Persistence Properties of Normally Hyperbolic Tori

Near-resonances between frequencies notoriously lead to small denominators when trying to prove persistence of invariant tori carrying quasi-periodic motion. In dissipative systems external parameters detuning the frequencies are needed so that Diophantine conditions can be formulated, which allow to solve the homological equation that yields a conjugacy between perturbed and unperturbed quasi-periodic tori. The parameter values for which the Diophantine conditions are not fulfilled form so-called resonance gaps. Normal hyperbolicity can guarantee invariance of the perturbed tori, if not their quasi-periodicity, for larger parameter ranges. For a 1-dimensional parameter space this allows to close almost all resonance gaps.     

Suppression of thermally excited capillary waves by shear flow

We investigate the thermal fluctuations of the colloidal gas-liquid interface subjected to a shear flow parallel to the interface. Strikingly, we find that the shear strongly suppresses capillary waves, making the interface smoother. This phenomenon can be described by introducing an effective interfacial tension that increases with the shear rate. The increase of sigma(eff) is a direct consequence of the loss of interfacial entropy caused by the flow, which affects especially the slow fluctuations. This demonstrates that the interfacial tension of fluids results from an intrinsic as well as a fluctuation contribution.     

Nonsmooth bifurcations of equilibria in planar continuous systems

In this paper we present a procedure to find all limit sets near bifurcating equilibria in a class of hybrid systems described by continuous, piecewise smooth differential equations. For this purpose, the dynamics near the bifurcating equilibrium is locally approximated as a piecewise affine systems defined on a conic partition of the plane. To guarantee that all limit sets are identified, conditions for the existence or absence of limit cycles are presented. Combining these results with the study of return maps, a procedure is presented for a local bifurcation analysis of bifurcating equilibria in continuous, piecewise smooth systems. With this procedure, all limit sets that are created or destroyed by the bifurcation are identified in a computationally feasible manner.     

The height of minimal Hilbert bases

For an integral polyhedral cone C = pos{a¹,…,a^m, a ⁱ ∈ ?^d, a subset $\cal B$ (C) ? C ∩ ?^d is called a minimal Hilbert basis of C iff (i) each element of C∩?^d can be written as a non-negative integral combination of elements of $\cal B$ (C) and (ii) $\cal B$ (C) has minimal cardinality with respect to all subsets of C ∩ ?^d for which (i) holds. We give a tight bound for the so-called height of an element of the basis which improves on former results.     

Formation of nematic liquid crystals of sterically stabilized layered double hydroxide platelets

Colloidal platelets of hydrotalcite, a layered double hydroxide, have been prepared by coprecipitation at pH 11-12 of magnesium nitrate and aluminum nitrate at two different magnesium to aluminum ratios. Changing the temperature and ionic strength during hydrothermal treatment, the platelets were tailored to different sizes and aspect ratios. Amino-modified polyisobutylene molecules were grafted onto the platelets following a convenient new route involving freeze-drying. Organic dispersions in toluene were prepared of the particles with the largest size and highest aspect ratio. The colloidal dispersions prepared in this way showed isotropic-nematic phase transitions above a limiting concentration in a matter of days. The number density at the transition and the width of the biphasic region were determined and compared to theory. The orientation of the platelets in nematic droplets (tactoids) and at the isotropic-nematic interface were analyzed by polarization microscopy. It was observed that sedimentation induces a nematic layer in samples that are below the limiting concentration for isotropic-nematic phase separation. No nematic phase was observed in the initial aqueous suspensions of the ungrafted particles.     

Screening of protein-ligand interactions using dynamic protein-affinity chromatography solid-phase extraction-liquid chromatography-mass spectrometry

A novel methodology is shown enabling the screening of mixtures of compounds for their affinity to a receptor protein. The system presented, dynamic protein-affinity chromatography solid-phase extraction (DPAC-SPE), overcomes the limitations of the existing methods by performing an incubation of the His-tagged protein with a mixture of possible ligands, which are still in their native conditions. This is followed by a fully automated affinity trapping step, coupled on-line to an LC-MS system in order to detect and identify the bound ligands. The system has been optimized using a commercially available on-line SPE system, using the estrogen receptor alpha (ERalpha) as model protein. A representative range of ligands with sub-nanomolar to millimolar affinities has been identified successfully from a mixture. The weakest binder that can be identified is norethindrone (approximately K(d)=0.1-1mM). The same setup also provides the possibilities to measure EC50 curves of both weak and strong binders.     

Liquid and gas chromatography coupled to isotope ratio mass spectrometry for the determination of 13C-valine isotopic ratios in complex biological samples

On-line gas chromatography-combustion-isotope ratio mass spectrometry (GC-C-IRMS) is commonly used to measure isotopic ratios at natural abundance as well as for tracer studies in nutritional and medical research. However, high-precision (13)C isotopic enrichment can also be measured by liquid chromatography-isotope ratio mass spectrometry (LC-IRMS). Indeed, LC-IRMS can be used, as shown by the new method reported here, to obtain a baseline separation and to measure (13)C isotopic enrichment of underivatised amino acids (Asp, Thr-Ser, Glu, Pro, Gly, Ala, Cys and Val). In case of Val, at natural abundance, the SD(delta(13)C) reported with this method was found to be below 1 per thousand . Another key feature of the new LC-IRMS method reported in this paper is the comparison of the LC-IRMS approach with the conventional GC-C-IRMS determination. To perform this comparative study, isotopic enrichments were measured from underivatised Val and its N(O, S)-ethoxycarbonyl ethyl ester derivative. Between 0.0 and 1.0 molar percent excess (MPE) (delta(13)C= -12.3 to 150.8 per thousand), the calculated root-mean-square (rms) of SD was 0.38 and 0.46 per thousand and the calculated rms of accuracy was 0.023 and 0.005 MPE, respectively, for GC-C-IRMS and LC-IRMS. Both systems measured accurately low isotopic enrichments (0.002 atom percent excess (APE)) with an SD (APE) of 0.0004. To correlate the relative (delta(13)C) and absolute (atom%, APE and MPE) isotopic enrichment of Val measured by the GC-C-IRMS and LC-IRMS devices, mathematical equations showing the slope and intercept of the curves were established and validated with experimental data between 0.0 to 2.3 MPE. Finally, both GC-C-IRMS and LC-IRMS instruments were also used to assess isotopic enrichment of protein-bound (13)C-Val in tibial epiphysis in a tracer study performed in rats. Isotopic enrichments measured by LC-IRMS and GC-C-IRMS were not statistically different (p>0.05). The results of this work indicate that the LC-IRMS was successful for high-precision (13)C isotopic measurements in tracer studies giving (13)C isotopic enrichment similar to the GC-C-IRMS but without the step of GC derivatisation. Therefore, for clinical studies requiring high-precision isotopic measurement, the LC-IRMS is the method of choice to measure the isotopic ratio.     

A supramolecularly-caged ionic iridium(III) complex yielding bright and very stable solid-state light-emitting electrochemical cells

A new iridium(III) complex showing intramolecular interligand pi-stacking has been synthesized and used to improve the stability of single-component, solid-state light-emitting electrochemical cell (LEC) devices. The pi-stacking results in the formation of a very stable supramolecularly caged complex. LECs using this complex show extraordinary stabilities (estimated lifetime of 600 h) and luminance values (average luminance of 230 cd m-2) indicating the path toward stable ionic complexes for use in LECs reaching stabilities required for practical applications.