The privileged spectrum of cnoidal ion holes and its extension by imperfect ion trapping

The fundamental properties of nonlinear ion hole modes propagating in current-driven collisionless plasmas are derived. Making use of Schamel's alternative method their spatial structure $?(x)$ and phase velocities $u_0$ are analyzed and found to depend crucially on the used trapped ion distribution $f_{it}$. A regular $f_{it}$ represents a continuous spectrum, which is called privileged or perfect since it yields a definite $u_0$ and appears most realistic. A singular $f_{it}$, on the other hand, involving jumps and moderate slope singularities at the separatrix, does reveal further classes of hole equilibria at the cost, however, of a well-defined $u_0$. This explains why Bernstein, Greene, Kruskal (BGK)-solutions of the Vlasov–Poisson system, exhibiting a strong slope singularity of their derived trapped particle distribution, can principally not provide definite $u_{0}s$. The nonlinear dispersion relation (or $u_0$) of privileged ion holes, on the other hand, is equivalent with that of cnoidal electron holes, i.e. in addition to the ordinary ion acoustic branch there exists a correspondence to the “Langmuir” branch and to the multiple “slow electron acoustic” branches, reflecting different trapping scenarios.     

Impact of local coupling on the vulnerability of 2D spatially embedded interdependent networks

Real networks are always interdependent and spatially embedded. Considering the space constraint, dependency links between networks may be established not globally but locally. In this paper, we study how the spatial coupling will impact the robustness of interdependent scale-free networks located in a 2D square plane where dependent nodes are connected within a connecting radius $r_{connect}$. Besides the traditional assortative degree–degree coupling (GD) and random coupling (GR), some novel spatial couplings are also introduced, i.e., spatial assortative degree–degree coupling (SD), spatial random coupling (SR) and nearest neighbor coupling (NN). Simulation results indicate that assortative couplings, GD and SD, can improve the robustness under topological attacks while under localized attacks, NN coupling is the best one. In addition, for SD coupling under topological attacks, we find that the robustness for small $r_{connect}$ decreases with $r_{connect}$ from 0 to the critical value $r_{c1}$, and for larger $r_{connect}$ gradually increases with $r_{connect}$ from $r_{c1}$ to the maximum value ${(r_{connect})}_{max}$. However, opposite results will be obtained under localized attacks. These findings may be helpful to understand and analyze some real interdependent infrastructures.     

On quasi-triviality and integrability of a class of scalar evolutionary PDEs

For a certain class of perturbations of the equation $u_t=f\left(u\right)u_x$, we prove the existence of change of coordinates, called quasi-Miura transformations, that reduce these perturbed equations to the unperturbed one. As an application, we propose a criterion for the integrability of these equations.     

Percolation on infinitely ramified fractal networks

We study how fractal features of an infinitely ramified network affect its percolation properties. The fractal attributes are characterized by the Hausdorff ($D_H$), topological Hausdorff ($D_{tH}$), and spectral ($d_s$) dimensions. Monte Carlo simulations of site percolation were performed on pre-fractal standard Sierpiński carpets with different fractal attributes. Our findings suggest that within the universality class of random percolation the values of critical percolation exponents are determined by the set of dimension numbers ($D_H$, $D_{tH}$, $d_s$), rather than solely by the spatial dimension (d). We also argue that the relevant dimension number for the percolation threshold is the topological Hausdorff dimension $D_{tH}$, whereas the hyperscaling relations between critical exponents are governed by the Hausdorff dimension $D_H$. The effect of the network connectivity on the site percolation threshold is revealed.     

Diffusion thermopower of the two-dimensional electron gas in GaN single quantum wells

Diffusion thermopower ($S_d$) of the two-dimensional (2D) electron gas in GaN single quantum wells is calculated in the temperature range 1 K–12 K using the Fermi–Dirac distribution function. Scattering of carriers through acoustic phonons via deformation potential and piezoelectric couplings, and through background and remote ionized impurities is included. $S_d$ is found to decrease with temperature and the 2D electron concentration, and is primarily controlled by deformation potential acoustic scattering. The dependence of $S_d$ on the well width and the ionized impurity concentration is found to be quite weak.     

Superfluidity of indirect excitons vs quantum Hall correlation in double Hall systems: Different types of physical mechanisms of correlation organization in Hall bilayers

Bilayer Hall systems can be divided into two groups—with and without tunneling of carriers across the barrier between layers. We demonstrate that these both classes differ in topology sense which leads to the distinct quantum Hall hierarchy. In the case of forbidden interlayer carrier tunneling we developed the Metropolis Monte Carlo simulation for an energy competition of the reentrant integer quantum Hall state against the superfluid Bose Einstein condensate of indirect excitons in double-layer 2D Hall systems, GaAs/GaAlAs/GaAs and b-graphene/hBN/b-graphene, with complementary layer filling, ${\nu }_{bot}+{\nu }_{top}=1$. The resulted phase diagrams for both systems have been determined in consistence with the experimental data.     

Shannon and Fisher entropies for a hydrogen atom under soft spherical confinement

We calculate Shannon and Fisher entropies in the position and momentum space, and some complexity measures for a variationally described hydrogen atom confined in soft and hard spherical boxes of varying dimension $r_c$ and selected values of strength $U_0$. We include calculations for a free particle trapped in impenetrable boxes. It is found that the Shannon entropy $S_r$ becomes negative for small cavity radii and large values of $U_0$, due to the highly localized nature of the particle. For soft confinement and small cavity dimensions, the entropies change very rapidly over short radial intervals.