Mathematical simulation of a profile cutter as a surface of revolution

Various types of cutters (spherical, toroidal, etc.) are used in surface processing of parts of a transmission mechanism. The cost of a special profile tool is somewhat higher than that of such cutters. But the increase in the cost of the tool is compensated by a significant reduction in the time of processing parts. The present paper deals with a mathematical model of a profile cutter surface (as a surface of revolution) for processing parts of a cylindrical transmission gear with an eccentrically cycloidal gearing (EC-gearing). A computer program for determining radii of the cutter's circular cross sections for a given set of axial displacements was created

Limit theorems for random point measures generated by cooperative sequential adsorption

We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity of the model is that the probability distribution of a point depends on previously allocated points. We assume that the dependence vanishes as the concentration of points tends to infinity. Under this assumption the law of large numbers, the central limit theorem and Poisson approximation are proved for the generated sequence of random point measures.Comment: 17 page

Threshold Resonant Structure of the 232Th Neutron-Induced Fission Cross Section

The structures observed in the sub-threshold neutron-induced fission of ^{232}Th were investigated employing a recent developed model. Theoretical single-particle excitations of a phenomenological two-humped barrier are determined by solving a system of coupled differential equations for the motion along the optimal fission path. A rather good agreement with experimental data was obtained using a small number of independent parameters. It is predicted that the structure at 1.4 and 1.6 MeV is mainly dominated by spin 3/2 partial cross-section with small admixture of spin 1/2, while the structure at 1.7 MeV is given by a large partial cross section of spin 5/2.Comment: 17 pages 11 figure

The mathematical model of the chevron-arch gearing transmitter

The teeth of herringbone transmission wheels are obtained by docking two helical wheels with an opposite arrangement of teeth, which can solve the problem of the axial force. The mathematical model of coupling chevron teeth of the driving wheel in the area of their docking using the arch tooth fragment is developed. The conjugacy area surface of the driven wheel chevron teeth is obtained as the envelope of the surfaces family formed by the arched tooth during the process of the parts motion

Critical Dynamics of Self-Organizing Eulerian Walkers

The model of self-organizing Eulerian walkers is numerically investigated on the square lattice. The critical exponents for the distribution of a number of steps ($\tau_l$) and visited sites ($\tau_s$) characterizing the process of transformation from one recurrent configuration to another are calculated using the finite-size scaling analysis. Two different kinds of dynamical rules are considered. The results of simulations show that both the versions of the model belong to the same class of universality with the critical exponents $\tau_l=\tau_s=1.75\pm 0.1$.Comment: 3 pages, 4 Postscript figures, RevTeX, additional information available at http://thsun1.jinr.dubna.su/~shche

Contribution of the magnetic resonance to the third harmonic generation from a fishnet metamaterial

We investigate experimentally and theoretically the third harmonic generated by a double-layer fishnet metamaterial. To unambiguously disclose most notably the influence of the magnetic resonance, the generated third harmonic was measured as a function of the angle of incidence. It is shown experimentally and numerically that when the magnetic resonance is excited by pump beam, the angular dependence of the third harmonic signal has a local maximum at an incidence angle of {\theta} \simeq 20{\deg}. This maximum is shown to be a fingerprint of the antisymmetric distribution of currents in the gold layers. An analytical model based on the nonlinear dynamics of the electrons inside the gold shows excellent agreement with experimental and numerical results. This clearly indicates the difference in the third harmonic angular pattern at electric and magnetic resonances of the metamaterial.Comment: 7 pages, 5 figure

EXTENDED COREY-CHAYKOVSKY REACTION AS A PATHWAY FOR THE SYNTHESIS OF SUBSTITUTED FURANS

This work was supported by RSF № 21-73-10063

Distribution of sizes of erased loops of loop-erased random walks in two and three dimensions

We show that in the loop-erased random walk problem, the exponent characterizing probability distribution of areas of erased loops is superuniversal. In d-dimensions, the probability that the erased loop has an area A varies as A^{-2} for large A, independent of d, for 2 <= d <= 4. We estimate the exponents characterizing the distribution of perimeters and areas of erased loops in d = 2 and 3 by large-scale Monte Carlo simulations. Our estimate of the fractal dimension z in two-dimensions is consistent with the known exact value 5/4. In three-dimensions, we get z = 1.6183 +- 0.0004. The exponent for the distribution of durations of avalanche in the three-dimensional abelian sandpile model is determined from this by using scaling relations.Comment: 25 pages, 1 table, 8 figure