Fractional Systems and Fractional Bogoliubov Hierarchy Equations

We consider the fractional generalizations of the phase volume, volume element and Poisson brackets. These generalizations lead us to the fractional analog of the phase space. We consider systems on this fractional phase space and fractional analogs of the Hamilton equations. The fractional generalization of the average value is suggested. The fractional analogs of the Bogoliubov hierarchy equations are derived from the fractional Liouville equation. We define the fractional reduced distribution functions. The fractional analog of the Vlasov equation and the Debye radius are considered.Comment: 12 page

Novel Nonreciprocal Acoustic Effects in Antiferromagnets

The possible occurrence of nonreciprocal acoustic effects in antiferromagnets in the absence of an external magnetic field is investigated using both (i) a microscopic formulation of the magnetoelastic interaction between spins and phonons and (ii) symmetry arguments. We predict for certain antiferromagnets the existence of two new nonreciprocal (non-time invariant) effects: A boundary-condition induced nonreciprocal effect and the occurrence of transversal phonon modes propagating in opposite directions having different velocities. Estimates are given and possible materials for these effects to be observed are suggested.Comment: Euro. Phys. Lett. (in press

New and Old Results in Resultant Theory

Resultants are getting increasingly important in modern theoretical physics: they appear whenever one deals with non-linear (polynomial) equations, with non-quadratic forms or with non-Gaussian integrals. Being a subject of more than three-hundred-year research, resultants are of course rather well studied: a lot of explicit formulas, beautiful properties and intriguing relationships are known in this field. We present a brief overview of these results, including both recent and already classical. Emphasis is made on explicit formulas for resultants, which could be practically useful in a future physics research.Comment: 50 pages, 15 figure

Atomic Force and Electron Scanning Microscopy of Silicone Composites

The conclusions of direct numerical simulation obtained earlier, within the cluster quantum-chemical approximation, are used in experimental investigations of polydimethylsiloxane composites with schungit or silica. The surface structure of these composites by atomic force and scanning electron microscopy was studied. Correlation of the distribution of micro- and nanodimensional fillers in the polymer matrix with the physical-mechanical properties of the composites was established

Scanning Probe Microscopy of Elastomers with Mineral Fillers

The results of a comprehensive study of the newly synthesized elastomeric composites filled with micro- and nanoscale modified shungite and also taurit, diatomit, and neosyl fillers are presented. The surface structure study of the prepared composites was conducted using scanning probe microscopy. The use of microscopy allowed visualization of the distribution patterns of filler aggregates and agglomerates in composites. The morphology and micro-nanometer size ranges of these aggregates in the synthesized materials are determined. The proposed method of grinding shungite, taurit, diatomit, and neosyl fillers allows significantly increasing the strength characteristics of these composites. The correlation between the reinforcement of the elastic-strength properties and the distribution of the used fillers in the rubber matrix was established

Status epilepticus: Analysis of refractory cases

Objective: to analyze refractory status epilepticus (SE) cases.Patients and methods. Fifteen female patients aged 21 to 62 years with refractory SE were comprehensively examined using long-term electroencephalography monitoring. The investigators evaluated the efficiency of treatment regimens with intravenous antiepileptic drugs (AEDs), such as diazepam (DZP); valproic acid (VPA); levetiracetam; and lacosamide and their combinations, at the prehospital and hospital stages, as well as SE therapy complications noted only in the intravenous administration of narcotics (propofol, sodium thiopental).Results and discussion. A fetal outcome due to multiple organ dysfunction indirectly related to SE was recorded in 2 (13.3%) patients with acute symptomatic status. SE was abolished in the other 13 cases. The preliminary findings may suggest that it is appropriate to prescribe VPA just at the prehospital stage. The co-administration of VPA and DZP substantially enhances the efficiency of SE therapy. The maximum acceptable doses of AEDs using the whole available therapeutic arsenal should be administered within the first hours of acute symptomatic SE

Faraday rotation, stochastic magnetic fields and CMB maps

The high- and low-frequency descriptions of the pre-decoupling plasma are deduced from the Vlasov-Landau treatment generalized to curved space-times and in the presence of the relativistic fluctuations of the geometry. It is demonstrated that the interplay between one-fluid and two-fluid treatments is mandatory for a complete and reliable calculation of the polarization observables. The Einstein-Boltzmann hierarchy is generalized to handle the dispersive propagation of the electromagnetic disturbances in the pre-decoupling plasma. Given the improved physical and numerical framework, the polarization observables are computed within the magnetized $\Lambda$CDM paradigm (m$\Lambda$CDM). In particular, the Faraday-induced B-mode is consistently estimated by taking into account the effects of the magnetic fields on the initial conditions of the Boltzmann hierarchy, on the dynamical equations and on the dispersion relations. The complete calculations of the angular power spectra constitutes the first step for the derivation of magnetized maps of the CMB temperature and polarization which are here obtained for the first time and within the minimal m$\Lambda$CDM model. The obtained results set the ground for direct experimental scrutiny of large-scale magnetism via the low and high frequency instruments of the Planck explorer satellite.Comment: 53 pages, 15 included figure

Investigation of oxidation process of mechanically activated ultrafine iron powders

The oxidation of mechanically activated ultrafine iron powders was studied using X-ray powder diffraction and thermogravimetric analyzes. The powders with average particles size of 100 nm were made by the electric explosion of wire, and were subjected to mechanical activation in planetary ball mill for 15 and 40 minutes. It was shown that a certain amount of FeO phase is formed during mechanical activation of ultrafine iron powders. According to thermogravimetric analysis, the oxidation process of non-milled ultrafine iron powders is a complex process and occurs in three stages. The preliminary mechanical activation of powders considerably changes the nature of the iron powders oxidation, leads to increasing in the temperature of oxidation onset and shifts the reaction to higher temperatures. For the milled powders, the oxidation is more simple process and occurs in a single step

Excitation Thresholds for Nonlinear Localized Modes on Lattices

Breathers are spatially localized and time periodic solutions of extended Hamiltonian dynamical systems. In this paper we study excitation thresholds for (nonlinearly dynamically stable) ground state breather or standing wave solutions for networks of coupled nonlinear oscillators and wave equations of nonlinear Schr\"odinger (NLS) type. Excitation thresholds are rigorously characterized by variational methods. The excitation threshold is related to the optimal (best) constant in a class of discr ete interpolation inequalities related to the Hamiltonian energy. We establish a precise connection among $d$, the dimensionality of the lattice, $2\sigma+1$, the degree of the nonlinearity and the existence of an excitation threshold for discrete nonlinear Schr\"odinger systems (DNLS). We prove that if $\sigma\ge 2/d$, then ground state standing waves exist if and only if the total power is larger than some strictly positive threshold, $\nu_{thresh}(\sigma, d)$. This proves a conjecture of Flach, Kaldko& MacKay in the context of DNLS. We also discuss upper and lower bounds for excitation thresholds for ground states of coupled systems of NLS equations, which arise in the modeling of pulse propagation in coupled arrays of optical fibers.Comment: To appear in Nonlinearit