifolds

In this paper, we study some intrinsic characterization of conformally compact manifolds. We show that, if a complete Riemannian manifold admits an essential set and its curvature tends to -1 at infinity in certain rate, then it is conformally compactifiable and the compactified metrics can enjoy some regularity at infinity. As consequences we prove some rigidity theorems for complete manifolds whose curvature tends to the hyperbolic one in a rate greater than 2.Comment: add reference and acknowledgement

Most memory efficient distributed super points detection on core networks

The super point, a host which communicates with lots of others, is a kind of special hosts gotten great focus. Mining super point at the edge of a network is the foundation of many network research fields. In this paper, we proposed the most memory efficient super points detection scheme. This scheme contains a super points reconstruction algorithm called short estimator and a super points filter algorithm called long estimator. Short estimator gives a super points candidate list using thousands of bytes memory and long estimator improves the accuracy of detection result using millions of bytes memory. Combining short estimator and long estimator, our scheme acquires the highest accuracy using the smallest memory than other algorithms. There is no data conflict and floating operation in our scheme. This ensures that our scheme is suitable for parallel running and we deploy our scheme on a common GPU to accelerate processing speed. We also describe how to extend our algorithm to sliding time. Experiments on several real-world core network traffics show that our algorithm acquires the highest accuracy with only consuming littler than one-fifth memory of other algorithms