Electron capture of iron group nuclei in magnetars

Using the theory of relativity in superstrong magnetic fields (SMFs) and nuclear shell model, we carry out estimation for electron capture (EC) rates on iron group nuclei in SMFs. The rates of change of electronic abundance (RCEA) due to EC are also investigated in SMFs. It is concluded that the EC rates of most iron group nuclides are increased greatly by SMFs and even exceeded by nine orders of magnitude. On the other hand, RCEA is influenced greatly by SMFs and even reduced by more than eight orders of magnitude in the EC reaction.We also compare our results with those of Fuller et al.(FFN) and Aufderheide et al.(AUFD) in the case with and without SMFs. The results show that our results are in good agreement with AUFD's, but the rates of FFN's are about close to one order of magnitude bigger than ours in the case without SMFs. On the contrary, our calculated rates for most nuclides in SMFs are increased and even exceeded as much as for nine and eight orders of magnitude of compared to FFN's and AUFD's results, which is in the case without SMFs, respectively.Comment: 8 pages, 13 figures, accepted by MNRA

Electron capture of strongly screening nuclides 56^{56}Fe, 56^{56}Co, 56^{56}Ni , 56^{56}Mn ,56^{56}Cr and 56^{56}V in presupernova

According to the Shell-Model Monte Carlo method, basing on the Random Phase Approximation and the linear response theory, we carried out an estimation on electron capture of strongly screening nuclides $^{56}$Fe, $^{56}$Co, $^{56}$Ni , $^{56}$Mn ,$^{56}$Cr and $^{56}$V in strong electron screening (SES)in presupernova. The EC rates are decreased greatly and even exceed $21.5\%$ in SES. We also compare our results with those of Aufderheide (AFUD), which calculated by the method of Aufderheide in SES. Our results are agreed reasonably well with AUFD at higher density-temperature surroundings (e.g. $\rho_7>60, T_9=15.40$) and the maximum error is $\sim$0.5$\%$. However, the maximum error is $\sim$13.0$\%$ at lower density surroundings (e.g. $^{56}$Cr at $\rho_7=10, T_9=15.40, Y_e=0.41$ ). On the other hand, we also compared our results in SES with those of FFN's and Nabi's, which is in the case without SES. The comparisons show that our results are lower more than one order magnitude than FFN's, but about $7.23\%$ than Nabi's.Comment: 6 pages,5 figures, MNRAS, Volume 433, Issue 2, p.1108-111

Strong screening effects on resonant nuclear reaction 23^{23}Mg (p,γ)(p,\gamma) 24^{24}Al in the surface of magnetars

Based on the theory of relativistic superstrong magnetic fields(SMFs), by using the method of the Thomas-Fermi-Dirac approximations, we investigate the problem of strong electron screening(SES) in SMFs, and the influence of SES on the nuclear reaction of $^{23}$Mg $(p, \gamma)$$^{24}$Al. Our calculations show that the nuclear reaction will be markedly effected by the SES in SMFs in the surface of magnetars. Our calculated screening rates can increase two orders of magnitude due to SES in SMFs

Supernova {\beta}^- decay of nuclides 53Fe, 54Fe, 55Fe, and 56Fe in strongly screened plasma

The electron screening strong effect on the electron energy and threshold energy of the beta decay reaction. in this paper, we study the $\beta^-$ decay rates of some iron isotopes. The electron screening beta decay rates increase by about two orders of magnitude. The strong screening beta decay rates due to Q-value correction are by more than one order of magnitude higher than those of without Q-value correction.Comment: 10 pages, 45 figures, accepted for publication in Resarch in Astronomy and Astrophysic

Phase matching condition for enhancement of phase sensitivity in quantum metrology

We find a phase matching condition for enhancement of sensitivity in a Mach-Zehnder interferometer illuminated by an arbitrary state in one input port and an odd(even) state in the other port. Under this condition, the Fisher information becomes maximal with respect to the relative phase of two modes and the phase sensitivity is enhanced. For the case with photon losses, we further find that the phase matching condition keeps unchanged with a coherent state and a coherent superposition state as the input states.Comment: 4 pages, 2 figure

Simultaneous approximation on affine subspaces

We solve the convergence case of the generalized Baker-Schmidt problem for simultaneous approximation on affine subspaces, under natural diophantine type conditions. In one of our theorems, we do not require monotonicity on the approximation function. In order to prove these results, we establish asymptotic formulae for the number of rational points close to an affine subspace. One key ingredient is a sharp upper bound on a certain sum of reciprocals of fractional parts associated with the matrix defining the affine subspace.Comment: To appear in IMR

Benchmark Tests of Convolutional Neural Network and Graph Convolutional Network on HorovodRunner Enabled Spark Clusters

The freedom of fast iterations of distributed deep learning tasks is crucial for smaller companies to gain competitive advantages and market shares from big tech giants. HorovodRunner brings this process to relatively accessible spark clusters. There have been, however, no benchmark tests on HorovodRunner per se, nor specifically graph convolutional network (GCN, hereafter), and very limited scalability benchmark tests on Horovod, the predecessor requiring custom built GPU clusters. For the first time, we show that Databricks' HorovodRunner achieves significant lift in scaling efficiency for the convolutional neural network (CNN, hereafter) based tasks on both GPU and CPU clusters, but not the original GCN task. We also implemented the Rectified Adam optimizer for the first time in HorovodRunner.Comment: AAAI 2020 W8 Deep Learning on Graphs: Methodologies and Applications Accepted Poster Number 2

A new insight into neutrino energy loss by electron capture of iron group nuclei in magnetars surface

Based on the relativistic mean-field effective interactions theory, and Lai dong model \citep{b37, b38, b39}, we discuss the influences of superstrong magnetic fields (SMFs) on electron Fermi energy, nuclear blinding energy, and single-particle level structure in magnetars surface. By using the method of Shell-Model Monte Carlo (SMMC), and the Random Phase Approximation (RPA) theory, we detailed analyze the neutrino energy loss rates(NELRs) by electron capture (EC) for iron group nuclei in SMFs.Comment: 22 pages, 8 figures, accepted for publication in ApJS. arXiv admin note: text overlap with arXiv:astro-ph/0606674, arXiv:nucl-th/9707052, arXiv:nucl-th/9801012, arXiv:1505.07304 by other author

Revisiting Optimal Power Control: its Dual Effect on SNR and Contention

In this paper we study a transmission power tune problem with densely deployed 802.11 Wireless Local Area Networks (WLANs). While previous papers emphasize on tuning transmission power with either PHY or MAC layer separately, optimally setting each Access Point's (AP's) transmission power of a densely deployed 802.11 network considering its dual effects on both layers remains an open problem. In this work, we design a measure by evaluating impacts of transmission power on network performance on both PHY and MAC layers. We show that such an optimization problem is intractable and then we investigate and develop an analytical framework to allow simple yet efficient solutions. Through simulations and numerical results, we observe clear benefits of the dual-effect model compared to solutions optimizing solely on a single layer; therefore, we conclude that tuning transmission power from a dual layer (PHY-MAC) point of view is essential and necessary for dense WLANs. We further form a game theoretical framework and investigate above power-tune problem in a strategic network. We show that with decentralized and strategic users, the Nash Equilibrium (N.E.) of the corresponding game is in-efficient and thereafter we propose a punishment based mechanism to enforce users to adopt the social optimal strategy profile under both perfect and imperfect sensing environments

Liouville correspondence between the Short-Pulse Hierarchy and the Sine-Gordon Hierarchy

This paper considers the whole hierarchy of bi-Hamiltonian integrable equations associated to each of the Short-Pulse (SP) equation and the Sine-Gordon (SG) equation. We prove that the transformation that relates the SP equation with the SG equation also serves to establish the correspondence between their flows and Hamiltonian conservation laws in respective hierarchy