Comparison of topologies on *-algebras of locally measurable operators

We consider the locally measure topology $t(\mathcal{M})$ on the *-algebra $LS(\mathcal{M})$ of all locally measurable operators affiliated with a von Neumann algebra $\mathcal{M}$. We prove that $t(\mathcal{M})$ coincides with the $(o)$-topology on $LS_h(\mathcal{M})=\{T\in LS(\mathcal{M}): T^*=T\}$ if and only if the algebra $\mathcal{M}$ is $\sigma$-finite and a finite algebra. We study relationships between the topology $t(\mathcal{M})$ and various topologies generated by faithful normal semifinite traces on $\mathcal{M}$.Comment: 21 page

Synthesis and characterisation of nanocrystalline ZrN PVD coatings on AISI 430 stainless steel

The nanocrystalline films of zirconium nitride have been synthesized using ion-plasma vacuum-arc deposition technique in combination with high-frequency discharge (RF) on AISI 430 stainless steel at 150oC. Structure examinations X-ray fluorescent analysis (XRF), X-ray diffraction analysis (XRD), scanning electron microscopy (SEM) with microanalysis (EDS), and transmission electron microscopy (TEM), nanoidentation method – were performed to study phase and chemical composition, surface morphology, microstructure and nanohardness of coatings. The developed technology provided low-temperature coatings synthesis, minimized discharge breakdown decreasing formation of macroparticles (MPs) and allowed to deposit ZrN coatings with hardness variation 26.6…31.5 GPa. It was revealed that ZrN single-phase coatings of cubic modification with finecrystalline grains of 20 nm in size were formed

Dynamic flexoelectric instabilities in nematic liquid crystals

Electro-hydrodynamic phenomena in liquid crystals constitute an old but still very active research area. The reason is that these phenomena play the key role in various applications of liquid crystals and due to the general interest of physical community to out-of-equilibrium systems. Nematic liquid crystals (NLCs) are ideally representative for such investigations. Our article aims to study theoretically the linear NLCs dynamics. We include into consideration orientation elastic energy, hydrodynamic motion, external alternating electric field, electric conductivity and flexoelectric polarization. We analyze the linear stability of the NLC film, determining dynamics of perturbations with respect to the homogeneous initial state of the NLC. For the purpose we compute eigen-values of the evolution matrix for a period of the external alternating electric field. These eigen-values determine the amplification factors for the modes during the period. The instability occurs when the principal eigen-value of the evolution matrix becomes unity by its absolute value. The condition determines the threshold (critical field) for the instability of the uniform state. It turns out that one might expect various types of the instability, only partially known and investigated in the literature. Particularly, we find that the flexoelectric instability may lead to two-dimensionally space modulated patterns exhibiting time oscillations. This type of the structures was somehow overlooked in the previous works.Comment: 26 pages, 12 figure

Nonlinear electro-hydrodynamics of liquid crystals

We present nonlinear dynamic equations for nematic and smectic $A$ liquid crystals in the presence of an alternating electric field and explain their derivation in detail. The local electric field acting in any liquid-crystalline system is expressed as a sum of external electric field and the fields originating from feedback of liquid crystal order parameter, and a field, created by charged impurities. The system tends to decrease the total electric field, because it lowers the energy density. This basically nonlinear problem is not a pure academic interest. In the realm of liquid crystals and their applications, utilized nowadays modern experimental techniques have progressed to the point where even small deviations from the linear behavior can be observed and measured with a high accuracy. Hydrodynamics is the macroscopic description of condensed matter systems in the low frequency, long wavelength limit. Nonlinear hydrodynamic equations are well established to describe simple fluids. Similar approaches (with degrees of freedom related to the broken orientational or translational symmetry included) have been used also for liquid crystals. However to study behavior of strongly perturbed well above the thresholds of various electro-hydrodynamic instabilities of liquid crystals the nonlinear equations should include soft electromagnetic degrees of freedom as well. The self-consistent derivation of the complete set of the nonlinear electro-hydrodynamic equations for liquid crystals became an actual task. The aim of our work is to present these equations, which is a mandatory step to handle any nonlinear phenomenon in liquid crystals.Comment: 12 pages, no figure

Amorphous VOx_x films with high temperature coefficient of the resistivity grown by reactive e-beam evaporation of V metal

Amorphous VO$_x$ films without a hysteretic phase transition are stable with respect to thermal cycling and highly demanded as sensitive elements of the resistive thermometers and microbolometers. In this paper we present simple and low-temperature growth of amorphous vanadium oxide films by reactive electron beam evaporation of vanadium metal in $\sim 10^{-4}$ mBar oxygen atmosphere. The temperature coefficient of the resistivity (TCR) of the films is weakly sensitive to substrate material and temperature and could be tuned by oxygen pressure in the growth chamber up to -2.2\% /K. The resistivity value is stable for months. It depends on the substrate material and substrate temperature during the evaporation. Simplicity and controllability of the method should lead to various laboratory and industrial applications

Self-similar dynamics of morphogen gradients

We discovered a class of self-similar solutions in nonlinear models describing the formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differention in developing tissues. These models account for diffusion and self-induced degration of locally produced chemical signals. When production starts, the signal concentration is equal to zero throughout the system. We found that in the limit of infinitely large signal production strength the solution of this problem is given by the product of the steady state concentration profile and a function of the diffusion similarity variable. We derived a nonlinear boundary value problem satisfied by this function and used a variational approach to prove that this problem has a unique solution in a natural setting. Using the asymptotic behavior of the solutions established by the analysis, we constructed these solutions numerically by the shooting method. Finally, we demonstrated that the obtained solutions may be easily approximated by simple analytical expressions, thus providing an accurate global characterization of the dynamics in an important class of non-linear models of morphogen gradient formation. Our results illustrate the power of analytical approaches to studying nonlinear models of biophysical processes.Comment: 17 pages, 5 figure

Steady operation of the electric drive of pipeline armature in the emergency situation at low ambient temperatures

This scientific work is devoted to the study of the electric drive operation of pipeline armature at low ambient temperatures. Hit of moisture into reducer and rare inclusions in operation of locking regulator are led to curdling lubricant that causes the increased wear of mechanical knots. There is a probability of freezing mechanical components; it leads to emergency situations. The problem of improving working efficiency of the electric drive of shut-off regulating armature at low ambient temperatures of the environment is solved in this work. A simulation model of the GUSAR electric drive was developed to solve this problem. Studies of the simulation model show the need to limit the torque increase rate on a drive motor shaft. The algorithm of setting of PI speed controller to obtain acceptable transient processes is suggested. Recommendations for the use of the algorithm in the microprocessor control system of electric drive are proposed. It is shown that the electric drive operation algorithm with torque increasing limitation on the motor shaft will be smoothly working off the perturbing actions that occur in pipeline armature

The effects of liquid-phase oxidation of multiwall carbon nanotubes on their surface characteristics

The development of new sorbents based on nanostructured carbon materials recently became a perspective field of research. Main topic of current study is to investigate the effect of different regimes of multiwall carbon nanotubes (MWCNT) surface modification process on their structural characteristics. MWCNT samples were treated with nitric acid at high temperature. Structural properties were studied using low temperature nitrogen adsorption and acid-base back titration methods. The study showed that diluted nitric acid does not affect MWCNT structure. Concentrated nitric acid treatment leads to formation of 2.8 carboxylic groups per 1 nm{2} of the sample surface

Scenarios of domain pattern formation in a reaction-diffusion system

We performed an extensive numerical study of a two-dimensional reaction-diffusion system of the activator-inhibitor type in which domain patterns can form. We showed that both multidomain and labyrinthine patterns may form spontaneously as a result of Turing instability. In the stable homogeneous system with the fast inhibitor one can excite both localized and extended patterns by applying a localized stimulus. Depending on the parameters and the excitation level of the system stripes, spots, wriggled stripes, or labyrinthine patterns form. The labyrinthine patterns may be both connected and disconnected. In the the stable homogeneous system with the slow inhibitor one can excite self-replicating spots, breathing patterns, autowaves and turbulence. The parameter regions in which different types of patterns are realized are explained on the basis of the asymptotic theory of instabilities for patterns with sharp interfaces developed by us in Phys. Rev. E. 53, 3101 (1996). The dynamics of the patterns observed in our simulations is very similar to that of the patterns forming in the ferrocyanide-iodate-sulfite reaction.Comment: 15 pages (REVTeX), 15 figures (postscript and gif), submitted to Phys. Rev.