Exact Solutions of Classical Electrodynamics and the Yang--Mills--Wong Theory in Even-Dimensional Spacetime

Exact solutions of classical gauge theories in even-dimensional (D=2n) spacetimes are discussed. Common and specific properties of these solutions are analyzed for the particular dimensions D=2, D=4, and D=6. A consistent formulation of classical gauge field theories with pointlike charged or colored particles is proposed for D=6. The particle Lagrangian must then depend on the acceleration. The self-interaction of a point particle is considered for D=2 and D=6. In D=2, radiation is absent and all processes are reversible. In D=6, the expression for the radiation rate and the equation of motion of a self-interacting particle are derived; from which follows that the Zitterbewegung always leads to radiation. It is shown that non-Abelian solutions are absent for any D not equal to 4; only Coulomb-like solutions, which correspond to the Abelian limit of the D-dimensional Yang--Mills--Wong theory, are admitted.Comment: LaTeX 2.09, 16 page

Probability of Incipient Spanning Clusters in Critical Square Bond Percolation

The probability of simultaneous occurence of at least k spanning clusters has been studied by Monte Carlo simulations on the 2D square lattice at the bond percolation threshold $p_c=1/2$. It is found that the probability of k and more Incipient Spanning Clusters (ISC) has the values $P(k>1) \approx 0.00658(3)$ and $P(k>2) \approx 0.00000148(21)$ provided that the limit of these probabilities for infinite lattices exists. The probability $P(k>3)$ of more than three ISC could be estimated to be of the order of 10^{-11} and is beyond the possibility to compute a such value by nowdays computers. So, it is impossible to check in simulations the Aizenman law for the probabilities when $k>>1$. We have detected a single sample with 4 ISC in a total number of about 10^{10} samples investigated. The probability of single event is 1/10 for that number of samples.Comment: 7 pages, 1 table, 5 figures (1PS+4*Latex),uses epsf.sty Int.J.Mod.Phys. C (submitted to

Radiation reaction and energy-momentum conservation

We discuss subtle points of the momentum balance for radiating particles in flat and curved space-time. An instantaneous balance is obscured by the presence of the Schott term which is a finite part of the bound field momentum. To establish the balance one has to take into account the initial and final conditions for acceleration, or to apply averaging. In curved space-time an additional contribution arises from the tidal deformation of the bound field. This force is shown to be the finite remnant from the mass renormalization and it is different both form the radiation recoil force and the Schott force. For radiation of non-gravitational nature from point particles in curved space-time the reaction force can be computed substituting the retarded field directly to the equations of motion. Similar procedure is applicable to gravitational radiation in vacuum space-time, but fails in the non-vacuum case. The existence of the gravitational quasilocal reaction force in this general case seems implausible, though it still exists in the non-relativistic approximation. We also explain the putative antidamping effect for gravitational radiation under non-geodesic motion and derive the non-relativistic gravitational quadrupole Schott term. Radiation reaction in curved space of dimension other than four is also discussedComment: Lecture given at the C.N.R.S. School "Mass and Motion in General Relativity", Orleans, France, 200

Self force in 2+1 electrodynamics

The radiation reaction problem for an electric charge moving in flat space-time of three dimensions is discussed. The divergences stemming from the pointness of the particle are studied. A consistent regularization procedure is proposed, which exploits the Poincar\'e invariance of the theory. Effective equation of motion of radiating charge in an external electromagnetic field is obtained via the consideration of energy-momentum and angular momentum conservation. This equation includes the effect of the particle's own field. The radiation reaction is determined by the Lorentz force of point-like charge acting upon itself plus a non-local term which provides finiteness of the self-action.Comment: 20 pages, 3 figure

Complex analysis of planning the power station equipment repair in generating companies

The problem of planning the thermal power station equipment repair in conditions of transition to adjustable markets of energy has been analyzed. The bases of applying the system approach in conditions of real restrictions by financial resources are stated. The method based on classification of sources of repair work initiation and considering priorities of works for different control levels is offered as a scheduling algorithm

Radiation reaction and renormalization in classical electrodynamics of point particle in any dimension

The effective equations of motion for a point charged particle taking account of radiation reaction are considered in various space-time dimensions. The divergencies steaming from the pointness of the particle are studied and the effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d=4. For the cases of three and six dimensions the covariant analogs of the Lorentz-Dirac equation are explicitly derived.Comment: minor changes in concluding section, misprints corrected, LaTeX2e, 15 page

Mechanism of Interaction Between Hydrolytic Lignin and Poly(acrylonitrile)

Interaction between polyacrylonitrile (PAN) and hydrolytic lignin (THL) in mixed binary solution dimethyl sulfoxide/water (70:30) allowed us to obtain homogeneous forming solution of the THL/PAN composite. This forming solution was used for preparation of fibers and films which served as precursors for carbon materials. In the present work, we considered and substantiated the proposed mechanism of the formation of the THL/PAN composite based on the structure of the initial polymers. We believe that interaction between reactive groups present in PAN and THL leads to the formation of graft copolymer. Fundamentally, this reaction is possible and may proceed according to the well-known Ritter mechanism It was demonstrated that the process of grafting nitrile groups to THL macromolecules is controlled by duration and temperature of interaction between the initial compounds in solution; this process is completed in 10 h at a temperature of 120 °C. Tentative calculation shows that for each statistically averaged PAN macromolecule there are five THL molecules with activated hydroxyl groups. These forming solutions are suitable for moulding fibers which serve as precursors for carbon fibrous materials

PROVIDING INDUSTRIAL SAFETY IN THE DESIGN OF CHEMICAL FACILITIES

Designing of chemical destination requires developers’ particular, careful approach, as malfunctions are dangerous for the whole area in which the facility is located. Efficient and uninterrupted operation of a chemical entity assumes certain tasks, and at the design stage, and during the construction, reconstruction, repair, and maintenance. When designing a crucial question: placing equipment in the technological scheme (nature and the order and connection of separate devices); determine the input parameters of raw materials; establishment of technological parameters of the system; determine the structural characteristics of the devices of the system; selection of process parameters in devices that affect the speed of the process, output and product quality. The main document containing the requirements of industrial safety, chemical and other dangerous objects is the Federal Law of July 21, 1997 № 116-FZ "On industrial safety of hazardous production facilities", as amended on December 31, 2014. It defines and regulates the framework for ensuring the safe operation of hazardous production facilities. The most important part in the development and design of hazardous chemicals is the examination of industrial safety, which is held on the basis of the principles of independence, objectivity, comprehensiveness and completeness of the research carried out by using modern science and technology. Design of chemical facilities is a complex, multifactorial and time-consuming process, which should be regarded as a series of socio-organizational and engineering stages. It is a systematic approach to solving design problems and control of all stages of the life cycle of chemical facilities will provide a high level of safe operation of industrial facilities

Effective dynamics of an electrically charged string with a current

Equations of motion for an electrically charged string with a current in an external electromagnetic field with regard to the first correction due to the self-action are derived. It is shown that the reparametrization invariance of the free action of the string imposes constraints on the possible form of the current. The effective equations of motion are obtained for an absolutely elastic charged string in the form of a ring (circle). Equations for the external electromagnetic fields that admit stationary states of such a ring are revealed. Solutions to the effective equations of motion of an absolutely elastic charged ring in the absence of external fields as well as in an external uniform magnetic field are obtained. In the latter case, the frequency at which one can observe radiation emitted by the ring is evaluated. A model of an absolutely nonstretchable charged string with a current is proposed. The effective equations of motion are derived within this model, and a class of solutions to these equations is found.Comment: 14 pages, 3 figures, format changed, minor change