Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms

We prove that every mapping torus of any free group endomorphism is residually finite. We show how to use a not yet published result of E. Hrushovski to extend our result to arbitrary linear groups. The proof uses algebraic self-maps of affine spaces over finite fields. In particular, we prove that when such a map is dominant, the set of its fixed closed scheme points is Zariski dense in the affine space.Comment: 18 page

A PIV comparison of the flow field and wall shear stress in rigid and compliant models of healthy carotid arteries

Certain systems relevant to circulatory disease have walls which are neither rigid nor static, for example, the coronary arteries, the carotid artery and the heart chambers. In vitro modeling allows the fluid mechanics of the circulatory system to be studied without the ethical and safety issues associated with animal and human experiments. Computational methods in which the equations are coupled governing the flow and the elastic walls are maturing. Currently there is a lack of experimental data in compliant arterial systems to validate the numerical predictions. Previous experimental work has commonly used rigid wall boundaries, ignoring the effect of wall compliance. Particle Image Velocimetry is used to provide a direct comparison of both the flow field and wall shear stress (WSS) observed in experimental phantoms of rigid and compliant geometries representing an idealized common carotid artery. The input flow waveform and the mechanical response of the phantom are physiologically realistic. The results show that compliance affects the velocity profile within the artery. A rigid boundary causes severe overestimation of the peak WSS with a maximum relative difference of 61% occurring; showing compliance protects the artery from exposure to high magnitude WSS. This is important when trying to understand the development of diseases like atherosclerosis. The maximum, minimum and time averaged WSS in the rigid geometry was 2.3, 0.51 and 1.03Pa and in the compliant geometry 1.4, 0.58 and 0.84Pa, respectively

Modelling nasal high flow therapy effects on upper airway resistance and resistive work of breathing

Aim The goal of this paper is to quantify upper airway resistance with and without nasal high flow (NHF) therapy. For adults, NHF therapy feeds 30–60 L/min of warm humidified air into the nose through short cannulas which do not seal the nostril. NHF therapy has been reported to increase airway pressure, increase tidal volume (Vt) and decrease respiratory rate (RR), but it is unclear how these findings affect the work done to overcome airway resistance to air flow during expiration. Also, there is little information on how the choice of nasal cannula size may affect work of breathing. In this paper, estimates of airway resistance without and with different NHF flow (applied via different cannula sizes) were made. The breathing efforts required to overcome airway resistance under these conditions were quantified. Method NHF was applied via three different cannula sizes to a 3-D printed human upper airway. Pressure drop and flow rate were measured and used to estimate inspiratory and expiratory upper airway resistances. The resistance information was used to compute the muscular work required to overcome the resistance of the upper airway to flow. Results NHF raises expiratory resistance relative to spontaneous breathing if the breathing pattern does not change but reduces work of breathing if peak expiratory flow falls. Of the cannula sizes used, the large cannula produced the greatest resistance and the small cannula produced the least. The work required to cause tracheal flow through the upper airway was reduced if the RR and minute volume are reduced by NHF. NHF has been observed to do so in COPD patients (Bräunlich et al., 2013). A reduction in I:E ratio due to therapy was found to reduce work of breathing if the peak inspiratory flow is less than the flow below which no inspiratory effort is required to overcome upper airway resistance. Conclusion NHF raises expiratory resistance but it can reduce the work required to overcome upper airway resistance via a fall in inspiratory work of breathing, RR and minute volume

Creation of dense polymer brush layers by the controlled deposition of an amphiphilic responsive comb polymer

We introduce a copolymer with a comb topology that has been engineered to assemble in a brush configuration at an air-water interface. The molecule comprises a 6.1 kDa poly(methyl methacrylate) backbone with a statistical amount of poly[2-(dimethyl amino)ethyl methacrylate] polybase side chains averaging 2.43 per backbone.. Brush layers deposited with the hydrophobic PMMA backbone adsorbed to hydrophobized silicon are stable in water even when stored at pH values less than 2.0 for over 24 h. The use of a Langmuir trough allows a simple controlled deposition of the layers at a variety of grafting densities. Depth profiling of brush layers was performed using neutron reflectometry and reveals a significant shifting of the responsiveness of the layer upon changing the grafting density. The degree of swelling of the layers at a pH value of 4 (below the pK(b)) decreases as grafting density increases. Lowering the pH of the subphase during deposition causes the side chains to become charged and more hydrophilic extending to a brush-like configuration while at neutral pH the side chains lie in a "pancake" conformation at the interface. (C) 2009 Elsevier Ltd. All rights reserved

Fabrication of a compliant phantom of the human aortic arch for use in Particle Image Velocimetry (PIV) experimentation

Compliant phantoms of the human aortic arch can mimic patient specific cardiovascular dysfunctions in vitro. Hence, phantoms may enable elucidation of haemodynamic disturbances caused by aortic dysfunction. This paper describes the fabrication of a thin-walled silicone phantom of the human ascending aorta and brachiocephalic artery. The model geometry was determined via a meta-analysis and modelled in SolidWorks before 3D printing. The solid model surface was smoothed and scanned with a 3D scanner. An offset outer mould was milled from Ebalta S-Model board. The final phantom indicated that ABS was a suitable material for the internal model, the Ebalta S-Model board yielded a rough external surface. Co-location of the moulds during silicone pour was insufficient to enable consistent wall thickness. The resulting phantom was free of air bubbles but did not have the desired wall thickness consistency

Effect of Salt on Phosphorylcholine-based Zwitterionic Polymer Brushes.

A quantitative investigation of the responses of surface-grown biocompatible brushes of poly(2-(methacryloyloxy)ethyl phosphorylcholine) (PMPC) to different types of salt has been carried out using ellipsometry, quartz crystal microbalance (QCM) measurements, and friction force microscopy. Both cations and anions of varying valency over a wide range of concentrations were examined. Ellipsometry shows that the height of the brushes is largely independent of the ionic strength, confirming that the degree of swelling of the polymer is independent of the ionic character of the medium. In contrast, QCM measurements reveal significant changes in mass and dissipation to the PMPC brush layer, suggesting that ions bind to phosphorylcholine (PC) groups in PMPC molecules, which results in changes in the stiffness of the brush layer, and the binding affinity varies with salt type. Nanotribological measurements made using friction force microscopy show that the coefficient of friction decreases with increasing ionic strength for a variety of salts, supporting the conclusion drawn from QCM measurements. It is proposed that the binding of ions to the PMPC molecules does not change their hydration state, and hence the height of the surface-grown polymeric brushes. However, the balance of the intra- and intermolecular interactions is strongly dependent upon the ionic character of the medium between the hydrated chains, modulating the interactions between the zwitterionic PC pendant groups and, consequently, the stiffness of the PMPC molecules in the brush layer

A Novel Fabrication Method for Compliant Silicone Phantoms of Arterial Geometry for Use in Particle Image Velocimetry of Haemodynamics

Cardiovascular diseases (CVDs) are one of the leading causes of death globally. In-vitro measurement of blood flow in compliant arterial phantoms can provide better insight into haemodynamic states and therapeutic procedures. However, current fabrication techniques are not capable of producing thin-walled compliant phantoms of complex shapes. This study presents a new approach for the fabrication of compliant phantoms suitable for optical measurement. Two 1.5× scaled models of the ascending aorta, including the brachiocephalic artery (BCA), were fabricated from silicone elastomer Sylgard-184. The initial phantom used the existing state of the art lost core manufacturing technique with simple end supports, an acrylonitrile butadiene styrene (ABS) additive manufactured male mould and Ebalta-milled female mould. The second phantom was produced with the same method but used more rigid end supports and ABS male and female moulds. The wall thickness consistency and quality of resulting stereoscopic particle image velocimetry (SPIV) were used to verify the fidelity of the phantom for optical measurement and investigation of physiological flow fields. However, the initial phantom had a rough surface that obscured SPIV analysis and had a variable wall thickness (range = 0.815 mm). The second phantom provided clear particle images and had a less variable wall thickness (range = 0.317 mm). The manufacturing method developed is suitable for fast and cost-effective fabrication of different compliant arterial phantom geometries

Nanoscale Contact Mechanics between Two Grafted Polyelectrolyte Surfaces

The adhesive and frictional behavior of end-grafted poly[2-(dimethylamino)ethyl methacrylate] (PDMAEMA) films (brushes) in contact with atomic force microscope tips from which PDMAEMA or poly(methacrylic acid) (PMAA) were grafted has been shown to be a strong function of pH in aqueous solution. The interaction between the brush-coated surfaces is determined by a combination of electrostatic and noncovalent interactions, modulated by the effect of the solvation state on the brush and the resulting area of contact between the probe and the surface. For cationic PDMAEMA-PDMAEMA contacts at low pH, the brushes are highly solvated; a combination of electrostatic repulsion and a high degree of solvation (leading to a significant osmotic pressure) leads to a small area of contact, weak adhesion, and energy dissipation through plowing. As the pH increases, the electrostatic repulsion and the osmotic pressure decrease, leading to an increase in the area of contact and a concomitant increase in the strength of adhesion through hydrophobic interactions; as a consequence, the friction-load relationship becomes nonlinear as shear processes contribute to friction and the mechanics are fitted by DMT theory and, at higher pH, by the JKR model. For PDMAEMA-PMAA, the electrostatic interaction is attractive at neutral pH, leading to a large adhesion force, a large area of contact, and a nonlinear friction-load relationship. However, as the pH becomes either very small or very large, a significant charge is acquired by one of the contacting surfaces, leading to a large amount of bound solvent and a significant osmotic pressure that resists deformation. As a consequence, the area of contact is small, adhesion forces are reduced, and the friction-load relationship is linear, with energy dissipation dominated by molecular plowing

The Substrate is a pH-Controlled Second Gate of Electrolyte-Gated Organic Field-Effect Transistor

Electrolyte-gated organic field-effect transistors (EGOFETs), based on ultra-thin pentacene films on quartz, were operated with electrolyte solutions whose pH was systematically changed. Transistor parameters exhibit non-monotonic variation vs pH, which cannot be accounted for by capacitive coupling through the Debye-Helmholtz layer. The data were fitted with an analytical model of the accumulated charge in the EGOFET where Langmuir adsorption was introduced to describe the (pH-dependent) charge build-up at the quartz surface. The model provides an excellent fit to the threshold voltage and transfer characteristics as a function of pH, which demonstrates that quartz acts as a second gate controlled by pH, and is mostly effective at neutral or alkaline pH. The effective capacitance of the device is always greater than the capacitance of the electrolyte, thus highlighting the role of the substrate as an important active element for amplification of the transistor response

Adhesive and conformational behaviour of mycolic acid monolayers

We have studied the pH-dependent interaction between mycolic acid (MA) monolayers and hydrophobic and hydrophilic surfaces using molecular (colloidal probe) force spectroscopy. In both cases, hydrophobic and hydrophilic monolayers (prepared by Langmuir-Blodgett and Langmuir-Schaefer deposition on silicon or hydrophobized silicon substrates, respectively) were studied. The force spectroscopy data, fitted with classical DLVO (Derjaguin, Landau, Verwey, and Overbeek) theory to examine the contribution of electrostatic and van der Waals forces, revealed that electrostatic forces are the dominant contribution to the repulsive force between the approaching colloidal probe and MA monolayers. The good agreement between data and the DLVO model suggest that beyond a few nm away from the surface, hydrophobic, hydration, and specific chemical bonding are unlikely to contribute to any significant extent to the interaction energy between the probe and the surface. The pH-dependent conformation of MA molecules in the monolayer at the solid-liquid interface was studied by ellipsometry, neutron reflectometry, and with a quartz crystal microbalance. Monolayers prepared by the Langmuir-Blodgett method demonstrated a distinct pH-responsive behaviour, while monolayers prepared by the Langmuir-Schaefer method were less sensitive to pH variation. It was found that the attachment of water molecules plays a vital role in determining the conformation of the MA monolayers. (C) 2010 Elsevier B.V. All rights reserved