Existence of Weak Solutions Up to Collision for Viscous Fluid‐Solid Systems with Slip

We study in this paper the movement of a rigid solid inside an incompressible Navier‐Stokes flow within a bounded domain. We consider the case where slip is allowed at the fluid/solid interface through a Navier condition. Taking into account slip at the interface is very natural within this model, as classical no‐slip conditions lead to unrealistic collisional behavior between the solid and the domain boundary. We prove for this model existence of weak solutions of Leray type, up to collision, in three dimensions. The key point is that, due to the slip condition, the velocity field is discontinuous across the fluid/solid interface. This prevents obtaining global H¹ bounds on the velocity, which makes many aspects of the theory of weak solutions for Dirichlet conditions inappropriate. © 2014 Wiley Periodicals, Inc.     

Local Regularity for Parabolic Nonlocal Operators

Weak solutions to parabolic integro-differential operators of order α ∈ (α₀, 2) are studied. Local a priori estimates of Hölder norms and a weak Harnack inequality are proved. These results are robust with respect to α↗2. In this sense, the presentation is an extension of Moser's result from [20 Moser , J. ( 1971 ). On a pointwise estimate for parabolic differential equations . Comm. Pure Appl. Math. 24 : 727 – 740 .[Crossref], [Web of Science ®] , [Google Scholar]].     

Supersymmetry and its spontaneous breaking in the random field Ising model

We provide a resolution of one of the long-standing puzzles in the theory of disordered systems. By reformulating the functional renormalization group for the critical behavior of the random field Ising model in a superfield formalism, we are able to follow the associated supersymmetry and its spontaneous breaking along the functional renormalization group flow. Breaking is shown to occur below a critical dimension d(DR) ? 5.1 and leads to a breakdown of the "dimensional reduction" property. We compute the critical exponents as a function of dimension and give evidence that scaling is described by three independent exponents.     

The RATIO method for time‐resolved Laue crystallography

A RATIO method for analysis of intensity changes in time‐resolved pump–probe Laue diffraction experiments is described. The method eliminates the need for scaling the data with a wavelength curve representing the spectral distribution of the source and removes the effect of possible anisotropic absorption. It does not require relative scaling of series of frames and removes errors due to all but very short term fluctuations in the synchrotron beam.     

Synthesis and characterization of variable-architecture thermosensitive polymers for complexation with DNA

Copolymers of N-isopropylacrylamide with a fluorescent probe monomer were grafted to branched poly(ethyleneimine) to generate polycations that exhibited lower critical solution temperature (LCST) behavior. The structures of these polymers were confirmed by spectroscopy, and their phase transitions before and after complexation with DNA were followed using ultraviolet and fluorescence spectroscopy and light scattering. Interactions with DNA were investigated by ethidium bromide displacement assays, while temperature-induced changes in structure of both polymers and polymer-DNA complexes were evaluated by fluorescence spectroscopy, dynamic light scattering, laser Doppler anemometry, and atomic force microscopy (AFM) in water and buffer solutions. The results showed that changes in polymer architecture were mirrored by variations in the architectures of the complexes and that the overall effect of the temperature-mediated changes was dependent on the graft polymer architecture and content, as well as the solvent medium, concentrations, and stoichiometries of the complexes. Furthermore, AFM indicated subtle changes in polymer-DNA complexes at the microstructural level that could not be detected by light scattering techniques. Uniquely, variable-temperature aqueous-phase AFM was able to show that changes in the structures of these complexes were not uniform across a population of polymer-DNA condensates, with isolated complexes compacting above LCST even though the sample as a whole showed a tendency for aggregation of complexes above LCST over time. These results indicate that sample heterogeneities can be accentuated in responsive polymer--DNA complexes through LCST-mediated changes--a factor that is likely to be important in cellular uptake and nucleic acid transport.     

On the predictive capabilities of the shear modified Gurson and the modified Mohr-Coulomb fracture models over a wide range of stress triaxialities and Lode angles

The predictive capabilities of the shear-modified Gurson model [Nielsen and Tvergaard, Eng. Fract. Mech. 77, 2010] and the Modified Mohr-Coulomb (MMC) fracture model [Bai and Wierzbicki, Int. J. Fract. 161, 2010] are evaluated. Both phenomenological fracture models are physics-inspired and take the effect of the first and third stress tensor invariants into account in predicting the onset of ductile fracture. The MMC model is based on the assumption that the initiation of fracture is determined by a critical stress state, while the shear-modified Gurson model assumes void growth as the governing mechanism. Fracture experiments on TRIP-assisted steel sheets covering a wide range of stress states (from shear to equibiaxial tension) are used to calibrate and validate these models. The model accuracy is quantified based on the predictions of the displacement to fracture for experiments which have not been used for calibration. It is found that the MMC model predictions agree well with all experiments (less than 4% error), while less accurate predictions are observed for the shear-modified Gurson model. A comparison of plots of the strain to fracture as a function of the stress triaxiality and the normalized third invariant reveals significant differences between the two models except within the vicinity of stress states that have been used for calibration.     

Frequency-coded quantum key distribution

We report an intrinsically stable quantum key distribution scheme based on genuine frequency-coded quantum states. The qubits are efficiently processed without fiber interferometers by fully exploiting the nonlinear interaction occurring in electro-optic phase modulators. The system requires only integrated off-the-shelf devices and could be used with a true single-photon source. Preliminary experiments have been performed with weak laser pulses and have demonstrated the feasibility of this new setup.     

Highly enantioselective and regioselective copper-catalyzed 1,4 addition of grignard reagents to cyclic enynones

In this letter we describe an unusual result in terms of regioselectivity with respect to copper-catalyzed conjugate additions of various Grignard reagents to cyclic enynones. The use of Cu(OTf)(2) and NHC ligand L1 as the catalyst combination in CH(2)Cl(2) led to the unique formation of the 1,4 adduct. This selectivity does not follow the general trend previously observed in the literature using extended Michael acceptors. Moreover these reactions allowed for the creation of a quarternary stereogenic center with enantioselectivities up to 97% ee.     

Surface and porosity of nanocrystalline boehmite xerogels

Boehmite xerogels are prepared by hydrolysis of Al(OC4H9)3 followed by peptization with HNO3 (H+/Al = 0, 0.07, 0.2). XRD and TEM show that these gels are made of nanosized crystals (5-9 nm in width and 3 nm thick). According to the amount of acid, no significant differences are found in size and shape, but only in the spatial arrangement of the crystallites. Nitrogen adsorption-desorption isotherms of nonpeptized gels are of type IV, whereas isotherms of peptized gels are of type I. These isotherms are analyzed by the t-plot method. The majority of pore volume results from intercrystalline mesopores, but the peptized gels also contain intercrystalline micropores. The particle packing is very dense for the gel peptized with H+/Al = 0.2 (porosity = 0.26), but it is less dense in non-peptized gel (porosity = 0.44). Heating these gels under vacuum creates, from 250 degrees C onwards, an intracrystalline microporosity resulting from the conversion of boehmite into transition alumina. But heating also causes intercrystalline micropores collapsing. The specific surface area increases up to a limit temperature (300 degrees C for nonpeptized gels and 400 degrees C for peptized) beyond which sintering of the particles begins and the surface decreases. The PSD are calculated assuming a cylindrical pore geometry and using the corrected Kelvin equation proposed by Kruk et al. Peptized xerogels give a monomodal distribution with a maximum near 2 nm and no pores are larger than 6 nm. Nonpeptized gels have a bimodal distribution with a narrow peak near to 2 nm and a broad unsymmetrical peak with a maximum at 4 nm. Heating in air above 400 degrees C has a strong effect on the porosity. As the temperature increases, there is a broadening of the distribution and a marked decrease of small pores (below 3 nm). However, even after treatment at 800 degrees C, micropores are still present.