The extended Malkus-Robbins dynamo as a perturbed Lorenz system

Recent investigations of some self-exciting Faraday-disk homopolar dynamo ([1-4]) have yielded the classic Lorenz equations as a special limit when one of the principal bifurcation parameters is zero. In this paper we focus upon one of those models [3] and illustrate what happens to some of the lowest order unstable periodic orbits as this parameter is increased from zero

The Malkus-Robbins dynamo with a nonlinear motor

In a recent paper Moroz \cite{m02} considered a simplified version of the third class of self-exciting Faraday-disk dynamo model, introduced by Hide \cite{h97}, in the limit in which the Malkus-Robbins dynamo \cite{m72,r77} results as a special case. In that study a linear series motor was incorporated which led to an enriching of the range of possible behaviour that the original Malkus-Robbins dynamo could support. In this paper, we replace the linear motor by a nonlinear motor and consider the consequences on the dynamics of the dynamo

Unstable periodic orbits of perturbed Lorenz equations

The extended Malkus-Robbins dynamo [Moroz, 2003] reduces to the Lorenz equations when one of the key parameters, $\beta$, vanishes. In a recent study [Moroz, 2004] investigated what happened to the lowest order unstable periodic orbits of the Lorenz limit as $\beta$ was increased to the end of the chaotic regime, using the classic Lorenz parameter values of r = 28; $\sigma$ = 10 and b = 8=3. In this paper we return to the parameter choices of [Moroz, 2003], reporting on two of the cases discussed therein

The Malkus–Robbins dynamo with a linear series motor

Hide [1997] has introduced a number of different nonlinear models to describe the behavior of n-coupled self-exciting Faraday disk homopolar dynamos. The hierarchy of dynamos based upon the Hide et al. [1996] study has already received much attention in the literature (see [Moroz, 2001] for a review). In this paper we focus upon the remaining dynamo, namely Case 3 of [Hide, 1997] for the particular limit in which the Malkus–Robbins dynamo [Malkus, 1972; Robbins, 1997] obtains, but now modified by the presence of a linear series motor. We compare and contrast the linear and the nonlinear behaviors of the two types of dynamo

Unstable periodic orbits of perturbed Lorenz equations

The extended Malkus-Robbins dynamo [Moroz, 2003] reduces to the Lorenz equations when one of the key parameters, $\beta$, vanishes. In a recent study [Moroz, 2004] investigated what happened to the lowest order unstable periodic orbits of the Lorenz limit as $\beta$ was increased to the end of the chaotic regime, using the classic Lorenz parameter values of r = 28; $\sigma$ = 10 and b = 8=3. In this paper we return to the parameter choices of [Moroz, 2003], reporting on two of the cases discussed therein

Inward and Outward Integral Equations and the KKR Method for Photons

In the case of electromagnetic waves it is necessary to distinguish between inward and outward on-shell integral equations. Both kinds of equation are derived. A correct implementation of the photonic KKR method then requires the inward equations and it follows directly from them. A derivation of the KKR method from a variational principle is also outlined. Rather surprisingly, the variational KKR method cannot be entirely written in terms of surface integrals unless permeabilities are piecewise constant. Both kinds of photonic KKR method use the standard structure constants of the electronic KKR method and hence allow for a direct numerical application. As a by-product, matching rules are obtained for derivatives of fields on different sides of the discontinuity of permeabilities. Key words: The Maxwell equations, photonic band gap calculationsComment: (to appear in J. Phys. : Cond. Matter), Latex 17 pp, PRA-HEP 93/10 (exclusively English and unimportant misprints corrected

Lie point symmetries and the geodesic approximation for the Schr\"odinger-Newton equations

We consider two problems arising in the study of the Schr\"odinger-Newton equations. The first is to find their Lie point symmetries. The second, as an application of the first, is to investigate an approximate solution corresponding to widely separated lumps of probability. The lumps are found to move like point particles under a mutual inverse-square law of attraction

Analysis of the level of labor potential development in higher educational institutions of Ukraine: competitiveness of university graduates

The article focuses on the possibility of using the criterion of competitiveness of domestic higher education institutions in the international labor market to analyze the level of development of labor potential of a particular university. In the article the relationship between the level of professional competence of future professionals and the quality of labor potential of universities which were involved in their formation and development. This article contains statistical information on the results of participation of Ukrainian university students in international student competitions, which the author used to characterize the quality of professional institutions in the field of competitiveness of future specialists. In addition, the article contains generalizations as for the possibility of usage the competitiveness feature level of graduates as an indicator (index) of the quality of university's labor potential

When are projections also embeddings?

We study an autonomous four-dimensional dynamical system used to model certain geophysical processes.This system generates a chaotic attractor that is strongly contracting, with four Lyapunov exponents $\lambda_i$ that satisfy $\lambda_1+ \lambda_2+\lambda_3<0$, so the Lyapunov dimension is $D_L=2+|\lambda_3|/\lambda_1 < 3$ in the range of coupling parameter values studied. As a result, it should be possible to find three-dimensional spaces in which the attractors can be embedded so that topological analyses can be carried out to determine which stretching and squeezing mechanisms generate chaotic behavior. We study mappings into $R^3$ to determine which can be used as embeddings to reconstruct the dynamics. We find dramatically different behavior in the two simplest mappings: projections from $R^4$ to $R^3$. In one case the one-parameter family of attractors studied remains topologically unchanged for all coupling parameter values. In the other case, during an intermediate range of parameter values the projection undergoes self-intersections, while the embedded attractors at the two ends of this range are topologically mirror images of each other