A fuzzy blue sky catastrophe

In this paper, a blue sky catastrophe of limit cycles of a Van der Pol system with fuzzy disturbances is studied by means of the fuzzy generalized cell mapping (FGCM) method. The blue sky catastrophe happens when a fuzzy limit cycle collides with a fuzzy saddle on the basin boundary as the intensity of fuzzy noise reaches a critical value. The fuzzy limit cycle, characterized by its global topology and membership function, suddenly loses stability and disappears into the blue sky after the collision. We illustrate this bifurcation event by considering the Van der Pol system under the multiplicative fuzzy noise. Such a bifurcation is a fuzzy noise-induced effect which cannot be seen in deterministic systems.     

On the steady motions of a flat domain wall in a ferromagnet

A new derivation is presented of Walker's exact solution to Gilbert equation, a solution which mimicks the travelling-wave motion of a flat domain wall at 180^°. It is shown that a process during which the working of the applied magnetic field exactly compensates dissipation (the Walker condition) exists both under the constitutive circumstances considered in the standard Gilbert equation and when either the internal free-energy or the dissipation, or both, are generalized by the introduction of higher-gradient terms; but that such a process cannot solve the generalized Gilbert equation. It is also shown that, when dry-friction dissipation is considered and a suitable magnetic field is applied, the associated Gilbert equation has a Walker-type solution mimicking a flat wall, at 90^° this time, which however does not satisfy the Walker condition. Received 16 November 2001     

An Efficient Geometric Integrator for Thermostatted Anti-/Ferromagnetic Models

(Anti)-/ferromagnetic Heisenberg spin models arise from discretization of Landau–Lifshitz models in micromagnetic modelling. In many applications it is essential to study the behavior of the system at a fixed temperature. A formulation for thermostatted spin dynamics was given by Bulgac and Kusnetsov, which incorporates a complicated nonlinear dissipation/driving term while preserving spin length. It is essential to properly model this term in simulation, and simplified schemes give poor numerical performance, e.g., requiring an excessively small timestep for stable integration. In this paper we present an efficient, structure-preserving method for thermostatted spin dynamics.     

Inhibition of domain wall formation and its effects on the bulk magnetic properties of certain spinels

It is shown that hysteresis and susceptibility studies at various temperatures could provide an idea whether a magnetic sample contains multidomain, single-domain or superparamagnetic particles. Our results on titanomagnetites with those of others on cobalt substituted magnesium ferrites suggest that domain wall formation is inhibited in some of them whereby only single-domain or superparamagnetic particles occur irrespective of the physical grain size of such materials. At high concentration of titanium in titanomagnetites, the magnetic behaviour is similar to a spin glass, which we interpret as a transition of optimum single-domains going over to superparamagnetic state.     

Label-free characterization of cell adhesion using reflectometric interference spectroscopy (RIfS)

Reflectometric interference spectroscopy (RIfS) is a label-free, time-resolved technique for detecting interactions of molecules immobilized on a surface with ligands in solution. Here we show that RIfS also permits the detection of the adhesion of tissue culture cells to a functionalized surface in a flow system. Interactions of T cells with other leukocytes or epithelial cells of blood vessels are crucial steps in the regulating immune response and inflammatory reactions. Jurkat T cell leukemia cells rapidly attached to a transducer functionalized with a monoclonal antibody directed against the T cell receptor (TCR)/CD3 complex, followed by activation-dependent cell spreading. RIfS curves were obtained for the Jurkat derivative JCaM 1.6 (which lacks the key signaling protein Lck), cells preincubated with cytochalasin D (an inhibitor of actin polymerization), and for surfaces functionalized with an antibody directed against the coreceptor CD28. These curves differed with respect to the maximum signal and the initial slope of the increase in optical thickness. The testing of chemical inhibitors, cell surface molecules and gene products relevant to a key event in T cell immunity illustrates the potential of label-free techniques for the analysis of activation-dependent cell-surface contacts. The first two authors contributed equally to this paper     

The influence of wire width on the charge distribution of transverse domain walls and their stray field interactions

We present here a numerical study of the magnetostatic charge distribution of transverse Néel type domain wall in permalloy nanowires. The calculations indicate that not only is the distribution highly non-uniform within a given transverse wall but it also varies dramatically with respect to the wire width. The implications of this for magnetostatic domain wall pinning are analyzed by considering the stray field interaction between a wall and another extended magnetic body for a particular domain wall chirality, where two distinct depinning mechanisms are observed depending on the wire width.     

The effects of temperature and frequency on the magnetization switching mode in circular MI sensors

This paper presents results computed using a meshless method in a point collocation formulation to investigate the effects of temperature and frequency on the magnetization switching mode in the circular amorphous magneto-impedance sensor (element). Specifically, the solutions characterizing the MI effect are solved from a set of coupled nonlinear equations consisting of the Maxwell’s equations, the Landau-Lifshitz-Gilbert equation, and the thermal diffusion equation. This coupled nonlinear space-time model predicts the formation and propagation of dynamic domain walls in switching and it is shown how they contribute to experimentally observed temperature and frequency effects. Computed results (that agree well with reported experimental data) suggest radial domain walls may play a larger role in the MI effect than originally believed even for the realistic conditions considered here at 1 MHz or more.     

Low-scale leptogenesis and the domain wall problem in models with discrete flavor symmetries

We propose a new mechanism for leptogenesis, which is naturally realized in models with a flavor symmetry based on the discrete group A₄$A_4$, where the symmetry breaking parameter also controls the Majorana masses for the heavy right-handed (RH) neutrinos. During the early universe, for T?TeV$T?\text{TeV}$, part of the symmetry is restored, due to finite temperature contributions, and the RH neutrinos remain massless and can be produced in thermal equilibrium even at temperatures well below the most conservative gravitino bounds. Below this temperature the phase transition occurs and they become massive, decaying out of equilibrium and producing the necessary lepton asymmetry. Unless the symmetry is broken explicitly by Planck-suppressed terms, the domain walls generated by the symmetry breaking survive till the quark–hadron phase transition, where they disappear due to a small energy splitting between the A₄$A_4$ vacua caused by the QCD anomaly.     

A first-order system approach for diffusion equation. II: Unification of advection and diffusion

In this paper, we unify advection and diffusion into a single hyperbolic system by extending the first-order system approach introduced for the diffusion equation [J. Comput. Phys., 227 (2007) 315–352] to the advection–diffusion equation. Specifically, we construct a unified hyperbolic advection–diffusion system by expressing the diffusion term as a first-order hyperbolic system and simply adding the advection term to it. Naturally then, we develop upwind schemes for this entire   system; there is thus no need to develop two different schemes, i.e., advection and diffusion schemes. We show that numerical schemes constructed in this way can be automatically uniformly accurate, allow O(h)$O(h)$ time step, and compute the solution gradients (viscous stresses/heat fluxes for the Navier–Stokes equations) simultaneously to the same order of accuracy as the main variable, for all Reynolds numbers. We present numerical results for boundary-layer type problems on non-uniform grids in one dimension and irregular triangular grids in two dimensions to demonstrate various remarkable advantages of the proposed approach. In particular, we show that the schemes solving the first-order advection–diffusion system give a tremendous speed-up in CPU time over traditional scalar schemes despite the additional cost of carrying extra variables and solving equations for them. We conclude the paper with discussions on further developments to come.