Invariance priors for Bayesian feed-forward neural networks.

Neural networks (NN) are famous for their advantageous flexibility for problems when there is insufficient knowledge to set up a proper model. On the other hand, this flexibility can cause overfitting and can hamper the generalization of neural networks. Many approaches to regularizing NN have been suggested but most of them are based on ad hoc arguments.

Statistical anisotropy of magnetohydrodynamic turbulence.

Direct numerical simulations of decaying and forced magnetohydrodynamic (MHD) turbulence without and with mean magnetic field are analyzed by higher-order two-point statistics. The turbulence exhibits statistical anisotropy with respect to the direction of the local magnetic field even in the case of global isotropy. A mean magnetic field reduces the parallel-field dynamics while in the perpendicular direction a gradual transition towards two-dimensional MHD turbulence is observed with k(-3/2) inertial-range scaling of the perpendicular energy spectrum.

Giant electron tails and passing electron pinch effects in tokamak-core turbulence.

The anomalous particle transport in a tokamak core is believed to be linked to the advection of magnetically trapped electrons alone, owing to the passing electrons maintaining a thermal equilibrium along the field lines. Surprisingly, in nonlinear numerical studies, the radial flux of passing electrons rivals that of the trapped ones. The strong interaction of passing electrons and electric fluctuations is mediated by long tails of the modes along the magnetic field, which are generated by the passing electrons in the first place.

Force field inside the void in complex plasmas under microgravity conditions.

Observations of complex plasmas under microgravity conditions onboard the International Space Station performed with the Plasma-Kristall experiment-Nefedov facility are reported. A weak instability of the boundary between the central void (region free of microparticles) and the microparticle cloud is observed at low gas pressures. The instability leads to periodic injections of a relatively small number of particles into the void region (by analogy this effect is called the "trampoline effect").

Coupled dust-lattice modes in complex plasmas.

The coupling between transverse and longitudinal dust-lattice modes due to the particle-wake interactions and vertical dust charge gradient is considered. It is shown that the dust-lattice waves can be subjected to a specific instability, the criterion for which has been derived. This instability can explain experimentally observed spontaneous excitation of vibrational modes in a plasma crystal when the pressure is decreased below a critical value.

Kinetic approach for the ion drag force in a collisional plasma.

The linear kinetic approach to calculate the ion drag force in a collisional plasma is generalized. The model collision integral (for ion-neutral collisions) is discussed and employed to calculate the plasma response for arbitrary velocity of the plasma flow and arbitrary frequency of the collisions. The derived plasma response is used to calculate the self-consistent force on the test charged particle.

Kinetics of ensembles with variable charges.

Kinetics of particle ensembles with variable charges is investigated. It is shown that the energy of such ensembles is not conserved in the interparticle collisions. The case when the equilibrium charge depends on the particle coordinate is studied, and the collision integral describing the momentum and energy transfer in collisions is derived.

Momentum transfer in complex plasmas.

Momentum transfer in complex plasmas (systems consisting of ions, electrons, neutrals, and charged macroscopic grains) is investigated assuming an interaction potential between the charged species of the screened Coulomb (Yukawa) type. Momentum transfer cross sections and rates are derived. Applications of the results are discussed; in particular, we classify the possible states of complex plasmas in terms of the momentum transfer due to grain-grain collisions and its competition with that due to interaction with the surrounding medium.

Diagnostics of the electronegative plasma sheath at low pressures using microparticles.

Levitated particles are a new powerful diagnostic of the midplasma sheath region. They can reveal features undetectable either to plasma or to surface measurements. The equilibrium position of microparticles suspended in an oxygen plasma sheath, together with a model of the levitation force and Langmuir probe measurements, gives evidence of secondary electropositive plasmas in the already established plasma sheath, in the range of parameters where the modified Bohm criterion breaks down into multiple solutions.

Wave dispersion relation of two-dimensional plasma crystals in a magnetic field.

The wave dispersion relation in a two-dimensional strongly coupled plasma crystal is studied by theoretical analysis and molecular dynamics simulation taking into account a constant magnetic field parallel to the crystal normal. The expression for the wave dispersion relation clearly shows that high-frequency and low-frequency branches exist as a result of the coupling of longitudinal and transverse modes due to the Lorenz force acting on the dust particles. The high-frequency and the low-frequency branches are found to belong to right-hand and left-hand polarized waves, respectively.

Bayesian neural-networks-based evaluation of binary speckle data.

We present a new method using Bayesian probability theory and neural networks for the evaluation of speckle interference patterns for an automated analysis of deformation and erosion measurements. The method is applied to the fringe pattern reconstruction of speckle measurements with a Twyman-Green interferometer. Given a binary speckle image, the method returns the fringe pattern without noise, thus removing the need for smoothing and allowing a straightforward unwrapping procedure and determination of the surface shape.

Thermodynamic potential in local turbulence simulations.

For the reduced local equations customary in, e.g., the computation of turbulence in tokamaks the energy is still a conserved quantity.

Experimental determination of dust-particle charge in a discharge plasma at elevated pressures.

The charge of dust particles is determined experimentally in a bulk dc discharge plasma in the pressure range 20-100 Pa. The charge is obtained by two independent methods: one based on an analysis of the particle motion in a stable particle flow and another on an analysis of the transition of the flow to an unstable regime. Molecular-dynamics simulations of the particle charging for conditions similar to those of the experiment are also performed.

Turbulent saturation of tokamak-core zonal flows.

Current theories of zonal flow dynamics focus on the transport of poloidal momentum. Different from a cylinder, stationary poloidal flows in a tokamak are accompanied by (possibly kinetic) flows along the magnetic field, which maintain incompressibility, and comprise the major part of the flow energy. In numerical turbulence studies, the flows saturate by the turbulent diffusion of the parallel flow, whereas the poloidal momentum transport continues to strongly drive the flows.

Dusty plasmas in a constant electric field: role of the electron drag force.

We investigate the forces experienced by a microparticle immersed in a weakly ionized plasma with constant electric field. These are electric force and the forces associated with the momentum transfer from electrons and ions drifting in the field (electron and ion drag forces). It is shown that the effect of the electron drag, which is often neglected, can be substantial in a certain parameter range.

Electrostatic modes in collisional complex plasmas under microgravity conditions.

A linear dispersion relation in a highly collisional complex plasma, including ion drift, was derived in the light of recent PKE-Nefedov wave experiment performed under microgravity conditions onboard the International Space Station. Two modifications of dust density waves with wave frequencies larger than the dust-neutral collision frequency were obtained. The relevance to the space observations was analyzed and a comparison of theory and observations was made for two different complex plasma domains formed by small and large microparticles.

Force on a charged test particle in a collisional flowing plasma.

The force on a charged test particle embedded in a flowing (electron-ion) plasma is calculated using the linear dielectric response formalism. This approach allows us to take into account ion-neutral collisions self-consistently. The effect of collisions on the ion drag force is analyzed.

Highly resolved fluid flows: "liquid plasmas" at the kinetic level.

Fluid flow around an obstacle was observed at the kinetic (individual particle) level using "complex (dusty) plasmas" in their liquid state. These "liquid plasmas" have bulk properties similar to water (e.g.

Vertical oscillations of paramagnetic particles in complex plasmas.

Vertical vibrations of a single magnetized dust grain and a one-dimensional string of magnetized particles in discharge plasmas are treated taking into account the magnetic force associated with gradients of an external magnetic field. For a single particle a novel type of oscillation associated with these gradients is found. Such vibrations can be stable or unstable depending on the distribution of the magnetic field inside the particle cloud.

Coupled dust-lattice solitons in monolayer plasma crystals.

Nonlinearly coupled dust-lattice (DL) waves in monolayer plasma crystals are studied theoretically. It is shown that the high-frequency transverse (vertical) oscillations can form localized wave envelopes--solitons coupled with "slow" longitudinal DL perturbations. Using the molecular dynamics simulations, the derived soliton solution is shown to be stable.

Melting of monolayer plasma crystals.

Melting of a monolayer plasma crystal in a radio-frequency discharge with no particles suspended above or below is studied. The experimental data are compared with results of molecular dynamics simulations and theory. It is shown that the melting is caused by the resonance coupling between the longitudinal and the transverse dust-lattice wave modes, due to the interaction of particles with the plasma wakes.

Rodlike particles in gas discharge plasmas: theoretical model.

Recently, complex plasmas with strongly asymmetric (rodlike) particles were investigated experimentally in rf and dc discharges [V. I. Molotkov et al.

Scattering in the attractive Yukawa potential in the limit of strong interaction.

Scattering in the attractive screened Coulomb (Yukawa) potential in the limit of strong interaction is investigated. It is shown that the scattering occurs mostly with large angles. The corresponding momentum-transfer cross section is calculated.

Kinetic measurements of shock wave propagation in a three-dimensional complex (dusty) plasma.

"Complex plasmas" consist of electrons, ions, and charged microparticles. The latter are individually observable, allowing kinetic measurements in plasmas. Using a sudden gas pulse, a traveling perturbation was initiated in such a complex plasma and its propagation, acceleration, and steepening-possibly into a shock was followed.

Decharging of complex plasmas: first kinetic observations.

The first experiment on the decharging of a complex plasma in microgravity conditions was conducted. After switching off the rf power, in the afterglow plasma, ions and electrons rapidly recombine and leave a cloud of charged microparticles. Because of microgravity, the particles remain suspended in the experimental chamber for a sufficiently long time, allowing precise measurements of the rest particle charge.