Normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems

This paper presents a unified framework for performing local analysis of grazing bifurcations in n-dimensional piecewise-smooth systems of ODEs. These occur when a periodic orbit has a point of tangency with a smooth (n−1)-dimensional boundary dividing distinct regions in phase space where the vector field is smooth. It is shown under quite general circumstances that this leads to a normal-form map that contains to lowest order either a square-root or a (3/2)-type singularity according to whether the vector field is discontinuous or not at the grazing point. In particular, contrary to what has been reported in the literature, piecewise-linear local maps do not occur generically. First, the concept of a grazing bifurcation is carefully defined using appropriate non-degeneracy conditions. Next, complete expressions are derived for calculating the leading-order term in the normal form Poincaré map at a grazing bifurcation point in arbitrary systems, using the concept of a discontinuity mapping. Finally, the theory is compared with numerical examples including bilinear oscillators, a relay feedback controller and general third-order systems.     

Zur Stickstoffbestimmung in Sprengstoffen von der Konstitution der Salpeters?ureester

Ohne Zusammenfassung     

Neuroprotection from NMDA excitotoxic lesion by Cu/Zn superoxide dismutase gene delivery to the postnatal rat brain by a modular protein vector

Background  

Superoxide mediated oxidative stress is a key neuropathologic mechanism in acute central nervous system injuries. We have analyzed the neuroprotective efficacy of the transient overexpression of antioxidant enzyme Cu/Zn Superoxide dismutase (SOD) after excitotoxic injury to the immature rat brain by using a recently constructed modular protein vector for non-viral gene delivery termed NLSCt. For this purpose, animals were injected with the NLSCt vector carrying the Cu/Zn SOD or the control GFP transgenes 2 hours after intracortical N-methyl-D-aspartate (NMDA) administration, and daily functional evaluation was performed. Moreover, 3 days after, lesion volume, neuronal degeneration and nitrotyrosine immunoreactivity were evaluated.     

Complex aggregation patterns in drying nanocolloidal suspensions: size matters when it comes to the thermomechanical stability of nanoparticle-based structures

We report the results of a model study on the interrelation among the occurrence of complex aggregation patterns in drying nanofluids, the size of the constitutive nanoparticles (NPs), and the drying temperature, which is a critical issue in the genesis of complex drying patterns that was never systematically reported before. We show that one can achieve fine control over the occurrence and topological features of these drying-mediated complex structures through the combination of the particle size, the drying temperature, and the substrate surface energy. Most importantly, we show that a transition in the occurrence of the patterns appears with the temperature and the particle size, which accounts for the size dependence of the thermomechanical stability of the aggregates in the nanoscale range. Using simple phenomenological and scaling considerations, we showed that the thermomechanical stability of the aggregates was underpinned by physical quantities that scale with the size of the NPs (R) either as R(-2) or R(-3). These insights into the size-dependent dissipation mechanisms in nanoclusters should help in designing NPs-based structures with tailored thermomechanical and environmental stability and hence with an optimized morphological stability that guarantees their long-term functional properties.     

Liquid-crystal phase equilibria of Lennard-Jones chains

Liquid-crystal phase equilibria of Lennard-Jones chain fluids and the solubility of a Lennard-Jones gas in the coexisting phases are calculated from Monte Carlo simulations. Direct phase equilibria calculations are performed using an expanded formulation of the Gibbs ensemble. Monomer densities, order parameters, and equilibrium pressures are reported for the coexisting isotropic and nematic phases of: (1) linear Lennard-Jones chains, (2) a partially-flexible Lennard-Jones chain, and (3) a binary mixture of linear Lennard-Jones chains. The effect of chain length is determined by calculating the isotropic-nematic coexistence of linear Lennard-Jones chain fluids made of 8, 10, and 12 segments (8-, 10-, 12-mer). The effect of molecular flexibility on the isotropic-nematic equilibrium is studied for a Lennard-Jones 10-mer chain fluid with one freely-jointed segment at the end of the chain. An isotropic-nematic phase split and fractionation are reported for a binary mixture of linear 7-mer and 12-mer chains. Simulation results are compared with theoretical results as obtained from a recently developed analytical equation of state based on perturbation theory. Excellent agreement between theory and simulations is observed. The solubility of a monomer Lennard-Jones gas in the coexisting isotropic and nematic phases is estimated using the Widom test-particle insertion method. A linear relationship between solubility difference and density difference at isotropic-nematic coexistence is observed. It is shown that gas solubility is independent of the nematic ordering of the fluid, at constant temperature and density conditions.     

Exploring lead exposure in ancient Chilean mummies using a single strand of hair by laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS)

Lead exposure has received increased attention over the past few decades since it has been shown to have adverse effects on physical and intellectual development in humans. The use of biological tissues such as blood, teeth, hair, and bone for assessment of lead exposure has been previously demonstrated. While analysis of blood for trace metals provides information concerning recent exposure, hair offers insight into a period of several months, and is preferable since it is non-invasively collected and easily stored. The present study analyzed total of 49 ancient hair samples for lead (Pb_H) using LA-ICP-MS. Samples belonged to an ancient fisher hunter–gatherer culture called the “Chinchorro,” and who occupied regions of the Atacama Desert on the northern coast of Chile from approximately 5000–1500 B.C. and practiced the first-known form of artificial mummification. Several samples from a post-Chinchorro agricultural community (n = 12) ca. 1000–1400 A.D. were also analyzed. A suite of hair standards was developed using contemporary hair from the same region and was subsequently used to make linear calibration functions for lead determination in single strands of hair using LA-ICP-MS. Three linear scans ranged from 500 to 1000 μm were performed for each sample and signal intensities were normalized over ¹³C. The distribution of lead in the central medulla in a 100 μm cross-section scan of hair strand demonstrated minimal exogenous contamination. Hair lead (Pb_H) concentrations ranged between 2.2 μg/g and 12.8 μg/g could be accurately quantified with these standards. Twenty one out of 49 samples (43%) showed Pb_H concentrations higher than the average value of 5 μg/g for unexposed individuals (range 1.1–228.0 μg/g). Median hair lead concentrations by burial sites and are shown in order of decreasing concentration: Morro (13.8 μg/g) > Iquique (6.6 μg/g) > Azapa (4.5 μg/g) > Yungay (4.1 μg/g) > Camarones (2.7 μg/g). Most of the burial sites showed Pb_H concentrations greater than the normal value for unexposed individuals and outliers heavily influenced average concentrations. The results suggest that the Chinchorro and later agro-pastoral populations were not widely exposed to naturally elevated lead.     

A Hot‐Segment‐Based Approach for the Design of Cross‐Amyloid Interaction Surface Mimics as Inhibitors of Amyloid Self‐Assembly

The design of inhibitors of protein–protein interactions mediating amyloid self‐assembly is a major challenge mainly due to the dynamic nature of the involved structures and interfaces. Interactions of amyloidogenic polypeptides with other proteins are important modulators of self‐assembly. Here we present a hot‐segment‐linking approach to design a series of mimics of the IAPP cross‐amyloid interaction surface with Aβ (ISMs) as nanomolar inhibitors of amyloidogenesis and cytotoxicity of Aβ, IAPP, or both polypeptides. The nature of the linker determines ISM structure and inhibitory function including both potency and target selectivity. Importantly, ISMs effectively suppress both self‐ and cross‐seeded IAPP self‐assembly. Our results provide a novel class of highly potent peptide leads for targeting protein aggregation in Alzheimer’s disease, type 2 diabetes, or both diseases and a chemical approach to inhibit amyloid self‐assembly and pathogenic interactions of other proteins as well.