Physics

We investigate time-resolved wave-packet transport in monolayer graphene patterned with asymmetric arrays of circular electrostatic scatterers. Using the Dirac continuum model with a split-operator scheme, we track how transmission evolves with scatterer radius and polarity sequence. To this end, we consider three potential configurations (Samples 1–3). The results reveal a geometry-controlled crossover from near-ballistic propagation at small radii to interference-dominated backscattering at large radii. Sample 1, where the potential exhibit two parallel lines of circles, each line sharing the same potential sign, preserves the highest transmission. Conversely, in Sample 3, where potential signs are intercalated between circles of the same line, the dwell time increases, which produces stronger confinement. As the radius increases, pronounced temporal oscillations emerge due to repeated internal reflections (similar to Fabry–Pérot interferometer), and the radius dependence of the saturated transmission probability exhibits anti-resonant dips that are tunable by geometry and potential magnitude. These behaviors establish simple design rules for graphene nanodevices: small-radius Sample 1 for high-throughput transport, Sample 2 (with inverted potential signs as compared to Sample 1) for broadband suppression, and Sample 3 for finely tunable, interference-based confinement.

We compare two different approaches to turbulence: the kinetic theory of solitons and the kinetic theory of quasi-particles. Using the same model equation as the starting point of both descriptions, we compare their properties, advantages, and limitations. We also address the question of whether a gas of solitons be seen as a particular case of a gas of quasi-particles and propose possible strategies leading to a more general theoretical model of wave turbulence.

We employ a two-dimensional fluid simulation approach to study the nonlinear turbulent dynamics of internal gravity waves (IGWs) in the weakly ionized Earth’s ionospheric F-layer with the effects of Pedersen conductivity. We observe that the presence of Pedersen conductivity leads to the formation of intermediate-scale structures in the velocity potential, along with the development of small-scale density fluctuations. The characteristic turbulent energy spectrum exhibits a non-Kolmogorov scaling of $k^{-2.40}$ in the presence of Pedersen conductivity, while a Kolmogorov-like $k^{-5/3}$ scaling is observed when it is absent, where k denotes the wave number. Due to energy loss caused by Pedersen conductivity, the wave’s amplitude reduces gradually with time. The cross-field diffusion coefficient related to the velocity potential also reduces as Pedersen conductivity increases. The results in the F-layer are compared with those in the literature, where the Ampère force and hence the Pedersen conductivity effect were ignored compared to the pressure gradient and gravity forces, as relevant in the Earth’s D-layer.