The aim of this exposition is to provide a detailed description of the use of combinatorial algebra in quantum field theory in the planar setting. Particular emphasis is placed on the relations between different types of planar Green’s functions. The primary object is a Hopf algebra that is naturally defined on variables representing non-commuting sources, and whose coproduct splits into two halfcoproducts. The latter give rise to the notion of an unshuffle bialgebra. This setting allows a description of the relation between full and connected planar Green’s functions to be given by solving a simple linear fixed point equation. We also include a brief outline of the consequences of our approach in the framework of ordinary quantum field theory.

In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations in the four-dimensional spacetime from the fivedimensional Einstein field equation. Besides the Einstein field equation in the four-dimensional spacetime, an electromagnetic field equation is obtained: ∇_aF^ab-ξR^b_aA^a =−4πJ^b with ξ =−2, where F^ab is the antisymmetric electromagnetic field tensor defined by the potential vector A^a, R_ab is the Ricci curvature tensor of the hypersurface, and J^a is the electric current density vector. The electromagnetic field equation differs from the Einstein–Maxwell equation by a curvature-coupled term ξR^b_aA^a, whose presence addresses the problem of incompatibility of the Einstein–Maxwell equation with a universe containing a uniformly distributed net charge, as discussed in a previous paper by the author [L.-X. Li, Gen. Relativ. Gravit. 48, 28 (2016)]. Hence, the new unified theory is physically different from Kaluza–Klein theory and its variants in which the Einstein–Maxwell equation is derived. In the four-dimensional Einstein field equation derived in the new theory, the source term includes the stress-energy tensor of electromagnetic fields as well as the stress-energy tensor of other unidentified matter. Under certain conditions the unidentified matter can be interpreted as a cosmological constant in the four-dimensional spacetime. We argue that, the electromagnetic field equation and hence the unified theory presented in this paper can be tested in an environment with a high mass density, e.g., inside a neutron star or a white dwarf, and in the early epoch of the universe.

In this study, we consider the emergence of explosive synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees and frustration is included in the system. This assumption can enhance or delay the explosive transition to synchronization. Interestingly, a de-synchronization phenomenon occurs and the type of phase transition is also changed. Furthermore, we provide an analytical treatment based on a star graph, which resembles that obtained in scale-free networks. Finally, a self-consistent approach is implemented to study the de-synchronization regime. Our findings have important implications for controlling synchronization in complex networks because frustration is a controllable parameter in experiments and a discontinuous abrupt phase transition is always dangerous in engineering in the real world.

The Dyson–Schwinger equation of the massless Wess–Zumino model is written as an equation over the anomalous dimension of the theory. Its asymptotic behavior is derived and the procedure to compute the perturbations of this asymptotic behavior is detailed. This procedure uses ill-defined objects. To solve this, the Dyson–Schwinger equation is rewritten for the Borel plane. It is shown that the illdefined procedure in the physical plane can be applied in the Borel plane. Other results obtained in the Borel plane are stated and the proof for one result is described.

In this study, we discover a mass space defined by generalized Koide relations, named here as k-relations, and achieve some new symmetric relations. These relations can be further used to predict the fourth-generation quark masses in terms of dilation magnitude and angular rotation ratios in the general mass space. Thus far, no theory has been proposed that can constrain the number of generations of quarks; this theory naturally limits the number of generations of quarks.

In many domains of physics, methods for dealing with non-perturbative aspects are required. Here, I want to argue that a good approach for this is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean Écalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.

Using a classical ensemble method, we have investigated sequential double ionization (SDI) of Ar atoms driven by elliptical laser pulses. The results show that the ion momentum distribution of the Ar atoms depends strongly on the pulse duration. As the pulse duration increases, the ion momentum distribution changes from two bands to four bands and then to six bands and finally to an eight-band structure. Back analysis of double ionization trajectories shows that the variation of the band structure originates from pulse duration dependent multiple ionization bursts of the second electron. Our calculations indicate that the subcycle electron emission in the SDI could be more easily accessed by using elliptical laser pulses with a longer wavelength. Moreover, we show that there is good correspondence between the scaled radial momentum and the ionization time.

We experimentally investigate probe transmission signals (PTS), the four-wave mixing photonic band gap signal (FWM BGS), and the fluorescence signal (FLS) in an inverted Y-type four level atomic system. For the first time, we compare the FLS of the two ground-state hyperfine levels of Rb 85. In particular, the second-order and the fourth-order fluorescence signals perform dramatic dressing discrepancies under the two hyperfine levels. Moreover, we find that the dressing field has some dressing effects on three such types of signals. Therefore, we demonstrate that the characteristics of PTS, FWM BGS, and FLS can be controlled by frequency detunings, the powers or phases of the dressing field. Such research could have potential applications in optical diodes, amplifiers, and quantum information processing.

In order to improve the resolution of digital holography with a common-dimension charge-coupled device (CCD) sensor, the point spread functions are briefly derived for the commonly used and practical post-magnification, pre-magnification, and image-plane digital holographic microscopic systems. The ultimate resolutions of these systems are analyzed and compared. The results show that the ultimate lateral resolution of pre-magnification digital holography is superior to that of post-magnification digital holography in the same conditions. We also demonstrate that the ultimate lateral resolution of image-plane digital holography has no correlation with the photosensitive dimension of the CCD sensor, and it is not significantly related to the pixel size of the sensor. Moreover, both the ultimate resolution and the imaging quality of image-plane digital holography are superior to that of pre- and post-magnification digital holographic microscopy. High-resolution imaging, whose resolution is close to the ultimate resolution of the microscope objective, can be achieved by image-plane digital holography even with a submillimeter-dimension sensor. This system, by which perfect imaging can be achieved, is optimal for commonly used digital holographic microscopy. Experimental results demonstrate the correctness of the theoretical analysis.

For the exploration of gas hydrate resources by measuring the dissolved methane concentration in seawater, a continuous-wave cavity ringdown spectroscopy (CW-CRDS) experimental setup was constructed for trace methane detection. A current-modulation method, rather than a cavity-modulation method using an optical switch and a piezoelectric transducer, was employed to realize the cavity excitation and shutoff. Such a current-modulation method enabled the improvement of the experimental setup construction and stability, and the system size and stability are critical for a sensor to be deployed underwater. Ringdown data acquisition and processing were performed, followed by an evaluation of the experimental setup stability and sensitivity. The obtained results demonstrate that great errors are introduced when a large fitting window is selected if the analog-to-digital converter has an insufficient resolution. The ringdown spectrum of methane corresponding to the 2v3 band R(4) branch was captured, and the methane concentration in lab air was determined to be 2.06 ppm. Further experiments for evaluating the quantitative ability of this CW-CRDS experimental setup are underway from which a high-sensitivity methane sensor that can be combined with a degassing system is expected.

We present a theoretical study of the propagation properties of polarized photons passing through the cavity with an anisotropic metamaterial. We find that the resonant peaks of transmission appear for photons polarized in a certain direction corresponding to a negative element of the permittivity tensor. This indicates the potential for applying such cavity structures as filters for photons with certain polarizations. The resonant peak of transmission for photons having a given frequency can be achieved by adjusting the thicknesses of the air and metamaterial. If the frequency of the incident photons and the thickness of the metamaterial are fixed, the cavity structure can be used as a photon switch controlled by the thickness of the air. The effect of the absorption is considered, and the result shows that the transmission peak always appears, even for metamaterials with large absorption. Finally, the polarization manipulation of such structures is explored.

Laser-induced breakdown spectroscopy (LIBS) is an emerging analytical spectroscopy technique. This review presents the main recent developments in China regarding the implementation of LIBS for coal analysis. The paper mainly focuses on the progress of the past few years in the fundamentals, data pretreatment, calibration model, and experimental issues of LIBS and its application to coal analysis. Many important domestic studies focusing on coal quality analysis have been conducted. For example, a proposed novel hybrid quantification model can provide more reproducible quantitative analytical results; the model obtained the average absolute errors (AREs) of 0.42%, 0.05%, 0.07%, and 0.17% for carbon, hydrogen, volatiles, and ash, respectively, and a heat value of 0.07 MJ/kg. Atomic/ionic emission lines and molecular bands, such as CN and C2, have been employed to generate more accurate analysis results, achieving an ARE of 0.26% and a 0.16% limit of detection (LOD) for the prediction of unburned carbon in fly ashes. Both laboratory and on-line LIBS apparatuses have been developed for field application in coal-fired power plants. We consider that both the accuracy and the repeatability of the elemental and proximate analysis of coal have increased significantly and further efforts will be devoted to realizing large-scale commercialization of coal quality analyzer in China.

Laser-induced breakdown spectroscopy (LIBS) is an analytical detection technique based on atomic emission spectroscopy to measure the elemental composition. LIBS has been extensively studied and developed due to the non-contact, fast response, high sensitivity, real-time and multi-elemental detection features. The development and applications of LIBS technique in Asia are summarized and discussed in this review paper. The researchers in Asia work on different aspects of the LIBS study in fundamentals, data processing and modeling, applications and instrumentations. According to the current research status, the challenges, opportunities and further development of LIBS technique in Asia are also evaluated to promote LIBS research and its applications.

Nuclear fusion has enormous potential to greatly affect global energy production. The next-generation tokamak ITER, which is aimed at demonstrating the feasibility of energy production from fusion on a commercial scale, is under construction. Wall erosion, material transport, and fuel retention are known factors that shorten the lifetime of ITER during tokamak operation and give rise to safety issues. These factors, which must be understood and solved early in the process of fusion reactor design and development, are among the most important concerns for the community of plasma–wall interaction researchers. To date, laser techniques are among the most promising methods that can solve these open ITER issues, and laser-induced breakdown spectroscopy (LIBS) is an ideal candidate for online monitoring of the walls of current and next-generation (such as ITER) fusion devices. LIBS is a widely used technique for various applications. It has been considered recently as a promising tool for analyzing plasma-facing components in fusion devices in situ. This article reviews the experiments that have been performed by many research groups to assess the feasibility of LIBS for this purpose.

Confinement can induce unusual behaviors of water. Inspired by the fabrication of carbon nanotubes with noncircular cross sections, we performed molecular dynamics simulations to investigate the mobilities of water confined in carbon nanochannels with circular, square, and equilateral triangular cross sections over a variety of dimensions. We find that water exhibits disparate mobilities across different types of channels below 0.796 nm². Notably, compared with the other two channels, water in equilateral triangular channels displays the greatest mobilities. Moreover, at 0.425 nm², different ordered structures are found in the three channels, and water inside the square channel exhibits an extremely low mobility. It is also found that above 0.796 nm², the mobilities along the tube axis of water converge to that of the bulk. These phenomena are understood by analyzing the structure, dynamics, and hydrogen bonding of water. Our work explores the mobilities of water across noncircular carbon nanochannels, which may expand the prospect of noncircular nanochannels in scientific studies and practical applications, such as desalination and drug delivery.

The two-dimensional Rayleigh–Taylor instability problem is simulated with a multiple-relaxation-time discrete Boltzmann model with a gravity term. Viscosity, heat conductivity, and Prandtl number effects are probed from macroscopic and nonequilibrium viewpoints. In the macro sense, both viscosity and heat conduction show a significant inhibitory effect in the reacceleration stage, which is mainly achieved by inhibiting the development of the Kelvin–Helmholtz instability. Before this, the Prandtl number effect is not sensitive. Viscosity, heat conductivity, and Prandtl number effects on nonequilibrium manifestations and the degree of correlation between the nonuniformity and the nonequilibrium strength in the complex flow are systematically investigated.

Grade assessment of steel is generally performed via the metallographic method, which is timeconsuming and is not able to provide the elemental distribution information. In this paper, we present a method to measure the globular oxide inclusion ratings in steel using laser-induced breakdown spectroscopy (LIBS). The measurement is performed in two basic steps: steel samples are polished using metallographic sand paper and the Al₂O₃ inclusion number and size distribution in a marked area are observed using scanning electron microscope/energy dispersive X-ray spectroscopy (SEM/EDS) for further LIBS scanning analysis. The threshold intensity that distinguishes soluble aluminum and insoluble aluminum inclusions is determined using LIBS combined with the SEM/EDS statistical data. Carbon steel (the sample number is S9256) and bearing steel (the sample number is GCr15) are analyzed in scanning mode, and the number of Al₂O₃ inclusions in different size ranges is obtained from the statistical information derived from the Al₂O₃ size calibration curve. According to heavy and thin series for globular oxide inclusions grade assessment, the method we propose is comparable to the traditional metallographic method in terms of accuracy; however, the process is simplified and the measurement speed is significantly improved.

Hydrodynamic properties and structure of strong shock waves in classical dense helium are simulated using non-equilibrium molecular dynamics methods. The shock speed in the simulation reaches 100 km/s and the Mach number is over 250, which are close to the parameters of shock waves in the implosion process of inertial confinement fusion. The simulations show that the high-Mach-number shock waves in dense media have notable differences from weak shock waves or those in dilute gases. These results will provide useful information on the implosion process, especially the structure of strong shock wave front, which remains an open question in hydrodynamic simulations.

Dopants and defects are important in semiconductor and magnetic devices. Strategies for controlling doping and defects have been the focus of semiconductor physics research during the past decades and remain critical even today. Co-doping is a promising strategy that can be used for effectively tuning the dopant populations, electronic properties, and magnetic properties. It can enhance the solubility of dopants and improve the stability of desired defects. During the past 20 years, significant experimental and theoretical efforts have been devoted to studying the characteristics of co-doping. In this article, we first review the historical development of co-doping. Then, we review a variety of research performed on co-doping, based on the compensating nature of co-dopants. Finally, we review the effects of contamination and surfactants that can explain the general mechanisms of co-doping.

It has been suggested that hydrogen-rich systems at high pressure may exhibit notably high super-conducting transition temperatures. One of the more interesting theoretical predictions was that hydrogen sulfide can be metallized and the high-temperature superconducting state can be induced. A record critical temperature (203 K) was later confirmed for H₃S in an experiment. In this paper, we investigated, within the framework of the Eliashberg formalism, the properties of compressed MgH₆, which is expected to be a very good candidate for room-temperature superconductivity. This applies particularly to the pressure range from 300 to 400 GPa, where the transition temperature is close to 400 K. Moreover, the estimated thermodynamic properties and the resulting dimensionless ratios exceed the predictions of the Bardeen–Cooper–Schrieffer theory. This behavior is attributed to the strong electron–phonon coupling and retardation effects existing in hydrogen-dominated materials under high pressure.

A framework for analytical studies of superconducting systems is presented and illustrated. The formalism, based on the conformal transformation of momentum space, allows one to study the effects of both the dispersion relation and the structure of the pairing interaction in two-dimensional anisotropic high-T_c superconductors. In this method, the number of employed degrees of freedom coincides with the dimension of the momentum space, which is different compared to that in the standard Van Hove scenario with a single degree of freedom. A new function, the kernel of the density of states, is defined and its relation to the standard density of states is explained. The versatility of the method is illustrated by analyzing coexistence and competition between spin-singlet and spin-triplet order parameters in superconducting systems with a tight-binding-type dispersion relation and an anisotropic pairing potential. Phase diagrams of stable superconducting states in the coordinates η (the ratio of hopping parameters) and η (the carrier concentration) are presented and discussed. Moreover, the role of attractive and repulsive on-site interactions for the stability of the s-wave order parameter is explained.

A Kondo-like effect, namely, the upturn of resistivity at low temperatures, is observed in perovskite manganite when nonmagnetic insulators are doped as secondary phase. In this paper, the low-temperature resistivity upturn effect has been argued to originate from interfacial magnetic phase reconstruction. Heisenberg spin lattices have been simulated using the Monte Carlo method to reveal phase competition around secondary phase boundary, namely, manganite-insulator boundary that behaves with a weak antiferromagnetic tendency. Moreover, the resistor network model based on double-exchange conductive mechanism reproduces the low-temperature resistivity upturn effect. Our work provides a reasonable physical mechanism to understand the novel transport behaviors in microstructures of correlated electron systems.