On the regularization mechanism for the periodic Korteweg–de Vries equation

In this paper we develop and use successive averaging methods for explaining the regularization mechanism in the the periodic Korteweg–de Vries (KdV) equation in the homogeneous Sobolev spaces Ḣ^s for s ≥ 0. Specifically, we prove the global existence, uniqueness, and Lipschitz‐continuous dependence on the initial data of the solutions of the periodic KdV. For the case where the initial data is in L₂ we also show the Lipschitz‐continuous dependence of these solutions with respect to the initial data as maps from Ḣ^s to Ḣ^s for s ∈(−1,0]. © 2010 Wiley Periodicals, Inc.     

Shallow Donors and Deep-Level Color Centers in Bulk AlN Crystals: EPR, ENDOR, ODMR and Optical Studies

The results of studies of shallow donors and deep-level color centers in bulk AlN crystals are presented. Two shallow donors (presumably oxygen located on the nitrogen site and carbon located on the aluminum site) are suggested to exhibit the DX-relaxation. Third shallow donor (presumably silicon on the Al site) shows the shallow donor behavior up to the room temperature and can be observed without light excitation at temperatures above 200 K. The values of the Bohr radius of the shallow donors are estimated. The structure of deep-level color centers (neutral nitrogen vacancy V _N) in bulk AlN crystals is determined and analyzed by electron paramagnetic resonance, electron-nuclear double resonance, optical absorption and thermoluminescence induced by X-ray irradiation. Spin-dependent recombination processes in AlN crystals are studied by means of optically detected magnetic resonance.     

Summary of the CMS potential for the Higgs boson discovery

The European Physical Journal C - This work summarizes the studies for the Higgs boson searches in CMS at the LHC collider. The main discovery channels are presented and the potential is given for...     

Optimum properties of extruding paste powders on the basis of TiO2, Al2O3 and other substances for production of honeycomb supports

Structure-mechanical and rheological characteristics of pastes on the basis of TiO₂ and Al₂O₃ are discussed. Optinum values to prepare honeycomb supports are determined.     

Investigation of ion-selective electrodes based on quanternary phosphonium salts: Part 3. An Ion-Selective Electrode for Hexafluorophosphate

A hexafluorophosphate-selective electrode based on the tetradecylphosphonium hexafluorophosphate(V) ion-pair complex in a PVC membrane is described. The active material is a white powder; its solution in dibutyl phthalate was used for the electrode membranes. The composition of the tetradecylphosphonium hexafluorophosphate was identified as its infrared and ³¹P-n.m.r. spectra. The calibration curves for the elelctrode were investigated and interpreted with respect to the hydrogen fluoride concentration of the sample solution. It is shown that the hydrolysis of hexafluorophosphate depends on the hydrofluoric acid content of the solution. The lifetime of the electrodes is about one month and the limits of detection vary from aobut 10^?7 mol 1^?1 to 10^?6 mol 1^?1 with 0–1 mol 1^?1 hydrofluoric acid present.     

Investigation of Eco-Friendly Gas Mixture for Gas Discharge Particle Detectors

Physics of Atomic Nuclei - The first results of studying the Ar/CO2/HFO1234ze eco-friendly gas mixture for gas discharge detectors are presented. The work is performed using a prototype multiwire...     

Rheological evidence for the existence of subphases in the liquid crystalline 4-n-alkoxybenzoic acids

The rheological behaviour of the homologous series, the alkyloxybenzoic acids, has been studied at steady flow and small amplitude oscillatory shear. The temperature dependencies of the viscosity were compared with differential scanning calorimetry data in order to estimate pretransitional phenomena in mesophases. The values of the viscosity and flow activation energy (E) can be indicative of the mesophase state. 4-n-pentyloxybenzoic acid yields a classic nematic (N) phase while the next homologues show a cybotactic nematic phase having a higher E value. The N phase is a Newtonian fluid of lower viscosity than that of the isotropic phase. The cybotactic nematic phase by its rheological properties takes an intermediate position between the N phase and a smectic C (SmC) phase. The SmC phase is a viscoelastic and viscoplastic medium. The SmC phase of 4-n-octyloxy-, 4-n-nonyloxy-, 4-n-decyloxy- and 4-n-dodecyloxybenzoic acid can exist in high- and low-ordered states. The more ordered smectic phase is characterised by higher stiffness, viscosity and yield stress than those of the less ordered. The SmC phase of 4-n-hexadecyloxybenzoic acid is characterised by the only state with unstable value of apparent viscosity. The phase state and the transition temperature can be dependent on the thermal history of the sample and a mechanical shear.     

On the closeness of trajectories for model quasi-gasdynamic equations

On a model example of a linear hyperbolic equation with small parameter multiplying the highest time derivative it is shown that the closeness of individual trajectories to the dynamics of the limiting parabolic equation essentially depends on the Fourier spectra of the initial data. The trajectories stay close if the higher modes decay sufficiently fast. If the initial data are irregular and there are relatively high modes, then the convergence of the trajectories becomes non-uniform. Namely, the boundary layer is formed and there exist small moments of time such that the difference of the solutions reaches in the mean a finite value as the coefficient of the highest time derivative tends to zero. These results reflect the difficulties that may arise in the analysis of the systems of non-linear quasi-gasdynamic equations.     

Atomic force microscopy imaging of novel macromolecular species,nanosponges, and their clusters

Atactic polystyrene of M = 330,000 Da and M_w/M_n = 1.04 was subjected to a complete chloromethylation. By heating the chloromethyl polystyrene with SnCl₄ in a very dilute solution in ethylene dichloride, the polymeric coils were converted into intramolecularly hypercrosslinked macromolecules, called “nanosponges.” These species have a molecular weight of about 370,000 Da and a diameter of about 17 nm. When in solution, the nanosponges display a tendency to reversibly self‐assemble into regular clusters. Preparative size‐exclusion chromatography isolates a fraction consisting predominantly of spherical clusters that are composed of 13 subunits and acquire a molecular weight of approximately 5.0 × 10⁶ Da and a diameter of 45 nm. Scanning atomic force microscopy (AFM) provides images of individual nanosponges, N = 13 clusters, as well as higher spherical clusters. The regular spherical species most probably belong to the cluster series N = 1 + ∑(10n² + 2), where n is the number of shells around the central nanosponge. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 1451–1455, 1999     

A modern look on yield stress fluids

A concept of viscoplasticity advanced exactly one century ago by Bingham appears very fruitful because there are many natural and artificial materials that demonstrate viscoplastic behavior, i.e., they are able to pass from a solid to a liquid state under the influence of applied stress. However, although this transition was originally considered as a jump-like phenomenon occurring at a certain stress—the yield stress—numerous subsequent studies have shown that the real situation is more complicated. A long-term discussion about the possibility of flow at low stresses less than the yield stress came to today’s conclusion denying this possibility as being opposite to the existence of the maximal Newtonian viscosity in viscoelastic polymeric fluids. So, there is a contradiction between the central dogma of rheology which says that “everything flows” and the alleged impossibility for flow at a solid-like state of viscoplastic fluids. Then, the concept of the fragile destruction of an inner structure responsible for a solid-like state at the definite (yield) stress was replaced by an understanding of the yielding as a transition extending over some stress range and occurring in time. So, instead of the yield stress, yielding is characterized by the dependence of durability (or time-to-break) on the applied stress. In this review, experimental facts and the new understanding of yielding as a kinetic process are discussed. Besides, some other alternative methods for measuring the yield stress are considered.