Kinetic Solvers with Adaptive Mesh in Phase Space

An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for solving multi-dimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a tree of trees data structure. The mesh in r-space is automatically generated around embedded boundaries and dynamically adapted to local solution properties. The mesh in v-space is created on-the-fly for each cell in r-space. Mappings between neighboring v-space trees implemented for the advection operator in configuration space. We have developed new algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive mesh in velocity space: importance sampling, multi-point projection method, and the variance reduction method. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions in a Lorentz gas. New AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce computational cost and memory usage for solving challenging kinetic problems

Electron Kinetics in a Positive Column of AC Discharges in a Dynamic Regime

We have performed hybrid kinetic-fluid simulations of a positive column in AC Argon discharges over a range of driving frequencies f and gas pressure p for the conditions when the spatial nonlocality of the Electron Energy Distribution Function (EEDF) is substantial. Our simulations confirmed that the most efficient conditions of plasma maintenance are observed in the dynamic regime when time modulations of mean electron energy (temperature) are substantial. The minimal values of the root mean square (rms) electric field and the electron temperature have been observed at f/p values of about 3 kHz/Torr in a tube of radius R = 1 cm. The ionization rate and plasma density reached maximal values under these conditions. The numerical solution of a kinetic equation allowed accounting for the kinetic effects associated with spatial and temporal nonlocality of the EEDF. Using the kinetic energy of electrons as an independent variable, we solved an anisotropic tensor diffusion equation in phase space. We clarified the role of different flux components during electron diffusion in phase space over surfaces of constant total energy. We have shown that the kinetic theory uncovers a more exciting and rich physics than the classical ambipolar diffusion (Schottky) model. Non-monotonic radial distributions of excitation rates, metastable densities, and plasma density have been observed in our simulations at pR > 6 Torr cm. The predicted off-axis plasma density peak in the dynamic regime has never been observed in experiments so far. We hope our results stimulate further experimental studies of the AC positive column. The kinetic analysis could help uncover new physics even for such a well-known plasma object as a positive column in noble gases

Ionization waves (striations) in low-current DC discharges in noble gases obtained with a hybrid kinetic-fluid model

A hybrid kinetic-fluid model is used to study ionization waves (striations) in a low-current plasma column of DC discharges in noble gases. Coupled solutions of a kinetic equation for electrons, a drift-diffusion equation of ions, and a Poisson equation for the electric field are obtained to clarify the nature of plasma stratification in the positive column and near-electrode effects. A simplified two-level excitation-ionization model is used for the conditions when the nonlinear effects due to stepwise ionization, gas heating, and Coulomb interactions among electrons are negligible. It is confirmed that the nonlocal effects are responsible for the formation of moving striations in DC discharges at low plasma densities. The calculated properties of self-excited waves of S, P, and R types in Neon and S type in Argon agree with available experimental data. The reason for Helium plasma stability to stratification is clarified. It is shown that sustaining stratified plasma is more efficient than striation-free plasma when the ionization rate is a nonlinear function of the electric field. However, the nonlinear dependence of the ionization rate on the electric field is not required for plasma stratification. Striations of S, P, and R types in Neon exist with minimal or no ionization enhancement. Effects of the column length on the wave properties have been demonstrated in our simulations

Distinct functional brain regional integration of Casp3, Ascl1 and S100a6 gene expression in spatial memory

Evaluating the brain structural expression of defined genes involved in basic biological processes of neurogenesis, apoptosis or neural plasticity may facilitate the understanding of genetic mechanisms underlying spatial memory. The aim of the present study was to compare Ascl1, Casp3 and S100a6gene expression in the hippocampus, prefrontal cortex and cerebellum of adult rats in water maze spatial memory performance. After four days training, the mean platform time (<10 s) was evidence of stable long-term spatial memory formation. Real time PCR analysis revealed a positive inter-structural correlation for S100a6/Caspgene expression between the prefrontal cortex and the cerebellum but a negative correlation for S100a6/Ascl1transcribed genes between the prefrontal cortex and hippocampus during swimming in the active controls. However, during spatial memory performance there was only one inter-structural correlation between the prefrontal cortex and cerebellum with respect to Casp3 expression, though there were intra-structural correlations between Casp3/Ascl1transcriptions within the prefrontal cortex and hippocampus as well as between Ascl1/S100a6in the cerebellum. In active learners versus naive controls, the transcrption of all genes was augmented in the prefrontal cortex but Casp3 and Ascl1were also elevated in hippocampus whilst only S100a6increased in the cerebellum. The findings endorsed the role of the hippocampus in memory acquisition in addition to an integrative relationship with the prefrontal cortex and cerebellum. This structural and molecular configuration is important for creation of novel neural circuitry for consolidation and reconsolidation of memory trace with an involvement of coupled processes of neurogenesis, apoptosis or neural plasticity