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By considering the general relativity effect, we calculated the dipolar toroidal magnetic field decay rates and investigated the L-X - L-rot relationship of 22 magnetars with soft X-ray luminosities. It is found that, for magnetars with L-X L-rot, the Ohmic decay of crustal toroidal magnetic fields can provide their observed isotropic soft X-ray luminosities and maintain high thermal temperatures.

Here, we summarize our recent work on the evolution of magnetic field and spin-down of young pulsars including high-B pulsars and magnetars. Our work includes the following three parts: (a) Based on the estimated ages of their potentially associated supernova remnants (SNRs), we estimate the values of the mean braking indices of eight magnetars with SNRs and find that fivemagnetars have smallermean braking indices of 1

By considering the combined effects of both the standard magnetic dipole model and the composite neutron superfluid vortex model on pulsar's spin-down, we study the evolution of pulsar's spin-down on the P - P diagram. The evolution path of each pulsar is dictated by a particular mechanism in our hybrid model within different parameter spaces. The valley of each curve is the most possible place for a neutron star (NS) to be observed as this is the place corresponding to the minimum value of the evolution speed (i.e., the time derivative P). In other words, pulsars would distribute around these valleys on the P - P diagram. The suppressed region in the lower-right part of the diagram can be explained by neutrino cyclotron emission from the S-1(0) neutron superfluid vortexes in NSs.

The pH responsive properties of poly[2-(methacryloyloxy)ethyl trimethylammonium chloride] (PMETAC) brushes have been manifested in an experiment carried out by Liu et al. (2017). In this paper, we have employed a molecular theory to study the pH response of strong polyelectrolyte brushes (SPBs), by considering both strong polyelectrolyte-OH− (P–O) hydrogen bonds and polyelectrolyte-counterions (P–C) bonds and their explicit coupling to the SPB conformation. It is found that, when at lower salt concentrations, the combination of P–O hydrogen bonds and P–C bonds results in the pH-responsive properties of a SPB, which are governed by the formation of interchain hydrogen bonds, while at higher salt concentrations, the pH response of the SPB is suppressed by the effect of salt ions. This finding agrees well with the experimental observation. We also investigate the OH−-mediated bridging effect on the structure of a SPB. Based on this theoretical perspective, we predict that the pH response of a SPB will depend on the identity of salt, and the OH−-mediated bridging interactions can induce a vertically phase segregation in a SPB.

There is accumulating evidence that scalar fields may exist in nature. The gravitational collapse of a boson cloud leads to the formation of a boson star just like white dwarfs and neutron stars. In general, as one of the candidates of dark matter, a boson star holds a stable configuration and has deserved intensive attention and extensive research in the past 50years. At first, we analyze the ground state solutions for a Boson-Fermi system using the metric tensor in the Newtonian approximation, then analyze the configuration of a star composed of bosons and fermions. At last, for the purpose of investigating the equilibrium geometry of a Boson-Fermi system, we construct the virial equations of a boson-Fermi system with different orders. In our future work, we will explore the equilibrium configuration and the stability of a Boson-Fermi star and how a scalar field affects the pressure of the system using higher-order virial equations of fluid motions.

Young pulsars are thought to be highly magnetized neutron stars (NSs). The crustal magnetic field of a NS usually decays at different timescales in the forms of Hall drift and Ohmic dissipation. The magnetization parameter &omega, B &tau, is defined as the ratio of the Ohmic timescale &tau, O h m to the Hall drift timescale &tau, H a l l . During the first several million years, the inner temperature of the newly born neutron star cools from T = 10 9 K to T = 1 . 0 &times, 10 8 K, and the crustal conductivity increases by three orders of magnitude. In this work, we adopt a unified equations of state for cold non-accreting neutron stars with the Hartree&ndash, Fock&ndash, Bogoliubov method, developed by Pearson et al. (2018), and choose two fiducial dipole magnetic fields of B = 1 . 0 &times, 10 13 G and B = 1 . 0 &times, 10 14 G, four different temperatures, T, and two different impurity concentration parameters, Q, and then calculate the conductivity of the inner crust of NSs and give a general expression of magnetization parameter for young pulsars: &omega, ≃ ( 1 &minus, 50 ) B 0 / ( 10 13 G) by using numerical simulations. It was found when B &le, 10 15 G, due to the quantum effects, the conductivity increases slightly with the increase in the magnetic field, the enhanced magnetic field has a small effect on the matter in the low-density regions of the crust, and almost has no influence the matter in the high-density regions. Then, we apply the general expression of the magnetization parameter to the high braking-index pulsar PSR J1640-4631. By combining the observed arrival time parameters of PSR J1640-4631 with the magnetic induction equation, we estimated the initial rotation period P 0 , the initial dipole magnetic field B 0 , the Ohm dissipation timescale &tau, O h m and Hall drift timescale &tau, H a l l . We model the magnetic field evolution and the braking-index evolution of the pulsar and compare the results with its observations. It is expected that the results of this paper can be applied to more young pulsars.

PSR J1640+2224 is a binary millisecond pulsar (BMSP) with a white dwarf (WD) companion. Recent observations indicate that the WD is very likely to be a $\sim 0.7\,M_{\odot}$ CO WD. Thus the BMSP should have evolved from an intermediate-mass X-ray binary (IMXB). However, previous investigations on IMXB evolution predict that the orbital periods of the resultant BMSPs are generally $2.0\,M_{\odot}$)., 24 pages, 5 figures, accepted for publication in ApJ

Magnetars are a kind of pulsars powered mainly by superhigh magnetic fields. They are popular sources with many unsolved issues in themselves, but also linked to various high energy phenomena, such as QPOs, giant flares, fast radio bursts and super-luminous supernovae. In this work, we first review our recent works on the dissipation of toroidal magnetic fields in magnetars and rotationally powered pulsars, then review the spin-down evolution of young and strongly magnetized pulsars, especially of magnetars. We present an interesting and important relation between the magnetization parameter, and magnetic field in the magnetar crust. Finally, we introduce our two works in progress: to explain the magnetar "anti-gltich" events in the thermal plastic flow model and to revisit the expression of braking index $n$, which is independent of the second derivative of spin frequency of a pulsar and give some proposals for our future work., Comment: 11pages,3figures

More and more problems related to Big Bang have been appeared in recent years. All the problems are due to the Doppler interpretation of redshift. The “tired light” theory, proposed in 1929 by Zwicky and most recently developed by Shao in 2013, gives a new explanation for redshift. The theory has shown that the redshift is induced from the energy loss of photons by the interaction with material particles on their journey through cosmological space. The basic principles related to the energy transfer are mainly the mass-energy equivalence and the Lorentz theory. Problems, such as super velocity, the horizon problem, the cosmological microwave background radiation, and Olbers’ paradox, vanish in the cosmological model of “tired light” theory. The model describes a boundless and timeless Cosmos.

Here we summarized our recent work on evolutions of magnetic field and spin-down of neutron stars. Our work includes the following three parts: (1) Based on the estimated ages of their potentially associated supernova remnants (SNRs), we estimate the values of the mean braking indices of eight magnetars with SNRs, and find that five magnetars have smaller mean braking indices of 1 3 for the other three magnetars are attributed to the magnetic field decay; (2) By introducing a mean rotation energy conversion coefficient, and combining the pulsar’s high-energy and timing observations with a reliable nuclear equation of state, we estimate the initial spin period, initial dipole magnetic field and true age PSR J1640 4631, The measured braking index of n = 3.15(3) for PSR J1640 4631 is attributed to its long-term dipole magnetic field decay and a low magnetic field decay rate; (3) The low braking index of n = 0.9(2) for PSR J1734 3333 could undergo a supercritical accretion soon after its formation in a supernova explosion. The buried multipole magnetic fields will merge into a dipole magnetic field. Keeping the current field-growth index e = 1.34, this pulsar will become a magnetar with dBp ∼ 6.2(2) × 1014 G and dBp ∼ 1.06(4) × 1015 G after next 50 kyrs and 100 kys, respectively.

According to the recycling model, neutron stars in low-mass X-ray binaries were spun up to millisecond pulsars (MSPs), which indicates that all MSPs in the Galactic plane ought to be harbored in binaries. However, about $20\%$ Galactic field MSPs are found to be solitary. To interpret this problem, we assume that the accreting neutron star in binaries may collapse and become a strange star when it reaches some critical mass limit. Mass loss and a weak kick induced by asymmetric collapse during the phase transition (PT) from neutron star to strange star can result in isolated MSPs. In this work, we use a population-synthesis code to examine the PT model. The simulated results show that a kick velocity of $\sim60~{\rm km~s}^{-1}$ can produce $\sim6\times10^3$ isolated MSPs and birth rate of $\sim6.6\times10^{-7} {\rm ~yr}^{-1}$ in the Galaxy, which is approximately in agreement with predictions from observations. For the purpose of comparisons with future observation, we also give the mass distributions of radio and X-ray binary MSPs, along with the delay time distribution., Comment: 9 pages, 11 figures, accepted to publish on A&A

We first deduce a uniform formula forthe Fermi energy of degenerate and relativistic electrons in the weak-magnetic field approximation. Then we obtain an expression of the special solution for the electron Fermi energy through this formula, and express the electron Fermi energy as a function of electron fraction and matter density. Our method is universally suitable for relativistic electron- matter regions in neutron stars in the weak-magnetic field approximation.

In this paper we discuss in detail the quantization of Landau energy levels of a strongly magnetized and completely degenerate relativistic electron gas in neutron stars. In particular, we focus on the Fermi energy dependence of the magnetic field for a relativistic electron gas in the superstrong magnetic field of magnetars. We would like to point out that some of the results concerning the microscopic number density of states of a strongly magnetized electron gas given by well-known statistical physics text books are incorrect. The repeated use of these results in the last five decades probably seriously affects the physics of neutron stars and magnetars. The quantization of Landau energy levels is accurately delineated in terms of the Dirac (delta) function. Relatively simple calculation shows that the Fermi energy of relativistic electron gas in magnetars with superstrong magnetic fields( B > Bcr , here Bcr is the Landau critical magnetic field) increases with magnetic fieldstrength as B**(1/4). On the basis of this simple but importantnew result we are leading naturally to propose a new mechanism for the production of high X-ray luminosity from magnetars., 7 pages, three figures

In this work, we investigate the effects of thiocyanate anions on the switching and the structure of poly (N-isopropylacrylamide) (PNIPAM) brushes using a molecular theory. Our model takes into consideration the PNIPAM–anion bonds, the electrostatic effects and their explicit coupling to the PNIPAM conformations. It is found that at low thiocyanate anion concentration, as the anion concentration of thiocyanate increases, thiocyanate anions are more associated with PNIPAM chains through the PNIPAM–anion bonds, which contributes to stronger electrostatic repulsion and leads to an increase of lower critical solution temperature (LCST). By analyzing the average volume fractions of PNIPAM brushes, it is found that the PNIPAM brush presents a plateau structure. Our results show that the thiocyanate anions promote phase segregation due to the PNIPAM–anion bonds and the electrostatic effect. According to our model, the reduction of LCST can be explained as follows: at high thiocyanate anion concentration, with the increase of thiocyanate concentration, more ion bindings occurring between thiocyanate anions and PNIPAM chains will result in the increase of the hydrophobicity of PNIPAM chains; when the increase of electrostatic repulsion is insufficient to overcome the hydrophobic interaction of PNIPAM chains, it will lead to the reduction of brush height and LCST at high thiocyanate anion concentration. Our theoretical results are consistent with the experimental observations, and provide a fundamental understanding of the effects of thiocyanate on the LCST of PNIPAM brushes.

Sprag overrunning clutch is one of key components in the drive system. Its a meaningful work to design and manufacture high performance sprag clutch to meet the practical working situation. In order to design reliable and durable clutch with good dynamic characteristics, this paper put forward a new type wedge surfaces which is a combination of involute and eccentric arc. On the basis of analysis of a clutch structure, work principles and failure modes, the sprag ,key element of the clutch, was demonstrated the feasibility of involute in the use of wedge surface design by analyzing the characteristics of involute, and the main sprag parameters were designed and analysized. The design of the new wedge surface, increasing the strut angle and effective cam rise, increased carrying capacity, reducing the contact stress, and extending service life, which laid the foundation for the sprag overrunning clutch design improvements.

In this work, we interpreted the high braking index of PSR J1640$-$4631 with a combination of the magneto-dipole radiation and dipole magnetic field decay models. By introducing a mean rotation energy conversion coefficient $\overline{\zeta}$, the ratio of the total high-energy photon energy to the total rotation energy loss in the whole life of the pulsar, and combining the pulsar's high-energy and timing observations with reliable nuclear equation of state, we estimate the pulsar's initial spin period, $P_{0}\sim (17-44)$ ms, corresponding to the moment of inertia $I\sim (0.8-2.1)\times 10^{45}$ g cm$^{2}$. Assuming that PSR J1640$-$4631 has experienced a long-term exponential decay of the dipole magnetic field, we calculate the true age $t_{\rm age}$, the effective magnetic field decay timescale $\tau_{D}$, and the initial surface dipole magnetic field at the pole $B_{p}(0)$ of the pulsar to be $(2900-3100)$ yrs, $1.07(2)\times10^{5}$ yrs, and $(1.84-4.20)\times10^{13}$ G, respectively. The measured braking index of $n=3.15(3)$ for PSR J1640$-$4631 is attributed to its long-term dipole magnetic field decay and a low magnetic field decay rate, $dB_{\rm p}/dt\sim -(1.66-3.85)\times10^{8}$ G yr$^{-1}$. Our model can be applied to both the high braking index ($n>3$) and low braking index ($n, Comment: Correspoding to the publication version: 2017, ApJ, 849, 19 (12pp)

Based on our previous work, we deduce a general formula for pressure of degenerate and relativistic electrons,Pe, which is suitable for superhigh magnetic fields, discuss the quantization of Landau levels of electrons, and consider the quantum electrodynam-ic(QED) effects on the equations of states (EOSs) for different matter systems. The main conclusions are as follows:Pe is related to the magnetic field B, matter density ?, and electron fraction Ye ; the stronger the magnetic field, the higher the electron pressure becomes; the high electron pressure could be caused by high Fermi energy of electrons in a superhigh magnetic field; compared with a common radio pulsar, a magnetar could be a more compact oblate spheroid-like deformed neutron star due to the anisotropic total pressure; and an increase in the maximum mass of a magnetar is expected because of the positive contribution of the magnetic field energy to the EOS of the star., 26 Papers, 5 Figures, Published in Modern Physics Letters A ., Vol.28, No.36, p.1350138 (2013)

In a superhigh magnetic field, direct Urca reactions can proceed for an arbitrary proton concentration. The magnetic field is the main energy source of all the persistent and bursting emissions observed in anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs). Employing the assumption of micro-state number, we deduce the formula of electron Fermi energy EF(e) in superhigh magnetic fields. Based on observing and introducing relevant parameters introduced, a approximate way of calculating the X-ray luminosity of a Magnetar LX in any superhigh magnetic field is introduced.