Bubble cell for magnetic bead trapping in capillary electrophoresis

A bubble cell capillary classically used to extend the optical path length for UV–vis detection is employed here to trap magnetic beads. With this system, a large amount of beads can be captured without inducing a strong pressure drop, as it is the case with magnetic beads trapped in a standard capillary, thereby having less effect on the experimental conditions. Using numerical simulations and microscopic visualizations, the capture of beads inside a bubble cell was investigated with two magnet configurations. Pressure-driven and electro-osmotic flow velocities were measured for different amounts of protein-A-coated beads or C18-functionalized beads (RPC-18). Solid-phase extraction of a model antibody on protein-A beads and preconcentration of fluorescein on RPC-18 beads were performed as proof of concept experiments.     

Homogenization of Non-linear Scalar Conservation Laws

We study the limit as ε → 0 of the entropy solutions of the equation . We prove that the sequence u ^ε two-scale converges toward a function u(t, x, y), and u is the unique solution of a limit evolution problem. The remarkable point is that the limit problem is not a scalar conservation law, but rather a kinetic equation in which the macroscopic and microscopic variables are mixed. We also prove a strong convergence result in .     

An investigation of the stored energy and thermal stability in a Cu–Ni–Si alloy processed by high-pressure torsion

ABSTRACT

The stored energy and activation energy for recrystallization were investigated for a Cu-Ni-Si alloy after high-pressure torsion processing for N?=?½, 1, 5 and 10 turns at room temperature. The contributions of geometrically necessary dislocations (GNDs), statistically stored dislocations (SSDs) and vacancies to the stored energy were calculated through the Vickers microhardness measurements, kernel average misorientation (KAM) measurements and an analysis by differential scanning calorimetry (DSC). The results show that the total stored energy decreases rapidly after equivalent strain of ε_eq?～?9 and then saturates through ε_eq?～?86 at ～70 J/mol. Concurrently, the local stored energy in GNDs and SSDs was found to depend strongly on the radial distance from the centre of the disc and increase with increasing equivalent strain at ε_eq?～?16 and saturate with further straining. Accordingly, the results indicate that the GNDs and vacancies are responsible for the high stored energy in the initial stage of deformation at equivalent strain range of ε_eq?=?8.6–16 and thereafter their contribution decreases slightly due to the occurrence of dynamic recrystallization and the formation of fine grains. At the same time, the contribution of the SSDs is similar to that of the GNDs only in high strain deformation as at ε_eq?=?49.3 to accommodate the deformation process. An activation energy for recrystallization was estimated in the range of ～?89.7–98.7 kJ/mol, thereby suggesting poor thermal stability.     

Mathematical study of rotating fluids with resonant surface stress

We are interested here in describing the linear response of a highly rotating fluid to some surface stress tensor, which admits fast time oscillations and may be resonant with the Coriolis force. In addition to the usual Ekman layer, we exhibit another - much larger - boundary layer, and we prove that for large times, the effect of the surface stress may no longer be localized in the vicinity of the surface. From a mathematical point of view, the main novelty here is to introduce some systematic approach for the study of boundary effects.     

Anomalous diffusion of water in [BMIM][TFSI] room-temperature ionic liquid

We have studied the self-diffusion properties of butyl-methyl-imidazolium bis(trifluoromethylsulfonyl)-imide ([BMIM][TFSI]) + water system. The self-diffusion coefficients of cations, anions, and water molecules were determined by pulsed field gradient NMR. These measures were performed with increased water quantity up to saturation (from 0.3 to 30 mol %). Unexpected variations have been observed. The self-diffusion coefficient of every species increases with the quantity of water but not in the same order of magnitude. Whereas very similar evolutions are observed for the anion and cation, the increase is 25 times greater for water molecules. We interpret our data by the existence of phase separation at microscopic scale.     

Initial layer for the Homogenization of a Conservation Law with Vanishing Viscosity

We study the limit as ε → 0 of the solutions of the equation . This problem has already been addressed in a previous article in the case of well-prepared initial data, i.e. when the microscopic profile of the solution is adapted to the medium at time t = 0. Here, we prove that when the initial data is not well prepared, there is an initial layer during which the solution adapts itself to match the profile dictated by the environment. The typical size of the initial layer is of order ε. The proof relies strongly on the parabolic form of the equation; in particular, no condition of nonlinearity on A is required.     

Molecule-Based Magnets: Ferro- and Antiferromagnetic Interactions in Copper(II)-Polyorganosiloxanolate Clusters

The magnetic behavior of the clusters [(PhSiO(2))(6)Cu(6)(O(2)SiPh)(6)].6EtOH (1), Na(4)[(PhSiO(2))(12)Cu(4)].8(n)()BuOH (2), and K(4)[(C(2)H(3)SiO(2))(12)Cu(4)].6(n)()BuOH (3) has been investigated by combined magnetic susceptibility measurements and variable-temperature EPR techniques (9.25 and 245 GHz). The six copper(II) ions in the core of 1, which approaches 6/mmm symmetry, are ferromagnetically coupled as a result of the geometry at the bridging siloxanolate oxygen atoms (Cu-O-Cu = 91.5-94.6 degrees; J = -42 cm(-)(1) with H = J S(i)().S(i)()(+1), S(7) = S(1)). The ground S = 3 spin state is split in zero field mainly due to anisotropic exchange contributions (D = 0.30 cm(-)(1)). Notably, both the magnitude and the sign of the zero-field splitting parameter have been determined from HF-EPR spectra. Large antiferromagnetic Cu-Cu interactions (J approximately 200 cm(-)(1)) and an S = 0 ground state have been detected in the tetranuclear clusters 2 and 3 as a consequence of the larger Cu-O-Cu angles. The results presented in the paper are relevant to the search for new molecule-based magnetic materials.     

Magnetic bistability of isolated giant-spin centers in a diamagnetic crystalline matrix

Polynuclear single-molecule magnets (SMMs) were diluted in a diamagnetic crystal lattice to afford arrays of independent and iso-oriented magnetic units. Crystalline solid solutions of an Fe(4) SMM and its Ga(4) analogue were prepared with no metal scrambling for Fe(4) molar fractions x down to 0.01. According to high-frequency EPR and magnetic measurements, the guest SMM species have the same total spin (S=5), anisotropy, and high-temperature spin dynamics found in the pure Fe(4) phase. However, suppression of intermolecular magnetic interactions affects magnetic relaxation at low temperature (40 mK), where quantum tunneling (QT) of the magnetization dominates. When a magnetic field is applied along the easy magnetic axis, both pure and diluted (x=0.01) phases display pronounced steps at evenly spaced field values in their hysteresis loops due to resonant QT. The pure Fe(4) phase exhibits additional steps which are firmly ascribed to two-molecule QT transitions. Studies on the field-dependent relaxation rate showed that the zero-field resonance sharpens by a factor of five and shifts from about 8 mT to exactly zero field on dilution, in agreement with the calculated variation of dipolar interactions. The tunneling efficiency also changes significantly as a function of Fe(4) concentration: the zero-field resonance is significantly enhanced on dilution, while tunneling at ±0.45 T becomes less efficient. These changes were rationalized on the basis of a dipolar shuffling mechanism and transverse dipolar fields, whose effect was analyzed by using a multispin model. Our findings directly prove the impact of intermolecular magnetic couplings on SMM behavior and disclose the magnetic response of truly isolated giant spins in a diamagnetic crystalline environment.     

Distances in evidence theory: Comprehensive survey and generalizations

The purpose of the present work is to survey the dissimilarity measures defined so far in the mathematical framework of evidence theory, and to propose a classification of these measures based on their formal properties. This research is motivated by the fact that while dissimilarity measures have been widely studied and surveyed in the fields of probability theory and fuzzy set theory, no comprehensive survey is yet available for evidence theory. The main results presented herein include a synthesis of the properties of the measures defined so far in the scientific literature; the generalizations proposed naturally lead to additions to the body of the previously known measures, leading to the definition of numerous new measures. Building on this analysis, we have highlighted the fact that Dempster’s conflict cannot be considered as a genuine dissimilarity measure between two belief functions and have proposed an alternative based on a cosine function. Other original results include the justification of the use of two-dimensional indexes as (cosine; distance) couples and a general formulation for this class of new indexes. We base our exposition on a geometrical interpretation of evidence theory and show that most of the dissimilarity measures so far published are based on inner products, in some cases degenerated. Experimental results based on Monte Carlo simulations illustrate interesting relationships between existing measures.     

Homogenization of Linear Transport Equations in a Stationary Ergodic Setting

We study the homogenization of a linear kinetic equation which models the evolution of the density of charged particles submitted to a highly oscillating electric field. The electric field and the initial density are assumed to be random and stationary. We identify the asymptotic microscopic and macroscopic profiles of the density, and we derive formulas for these profiles when the space dimension is equal to one.