Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation

Nonlinear Dynamics - This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the...     

Focusing of Fe3O4 nanoparticles using a rotating magnetic field in various environments

The paper shows the application of a new method – Magnetic Nanoparticles Focusing 3D, MNF-3D – for focusing of magnetic nanoparticles at any point in a three-dimensional space between the rotating magnet system. The results of focusing process of nanoparticles in water, human blood, human serum and polyurethane sponge are presented. Additionally, blood flow was also considered. The effectiveness of nanoparticle focusing was monitored optically and quantitatively by electron spin resonance method. The method enabled focusing of magnetic nanoparticles within a few minutes in different environments. A good efficiency of focusing process was observed for all the samples.     

Statistical approach to multiple-q modulated structures: average Patterson analysis

Using a statistical approach, the average unit cells have been constructed for modulated structures with different types of modulation, from simple sinusoidal to square-wave functions. The obtained unit cells fully describe diffraction intensities of the main reflections and their satellites. A universal distribution, valid for different lengths of the modulation vector, has been found. Average Patterson functions have been constructed and used to distinguish between different types of modulation.     

A dichotomy for the convex spaces of probability measures

We show that every nonempty compact and convex space M of probability Radon measures either contains a measure which has ‘small’ local character in M or else M contains a measure of ‘large’ Maharam type. Such a dichotomy is related to several results on Radon measures on compact spaces and to some properties of Banach spaces of continuous functions.     

Critical circle maps near bifurcation

We estimate harmonic scalings in the parameter space of a one-parameter family of critical circle maps. These estimates lead to the conclusion that the Hausdorff dimension of the complement of the frequency-locking set is less than 1 but not less than 1/3. Moreover, the rotation number is a Hölder continuous function of the parameter.Partially supported by KBN grant Iteracje i Fraktale #210909101.Partially supported by NSF Grant #DMS-9206793 and the Sloan Research Fellowship.     

An Asymptotic Ratio in the Complete Binary Tree

Let T _n be the complete binary tree of height n considered as the Hasse-diagram of a poset with its root 1 _n as the maximum element. For a rooted tree T, define two functions counting the embeddings of T into T _n as follows A(n;T)=|{S T _n  : 1 _n ∈S, S≅T}|, and B(n;T)=|{S T _n :1 _n ∉S, S≅T}|. In this paper we investigate the asymptotic behavior of the ratio A(n;T)/B(n;T), and we show that lim  _n→∞[A(n;T)/B(n;T)]=2^ℓ;−1−1, for any tree T with ℓ leaves. This revised version was published online in June 2006 with corrections to the Cover Date.     

Uniqueness of minimal Fourier-type extensions in L_1-spaces

We give a characterization of uniqueness of finite rank Fourier-type minimal extensions in $L_1$ -norm. This generalizes the main result obtained by Lewicki (Proceedings of the Fifth International Conference on Function Spaces, Lecture Notes in Pure and Applied Mathematics, vol. 213, pp. 337–345, 1998) to the case of $n$ -circular sets in $\mathbb{C }^n$ .     

Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains

In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. Finally, we prove the existence of a pullback attractor for a non-autonomous 2D Navier–Stokes model in an unbounded domain, a case in which the theory of uniform attractors does not work since the non-autonomous term is quite general. To cite this article: T. Caraballo et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Improving the dielectric constant of Al2O3 by cerium substitution for high-k MIM applications

Process compatible high-k dielectric thin films are one of the key solutions to develop high performance metal–insulator–metal (MIM) structures for future microelectronic devices. Engineered cerium–aluminate (Ce_xAl_2–xO₃) thin films were deposited on titanium nitride metal electrodes by electron-beam co-evaporation of ceria and alumina in a molecular beam deposition chamber. X-ray photoelectron spectroscopy clearly reveals that Ce cations can be stabilized in the 3+ valence state in Ce_xAl_2–xO₃ up to x = 0.7 by accommodation in the alumina host matrix. Higher Ce content was observed to result in cerium dioxide segregation in cerium aluminate matrix, probably due to the chemical tendency of Ce cations to exist rather in the 4+ than in the 3+ state. Electrical characterization of the X-ray amorphous Ce_0.7Al_1.3O₃ films reveals a dielectric constant value of about 11 and leakage current lower than 10^?4 A/cm². No parasitic low-k interface formation between the high-k Ce_0.7Al_1.3O₃ film and the TiN metal electrode is detected.     

The power of adaptive algorithms for functions with singularities

This is an overview of recent results on complexity and optimality of adaptive algorithms for integrating and approximating scalar piecewise r-smooth functions with unknown singular points. We provide adaptive algorithms that use at most n function samples and have the worst case errors proportional to n^−r for functions with at most one unknown singularity. This is a tremendous improvement over nonadaptive algorithms whose worst case errors are at best proportional to n⁻¹ for integration and n^−1/p for the L^p approximation problem. For functions with multiple singular points the adaptive algorithms cease to dominate the nonadaptive ones in the worst case setting. Fortunately, they regain their superiority in the asymptotic setting. Indeed, they yield convergence of order n^−r for piecewise r-smooth functions with an arbitrary (unknown but finite) number of singularities. None of these results hold for the L^∞ approximation. However, they hold for the Skorohodmetric, which we argue to be more appropriate than L^∞ for dealing with discontinuous functions. Numerical test results and possible extensions are also discussed.