Polar propagating optical phonon states and their dispersive spectra in wurtzite nitride superlattices: Quantum size effect

The polar optical phonon states of propagating (PR) modes in wurtzite GaN/Al_xGa_1−xN superlattices (SLs) are investigated within the dielectric continuum model framework. It is proved that the PR phonon modes only appear in wurtzite GaN/Al_xGa_1−xN SL with a small x$x$ Al mole ratio concentration (such as x<0.34$x<0.34$). The analytical phonon states of PR modes and their dispersive equation in the wurtzite GaN/Al_xGa_1−xN SL structures are obtained. Numerical calculations on the dispersive spectra of PR modes and their electrostatic potential properties as well as the quantum size effect are performed for a wurtzite GaN/Al_0.15Ga_0.85N SL. Results reveal that dispersive curves of PR modes in SLs form frequency bands. As the well width of GaN well-layer increases, the frequency bands of PR modes become steeper and narrower. The discussion of electrostatic potentials shows that the wavelength of PR phonon modes with a phase qL=π$qL=\pi$ (0) is 2L$2L$ (L$L$). With the increase of the SL well width, the wave-node number of the PR phonon modes in the barrier regions increases. The present theoretical scheme and numerical results are quite useful for analyzing the dispersive spectra of PR phonon modes and their polaronic effect in wurtzite GaN/AlGaN SL structures.     

Effect of pressure on intersubband optical absorption coefficients and refractive index changes in a V-groove quantum wire

In this paper, the effect of hydrostatic pressure on the intersubband optical absorption and the refractive index changes in a GaAs/Ga_1−xAl_xAs ridge quantum wire are studied. We use analytical expressions for the linear and third-order nonlinear intersubband absorption coefficients and refractive index changes obtained by the compact-density matrix formalism. The linear, third-order nonlinear, and total intersubband absorption coefficients and refractive index changes are investigated at different pressures as a function of photon energy with known values of width wire (b$b$), the incident optical intensity (I$I$), and the angle θ$\theta$. According to the results obtained from the present work, we have found that the pressure plays an important role in the intersubband optical absorption coefficients and refractive index changes in a V-groove quantum wire.     

Third-harmonic generation in asymmetric coupled quantum wells

The third-harmonic generation (THG) in asymmetric coupled quantum wells (ACQWs) for different values of the well parameter Δ$\Delta$ and width of barrier (_WB)$\left(W_B\right)$ are theoretically studied. The analytical expression of the third-harmonic generation is derived by using the compact density-matrix approach and the iterative method. Finally, the numerical calculations are presented for typical GaAs/Al_xGa_1−xAs asymmetric coupled quantum wells. Results obtained show that the third-harmonic generation in the asymmetric coupled quantum wells can be importantly modified by the parameter Δ$\Delta$ and _WB$W_B$. Moreover, third-harmonic generation also depends on the relaxation rate of the asymmetric coupled quantum wells.     

Magnetic entropy-change in La0.67−xBixCa0.33MnO3 compound

Bi doped lanthanum manganites with the chemical composition of La_0.67−xBi_xCa_0.33MnO₃ (x=0$x=0$, 0.05, 0.1, 0.2) were prepared by the standard solid-state process. The Curie temperatures were measured to be 267 K for x=0$x=0$, 248 K for x=0.05$x=0.05$, 244 K for x=0.1$x=0.1$ and 229 K for x=0.2$x=0.2$ samples. It was found that the maximum value of the magnetic entropy change ∣ΔS_m∣ has reached the highest value of 6.08 J/kg K at 3 T for the composition with x=0.05$x=0.05$. Nearly the same maximum entropy change was observed for the x=0$x=0$ sample. A large decrease in the magnitude of the entropy change was observed for the x=0.2$x=0.2$ sample.     

Intertwining operators for Sklyanin algebra and elliptic hypergeometric series

Intertwining operators for infinite-dimensional representations of the Sklyanin algebra with spins ?$?$ and −?−1$-?-1$ are constructed using the technique of intertwining vectors for elliptic L$L$-operator. They are expressed in terms of elliptic hypergeometric series with operator argument. The intertwining operators obtained (W$W$-operators) serve as building blocks for the elliptic R$R$-matrix which intertwines tensor product of two L$L$-operators taken in infinite-dimensional representations of the Sklyanin algebra with arbitrary spin. The Yang–Baxter equation for this R$R$-matrix follows from simpler equations of the star–triangle type for the W$W$-operators. A natural graphic representation of the objects and equations involved in the construction is used.     

On the parallel transport of the Ricci curvatures

Geometrical characterizations are given for the tensor R⋅S$R\cdot S$, where S$S$ is the Ricci tensor   of a (semi-)Riemannian manifold (M,g)$(M,g)$ and R$R$ denotes the curvature operator   acting on S$S$ as a derivation, and of the Ricci Tachibana tensor  _∧g⋅S${\wedge }_g\cdot S$, where the natural metrical operator  _∧g${\wedge }_g$ also acts as a derivation on S$S$. As a combination, the Ricci curvatures   associated with directions on M$M$, of which the isotropy determines that M$M$ is Einstein, are extended to the Ricci curvatures of Deszcz   associated with directions and planes on M$M$, and of which the isotropy determines that M$M$ is Ricci pseudo-symmetric in the sense of Deszcz.     

Thermodynamics properties of an anisotropic Ising antiferromagnet in both external longitudinal and transverse fields

We have studied the anisotropic two-dimensional nearest-neighbor Ising model with competitive interactions in both uniform longitudinal field H$H$ and transverse magnetic field Ω$\Omega$. Using the effective-field theory (EFT) with correlation in cluster with N=1$N=1$ spin we calculate the thermodynamic properties as a function of temperature with values H$H$ and Ω$\Omega$ fixed. The model consists of ferromagnetic interaction _Jx$J_x$ in the x$x$ direction and antiferromagnetic interaction _Jy$J_y$ in the y$y$ direction, and it is found that for H/_Jy∈[0,2]$H/J_y\in [0,2]$ the system exhibits a second-order phase transition. The thermodynamic properties are obtained for the particular case of λ=_Jx/_Jy=1$\lambda =J_x/J_y=1$ (isotropic square lattice).     

Magnetic properties of novel FeSe(Te) superconductors

Magnetization studies were carried out for the novel FeSe_1−xTe_x superconductors (0≤x≤1$0\le x\le 1$) to investigate a behavior of the intrinsic magnetic susceptibility χ$\chi$ in the normal state. The magnetic susceptibility was found to increase gradually with Te content. The temperature dependencies of the magnetic susceptibility χ$\chi$ and its anisotropy Δχ=_χ∥−_χ⊥$\mathrm{\Delta }\chi ={\chi }_{\parallel }-{\chi }_{\perp }$ were measured for FeSe in the temperature range 4.2–300 K, and a growth of susceptibility with temperature was revealed. For FeTe a substantial increase of χ$\chi$ under pressure was found. Ab initio calculations of the band structure and magnetic susceptibility have shown, that FeSe_1−xTe_x systems are close to magnetic instability with dominating enhanced spin paramagnetism. The calculated paramagnetic susceptibility exhibits a strong dependence on the unit cell volume V   and especially the height of chalcogen species from the Fe plane. With appropriate values of these parameters the calculations have reproduced the experimental data on χ(T)$\chi (T)$ and χ(P)$\chi (P)$ for FeSe and FeTe, respectively.     

Target mass corrections for spin-dependent structure functions in collinear factorization

We derive target mass corrections (TMC) for the spin-dependent nucleon structure function g₁$g_1$ and polarization asymmetry A₁$A_1$ in collinear factorization at leading twist. The TMCs are found to be significant for g₁$g_1$ at large xB$x_B$, even at relatively high Q²$Q^2$ values, but largely cancel in A₁$A_1$. A comparison of TMCs obtained from collinear factorization and from the operator product expansion shows that at low Q²$Q^2$ the corrections drive the proton A₁$A_1$ in opposite directions.     

Exact solution of the alternating XXZ spin chain with generic non-diagonal boundaries

The integrable XXZ alternating spin chain with generic non-diagonal boundary terms specified by the most general non-diagonal K$K$-matrices is studied via the off-diagonal Bethe Ansatz method. Based on the intrinsic properties of the fused R$R$-matrices and K$K$-matrices, we obtain certain closed operator identities and conditions, which allow us to construct an inhomogeneous T−Q$T-Q$ relation and the associated Bethe Ansatz equations accounting for the eigenvalues of the transfer matrix.     

Quantum information entropies for a squared tangent potential well

The particle in a symmetrical squared tangent potential well is studied by examining its Shannon information entropy and standard deviations. The position and momentum information entropy densities _ρs(x)${\rho }_s(x)$, _ρs(p)${\rho }_s(p)$ and probability densities ρ(x)$\rho (x)$, ρ(p)$\rho (p)$ are illustrated with different potential range L and potential depth U  . We present analytical position information entropies _Sx$S_x$ for the lowest two states. We observe that the sum of position and momentum entropies _Sx$S_x$ and _Sp$S_p$ expressed by Bialynicki-Birula–Mycielski (BBM) inequality is satisfied. Some eigenstates exhibit entropy squeezing in the position. The entropy squeezing in position will be compensated by an increase in momentum entropy. We also note that the _Sx$S_x$ increases with the potential range L, while decreases with the potential depth U  . The variation of _Sp$S_p$ is contrary to that of _Sx$S_x$.     

Weak mirror symmetry of complex symplectic Lie algebras

A complex symplectic structure on a Lie algebra h$\mathfrak{h}$ is an integrable complex structure J$J$ with a closed non-degenerate (2,0)$(2,0)$-form. It is determined by J$J$ and the real part Ω$\Omega$ of the (2,0)$(2,0)$-form. Suppose that h$\mathfrak{h}$ is a semi-direct product g?V$\mathfrak{g}?V$, and both g$\mathfrak{g}$ and V$V$ are Lagrangian with respect to Ω$\Omega$ and totally real with respect to J$J$. This note shows that g?V$\mathfrak{g}?V$ is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω$\Omega$ and J$J$ are isomorphic.     

Critical behavior of an anisotropic Ising antiferromagnet in both external longitudinal and transverse fields

In this paper we study the critical behavior of a two-sublattice Ising model on an anisotropic square lattice in both uniform longitudinal (H  ) and transverse (Ω$\Omega$) fields by using the effective-field theory. The model consists of ferromagnetic interaction J_x in the x direction and antiferromagnetic interaction J_y in the y direction in the presence of the H   and Ω$\Omega$ fields. We obtain the phase diagrams in the H–T$H–T$ and Ω–T$\Omega –T$ planes changing values of the Ω$\Omega$ and H   parameters, respectively for fixed value at λ=_Jx/_Jy=1$\lambda =J_x/J_y=1$. At null temperature, the ground state phase diagram in the Ω–H$\Omega –H$ plane for several values of λ$\lambda$ parameter is analyzed. In the particular case of λ=1$\lambda =1$ we compare our results with mean-field theory (MFT) and was not observed reentrant behavior around of the critical field _Hc/_Jy=2.0$H_c/J_y=2.0$ for Ω=0$\Omega =0$ by using EFT.     

Post-breakthrough scaling in reservoir field simulation

We study the oil displacement and production behavior in an isothermal thin layered reservoir model subjected to water flooding. We use the CMG’s (Computer Modelling Group  ) numerical simulators to solve mass balance equations. The influences of the viscosity ratio (m≡_μoil/_μwater$m\equiv {\mu }_{oil}/{\mu }_{water}$) and the inter-well (injector-producer) distance r$r$ on the oil production rate C(t)$C\left(t\right)$ and the breakthrough time _tbr$t_{br}$ are investigated. Two types of reservoir configuration are used, namely one with random porosities and another with a percolation cluster structure. We observe that the breakthrough time follows a power-law of m$m$ and r$r$, _tbr∝r^αm^β$t_{br}\propto r^{\alpha }{m}^{\beta }$, with α=1.8$\alpha =1.8$ and β=−0.25$\beta =-0.25$ for the random porosity type, and α=1.0$\alpha =1.0$ and β=−0.2$\beta =-0.2$ for the percolation cluster type. Moreover, our results indicate that the oil production rate is a power law of time. In the percolation cluster type of reservoir, we observe that P(t)∝t^γ$P\left(t\right)\propto t^{\gamma }$, with γ=−1.81$\gamma =-1.81$, where P(t)$P\left(t\right)$ is the time derivative of C(t)$C\left(t\right)$. The curves related to different values of m$m$ and r$r$ may be collapsed suggesting a universal behavior for the oil production rate.     

Partition function zeros of the antiferromagnetic Ising model on triangular lattice in the complex temperature plane for nonzero magnetic field

The grand partition functions Z(T,B)$Z(T,B)$ of the Ising model on L×L$L\times L$ triangular lattices with fully periodic boundary conditions, as a function of temperature T and magnetic field B  , are evaluated exactly for L<12$L<12$ (using microcanonical transfer matrix) and approximately for L?12$L?12$ (using Wang–Landau Monte Carlo algorithm). From Z(T,B)$Z(T,B)$, the distributions of the partition function zeros of the triangular-lattice Ising model in the complex temperature plane for real B≠0$B\ne 0$ are obtained and discussed for the first time. The critical points aN(x)$a_N(x)$ and the thermal scaling exponents yt(x)$y_t(x)$ of the triangular-lattice Ising antiferromagnet, for various values of x=e−2βB$x=e^{-2\beta B}$, are estimated using the partition function zeros.     

On analogues of black brane solutions in the model with multicomponent anisotropic fluid

A family of spherically symmetric solutions with horizon in the model with m  -component anisotropic fluid is presented. The metrics are defined on a manifold that contains a product of n−1$n-1$ Ricci-flat “internal” spaces. The equation of state for any s  -th component is defined by a vector Us$U^s$ belonging to Rn+1${\mathbb{R}}^{n+1}$. The solutions are governed by moduli functions Hs$H_s$ obeying non-linear differential equations with certain boundary conditions imposed. A simulation of black brane solutions in the model with antisymmetric forms is considered. An example of solution imitating M₂–M₅$M_2\text{–}{M}_5$ configuration (in D=11$D=11$ supergravity) corresponding to Lie algebra A₂$A_2$ is presented.     

An efficient community detection method based on rank centrality

Community detection is a very important problem in social network analysis. Classical clustering approach, K$K$-means, has been shown to be very efficient to detect communities in networks. However, K$K$-means is quite sensitive to the initial centroids or seeds, especially when it is used to detect communities. To solve this problem, in this study, we propose an efficient algorithm K$K$-rank, which selects the top-K$K$ nodes with the highest rank centrality as the initial seeds, and updates these seeds by using an iterative technique like K$K$-means. Then we extend K$K$-rank to partition directed, weighted networks, and to detect overlapping communities. The empirical study on synthetic and real networks show that K$K$-rank is robust and better than the state-of-the-art algorithms including K$K$-means, BGLL, LPA, infomap and OSLOM.     

Complex scale-free networks with tunable power-law exponent and clustering

We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network. This set includes m$m$ “ambassador” nodes and l$l$ of each ambassador’s descendants where m$m$ and l$l$ are random variables selected from any choice of distributions _pl$p_l$ and _qm$q_m$. The process mimics the tendency of authors to cite varying numbers of papers included in the bibliographies of the other papers they cite. We show that the degree distributions of the networks generated after a large number of iterations are scale-free and derive an expression for the power-law exponent. In a particular case of the model where the number of ambassadors is always the constant m$m$ and the number of selected descendants from each ambassador is the constant l$l$, the power-law exponent is (2l+1)/l$(2l+1)/l$. For this example we derive expressions for the degree distribution and clustering coefficient in terms of l$l$ and m$m$. We conclude that the proposed model can be tuned to have the same power law exponent and clustering coefficient of a broad range of the scale-free distributions that have been studied empirically.