Modern Physics Letters B

This review is an expansion of my talk at the conference on Sixty Years of Yang–Mills Theory. I review and explain the line of thoughts that lead to a recent joint work with Hu and Geer [Hu et al., arXiv:1502.03433] on the construction, exact solutions and ubiquitous properties of a class of quantum group gauge models on a honey-comb lattice. Conceptually the construction achieves a synthesis of the ideas of Yang–Baxter equations with those of Yang–Mills theory. Physically the models describe topological anyonic states in 2D systems.

In this paper, based on the fact that the inductors and capacitors are of fractional order in nature, the four-order mathematical model of the fractional order quadratic Boost converter in type I and type II discontinuous conduction mode (DCM) — DCM is established by using fractional calculus theory. Direct current (DC) analysis is conducted by using the DC equivalent model and the transfer functions are derived from the corresponding alternating current (AC) equivalent model. The DCM–DCM regions of type I and type II are obtained and the relations between the regions and the orders are found. The influence of the orders on the performance of the quadratic Boost converter in DCM–DCM is verified by numerical and circuit simulations. Simulation results demonstrate the correctness of the fractional order model and the efficiency of the proposed theoretical analysis.

Starting from a first-order approximate field description function for laser pulses, the method currently used to approximate chirped laser pulse (CLP) substitutes frequency and wave vector related variables with spatiotemporally varying functions. We investigated the error involved by calculating the relative deviation from Maxwell equations. Errors for the electric and magnetic fields are analyzed separately, and behaviors related to parameter changes (that is, in laser width, pulse duration and chirp parameter) were studied. Results show that aberration associated with currently used field-description functions for CLP increases monotonically with chirp parameter, and the deviation introduced by chirping is proportional to the relative frequency span of the laser. Simulations based on these functions will lead to considerable error, especially for laser pulses with large chirping.

In order to study the effects of processing parameters on the continuous variable cross-section direct extrusion (CVCDE), taking 7A09 aluminium alloy for example, the extrusion speed and forming temperature and the friction factor as key processing parameters are applied to research by finite element (FE) simulation. The research result showed that the extrusion speed had a significant influence on the maximum temperature of the billet, at the same time, both decreasing the friction factor and increasing forming temperature within a certain range were beneficial to reduce extrusion load. Both forming temperature and the extrusion speed were inversely linked to extrusion load, but the friction factor was directly proportional to extrusion load. Forming temperature had a far more important influence on extrusion load by comparison: when forming temperature increased from 380${}^{\circ }$ to 430${}^{\circ }$C, the peak value of extrusion load decreased by 25.6% and the flow uniformity of extruded product got improved. The process window based on both the press limit and surface defects limit was established and the most reasonable forming temperature was 405${}^{\circ }$C under this process condition, which provided theoretical basis for formulation process of 7A09 aluminium alloy on the CVCDE extrusion.

A direct current of 5 A was applied to narrow strips of iron foil in air to synthesize iron oxide nanowires (NWs) via thermal oxidation route of resistive heating. Transverse electric fields of 0–4000 V/m were applied perpendicularly to the surface of the iron foil during thermal oxidations. Results showed that the Fe₂O₃ NW array can grow perpendicularly on that surface by using this kind of thermal oxidation method. Transverse electric fields applied during thermal oxidation significantly affected the morphology of the Fe₂O₃ NW array. With increasing strength of the transverse electric fields, the Fe₂O₃ NWs became much longer, thinner and denser in distribution, and the diameters became more uniform. Furthermore, solid state based-up diffusion growth mechanism for the Fe₂O₃ NW array was confirmed by thermal oxidation.

We study polarization squeezing of a light beam initially in the coherent state using the nonlinear interaction Hamiltonian $H=k({â}_x^{†2}+{â}_x^2)$. For the degree of polarization squeezing, we use a definition written in the final form by the authors and also used in earlier papers. We find that the polarization squeezing can be very high and the degree of polarization squeezing can be less than unity by a very small amount. We achieve the polarization squeezing even for very low beam intensity under some conditions involving phase angles in the polarization modes.

Cerium-doped 0.8BaTiO₃-0.2Bi${}_{0.5}$K${}_{0.5}$TiO₃ with composition 0.8Ba0.2(Bi${}_{0.5}$K${}_{0.5}$)Ti${}_{1-x}$Ce${}_x$O₃ where x = 0.01, 0.02, 0.03, 0.04, 0.05, 0.06 lead free ceramics were prepared by conventional solid state reaction method followed by high energy ball milling. X-ray diffraction studies confirm the tetragonal structure at room temperature for all the Ce-doped samples. Lattice parameters and density were increasing with increase of Ce doping. Frequency and temperature dependent dielectric studies were carried out and indicate that the dielectric constant and Curie temperature are decreasing with increasing of Ce doping. All the Ce-doped samples exhibiting diffused and dispersive phase transitions with degree of diffuseness ranging from 1.4 to 2 calculated from the modified Curie–Weiss law. Impedance studies confirms the temperature dependent non-Debye kind of relaxation process in the material. From the Cole–Cole plots measured at high temperatures, reveals that the grain effect in the all Ce-doped samples. Impedance analysis studies also support the X-ray diffraction and dielectric studies that occupation of Ce both at A-site and B-site for small values of Ce doping.

The study of the influence of the surface and bulk parameters on the depletion region, created by electronic excitation, has been performed on $p$-type CdTe. The surface effect is given by two parameters: the energy of surface defects $(E_t)$ and their surface state density $(N_t)$. However the volume effect is characterized by the diffusion length $(L_n)$ and the concentration of acceptors $(N_a)$. This investigation demonstrated that, for high values of the excitation beam intensity, the depth of the depletion region $(Z_d)$ decreases as $E_t$ and $N_t$ decrease and when $N_a$ and $L_n$ increase.

It is known that gauge potentials/spin-orbit couplings can be simulated for ultracold atoms through their interaction with laser fields. Tripod and Lambda $(\mathrm{\Lambda })$ are two typical configurations of atom–field interaction in the simulations. We find that there is a similarity between the two configurations if we parametrize Rabi frequencies properly. Based on the similarity, we can transform a gauge potential/spin-orbit coupling simulation scheme in the tripod configuration into a scheme in the $\mathrm{\Lambda }$ configuration.

The convection of ambient flow field has a significant influence on the pattern formation of growing particles. In this paper, we investigate the shape evolution of particles growing in supersaturated solution affected by straining flows. By using the multiple variable asymptotic expansion method, we obtain the asymptotic solution. The solution indicates that the interface microstructure is greatly affected by the straining flows. The flow results in a higher growth rate in the surface where it is incoming and a lower growth rate where it is outgoing. Besides, the flow also has effects on the concentration distribution.

The angular distribution of W-$L_{\alpha }$, $L_{\beta 1}$ and $L_{\beta 2}$ X-rays induced by 13.1 keV bremsstrahlung has been measured at different emission angles from 110${}^{\circ }$ to 140${}^{\circ }$ at intervals of 10${}^{\circ }$. The investigation of angular dependence of $L$ X-ray intensity ratios by bremsstrahlung is barely found in previous works. The $L_{\beta 1}$ X-ray yield shows isotropic emission, while the measured $L_{\alpha }$ and $L_{\beta 2}$ X-ray yields are found to be spatially anisotropic. At last, the anisotropy parameters for $L_{\alpha }$ and $L_{\beta 2}$ X-rays have been derived.

In this paper, we design a scheme where a polarization Greenberger–Horne–Zeilinger (GHZ) state can be completely and deterministically distinguished by adopting linear momentum degree of freedom as the ancillary qubits or change of roles between the momentum and polarization degrees of freedom. Two ways for distinguishing three-photon GHZ state can be achieved in just one quantum circuit.

Here, we investigate the following key prediction of a thermodynamical model that interrelates the defect parameters with the bulk elastic and expansivity data: for various defect processes in a given matrix material, a proportionality exists between defect entropies and enthalpies. The investigation is focused on BaF₂ for which ab initio calculations within density functional theory and the generalized-gradient approximation have been recently made as far as the formation and migration of intrinsic defects are concerned, as well as for the elastic constants. Four defect processes have been studied in BaF₂: anion Frenkel formation, fluorine vacancy migration, fluorine interstitial motion and electrical relaxation associated with a single tetravalent uranium. For these processes, the entropies and enthalpies vary by almost two orders of magnitude and reveal a proportionality between them. We find that this proportionality is solely governed by the bulk elasticity and expansivity data, which conforms to the aforementioned thermodynamical model.

A low-cost and high-speed electro-optic (EO) switch using the guest–host EO material Disperse Red 1/Polymethyl Methacrylate (DR1/PMMA) was designed and fabricated. The DR1/PMMA material presented a low processing cost, an excellent photostability and a large EO coefficient of 13.1 pm/V. To improve the performance of the switch, the in-plane buried electrode structure was introduced in the polymer Mach–Zehnder waveguide to improve the poling and modulating efficiency. The characteristic parameters of the waveguide and the electrodes were carefully designed and the fabrication process was strictly controlled. Under 1550 nm, the insertion loss of the device was 12.7 dB. The measured switching rise time and fall time of the switch were 50.00 ns and 54.29 ns, respectively.

Highly efficient coupling outer electromagnetic (EM) waves into photonic crystal (PhC) waveguides (PhCWs) is critical to the applications of PhCs in photonic integrated circuits. We investigate and simulate an efficient way of coupling EM waves into PhCWs of air holes array by using surface dielectric margin based on all-PhCs structure. Good matching of modal field profiles on both sides of the interface is obtained by adjusting the surface dielectric margin along the propagation direction. The coupling efficiency can be highly enhanced by suppressing the surface field propagating along the transverse margin at the interface. The numerical results using finite-difference time-domain simulations show that the bandwidth for coupling efficiency larger than 90% can be as broad as about 100nm.

The magnetic properties of MnP:GaP nanoparticles are calculated using a statistical mechanical approach and effect of various factors on magnetization of nanoparticles is studied. The calculation is based on solution of localized partition function and evolution of magnetic moment affected by thermal fluctuation and external field is included by solving master equation. Instead of constant magnetic saturation approximation, a temperature dependent magnetic moment saturation is included to improve calculation efficiency for larger nanoparticles. In the present work, the field-cooled and zero-field-cooled (FC/ZFC) magnetization of randomly oriented anisotropy and log-normal volume distributed nanoparticles are calculated.

This work presents the results of synthesis and characterization of polycrystalline $n$-type Bi₂S₃ thin films. The films were grown through a chemical reaction from co-evaporation of their precursor elements in a soda-lime glass substrate. The effect of the experimental conditions on the optical, morphological structural properties, the growth rate, and the electrical conductivity $(\sigma )$ was studied through spectral transmittance, X-ray diffraction (XRD), atomic force microscopy (AFM) and $\sigma$ versus $T$ measurements, respectively. The results showed that the films grow only in the orthorhombic Bi₂S₃ bismuthinite phase. It was also found that the Bi₂S₃ films present an energy band gap $(E_g)$ of about 1.38 eV. In addition to these results, the electrical conductivity of the Bi₂S₃ films was affected by both the transport of free carriers in extended states of the conduction band and for variable range hopping transport mechanisms, each one predominating in a different temperature range.

Multi-wave resonant solutions of a class of nonlinear heat-type equations are investigated by their corresponding generalized bilinear equations. We develop a new technique for searching for resonant solutions to those generalized bilinear equations, using the idea of weights of dependent variables. The results show that generalized bilinear operators and generalized bilinear equations are powerful and irreplaceable tools for dealing with nonlinear differential equations.

This paper is concerned with the network-based $H_{\infty }$ synchronization control for a class of discrete time-delay neural networks, and attention is focused on how to reduce the communication rate since the communication resource is limited. Techniques such as the measurement size reduction, signal quantization and stochastic signal transmission are introduced to achieve the above goal. An uncertain switched system model is first proposed to capture the above-networked uncertainties. Based on the switched system theory and Lyapunov stability approach, a sufficient condition is obtained such that the closed-loop synchronization system is exponentially stable in the mean-square sense with a prescribed $H_{\infty }$ performance level. The controller gains are determined by solving a set of linear matrix inequalities (LMIs). A numerical example is finally presented to show the effectiveness of the proposed design method.

An encapsulated grating with a metal slab is designed as a reflection three-port beam splitter at the wavelength of 1550 nm under normal incidence. Such a new grating is aimed to separate energies into the ±1st and the 0th orders for both TE and TM polarizations. The grating parameters such as grating period, duty cycle and grating depth are optimized by using rigorous coupled-wave analysis. Based on optimized grating parameters, efficiencies can reach more than 32% with the polarization-independent property. It indicates that reflection three-port beam splitter with high efficiency can be obtained by the encapsulated grating. Moreover, the presented reflection three-port grating has advantages of wide incident wavelength range and angular bandwidth, which would be useful in practical application.