International Journal of Modern Physics B

The nonlocal symmetry of the new integrable $(2+1)$-dimensional Boussinesq equation is studied by the standard truncated Painlevé expansion. This nonlocal symmetry can be localized to the Lie point symmetry of the prolonged system by introducing two auxiliary dependent variables. The corresponding finite symmetry transformation and similarity reduction related to the nonlocal symmetry of the new integrable $(2+1)$-dimensional Boussinesq equation are studied. The rational solution, the triangle solution, two solitoff-interaction solution and the soliton–cnoidal interaction solutions for the new $(2+1)$-dimensional Boussinesq equation are presented analytically and graphically by selecting the proper arbitrary constants.

This paper deals with the optical solitons of fractional coupled Boussinesq, Burgers-type and mKdV equations by the hypothesis of traveling wave and $\frac{G^{\prime }}{G^2}$-expansion scheme. These equations are important in different fields such as propagation of long water waves, fluid dynamics, and shallow water wave propagation. In comparison to other analytical procedures, the analytical methodology $\frac{G^{\prime }}{G^2}$ is an incredibly beneficial approach. This technique can also be used with other nonlinear fractional models. The suggested method generates three distinct solutions such as trigonometric, hyperbolic, and rational. Moreover, graphical representation has been used to portray the physical significance of the constructed solutions. Finally, a comprehensive study is made by using a definition of Beta fractional derivative and obtained solutions are represented graphically to understand considered models.

Anisotropy parabolic potential (APP) effects on ground state (GS) energy $E_0$ and the vibration frequency (VF) $\lambda$ of weak-coupled magnetopolaron (MP) in asymmetric Gaussian quantum wells (AGQWs) were investigated using the linear combination operator and unitary transformation method. The obtained results showed that $E_0$ and $\lambda$ were increased by increasing the barrier height $V_0$ of AGQWs as well as transverse and longitudinal confined strengths ${\omega }_x$ and ${\omega }_y$ of APP and decreased with increase in the asymmetric Gaussian confinement potential (AGCP) range $R$ and transverse and longitudinal effective confined lengths $l_x$ and $l_y$ of APP. Thus, the GS energy and VF of MP could be changed by adjusting the confinement parameters of the APP and AGCP. The study of quantum wells’ semiconductor materials has broad potential applications in semiconductor lasers, optoelectronic devices and quantum information.

This paper studies the exact traveling wave solutions to the nonlinear Dullin–Gottwald–Holm model which has the application in shallow-water waves in which the fractional derivative is considered in the sense of conformable derivative. Diverse exact solutions in hyperbolic, trigonometric and plane wave forms are obtained using two integration norms. For this purpose $G^{{}^{\prime }}/G$-expansion method and reccati mapping techniques are used. The 3D plots and their corresponding contour graphs are also depicted. Being concise and straightforward, the calculations demonstrate the effectiveness and convenience of the method for solving other nonlinear partial differential equations.

Inspired by infectious disease dynamics and modern psychology, this paper aims at constructing a multi-dimensional function to get the model of information dissemination on social networks under epidemic-related panic base on the characteristics of individual differences and global characteristics, like emotional cumulative effect, herd effect, time-sensitive decline effect, cognitive level, intimacy, personal influence, etc. The results show that the psychological effect has a significant effect on the increase of the spread of panic news; When netizens are in an emotional atmosphere, their emotional self-regulation ability is limited; when the infection rate is relatively low, the characteristics of individual differences play a leading role in affecting the spreading process. When the infection rate is high enough, the herd effect and emotional cumulative effect play a major role in promoting information dissemination; In a society with a higher rate of emotional contact, it is easier to form a kind of collective wisdom, which can help the collective quickly identify rumors. Moreover, in this kind of society, the role of opinion leaders is limited, and timely refutation of rumors can significantly reduce the spread of panic news.

The addition of porous nanomaterials is promising to enhance the thermal energy property of the organic working fluid. In this paper, molecular dynamics (MD) and grand canonical Monte Carlo simulations are employed to investigate the adsorption and energy storage properties of R32, R134a and R1234yf in MOF-5 and MOF-177. The results showed that the working fluid with small molecular size is easier to absorb and desorb in MOF structure. Besides, the MOF with larger specific surface area and pore size can absorb more organic working fluids, which can result in the larger enhancement of energy storage.

In this paper, the properties of two-dimensional (2D) gallium nitride (GaN) photocathodes with a uniform doping and variable doping structure are studied by using Mg as a doping element based on first principles. The stability, bandstructure, work function, density of state and optical properties of the GaN bilayer and GaN trilayer in two-doped ways are investigated. The results show that formation energy of variable doping structure is less than that of the uniform doping structure, which means that the variable doping structure is more stable. At the same time, the formation energy increases with increase of layers. The pristine GaN bilayer has an indirect bandgap, while the doped GaN bilayer transforms into a direct bandgap. The impurity levels appear in a forbidden band of doped GaN trilayers, which is favorable for electron transition. The results of work function reveal that variable doping structure has lower vacuum barriers and more electron escape numbers, which proves that it can improve the quantum efficiency of photocathodes. Finally, the analysis of optical properties shows that the uniform doping structure has better optical properties than that of the variable doping structure.

In this paper, we introduce a class of double-weighted polygon networks with two different meanings of weighted factors $\omega$ and $r$, which represent path-difficulty and path-length, respectively, based on actual traffic networks. Picking an arbitrary node from the hub nodes set as the trap node, and the double-weighted polygon networks are divided into $nt+1$ blocks by combining with the iterative method. According to biased random walks, the calculation expression of average receiving time (ART) of any polygon networks is given by using the intermediate quantity the mean first-passage time (MFPT), which is applicable to any $n$ ($n\ge 3$) polygon networks. What is more, we display the specific calculation process and results of ART of the double-weighted quadrilateral networks, indicating that ART grows exponentially with respect to the networks order and the exponent is $𝜃={log}_5(1+4\omega r)$ which grows with the product of $\omega r$. When $\omega r$ increases, ART increases linearly ($\omega =r=1$) or sublinearly ($0<\omega r<1$) with the size of networks, and the smaller value of $\omega r$, the higher transportation efficiency.

Based on the quantum kinetic equation (QKE) for electron, we have theoretically studied the theory of photo-stimulated Ettingshausen effect in a one-dimensional cylindrical quantum wire (CQW). The strong electromagnetic wave (EMW) $E=(E_{0}sin\mathrm{\Omega }t,0,0)$ plays a role as photo-stimulation source. We obtain the analytic expressions for the kinetic tensors $\alpha$, $\beta$, $\gamma$, $\xi$ and the Ettingshausen coefficient (EC) in the CQW with the dependence on the amplitude and the energy of EMW, the CQW radius, the magnetic field and the temperature for two cases: optical phonon and acoustic phonon. The results are numerically evaluated and graphed for GaAs/AlGaAs CQW model. It is shown that we observe the cyclotron resonance and magneto-phonon resonance effect while surveying EC in terms of magnetic field (with and without EMW) and EMW energy, considered the electron-optical phonon scattering. In case of electron-acoustic phonon scattering, the oscillation of EC is obtained with the transition between low Landau levels (LLs). We also clarify the impact of quantum size effect (QSE) on EC by surveying the influence of EC on the radius of CQW.

Surface plasmon resonance (SPR)-based single-core photonic crystal fiber (PCF) biosensor is investigated with external gold coating. All the geometrical parameters such as a gold layer, an analyte layer, a lattice period and cladding air holes are optimized to enhance the sensing ability of the sensor by introducing the finite element method. The designed sensor is able to achieve the highest amplitude sensitivity (AS) of 2258.95 RIU${}^{-1}$ with an acceptable refractive index sensitivity (RIS) of 6000 nm/RIU over the analyte refractive index (ARI) span of 1.31–1.40. This sensor can detect a slight index alteration in the sensing medium using a resolution of $1.66\times 10^{-5}$ and a high figure of merit (FOM) of 79.01. With the enhanced modal behavior with simple geometry, the resulting sensor can be suitable for real-time monitoring in biological, biochemical and bio-imaging applications.