Wavelet-Based Estimation of Anisotropic Spatiotemporal Long-Range Dependence

In this article, the estimation of spatiotemporal long-range dependence is formulated in the spectral wavelet domain. Sample information is provided by functional spectral data. Their high local singularity at the origin is captured by the wavelet transform. Weak consistency of the spectral wavelet estimators proposed is derived. Two functional estimation algorithms are implemented. A simulation study is developed to illustrate the efficiency of the computational methods derived. An approximation to the empirical convergence rate of the spectral wavelet periodogram is computed in some simulated examples.     

Quantitative description of the T1 formation kinetics in an Al–Cu–Li alloy using differential scanning calorimetry,small-angle X-ray scattering and transmission electron microscopy

The object of the present study is to design a methodology to follow the kinetics of T₁ precipitation, in an AA2198 alloy, in terms of precipitate size, morphology (thickness, diameter) and volume fraction, during a two-temperature isothermal heat treatment. We used in situ small-angle X-ray scattering (SAXS) as a way to measure the evolution of the T₁ mean thickness and diameter during the heat treatment. Transmission electron microscopy (TEM) was then performed in order to calibrate these evolutions. Furthermore, we demonstrate that the volume fraction evolution can be described successfully using a simple analysis of the differential scanning calorimetry (DSC) thermograms. The latter was calibrated by selected observations in high angular annular dark field scanning transmission electron microscopy (HAADF-STEM). Microstructure evolution during DSC heating ramps was analysed using in situ SAXS: the T₁ phase transformation is found to consist in a two-step thickening process explained by two consecutive diffusion stages. The enthalpy of formation of the T₁ phase is deduced from the DSC measurements.     

Iterative deconvolution of quadrupole split NMR spectra

We propose a simple method to deconvolute NMR spectra of quadrupolar nuclei in order to separate the distribution of local magnetic hyperfine field from the quadrupole splitting. It is based on an iterative procedure which allows to express the intensity of a single NMR line directly as a linear combination of the intensities of the total experimental spectrum at a few related frequencies. This procedure is argued to be an interesting complement to Fourier transformation since it can lead to a significant noise reduction in some frequency ranges. This is demonstrated in the case of the ¹¹B-NMR spectrum in SrCu₂(BO₃)₂ at a field of 31.7 T, where a magnetization plateau at 1/6 of the saturation has been observed.     

Tailoring Anderson localization by disorder correlations in 1D speckle potentials

We study Anderson localization of single particles in continuous, correlated, one-dimensional disordered potentials. We show that tailored correlations can completely change the energy-dependence of the localization length. By considering two suitable models of disorder, we explicitly show that disorder correlations can lead to a nonmonotonic behavior of the localization length versus energy. Numerical calculations performed within the transfer-matrix approach and analytical calculations performed within the phase formalism up to order three show excellent agreement and demonstrate the effect. We finally show how the nonmonotonic behavior of the localization length with energy can be observed using expanding ultracold-atom gases.     

Phase transformations and structural characteristics of AL–Cu–Co(–Si) decagonal phase

The phase transformations and structural characteristics of the Al-Cu-Co-Si alloy have been studied by neutron diffraction and high-resolution electron microscopy. The Al₆₅Cu_17.5Co_17.5 decagonal phase is stable in the temperature range between 973 K and 1350 K. At the low-temperature end, it relaxes to a microcrystalline approximant structure. At the high-temperature end, it melts directly into liquid. Two distinct orthorhombic phases are identified in the Al₆₃Cu_17.5Co_17.5Si₂ microcrystalline structure. They are composed of several structure units that can also construct the Penrose tiling. Because of lack of units, a single orthorhombic phase cannot undergo the transformation towards the high-temperature decagonal phase. An analysis of the orientation relationships between the CsCl and orthorhombic phases leads to the definition of Penrose tiling-like subnetworks inside the orthorhombic unit cells so that these orthorhombic phases can be regarded as the periodic patchworks of quasiperiodic subnetworks.     

Spin-dependent and Coriolis interactions by an improved configuration interaction treatment: predissociation of excited fine structure levels of OH/OD

The state specific predissociation of OH/OD in its lowest electronically excited state (A²Σ⁺,v',N',F₁/F₂) is investigated by time dependent wave packet propagation techniques. To improve the accuracy of the potential energy curves, spin-orbit, spin-spin and rotational interactions required for the treatment, we have refined our CI techniques, using optimal orbitals for each of the electronic states. Potential energy curves, matrix elements and lifetimes of the rotational sublevels are compared with experiment and with theoretical values from multichannel scattering theory     

Extensions of Superalgebras of Krichever–Novikov Type

An explicit construction of central extensions of Lie superalgebras of Krichever–Novikov type is given. In the case of Jordan superalgebras related to the superalgebras of Krichever–Novikov type we calculate a 1-cocycle with coefficients in the dual space.     

Time-Ordering and a Generalized Magnus Expansion

Both the classical time-ordering and the Magnus expansion are well known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in statistical physics, we introduce a generalization of the Magnus expansion. Whereas the classical expansion computes the logarithm of the evolution operator of a linear differential equation, our generalization addresses the same problem, including, however, directly a non-trivial initial condition. As a by-product we recover a variant of the time-ordering operation, known as ${\mathsf{T}^\ast}$ -ordering. Eventually, placing our results in the general context of Rota–Baxter algebras permits us to present them in a more natural algebraic setting. It encompasses, for example, the case where one considers linear difference equations instead of linear differential equations.     

Higher order symmetrizer and application to an unusual transport equation

We study a class of stationary transport equation with nonlocal low-order tems We obtain the existence and uniqueness of a solution in sobolev spaces