On the use of blow up to study regularizations of singularities of piecewise smooth dynamical systems in R3\mathbb{R}^3

In this paper we use the blow up method of Dumortier and Roussarie \cite{dumortier_1991,dumortier_1993,dumortier_1996}, in the formulation due to Krupa and Szmolyan \cite{krupa_extending_2001}, to study the regularization of singularities of piecewise smooth dynamical systems \cite{filippov1988differential} in $\mathbb R^3$. Using the regularization method of Sotomayor and Teixeira \cite{Sotomayor96}, first we demonstrate the power of our approach by considering the case of a fold line. We quickly recover a main result of Bonet and Seara \cite{reves_regularization_2014} in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided a certain non-resonance condition holds. Finally, we provide numerical evidence for the existence of secondary canards near resonance.Comment: To appear in SIAM Journal of Applied Dynamical System

Brain-specific tropomyosins TMBr-1 and TMBr-3 have distinct patterns of expression during development and in adult brain

In this study we report on the developmental and regional expression of two brain-specific isoforms of tropomyosin, TMBr-1 and TMBr-3, that are generated from the rat alpha-tropomyosin gene via the use of alternative promoters and alternative RNA splicing. Western blot analysis using an exon-specific peptide polyclonal antibody revealed that the two isoforms are differentially expressed in development with TMBr-3 appearing in the embryonic brain at 16 days of gestation, followed by the expression of TMBr-1 at 20 days after birth. TMBr-3 was detected in all brain regions examined, whereas TMBr-1 was detected predominantly in brain areas that derived from the prosencephalon. Immunocytochemical studies on mixed primary cultures made from rat embryonic midbrain indicate that expression of the brain-specific epitope is restricted to neurons. The developmental pattern and neuronal localization of these forms of tropomyosin suggest that these isoforms have a specialized role in the development and plasticity of the nervous system

Set-up of the cryogenic phase equilibria test stand CryoPHAEQTS

The design of processes using cryogenic fluid mixtures requires fluid property data, which is unavailable today. In particular, this data is crucial to develop cryogenic mixed-refrigerant cycles for high-temperature superconductor (HTS) applications and to further optimize hydrogen liquefaction processes. CryoPHAEQTS, which is currently being built at KIT, will provide physical property data for fluid mixtures in a temperature range of 15–300K and at pressures up to 15 MPa, including also mixtures with either flammable or oxidizing components (e.g. hydrogen, deuterium, oxygen). By direct sampling from an equilibrium cell, vapor-liquid equilibria (VLE) and vapor-liquid-liquid equilibria (VLLE) can be determined using gas chromatography. Solid-liquid equilibria (SLE) are measured using a calorimetric method. The measurement of heat capacities is implemented by combining two different flow measurement principles. In addition, the test stand offers optical access for a future upgrade with an optical measurement system that allows in-equilibrium measurements of both bulk transport properties by dynamic light scattering (DLS) and surface tension by surface light scattering (SLS)

Imperfect Homoclinic Bifurcations

Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an explicit mathematical model of the system.Comment: 8 pages, 11 figures, submitted to PR

Harvest Method, Cultivar, and Time of Swathing Effects on Yield and Oil Content of Winter Canola

Producers want to achieve the highest yield and oil content possible using either swathing or direct cutting to harvest winter canola. Multi-year experiments were conducted to evaluate the effects of harvest method (swathing versus direct cutting) and cultivar on seed moisture, yield, and oil content; and to evaluate the effects of swathing timing on yield and oil content. The harvest method experiments were conducted for two seasons at the Redd Foundation Field near Partridge, KS. The time of swathing experiments were conducted for two seasons near Manhattan, KS. In 2016 and 2017, harvest method had a significant effect on seed moisture, yield, and oil content. Swathing produced seed with lower moisture content and greater yield, but direct cutting produced seed with the highest oil content. Cultivars differed in their response to yield depending on the harvest method used. Some cultivars responded positively to swathing, others responded positively to direct cutting, and some showed no response to harvest method. Time of swathing had a significant effect on yield and oil content. As a rule, as seed color change progressed, yield and oil content increased. All swathing treatments had greater yield than direct cutting except when swathing was done at green seed. Seed from direct cutting had significantly greater oil content than seed from all swathing treatments. Both swathing and direct cutting can be used effec­tively to harvest winter canola

Insights on Water Interaction at the Interface of Nitrogen Functionalized Hydrothermal Carbons

Hydrothermal carbon (HTC) derived from biomass is a class of cost-efficient, eco-friendly functional carbon materials with various potential applications. In this work, solid-state nuclear magnetic resonance (NMR), longitudinal (T1) relaxation time and diffusion NMR were employed to investigate the structure and water dynamics for HTC and nitrogen-functionalized hydrothermal carbon (N-HTC) samples ((N)-HTC). Results showed that the presence of N-functional groups influences the water interaction with (N)-HTC more strongly than surface area, pore size distribution or oxygenated functional groups. Furthermore, the degree of water interaction can be tuned by adjusting the synthesis temperature and the precursor ratio. Water motion was more strongly inhibited in N-HTC than in N-free HTC, thereby suggesting the existence of a differently structured hydration shell around N-HTC particles. In addition, the diffusion data of water in the N-HTC material shows two components that do not exchange on the time scale of the experiment (tens of milliseconds), indicating a significant fraction of slow mobile water that exists inside the structure of N-HTC. 1H–2H isotope exchange and cross-polarization NMR results show this internal water only in a near-surface layer of the N-HTC particles. Based on these findings, a model for water interaction with (N)-HTC particles is proposed

Fabrication of Highly Ordered Polymeric Nanodot and Nanowire Arrays Templated by Supramolecular Assembly Block Copolymer Nanoporous Thin Films

Realizing the vast technological potential of patternable block copolymers requires both the precise controlling of the orientation and long-range ordering, which is still a challenging topic so far. Recently, we have demonstrated that ordered nanoporous thin film can be fabricated from a simple supramolecular assembly approach. Here we will extend this approach and provide a general route to fabricate large areas of highly ordered polymeric nanodot and nanowire arrays. We revealed that under a mixture solvent annealing atmosphere, a near-defect-free nanoporous thin film over large areas can be achieved. Under the direction of interpolymer hydrogen bonding and capillary action of nanopores, this ordered porous nanotemplate can be properly filled with phenolic resin precursor, followed by curation and pyrolysis at middle temperature to remove the nanotemplate, a perfect ordered polymer nanodot arrays replication was obtained. The orientation of the supramolecular assembly thin films can be readily re-aligned parallel to the substrate upon exposure to chloroform vapor, so this facile nanotemplate replica method can be further extend to generate large areas of polymeric nanowire arrays. Thus, we achieved a successful sub-30 nm patterns nanotemplates transfer methodology for fabricating polymeric nanopattern arrays with highly ordered structure and tunable morphologies