Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues

Theory of current-driven motion of Skyrmions and spirals in helical magnets

We study theoretically the dynamics of the spin textures, i.e., Skyrmion crystal (SkX) and spiral structure (SS), in two-dimensional helical magnets under external current. By numerically solving the Landau-Lifshitz-Gilbert equation, it is found that (i) the critical current density of the motion is much lower for SkX compared with SS in agreement with the recent experiment, (ii) there is no intrinsic pinning effect for SkX and the deformation of the internal structure of Skyrmion reduces the pinning effect dramatically, (iii) the Bragg intensity of SkX shows strong time-dependence as can be observed by neutron scattering experiment.Comment: 4 pages, 3 figure

Magnetic Vortex Core Reversal by Excitation of Spin Waves

Micron-sized magnetic platelets in the flux closed vortex state are characterized by an in-plane curling magnetization and a nanometer-sized perpendicularly magnetized vortex core. Having the simplest non-trivial configuration, these objects are of general interest to micromagnetics and may offer new routes for spintronics applications. Essential progress in the understanding of nonlinear vortex dynamics was achieved when low-field core toggling by excitation of the gyrotropic eigenmode at sub-GHz frequencies was established. At frequencies more than an order of magnitude higher vortex state structures possess spin wave eigenmodes arising from the magneto-static interaction. Here we demonstrate experimentally that the unidirectional vortex core reversal process also occurs when such azimuthal modes are excited. These results are confirmed by micromagnetic simulations which clearly show the selection rules for this novel reversal mechanism. Our analysis reveals that for spin wave excitation the concept of a critical velocity as the switching condition has to be modified.Comment: Minor corrections and polishing of previous versio

Soliton pair dynamics in patterned ferromagnetic ellipses

Confinement alters the energy landscape of nanoscale magnets, leading to the appearance of unusual magnetic states, such as vortices, for example. Many basic questions concerning dynamical and interaction effects remain unanswered, and nanomagnets are convenient model systems for studying these fundamental physical phenomena. A single vortex in restricted geometry, also known as a non-localized soliton, possesses a characteristic translational excitation mode that corresponds to spiral-like motion of the vortex core around its equilibrium position. Here, we investigate, by a microwave reflection technique, the dynamics of magnetic soliton pairs confined in lithographically defined, ferromagnetic Permalloy ellipses. Through a comparison with micromagnetic simulations, the observed strong resonances in the subgigahertz frequency range can be assigned to the translational modes of vortex pairs with parallel or antiparallel core polarizations. Vortex polarizations play a negligible role in the static interaction between two vortices, but their effect dominates the dynamics.Comment: supplemental movies on http://www.nature.com/nphys/journal/v1/n3/suppinfo/nphys173_S1.htm

Serum amyloid A primes microglia for ATP-dependent interleukin-1\u3b2 release

Acute-phase response is a systemic reaction to environmental/inflammatory insults and involves production of acute-phase proteins, including serum amyloid A (SAA). Interleukin-1\u3b2 (IL-1\u3b2), a master regulator of neuroinflammation produced by activated inflammatory cells of the myeloid lineage, in particular microglia, plays a key role in the pathogenesis of acute and chronic diseases of the peripheral nervous system and CNS. IL-1\u3b2 release is promoted by ATP acting at the purinergic P2X7 receptor (P2X7R) in cells primed with toll-like receptor (TLR) ligands

Inertia-driven resonant excitation of a magnetic skyrmion

Topological spin structures such as magnetic domain walls, vortices, and skyrmions, have been receiving great interest because of their high potential application in various spintronic devices. To utilize them in the future spintronic devices, it is first necessary to understand the dynamics of the topological spin structures. Since inertial effect plays a crucial role in the dynamics of a particle, understanding the inertial effect of topological spin structures is an important task. Here, we report that a strong inertial effect appears steadily when a skyrmion is driven by an oscillating spin-Hall-spintorque (SHST). We find that the skyrmion exhibits an inertia-driven hypocycloid-type trajectory when it is excited by the oscillating SHST. This motion has not been achieved by an oscillating magnetic field, which only excites the breathing mode without the inertial effect. The distinct inertial effect can be explained in terms of a spin wave excitation in the skyrmion boundary which is induced by the non-uniform SHST. Furthermore, the inertia-driven resonant excitation provides a way of experimentally estimating the inertial mass of the skyrmion. Our results therefore pave the way for the development of skyrmion-based device applications

Wave modes of collective vortex gyration in dipolar-coupled-dot-array magnonic crystals

Lattice vibration modes are collective excitations in periodic arrays of atoms or molecules. These modes determine novel transport properties in solid crystals. Analogously, in periodical arrangements of magnetic vortex-state disks, collective vortex motions have been predicted. Here, we experimentally observe wave modes of collective vortex gyration in one-dimensional (1D) periodic arrays of magnetic disks using time-resolved scanning transmission x-ray microscopy. The observed modes are interpreted based on micromagnetic simulation and numerical calculation of coupled Thiele equations. Dispersion of the modes is found to be strongly affected by both vortex polarization and chirality ordering, as revealed by the explicit analytical form of 1D infinite arrays. A thorough understanding thereof is fundamental both for lattice vibrations and vortex dynamics, which we demonstrate for 1D magnonic crystals. Such magnetic disk arrays with vortex-state ordering, referred to as magnetic metastructure, offer potential implementation into information processing devices.open8

Genome-scale modeling of the protein secretory machinery in yeast

The protein secretory machinery in Eukarya is involved in post-translational modification (PTMs) and sorting of the secretory and many transmembrane proteins. While the secretory machinery has been well-studied using classic reductionist approaches, a holistic view of its complex nature is lacking. Here, we present the first genome-scale model for the yeast secretory machinery which captures the knowledge generated through more than 50 years of research. The model is based on the concept of a Protein Specific Information Matrix (PSIM: characterized by seven PTMs features). An algorithm was developed which mimics secretory machinery and assigns each secretory protein to a particular secretory class that determines the set of PTMs and transport steps specific to each protein. Protein abundances were integrated with the model in order to gain system level estimation of the metabolic demands associated with the processing of each specific protein as well as a quantitative estimation of the activity of each component of the secretory machinery

Optimal control of vortex core polarity by resonant microwave pulses

In a vortex-state magnetic nano-disk, the static magnetization is curling in the plane, except in the core region where it is pointing out-of-plane, either up or down leading to two possible stable states of opposite core polarity p. Dynamical reversal of p by large amplitude motion of the vortex core has recently been demonstrated experimentally,raising fundamental interest for potential application in magnetic storage devices. Here we demonstrate coherent control of p by single and double microwave pulse sequences, taking advantage of the resonant vortex dynamics in a perpendicular bias magnetic field. Optimization of the microwave pulse duration required to switch p allows to experimentally infer the characteristic decay time of the vortex core in the large oscillation regime. It is found to be more than twice shorter than in the small oscillation regime, raising the fundamental question of the non-linear behaviour of magnetic dissipation