Parallelization of matrix algorithms for Gröbner basis computation

Sequential and parallel implementations of the F4 algorithm for computing Gröbner bases of polynomial ideals are discussed.     

Numerical simulation of spinning detonation in circular section channels

Numerical simulation of three-dimensional structures of gas detonation in circular section channels that emerge due to the instability when the one-dimensional flow is initiated by energy supply at the closed end of the channel is performed. It is found that in channels with a large diameter, an irregular three-dimensional cellular detonation structure is formed. Furthermore, it is found that in channels with a small diameter circular section, the initially plane detonation wave is spontaneously transformed into a spinning detonation wave, while passing through four phases. A critical value of the channel diameter that divides the regimes with the three-dimensional cellular detonation and spinning detonation is determined. The stability of the spinning detonation wave under perturbations occurring when the wave passes into a channel with a greater (a smaller) diameter is investigated. It is found that the spin is preserved if the diameter of the next channel (into which the wave passes) is smaller (respectively, greater) than a certain critical value. The computations were performed on the Lomonosov supercomputer using from 0.1 to 10 billions of computational cells. All the computations of the cellular and spinning detonation were performed in the whole long three-dimensional channel (up to 1 m long) rather than only in its part containing the detonation wave; this made it possible to adequately simulate and investigate the features of the transformation of the detonation structure in the process of its propagation.     

Numerical investigation of surface wave generation upon solid body immersion in water

The immersion of a cylindrical solid in an undisturbed fluid is numerically investigated. Wave formation accompanying this process and the dependence of the wave parameters on those of the body are studied. The shallow water model in a cylindrical coordinate system is used. A total variation diminishing (TVD) scheme is applied on a C-type difference grid, according to Arakawa’s classification.     

Superdiffusion and encounter rates in diluted,low dimensional worlds

Rate limitation due to encounters is fundamental to many ecological interactions. Since encounter rate governs reaction rates, and thus, dynamics of systems, it deserves systematic study. In classical population biology, ecological dynamics rely on the assumption of perfectly mixed interacting entities (e.g., individuals, populations, etc.) in a spaceless world. The so-called mean field assumption assumes that encounter rates are driven exclusively by changes in the density of the interacting entities and not on how they are distributed or move in space. Therefore, the mean field assumption does not give any insight into relevant spatiotemporal statistical properties produced by the trajectories of moving entities through space. In the present study, we develop spatially explicit simulations of random walking particles (i.e., Lévy walkers) to evaluate encounter rate constraints beyond the mean field assumption. We show that encounter rate fluctuations are driven not only by physical aspects such as the size or the velocity of the interacting particles, but also by different motion patterns. In particular, superdiffusion phenomena might be relevant at low densities and/or low spatial dimensionality. Finally, we discuss potential adaptive responses of living organisms that may allow individuals to control how they diffuse through space and/or the spatial dimensions employed in the exploration process.     

The Newton Bracketing Method for Convex Minimization

An iterative method for the minimization of convex functions f :ⁿ , called a Newton Bracketing (NB) method, is presented. The NB method proceeds by using Newton iterations to improve upper and lower bounds on the minimum value. The NB method is valid for n = 1, and in some cases for n > 1 (sufficient conditions given here). The NB method is applied to large scale Fermat–Weber location problems.     

On dynamics of vertices of locally connected polynomial Julia sets

Let be a polynomial whose Julia set is locally connected. Then a non-preperiodic non-precritical vertex of must have the limit set which coincides with the limit set of an appropriately chosen recurrent critical point of . In particular, if all critical points of are non-recurrent then all vertices of are preperiodic or precritical.