Stability of the vortex defect in the Landau–de Gennes theory for nematic liquid crystals

We analyze the radially symmetric solution corresponding to the vortex defect (the so-called melting hedgehog) in the Landau–de Gennes theory for nematic liquid crystals. We prove the existence, uniqueness and stability results of the melting hedgehog.     

Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators

Noncompact convexificators, which provide upper convex and lower concave approximations for a continuous function, are defined. Various calculus rules, including extremality and mean-value properties, are presented. Regularity conditions are given for convexificators to be minimal. A characterization of quasiconvexity of a continuous function is obtained in terms of the quasimonotonicity of convexificators.     

Kernel Characterization of an Interval Function

This paper proposes a set-membership approach to characterize the kernel of an interval-valued function. In the context of a bounded-error estimation, this formulation makes it possible to embed all uncertainties of the problem inside the interval function and thus to avoid bisections with respect to all these uncertainties. To illustrate the principle of the approach, two testcases taken from robotics will be presented. The first testcase deals with the characterization of all loops of a mobile robot from proprioceptive measurements only. The second testcase is the localization of a robot from range-only measurements.     

Numerical experiments on a flexible variant of GMRES-DR

The Flexible GMRES (FGMRES [1]) and the GMRES with deflated restarting (GMRES-DR [2]) methods are two algorithms derived from GMRES [3], that are considered as powerful when solving large non hermitian systems of linear equations. GMRES-DR is a variant of GMRES with an improved restarting technique that maintains in the Krylov subspace harmonic Ritz vector from the previous restart. In situations where the convergence of restarted GMRES is slow and where the matrix has few eigenvalues close to the origin, this technique has proved very efficient. The new method that we propose is the Flexible GMRES with deflated restarting (FGMRES-DR [6]), which combines the two above mentioned algorithms in order to yield better performance. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

SMIREP: predicting chemical activity from SMILES

Most approaches to structure-activity-relationship (SAR) prediction proceed in two steps. In the first step, a typically large set of fingerprints, or fragments of interest, is constructed (either by hand or by some recent data mining techniques). In the second step, machine learning techniques are applied to obtain a predictive model. The result is often not only a highly accurate but also hard to interpret model. In this paper, we demonstrate the capabilities of a novel SAR algorithm, SMIREP, which tightly integrates the fragment and model generation steps and which yields simple models in the form of a small set of IF-THEN rules. These rules contain SMILES fragments, which are easy to understand to the computational chemist. SMIREP combines ideas from the well-known IREP rule learner with a novel fragmentation algorithm for SMILES strings. SMIREP has been evaluated on three problems: the prediction of binding activities for the estrogen receptor (Environmental Protection Agency's (EPA's) Distributed Structure-Searchable Toxicity (DSSTox) National Center for Toxicological Research estrogen receptor (NCTRER) Database), the prediction of mutagenicity using the carcinogenic potency database (CPDB), and the prediction of biodegradability on a subset of the Environmental Fate Database (EFDB). In these applications, SMIREP has the advantage of producing easily interpretable rules while having predictive accuracies that are comparable to those of alternative state-of-the-art techniques.     

On the null-controllability of the heat equation in unbounded domains

We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting) which implies that one cannot go infinitely far away from the control region without tending to the boundary (if any), but also applies when the distance to the control region is bounded. The proof builds on heat kernel estimates. Secondly, we describe a class of null-controllable heat equations on unbounded product domains. Elementary examples include an infinite strip in the plane controlled from one boundary and an infinite rod controlled from an internal infinite rod. The proof combines earlier results on compact manifolds with a new lemma saying that the null-controllability of an abstract control system and its null-controllability cost are not changed by taking its tensor product with a system generated by a non-positive self-adjoint operator.     

Using self-similar properties of turbulent premixed flames to downsize chemical tables in high-performance numerical simulations

Detailed chemical mechanisms have to be incorporated in turbulent combustion modelling to predict flame propagation, ignition, extinction or pollutant formation. Unfortunately, hundreds of species and thousands of elementary reactions are involved in hydrocarbon chemical schemes and cannot be handled in practical simulations, because of the related computational costs and the need to model the complexity of their interaction with turbulent motions. Detailed chemistry may be handled using look-up tables, where chemical parameters such as reaction rates and/or species mass fractions are determined from a reduced set of coordinates, progress variables or mixture fractions, as proposed in ILDM, FPI or FGM methods. Nevertheless, these tables may require large computer memory spaces and non-negligible access times. This issue becomes of crucial importance when running on massively parallel computers: to implement these databases in shared memories would induce a large number of data exchanges, reducing the overall code performance; on the other hand duplicating databases in every local processor memory may become impossible either for large databases or small local memories. This work proposes to take advantage of the self-similar behaviour of turbulent premixed flames to reduce the size of these chemical databases, specifically when running on massively parallel machines, under the FPI (Flame Prolongation of ILDM) framework. Several approaches to reduce the database are investigated and discussed both in terms of memory requirements and access times. A very good compromise is obtained for methane–air turbulent premixed flames, where the size of the database is decreased by a factor of 1000, while the access time is reduced by about 60%.     

Reexamination of the I2 spectrum near the B(3Π0u+) state dissociation limit

The disagreement of Danyluk and King's (Chem. Phys.25, 343 (1977)) rotational constants for levels lying near the dissociation limit of B-state I₂ with the mechanical behavior predicted by near-dissociation theory is investigated. The discrepancies are shown to be much too large to be explained by either the neglect of centrifugal distortion effects in the original analysis or by rotational or spin-rotation coupling to a nearby repulsive 1_u state. These differences are therefore attributed to experimental error, a conclusion which is confirmed by more recent experimental results. A reanalysis of the best available data for levels near the dissociation limit of B-state I₂ then yields improved values for the B-state dissociation limit $\text{D}$ = 20 043.16 (±0.02) cm^?1 of the vibrational index at dissociation v_$\text{D}$ = 87.32 (±0.04) and of the long-range potential constant $\text{C}{}_5\text{= 2.88 (±0.03) × 10}{}^5\text{cm}{}^{\mathrm{?1}}\text{A}\text{?}{}^5$. This in turn implies a slightly improved ground-state dissociation energy of $\text{D}$₀ = 12 440.18 (±0.02) cm^?1.     

Photoluminescence properties of Co-doped ZnO nanocrystals

We performed photoluminescence experiments on colloidal, Co²⁺-doped ZnO nanocrystals in order to study the electronic properties of Co²⁺ in a ZnO host. Room temperature measurements showed, next to the ZnO exciton and trap emission, an additional emission related to the Co²⁺ dopant. The spectral position and width of this emission does not depend on particle size or Co²⁺ concentration. At 8 K, a series of ZnO bulk phonon replicas appear on the Co²⁺-emission band. We conclude that Co²⁺ ions are strongly localized in the ZnO host, making the formation of a Co²⁺d-band unlikely. Magnetic measurements revealed a paramagnetic behaviour.     

Synthesis of PEDOT Nanoparticles and Vesicles by Dispersion Polymerization in Alcoholic Media

Summary: The synthesis of PEDOT nanoparticles and vesicles by dispersion polymerization in a methanol/water mixture (3/2, v/v) is reported, using either ammonium persulfate or iron(III) p‐toluenesulfonate as oxidants and α‐EDOT‐PEO as a reactive stabilizer. The influence of the oxidant as well as the α‐EDOT‐PEO molar mass and concentration on the core‐shell particle morphology and conductivity properties have been investigated. PEDOT particles with conductivities up to 1.5 × 10⁻² S · cm⁻¹ have been obtained in high yield.

TEM image of PEDOT vesicles prepared using PEO‐based stabilizers of 25 000 g · mol⁻¹ in water/methanol mixture (2:3 v/v) at room temperature using ammonium persulfate as an oxidant.