Polaronic and charge ordering effects in Pr 0.5 Sr 0.5 Mn 1− x Fe x O 3

In this work we report the results of X-ray diffraction and Mössbauer spectroscopy for the systems Pr_0.5Sr_0.5Mn_1???x Fe _x O₃ (with x?=?0.05, 0.10, 0.15, 0.20, 0.25, 0.30). XRD patterns indicated that all samples were single phase with slightly distorted orthorhombic symmetry. Room temperature Mössbauer spectra are all quadrupole split, indicating paramagnetic relaxation of the Fe moment for all values of Fe concentrations. The spectra are fitted with two doublet components associated with Fe^3?+? ions in octahedral sites with different distortions. Mössbauer spectra recorded at liquid nitrogen temperature for this system also indicate paramagnetic relaxation of the Fe moments down to liquid nitrogen temperature (LNT). In these spectra a third quadrupole component with quadrupole splitting close to zero develops. This component is associated with the delocalization of the charge carriers and the consequent disappearance of lattice distortions produced by the polaronic effect at room temperature. The component with the high quadrupole splitting (0.81 to 1.07 mm/s) results from Jahn–Teller distortion as a consequence of charge ordering transition at low temperature.     

Observation and modelling of magnetic vortex core structure in Permalloy nanoparticles

We use an approximate micromagnetic model, based on geometrical simplifications of the problem, to describe the vortex core structure observed in spherical Permalloy nanoparticles using off-axis electron holography. The magnetisation distribution inside the vortex core is directly calculated by minimising the micromagnetic energy functional and is compared with the experimental results. The symmetry constraints underlying the model are discussed envisaging possible generalisation to the case of vortex cores with structure strongly dependent on the coordinate directed along the axis of the vortex. Moreover the many-body effect associated with the presence of two small satellite particles is described by rescaling the size of the particle.     

Numerical Simulation of Highly Viscoelastic Polymer Melts using VF and DEVSS Methods

Viscoelastic polymer melts are usually modeled with a macro approch. This is done using an anisotropic mobility tensor to generalize the Maxwell model. In recent works the use of micro approches is increasing, e.g. the so-called POM-POM model. In this work a frame independent flow type property is introduced in order to help visualizing the elongation and shear regions in a 3D flow. Which in turn helps to choose the right material model, since the model parameters are adjusted with 1D shear flows and the elongation properties are mostly neglected. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On nonlinear diffusion problems with strong degeneracy

In this Note, we study the ‘triply’ degenerate problem: $b{(v)}_t?\mathrm{\Delta }g(v)+\mathrm{div}\Phi (v)=f$ on $Q:=(0,T)\times \Omega$, $b(v(0,?))=b(v_0)$ on Ω and $g(v)=g(a)$ ‘on some part of the boundary’ $(0,T)\times ?\Omega$, in the case of continuous nonhomogenous and nonstationary boundary data a. The functions $b,g$ are assumed to be continuous nondecreasing and to verify the normalisation condition $b(0)=g(0)=0$ and the range condition $R(b+g)=\mathbb{R}$. Using monotonicity and penalization methods, we prove existence of a weak entropy solution in the spirit of F. Otto (1996). To cite this article: K. Ammar, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Variational Primitive of a Differential Form

In this paper, a Dirichlet-to-Neumann operator related to the Cauchy problem for the gradient operator with data on a part of the boundary is defined. To this end, a nonlinear relaxation of this problem, which is a mixed boundary problem of Zaremba type for the p-Laplace equation, is considered.     

The Hilbert number of a class of differential equations

The notion of Hilbert number from polynomial differential systems in the plane of degree $n$ can be extended to the differential equations of the form \[\dfrac{dr}{d\theta}=\dfrac{a(\theta)}{\displaystyle \sum_{j=0}^{n}a_{j}(\theta)r^{j}} \eqno(*)\] defined in the region of the cylinder $(\tt,r)\in \Ss^1\times \R$ where the denominator of $(*)$ does not vanish. Here $a, a_0, a_1, \ldots, a_n$ are analytic $2\pi$--periodic functions, and the Hilbert number $\HHH(n)$ is the supremum of the number of limit cycles that any differential equation $(*)$ on the cylinder of degree $n$ in the variable $r$ can have. We prove that $\HHH(n)= \infty$ for all $n\ge 1$.     

Perturbation of unbounded linear operators by $$\gamma $$-relative boundedness

Diagana (Handbook on operator theory. Springer, Basel, pp 875–880, 2015) studied some sufficient conditions such that if S,  T and K are three unbounded linear operators with S being a closed operator, then their algebraic sum \(S+T+K\) is also a closed operator. The main focus of this paper is to extend these results to the closable operator by adding a new concept of the gap and the \(\gamma \)-relative boundedness inspired by the work of Jeribi et al. (Linear Multilinear Algebra 64:1654–1668, 2015). After that, we apply the obtained results to study the specific properties of some block operator matrices.