Capacitively-coupled rf discharge with a large amount of microparticles: spatiotemporal emission pattern and microparticle arrangement

The effect of micron-sized particles on a low-pressure capacitively-coupled rf discharge is studied both experimentally and using numerical simulations. In the laboratory experiments, microparticle clouds occupying a considerable fraction of the discharge volume are supported against gravity with the help of the thermophoretic force. The spatiotemporally resolved optical emission measurements are performed with different arrangements of microparticles. The numerical simulations are carried out on the basis of a one-dimensional hybrid (fluid-kinetic) discharge model describing the interaction between plasma and microparticles in a self-consistent way. The study is focused on the role of microparticle arrangement in interpreting the spatiotemporal emission measurements. We show that it is not possible to reproduce simultaneously the observed microparticle arrangement and emission pattern in the framework of the considered one-dimensional model. This disagreement is discussed and attributed to two-dimensional effects, e.g., radial diffusion of the plasma components

Dust density waves in a dc flowing complex plasma with discharge polarity reversal

We report on the observation of the self-excited dust density waves in the dc discharge complex plasma. The experiments were performed under microgravity conditions in the Plasmakristall-4 facility on board the International Space Station. In the experiment, the microparticle cloud was first trapped in an inductively coupled plasma, then released to drift for some seconds in a dc discharge with constant current. After that the discharge polarity was reversed. DC plasma containing a drifting microparticle cloud was found to be strongly non-uniform in terms of microparticle drift velocity and plasma emission in accord with [Zobnin et.al., Phys. Plasmas 25, 033702 (2018)]. In addition to that, non-uniformity in the self-excited wave pattern was observed: In the front edge of the microparticle cloud (defined as head), the waves had larger phase velocity than in the rear edge (defined as tail). Also, after the polarity reversal, the wave pattern exhibited several bifurcations: Between each of the two old wave crests, a new wave crest has formed. These bifurcations, however, occurred only in the head of the microparticle cloud. We show that spatial variations of electric field inside the drifting cloud play an important role in the formation of the wave pattern. Comparison of the theoretical estimations and measurements demonstrate the significant impact of the electric field on the phase velocity of the wave. The same theoretical approach applied to the instability growth rate, showed agreement between estimated and measured values.Comment: 7 pages, 4 figure

Shear flow in a three-dimensional complex plasma in microgravity conditions

Shear flow in a three-dimensional complex plasma was experimentally studied in microgravity conditions using Plasmakristall-4 (PK-4) instrument on board the International Space Station (ISS). The shear flow was created in an extended suspension of microparticles by applying the radiation pressure force of the manipulation-laser beam. Individual particle trajectories in the flow were analyzed and from these, using the Navier-Stokes equation, an upper estimate of the complex plasma's kinematic viscosity was calculated in the range of $0.2$--$6.7~{\rm mm^2/s}$. This estimate is much lower than previously reported in ground-based experiments with 3D complex plasmas. Possible reasons of this difference are discussed.Comment: 5 pages, 4 figure

Towards a unified theory of Sobolev inequalities

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1

CoRoT photometry and high-resolution spectroscopy of the interacting eclipsing binary AU Mon

Analyses of very accurate CoRoT space photometry, past Johnson V photoelectric photometry and high-resolution \'echelle spectra led to the determination of improved and consistent fundamental stellar properties of both components of AU Mon. We derived new, accurate ephemerides for both the orbital motion (with a period of 11.113d) and the long-term, overall brightness variation (with a period of 416.9d) of this strongly interacting Be + G semi-detached binary. It is shown that this long-term variation must be due to attenuation of the total light by some variable circumbinary material. We derived the binary mass ratio $M_{\rm G}/M_{\rm B}$ = 0.17\p0.03 based on the assumption that the G-type secondary fills its Roche lobe and rotates synchronously. Using this value of the mass ratio as well as the radial velocities of the G-star, we obtained a consistent light curve model and improved estimates of the stellar masses, radii, luminosities and effective temperatures. We demonstrate that the observed lines of the B-type primary may not be of photospheric origin. We also discover rapid and periodic light changes visible in the high-quality residual CoRoT light curves. AU Mon is put into perspective by a comparison with known binaries exhibiting long-term cyclic light changes.Comment: Accepted for publication in MNRA

Physics and applications of dusty plasmas: The Perspectives 2023

Dusty plasmas are electrically quasi-neutral media that, along with electrons, ions, neutral gas, radiation, and electric and/or magnetic fields, also contain solid or liquid particles with sizes ranging from a few nanometers to a few micrometers. These media can be found in many natural environments as well as in various laboratory setups and industrial applications. As a separate branch of plasma physics, the field of dusty plasma physics was born in the beginning of 1990s at the intersection of the interests of the communities investigating astrophysical and technological plasmas. An additional boost to the development of the field was given by the discovery of plasma crystals leading to a series of microgravity experiments of which the purpose was to investigate generic phenomena in condensed matter physics using strongly coupled complex (dusty) plasmas as model systems. Finally, the field has gained an increasing amount of attention due to its inevitable connection to the development of novel applications ranging from the synthesis of functional nanoparticles to nuclear fusion and from particle sensing and diagnostics to nano-contamination control. The purpose of the present perspectives paper is to identify promising new developments and research directions for the field. As such, dusty plasmas are considered in their entire variety: from classical low-pressure noble-gas dusty discharges to atmospheric pressure plasmas with aerosols and from rarefied astrophysical plasmas to dense plasmas in nuclear fusion devices. Both fundamental and application aspects are covered

A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type

summary:The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations

On Strictly Singular and Strictly Cosingular Embeddings Between Banach Lattices of Functions

Let E be a Banach function lattice such that L1[0; 1] ,! E ,! L1[0; 1]. We characterize the strict singularity of the embedding L1[0; 1] ,! E and the strict cosingularity of E ,! L1[0; 1] in terms of functionals de_ned by using characteristic functions