International Journal of Modern Physics B

We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of representation theory in terms of tensor categories is emphasized. Connections to two-dimensional conformal field theory are also presented. In particular, we discuss anyon condensation, gapped domain walls and matrix product operators in terms of operator algebras.

Effect of 2 MeV electron beam at the current density 0.09 nA/cm² on surface structure, nanocrystallite size of (ZrTi)CN nanocomposite coating on steel was investigated at Scanning Electron and Atomic Force microscopes, and also X-ray diffractometer. Using the Rietveld method, two structure phases were indentified in the pristine samples: (ZrTi)(CN)-cubic (space group Fm-3m) and TiC — trigonal (sp.gr.R-3m). Electron beam irradiation to the fluency of $4.1\times 10^{17}$ electron/cm² resulted in the phase transition of TiC from trigonal (sp.gr.R-3m) to cubic structure (sp.gr.Fm-3m). Besides, nanocrystallite size and shape have changed after the fluency $2.3\times 10^{17}$ electron/cm². The lattice parameters have increased up to $3.1\times 10^{17}$ electron/cm² fluence and the nanorcrystallite size of nanocomposite was enlarged 26%, which was attributed to generation of defects.

In order to meet the requirements of “wide, thin, strong and light” for military stealth materials, it is of great practical value to study the absorbing characteristics of multi-layer MWCNTs/Fe₃O₄/NBR absorbing materials in space. First, we use the large-scale software COMSOL Multiphysics to simulate the absorbing characteristics of the composite thin plate in space. Then the four-port network matrix is used to calculate the absorbing characteristics of the composite plate in space. Finally, the Free-Space method is used to measure the reflection attenuation loss, and the results of the three methods are compared and analyzed. The results show that when the frequency is 10 GHz, the reflection loss of multi-layer MWCNTs/Fe₃O₄/NBR reaches the maximum value of −27.91, −27.01 and −22.56 dB by COMOSL numerical simulation, four-port network the matrix and Free-Space experimental measurement. The results of the three methods show that the reflection loss is less than −10 dB in the frequency band of 6–14 GHz.

Cu₂Te single crystal was grown by the Bridgman method. X-ray diffraction (XRD) study of Cu₂Te single crystals in the temperature range of 293–893 K was performed and possible phase transitions in the mentioned range of temperature have been investigated. (Cu₂Te)${}_{2-x}$(ZnTe)${}_x$ single crystals also were grown with $x=0.00$, 0.05, 0.10 concentrations and structural properties of the obtained single crystals were investigated by the XRD method in the temperature range 293–893 K. Lattice parameters and possible phase transitions in the mention temperature range were determined for (Cu₂Te)${}_{2-x}$(ZnTe)${}_x$ single crystals for $x=0.00$, 0.05, 0.10 concentrations.

We study a $(1+1)$-dimensional field theory based on the ${\psi }^2{ln}^2{\psi }^2$ potential which represents minimal nonlinearity in the context of phase transitions. There are three degenerate minima at $\psi =0$ and $\psi =\pm 1$. There are novel, asymmetric kink solutions of the form $\psi =\mp exp(-exp(\pm x))$ connecting the minima at $\psi =0$ and $\psi =\mp 1$. The domains with $\psi =0$ repel the linear excitations, the waves (e.g., phonons). Topology restricts the domain sequences and therefore the ordering of the domain walls. Collisions between domain walls are rich for properties such as transmission of kinks and particle conversion, etc. For illustrative purposes we provide a comparison of these results with the ${\varphi }^6$ model and its half-kink solution, which has an exponential tail in contrast to the super-exponential tail for the ${\psi }^2{ln}^2{\psi }^2$ potential. Finally, we place the results in the context of other logarithmic models.

Baidu search engine is the most common one adopted by Chinese Internet users, and Baidu index provides a platform to capture the behaviors of massive users on Baidu, which is one important statistical tool to mine the Internet users’ behaviors and characteristics in China. Here, we utilize the Baidu index data on greenhouse gas from January 1, 2011 to November 29, 2019, to perform the related statistical analyses at first. Then, on the basis of Baidu index time series data, the corresponding network is constructed by use of the visibility graph method. Finally, the topology of the generated network is analyzed from different perspectives. Our results indicate that people’s attention to greenhouse gases obeys the power-law distribution, and we can identify the significant nodes and find some outliers in time series data by use of the topological properties of networks. Taking together, the current model offers a novel means to represent and depict the time series data of Baidu index through the complex network analysis.

The excellent performance of carbon nanotubes (CNTs) allows them to be widely employed in various micro- and nano-electromechanical devices. However, different imperfections such as Stone–Wales (S-W) defects often arise in these structures during the preparation process. In this paper, special attention is paid to the effects of the number and location of defects as well as the diameter and chiral angle of CNTs on the static and dynamic buckling of CNTs with S-W defects. First, LAMMPS software is used to simulate the molecular dynamics (MDs) of CNTs with S-W defects, and their static buckling performances are discussed. Then based on the static buckling data, the dynamic buckling vibration performance of CNTs with S-W defects is analyzed in the context of the nonlocal elastic theory. Finally, the effective range of nonlocal parameters is established via the MD modeling. The results show that the existence of S-W defects will reduce the buckling performance and vibration characteristics of CNTs, and an increase in the number of defects will aggravate the influence of diameter and chiral angle on the buckling performance as well as the natural frequency and amplitude of the nanotube’s axial vibration.

Based on the three-dimensional memristive Hindmarsh–Rose model, the effects of Gaussian colored noise and electromagnetic induction on memory function of the memristor and neural firing states are investigated in this paper. It is found that the memory function of memristor can be suppressed by a higher signal frequency, while enhanced by a relatively larger coefficient of the memristor. The memory function of memristor is destroyed by larger values of noise intensity and correlation rate between noises. The neural firing state can be transformed from the spiking state to the chaotic state with the increase of noise intensity or correlation rate. The firing states transition induced by the higher electromagnetic induction intensity is opposite to that by the stronger Gaussian colored noise.

The objective of this paper is to study the mixed convective nonsimilar flow above an exponentially stretching sheet saturated by nanofluid. The leading partial differential equations (PDEs) of the problem have been modified towards dimensionless nonlinear PDEs utilizing newly proposed nonsimilarity transformations. Furthermore, local nonsimilarity procedure up to-second truncation has been operated to change the dimensionless PDEs into ordinary differential equations (ODEs). MATLAB-based algorithm bvp4c is used to observe the consequences of the distinct parameters namely Prandlt number $(\mathrm{\text{Pr}})$, magnetic field $(M)$, Lewis number $(\mathrm{\text{Le}})$, Brownian motion $(N_b)$, Eckert number $(\mathrm{\text{Ec}})$, thermophoresis $(N_t)$ on velocity, concentration and temperature distribution are shown in graphical portray. Additional outcomes presume the heat penetration into the fluid enhances with increase in Biot number and Brownian motion. Increasing values of $M$ and $\xi$ cause decrease of temperature profile.

The iterative propagation of information between nodes will strengthen the connection strength between nodes, and the network can evolve into different groups according to difference edge strength. Based on this observation, we present the user engagement to quantify the influences of users different propagation modes to network propagation, and construct weight network to simulate real social network, and proposed the community detection method in social networks based on information propagation and user engagement. Our method can produce different scale communities and overlapping community. We also applied our method to real-world social networks. The experiment proved that the network spread and the community division interact with each other. The community structure is significantly different in the network propagation of different scales.

Local community detection algorithms are an important type of overlapping community detection methods. Local community detection methods identify local community structure through searching seeds and expansion process. In this paper, we propose a novel local community detection method on line graph through degree centrality and expansion (LCDDCE). We firstly employ line graph model to transfer edges into nodes of a new graph. Secondly, we evaluate edges relationship through a novel node similarity method on line graph. Thirdly, we introduce local community detection framework to identify local node community structure of line graph, combined with degree centrality and PageRank algorithm. Finally, we transfer them back into original graph. The experimental results on three classical benchmarks show that our LCDDCE method achieves a higher performance on normalized mutual information metric with other typical methods.

In order to obtain some novel analytical solutions for fractional improved nonlinear Schrodinger equation with perturbation, the polynomial expansion, simplest equation and extended sine-Gordon expansion schemes are utilized. A collection of different types of solitons are reported with a physical and important perspective, containing optical dark solitons. The methods reveal the solutions in a structure of rapidly converging series. This research highlights additional important features of the methods being considered. In addition, the modulation instability analysis is carried out to discuss the stability analysis of the solutions reached, and the movement role of the waves is examined, which affirms that all the established solutions are exact and stable.

The purification process of polycyclic aromatic hydrocarbons was carried out by extraction of diesel fraction from the primary oil refining using the effect of magnetic field. A mixture of N-methylpyrrolidone with sulfuric acid was used as an extractant. The content of aromatic hydrocarbons in the diesel fraction decreased by 39.8% under normal conditions and by 50.8% under the influence of magnetic field after extraction. The samples were investigated by infrared (IR) spectroscopy method before and after extraction. Vibartional modes corresponding to different atomic bonds have been observed. Deodorization of diesel was determined by interpreting obtained modes.

The effects of Ti and Zr doping concentrations on the mechanical properties and electronic structure of the reduced Ce${}_{1-x}$M${}_x$O${}_{1.785}$ were studied. The calculated results show that elastic moduli of Ce${}_{1-x}$Ti${}_x$O${}_{1.875}$ decreased, while those of Ce${}_{1-x}$Zr${}_x$O${}_{1.875}$ increased. Ce${}_{0.625}$Ti${}_{0.375}$O${}_{1.875}$ that undergoes structural transformation at 37.5 at.% Ti. Ce${}_{1-x}$M${}_x$O${}_{1.875}$ is ductile material. The degree of anisotropy of Ce${}_{1-x}$Ti${}_x$O${}_{1.875}$ decreased sharply at 25 at.% Ti, while that of Ce${}_{1-x}$Zr${}_x$O${}_{1.875}$ almost unchanged with the increase of Zr concentration. Ti and Zr doping has little effect on the electronic structure of the unreduced Ce${}_{1-x}$M${}_x$O₂. Ti and Zr doping reduced the formation energy of O vacancy, and Ti doping was more conducive to the formation of O vacancy. The density of states of the reduced Ce${}_{1-x}$M${}_x$O${}_{1.875}$ exhibited spin splitting and was magnetic. Zr atom transferred 0.24–0.27 e more than Ti atom to the nearest O atoms, and Zr–O bond has stronger covalency and higher bond energy.

Elongated colloids with a permanent magnetic moment and immersed in a nematic liquid crystal are studied numerically using a mesoscopic scheme that supports fluctuations, hydrodynamics, and topological defects. Colloids are accompanied by disclinations curves and subjected to an effective torque caused by the nematic environment and to a magnetic torque due to an external magnetic field. The case is analyzed where these torques compete to bring colloids to two different mutually perpendicular equilibrium states. The fluctuating dynamics of the colloid-defect pair is studied in terms of orientational correlation functions. Analytical expressions for these correlations are derived on the basis of an approximated planar lineal model. A good agreement is found between the numerical and analytical methods when magnetic torques are much larger than nematic torques, while for smaller magnetic torques nonlinear effects are demonstrated to be important. As conclusion, the numerical technique could be considered a reliable approach to the rotational motion of polar nanoparticles in liquid crystals.

Understanding the appearance and maintenance of cooperation behavior is one of the most interesting challenges in natural and social sciences. Evolutionary game is a useful tool to study this issue. Here, we consider a basic strategy updating rule: the probability of a player updating its strategy is affected by the learning ability, which is determined by payoffs and an aspiration parameter $w$. For positive $w$, learning ability is directly proportional to player’s own payoff. When $w$ equals 0, it returns to traditional situation. It is found that increasing the value of $w$ can promote the cooperation. With the increase of $w$, the player’s learning ability is continuously enhanced, and the probability of changing strategies is also increased. This paper verifies the influence of the introduced selection parameter $w$ on the cooperation rate from different aspects. We tested this hypothesis through the Monte Carlo simulation, and demonstrated that introducing $w$ changed the network of interaction effectively, therefore changing the effect of the adoption of the strategy on the uncertainty of cooperation evolution. This paper analyzed the results of the payoff-dependence learning ability of different players when they imitate the strategies of their opponents, which can effectively promote the evolution of cooperation.