A Study of deuteron electromagnetic form factors with light-front approach

The electromagnetic form factors and low-energy observables of deuteron are studied with the help of the light-front approach, where the deuteron is regarded as a weekly bound state of a proton and a neutron. Both the $S-$ and $D-$wave interacting vertexes among deuteron, proton, and neutron are taken into account. Moreover, the regularization functions are also introduced. In our calculations, the vertex and the regularization functions are employed to simulate the momentum distribution inside the deuteron. Our numerical results show that the light-front approach can roughly reproduce the deuteron electromagnetic form factors, like charge $G_0$, magnetic $G_1$, and quadrupole $G_2$, in the low $Q^2$ region. The important role of the $D-$wave vertex on $G_2$ is also addressed

Polarized GPDs and structure functions of ρ\rho meson

The $\rho$ meson polarized generalized parton distribution functions, its structure functions $g_1$ and $g_2$ and its axial form factors ${\tilde G}_{1,2}$ are studied based on a light-front quark model for the first time. Comparing our obtained moments of $g_1$ to lattice QCD calculation, we find that our results are reasonably consistent to the Lattice predictions

Distributed Real-Time Power Balancing in Renewable-Integrated Power Grids with Storage and Flexible Loads

The large-scale integration of renewable generation directly affects the reliability of power grids. We investigate the problem of power balancing in a general renewable-integrated power grid with storage and flexible loads. We consider a power grid that is supplied by one conventional generator (CG) and multiple renewable generators (RGs) each co-located with storage,and is connected with external markets. An aggregator operates the power grid to maintain power balance between supply and demand. Aiming at minimizing the long-term system cost, we first propose a real-time centralized power balancing solution, taking into account the uncertainty of the renewable generation, loads, and energy prices. We then provide a distributed implementation algorithm, significantly reducing both computational burden and communication overhead. We demonstrate that our proposed algorithm is asymptotically optimal as the storage capacity increases and the CG ramping constraint loosens. Moreover, the distributed implementation enjoys a fast convergence rate, and enables each RG and the aggregator to make their own decisions. Simulation shows that our proposed algorithm outperforms alternatives and can achieve near-optimal performance for a wide range of storage capacity.Comment: To appear in IEEE Transactions on Smart Grid, 201

Real-Time Welfare-Maximizing Regulation Allocation in Dynamic Aggregator-EVs System

The concept of vehicle-to-grid (V2G) has gained recent interest as more and more electric vehicles (EVs) are put to use. In this paper, we consider a dynamic aggregator-EVs system, where an aggregator centrally coordinates a large number of dynamic EVs to perform regulation service. We propose a Welfare-Maximizing Regulation Allocation (WMRA) algorithm for the aggregator to fairly allocate the regulation amount among its EVs. Compared to previous works, WMRA accommodates a wide spectrum of vital system characteristics, including dynamics of EV, limited EV battery size, EV battery degradation cost, and the cost of using external energy sources for the aggregator. The algorithm operates in real time and does not require any prior knowledge of the statistical information of the system. Theoretically, we demonstrate that WMRA is away from the optimum by O(1/V), where V is a controlling parameter depending on EV's battery size. In addition, our simulation results indicate that WMRA can substantially outperform a suboptimal greedy algorithm.Comment: 13 page

WENO interpolation-based and upwind-biased schemes with free-stream preservation

Based on the understandings regarding linear upwind schemes with flux splitting to achieve free-stream preservation (Q. Li, etc. Commun. Comput. Phys., 22 (2017) 64-94), a series of WENO interpolation-based and upwind-biased nonlinear schemes are proposed in this study. By means of engagement of fluxes on midpoints, the nonlinearity of schemes is introduced through WENO interpolations, and upwind-biased features are acquired through the choice of dependent grid stencil. Regarding the third- and fifth-order versions, schemes with one and two midpoints are devised and carefully tested. With the integration of the piecewise-polynomial mapping function methods (Q. Li, etc. Commun. Comput. Phys. 18 (2015) 1417-1444), the proposed schemes are found to achieve the designed orders and free-stream preservation property. In 1-D Sod and Shu-Osher problems, all schemes succeed in yielding well predictions. In 2-D cases, the vortex preservation, supersonic inviscid flow around cylinder at M=4, Riemann problem and Shock-vortex interaction problems are tested. In each problem, two types of grids are employed, i.e. the uniformed/smooth grids and the randomized/partially-randomized grids. On the latter, the shock wave and complex flow structures are located/partially located. All schemes fulfill computations in uniformed/smooth grids with satisfactory results. On randomized grids, all schemes accomplish computations and yield reasonable results except the third-order one with two midpoints engaged fails in Riemann problem and shock-vortex interaction problem. Overall speaking, the proposed schemes manifest the capability to solve problems on grids with bad quality, and therefore indicate their potential in engineering applications

Hybridizing WENO implementations of interpolation and reconstruction-wise operation for upwind-biased schemes with free-stream preservation

Cases have shown that WENO schemes usually behave robustly on problems containing shocks with high pressure ratios when uniformed or smooth grids are present, while nonlinear schemes based on WENO interpolations might relatively be liable to numerical instability. In the meanwhile, the latter have manifested their advantages in computations on grids of bad quality, because the free-stream preservation is easily realized there, and what is more flux-splitting schemes with low dissipations can be engaged inherently as well. Targeting at above dissatisfactions, a method by hybridizing WENO implementations of interpolation and reconstruction-wise operation for upwind-biased schemes with flux splitting employed is proposed and corresponding third-, fifth- and seventh-order upwind-biased schemes are proposed. Based on the understandings of [Q. Li, et al. Commun. Comput. Phys. 22 (2017) 64-94], the free-stream preservation of proposed schemes is achieved with incorporation of frozen grid metrics in WENO reconstructions-wise operations on split fluxes. In proposed schemes, flux-splitting schemes with low dissipation can also be applied for the flux on a cell edge. As a byproduct, an implementation of WENO scheme with free-stream preservation is obtained. Numerical examples are provided as following with the third- and fifth-order schemes being tested. In tests of free-stream preservation, the property is achieved as expected (including two implementations of WENO). The computation of 1-D Sod problem shows the capability of proposed schemes on solving ordinary shock discontinuity. 2-D vortex preservation and double Mach reflection are tested on uniformed and randomized grids. The accomplishment by proposed schemes manifests their capability and robustness on solving problems under rigorous circumstances

Representations by x12+2x22+x32+x42+x1x3+x1x4+x2x4x_1^2+2x_2^2+x_3^2+x_4^2+x_1x_3+x_1x_4+x_2x_4

Let $r_Q(n)$ be the representation number of a nonnegative integer $n$ by the quaternary quadratic form $Q=x_1^2+2x_2^2+x_3^2+x_4^2+x_1x_3+x_1x_4+x_2x_4$. We first prove the identity $r_Q(p^2n)=r_Q(p^2)r_Q(n)/r_Q(1)$ for any prime $p$ different from 13 and any positive integer $n$ prime to $p$, which was conjectured in [Eum et al, A modularity criterion for Klein forms, with an application to modular forms of level 13, J. Math. Anal. Appl. 375 (2011), 28--41]. And, we explicitly determine a concise formula for the number $r_Q(n^2)$ as well for any integer $n$

Phase Balancing Using Energy Storage in Power Grids under Uncertainty

Phase balancing is essential to safe power system operation. We consider a substation connected to multiple phases, each with single-phase loads, generation, and energy storage. A representative of the substation operates the system and aims to minimize the cost of all phases and to balance loads among phases. We first consider ideal energy storage with lossless charging and discharging, and propose both centralized and distributed real-time algorithms taking into account system uncertainty. The proposed algorithm does not require any system statistics and asymptotically achieves the minimum system cost with large energy storage. We then extend the algorithm to accommodate more realistic non-ideal energy storage that has imperfect charging and discharging. The performance of the proposed algorithm is evaluated through extensive simulation and compared with that of a benchmark greedy algorithm. Simulation shows that our algorithm leads to strong performance over a wide range of storage characteristics

The Spin-weighted Spheroidal Wave functions in the Case of s=1/2

The spin-weighted spheroidal equations in the case s=1/2 is thoroughly studied in the paper by means of the perturbation method in supersymmetry quantum mechanics. The first-five terms of the super-potential in the series of the parameter beta are given. The general form of the nth term of the superpotential is also obtained, which could derived from the previous terms W_{k}, k<n. From the results, it is easy to give the ground eigenfunction of the equation. Furthermore, the shape-invariance property is investigated in the series form of the parameter beta and is proven kept in this series form for the equations. This nice property guarantee one could obtain the excited eigenfunctions in the series form from the ground eigenfunctions by the method in supersymmetry quantum mechanics. This shows the perturbation method method in supersymmetry quantum mechanics could solve the spin-weight spheroidal wave equations completely in the series form of the small parameter beta

Exploration quantum steering, nonlocality and entanglement of two-qubit X-state in structured reservoirs

In this work, there are two parties, Alice on Earth and Bob on the satellite, which initially share an entangled state, and some open problems, which emerge during quantum steering that Alice remotely steers Bob, are investigated. Our analytical results indicate that all entangled pure states and maximally entangled evolution states (EESs) are steerable, and not every entangled evolution state is steerable and some steerable states are only locally correlated. Besides, quantum steering from Alice to Bob experiences a "sudden death" with increasing decoherence strength. However, shortly after that, quantum steering experiences a recovery with the increase of decoherence strength in bit flip (BF) and phase flip (PF) channels. Interestingly, while they initially share an entangled pure state, all EESs are steerable and obey Bell nonlocality in PF and phase damping channels. In BF channels, all steerable states can violate Bell-CHSH inequality, but some EESs are unable to be employed to realize steering. However, when they initially share an entangled mixed state, the outcome is different from that of the pure state. Furthermore, the steerability of entangled mixed states is weaker than that of entangled pure states. Thereby, decoherence can induce the degradation of quantum steering, and the steerability of state is associated with the interaction between quantum systems and reservoirs.Comment: 17 pages, 4 figures and 3 table