Physics

Partially ionized plasma physics has attracted increased attention recently due to numerous technological applications made possible by the increased sophistication of computer modelling, the depth of the theoretical analysis, and the technological applications to a vast field of manufacturing for computer components. Partially ionized plasma is characterized by a significant presence of neutral particles in contrast to the fully ionized plasma. The theoretical analysis is based upon solutions of the kinetic Boltzmann equation, yielding the non-Maxwellian electron energy distribution function (EEDF), thereby emphasizing the difference with a fully ionized plasma. The impact of the effect on discharges in inert and molecular gases is described in detail, yielding the complex nonlinear phenomena resulting in plasma selforganization. A few examples of such phenomena are given, including the non-monotonic EEDFs in the discharge afterglow in a mixture of argon with the molecular gas NF₃; the explosive generation of cold electron populations in capacitive discharges, hysteresis of EEDF in inductively coupled plasmas. Recently, highly advanced computer codes were developed in order to address the outstanding challenges in plasma technology. These developments are briefly described in general terms.

Polynomial exact solutions of the Navier–Stokes equations for describing micropolar incompressible fluid flows with energy dissipation are reported. The transformation of mechanical energy into thermal energy is taken into account. The heat equation for the Rayleigh function contains the sum of the squares of the components of the Cauchy velocity tensor (the main component for the dissipative function). Unidirectional homogeneous and non-homogeneous fluid flows with moment stresses are considered. The solvability of overdetermined systems for studying homogeneous and non-homogeneous shear flows is studied. The paper pays attention to the exact integration of equations for three-dimensional flows. The construction of classes of exact solutions is carried out first using the Lin–Sidorov–Aristov solution family. In other words, the velocity field depends linearly on part of the coordinates. The coefficients of the linear forms of the velocity field depend on the third coordinate and time. The pressure field and the temperature field are quadratic forms with similar functional arbitrariness. In addition, exact solutions for the velocity field with a nonlinear dependence on part of the coordinates are considered.

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.