Stability of the magnetic domain structure of nanoparticle thin films against external fields

We investigate the effect of external magnetic fields on the magnetic structure of thin films from magnetic nanoparticles (MNP) with dipolar interaction. Such fields are present, for example, if samples are scanned with magnetic probes. Numerical simulations and experimental magnetic force microscopy (MFM) studies are presented. Numerically, we have calculated the magnetization pattern of single-layer and multilayer MNP thin films. The calculations show that unperturbed single-layer MNP films have an in-plane orientation of the magnetization with a flux-closure-domain pattern. An external field generated by a point dipole above the film induces locally an out-of-plane configuration of the magnetization. In the corresponding MFM images, the domain pattern in the film is erased and a stripe-like contrast enhancement at the edges appears. Multilayer films are found to be more robust against external fields than monolayers.     

Bergman polynomials on an archipelago: Estimates, zeros and shape reconstruction

Growth estimates of complex orthogonal polynomials with respect to the area measure supported by a disjoint union of planar Jordan domains (called, in short, an archipelago) are obtained by a combination of methods of potential theory and rational approximation theory. The study of the asymptotic behavior of the roots of these polynomials reveals a surprisingly rich geometry, which reflects three characteristics: the relative position of an island in the archipelago, the analytic continuation picture of the Schwarz function of every individual boundary and the singular points of the exterior Green function. By way of explicit example, fine asymptotics are obtained for the lemniscate archipelago |z^m−1|<r^m, 0<r<1, which consists of m islands. The asymptotic analysis of the Christoffel functions associated to the same orthogonal polynomials leads to a very accurate reconstruction algorithm of the shape of the archipelago, knowing only finitely many of its power moments. This work naturally complements a 1969 study by H. Widom of Szegő orthogonal polynomials on an archipelago and the more recent asymptotic analysis of Bergman orthogonal polynomials unveiled by the last two authors and their collaborators.     

Applications holomorphes propres d'un domaine quasi-disqué sur un domaine disqué

A result of F. Berteloot and G. Patrizio [F. Berteloot, G. Patrizio, A cartan theorem for proper holomorphic mappings of complete circular domains, Adv. Math. 153 (2000) 342-352] states that if f is a proper holomorphic map between two bounded complete circular domains Ω₁ and Ω₂ in Cn+1 (n?1), such that f−1{0}={0} and such that the principal part fp of the Taylor expansions of f at the origine is nondegenerated i.e. fp−1{0}={0}, then f=fp.Here, we give a partial extension of this result to the case where f is a nondegenerated proper holomorphic map between a quasi-circular domain Ω₁ and a complete circular domain Ω₂, which are pseudo-convex but not necessarily bounded.We show that if f and its principal part fp are nondegenerated at the origine, then fp−1(Ω₂)=Ω₁.     

Reachability sets of hybrid systems in the presence of successive switchings

The concept of reachability domains of hybrid systems is described together with the use of ellipsoidal methods for calculation of such domains in the case when there are successive switchings on several given hyperplanes or bands. An algorithm for calculation of the reachability sets for a hybrid system that uses ellipsoidal approximations is given for the cases in which the switching sets are planes or bands. The parametrization of nonconvex reachability domains is obtained as a union of intersections of the corresponding ellipsoidal estimates.     

Robust stability analysis of static neural network with S-type distributed delays

In this paper, we investigate local robust stability of static neural network (SNN) with S-type distributed delays. We derive some new sufficient conditions for local robust stability of equilibrium points and estimate attracting domains of equilibrium points except isolated equilibrium points. Our results not only show local robust stability of equilibrium points but also allow much broader application for static neural network with or without delays. It is shown that our results are new and improve corresponding results existing in the previous literature.     

On k-uniformly close-to-convex functions of complex order

In this paper, we define and study some subclasses of analytic functions by using fractional derivative operator. Some interesting properties, coefficients problems and inclusion results of these classes are investigated. It is also shown that these classes are closed under convolution with convex functions and some applications are given.     

An L p -theory of Stochastic PDEs of Divergence Form on Lipschitz Domains

Stochastic partial differential equations of divergence form are considered on Lipschitz domains. Existence and uniqueness results are given in weighted Sobolev spaces. It is allowed that the coefficients of the equations substantially oscillate or blow up near the boundary.      

The Pullback Asymptotic Behavior of the Solutions for 2D Nonautonomous G-Navier-Stokes Equations

The pullback asymptotic behavior of the solutions for 2D Nonautonomous G-Navier-Stokes equations is studied, and the existence of its $L^2$-pullback attractors on some bounded domains with Dirichlet boundary conditions is investigated by using the measure of noncompactness. Then the estimation of the fractal dimensions for the 2D G-Navier-Stokes equations is given.     

A conservative,thermodynamically consistent numerical approach for low Mach number combustion. Part I: Single-level integration

We present a numerical approach for low Mach number combustion that conserves both mass and energy while remaining on the equation of state to a desired tolerance. We present both unconfined and confined cases, where in the latter the ambient pressure changes over time. Our overall scheme is a projection method for the velocity coupled to a multi-implicit spectral deferred corrections (SDC) approach to integrate the mass and energy equations. The iterative nature of SDC methods allows us to incorporate a series of pressure discrepancy corrections naturally that lead to additional mass and energy influx/outflux in each finite volume cell in order to satisfy the equation of state. The method is second order, and satisfies the equation of state to a desired tolerance with increasing iterations. Motivated by experimental results, we test our algorithm on hydrogen flames with detailed kinetics. We examine the morphology of thermodiffusively unstable cylindrical premixed flames in high-pressure environments for confined and unconfined cases. We also demonstrate that our algorithm maintains the equation of state for premixed methane flames and non-premixed dimethyl ether jet flames.