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The equilibrium equations for an isotropic Kirchhoff rod are known to be completely integrable. It is also known that neither the effects of extensibility and shearability nor the effects of a uniform magnetic field individually break integrability. Here we show, by means of a Melnikov-type analysis, that, when combined, these effects do break integrability giving rise to spatially chaotic configurations of the rod. A previous analysis of the problem suffered from the presence of an Euler-angle singularity. Our analysis provides an example of how in a system with such a singularity a Melnikov-type technique can be applied by introducing an artificial unfolding parameter. This technique can be applied to more general problems.

We present experimental results on thermoelectric power ({\em S}) and electrical resistivity ($\rho $) of pseudobinary alloys Ho(Al$_x$Co$_{1-x}$)$_2$ ($0 \leq x \leq 0.1 $), in the temperature range 4.2 K to 300 K. The work focuses on the effects of static (induced by alloying) and dynamic (induced by temperature) disorder on the magnetic state and electronic transport in a metallic system with itinerant metamagnetic instability. Spatial fluctuations of the local magnetic susceptibility in the alloys lead to a development of a partially ordered magnetic ground state of the itinerant 3d electron system. This results in a strong increase of the residual resistivity and a suppression of the temperature-dependent resistivity. Thermopower exhibits a complex temperature variation in both the magnetically ordered and in the paramagnetic state. This complex temperature variation is referred to the electronic density of states features in vicinity of Fermi energy and to the interplay of magnetic and impurity scattering. Our results indicate that the magnetic enhancement of the Co 3d-band in RCo$_{\rm 2}$--based alloys upon a substitution of Co by non-magnetic elements is mainly related to a progressive localization of the Co -- 3d electrons caused by disorder. We show that the magnitude of the resistivity jump at the Curie temperature for RCo$_{\rm 2}$ compounds exhibiting a first order phase transition is a non-monotonic function of the Curie temperature due to a saturation of the 3d--band spin fluctuation magnitude at high temperatures., Comment: 10 pages, 12 figures

Solitons are studied in a model of a fiber Bragg grating (BG) whose local reflectivity is subjected to periodic modulation. The superlattice opens an infinite number of new bandgaps in the model's spectrum. Averaging and numerical continuation methods show that each gap gives rise to gap solitons (GSs), including asymmetric and double-humped ones, which are not present without the superlattice.Computation of stability eigenvalues and direct simulation reveal the existence of completely stable families of fundamental GSs filling the new gaps - also at negative frequencies, where the ordinary GSs are unstable. Moving stable GSs with positive and negative effective mass are found too., Comment: 7 pages, 3 figures, submitted to EPL

New mechanism of magnetoresistivity in itinerant metamagnets with a structural disorder is introduced basing on analysis of experimental results on magnetoresistivity, susceptibility, and magnetization of structurally disordered alloys (Y$_{1-x}$Gd$_{x}$)Co$_{2}$. In this series, YCo$_{2}$ is an enhanced Pauli paramagnet, whereas GdCo$_{2}$ is a ferrimagnet (T$_{\rm c}$=400 K) with Gd sublattice coupled antiferromagnetically to the itinerant Co-3d electrons. The alloys are paramagnetic for $x < 0.12$. Large positive magnetoresistivity has been observed in the alloys with magnetic ground state at temperatures T$<$T$_{\rm c}$. We show that this unusual feature is linked to a combination of structural disorder and metamagnetic instability of itinerant Co-3d electrons. This new mechanism of the magnetoresistivity is common for a broad class of materials featuring a static magnetic disorder and itinerant metamagnetism., Comment: 7 pages 7 figures