1,303 research outputs found
Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion
In this tutorial, we discuss self-excited and hidden attractors for systems
of differential equations. We considered the example of a Lorenz-like system
derived from the well-known Glukhovsky--Dolghansky and Rabinovich systems, to
demonstrate the analysis of self-excited and hidden attractors and their
characteristics. We applied the fishing principle to demonstrate the existence
of a homoclinic orbit, proved the dissipativity and completeness of the system,
and found absorbing and positively invariant sets. We have shown that this
system has a self-excited attractor and a hidden attractor for certain
parameters. The upper estimates of the Lyapunov dimension of self-excited and
hidden attractors were obtained analytically.Comment: submitted to EP
Crossover of skyrmion and helical modulations in noncentrosymmetric ferromagnets
The coupling between angular (twisting) and longitudinal modulations arising
near the ordering temperature of noncentrosymmetric ferromagnets strongly
influences the structure of skyrmion states and their evolution in an applied
magnetic field. In the precursor states of cubic helimagnets, a continuous
transformation of skyrmion lattices into the saturated state is replaced by the
first-order processes accompanied by the formation of multidomain states.
Recently the effects imposed by dominant longitudinal modulations have been
reported in bulk MnSi and FeGe. Similar phenomena can be observed in the
precursor regions of cubic helimagnet epilayers and in easy-plane chiral
ferromagnets (e.g. in the hexagonal helimagnet CrNb3S6)
Electronic structure of charge-ordered Fe3O4 from calculated optical, megneto-optical Kerr effect, and O K-edge x-ray absorption spectra
The electronic structure of the low-temperature (LT) monoclinic magnetite,
Fe3O4, is investigated using the local spin density approximation (LSDA) and
the LSDA+U method. The self-consistent charge ordered LSDA+U solution has a
pronounced [001] charge density wave character. In addition, a minor [00{1/2}]
modulation in the phase of the charge order (CO) also occurs. While the
existence of CO is evidenced by the large difference between the occupancies of
the minority spin t_{2g} states of ``2+'' and ``3+'' Fe_B cations, the total 3d
charge disproportion is small, in accord with the valence-bond-sum analysis of
structural data. Weak Fe orbital moments of ~0.07 mB are obtained from
relativistic calculations for the CO phase which is in good agreement with
recent x-ray magnetic circular dichroism measurements. Optical, magneto-optical
Kerr effect, and O K-edge x-ray absorption spectra calculated for the charge
ordered LSDA+U solution are compared to corresponding LSDA spectra and to
available experimental data. Reasonably good agreement between the theoretical
and experimental spectra supports the relevance of the CO solution obtained for
the monoclinic LT phase. The results of calculations of effective exchange
coupling constants between Fe spin magnetic moments are also presented.Comment: 32 pages, 10 figure
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