A theorem on planar continua and an application to automorphisms of the field of complex numbers

Let K be a continuum in the plane which does not lie on a line. Then the set of differences, K - K, contains an open set. Let ψ be an automorphism of the field of complex numbers which is bounded on an F_σ set of positive inductive dimension. Then ψ is continuous.     

Cooperative engineering as a specific design-based research

In this paper, we first describe what are the main constituents of what we term cooperative engineering, between teachers and researchers, from an epistemological and theoretical viewpoint. We show that this kind of research tries to dilute the ancient dualisms of Western Thought, and we present some features that may contribute to specifying cooperative engineering within the general paradigm of design-based research. In the second part of the paper, we give an empirical account of such a process of engineering at primary school level in mathematics, by focusing on the co-elaboration, between teachers and researchers, of learning sequences at kindergarten (the Treasures Games, situations of graphical representations) and at grade 1 (The Arithmetic and Comprehension at Elementary School program, building of basic numerical capacities). At the end of the paper, we briefly elaborate on what we consider to be major issues relating to cooperative engineering.     

Gas sensing mechanism in chemiresistive cobalt and metal-free phthalocyanine thin films

The gas sensing behaviors of cobalt phthalocyanine (CoPc) and metal-free phthalocyanine (H2Pc) thin films were investigated with respect to analyte basicity. Chemiresistive sensors were fabricated by deposition of 50 nm thick films on interdigitated gold electrodes via organic molecular beam epitaxy (OMBE). Time-dependent current responses of the films were measured at constant voltage during exposure to analyte vapor doses. The analytes spanned a range of electron donor and hydrogen-bonding strengths. It was found that, when the analyte exceeded a critical base strength, the device responses for CoPc correlated with Lewis basicity, and device responses for H2Pc correlated with hydrogen-bond basicity. This suggests that the analyte-phthalocyanine interaction is dominated by binding to the central cavity of the phthalocyanine with analyte coordination strength governing CoPc sensor responses and analyte hydrogen-bonding ability governing H2Pc sensor responses. The interactions between the phthalocyanine films and analytes were found to follow first-order kinetics. The influence of O2 on the film response was found to significantly affect sensor response and recovery. The increase of resistance generally observed for analyte binding can be attributed to hole destruction in the semiconductor film by oxygen displacement, as well as hole trapping by electron donor ligands.     

A finite element implementation of the stress gradient theory

In this contribution, a finite element implementation of the stress gradient theory is proposed. The implementation relies on a reformulation of the governing set of partial differential equations in terms of one primary tensor-valued field variable of third order, the so-called generalised displacement field. Whereas the volumetric part of the generalised displacement field is closely related to the classic displacement field, the deviatoric part can be interpreted in terms of micro-displacements. The associated weak formulation moreover stipulates boundary conditions in terms of the normal projection of the generalised displacement field or of the (complete) stress tensor. A detailed study of representative boundary value problems of stress gradient elasticity shows the applicability of the proposed formulation. In particular, the finite element implementation is validated based on the analytical solutions for a cylindrical bar under tension and torsion derived by means of Bessel functions. In both tension and torsion cases, a smaller is softer size effect is evidenced in striking contrast to the corresponding strain gradient elasticity solutions.

     

Microfluidic system for simultaneous optical measurement of platelet aggregation at multiple shear rates in whole blood

Thrombosis is the pathological formation of platelet aggregates which occlude blood flow causing stroke and heart attack-the leading causes of death in developed nations. Instrumentation for diagnosing and exploring treatments for pathological platelet aggregation thus has the potential for major clinical impact. Most current thrombosis methods focus on single flow conditions, non-occlusive platelet adhesion, or low shear rates and so are limited in their application to comparative studies involving multiple, pathological test conditions (e.g., shear rate, stenotic geometries that mimic arteries, and rapid platelet accumulation to occlusion). The field could benefit from a low volume, high throughput, short analysis time, and low cost system while minimizing sample handling. We report on the design, fabrication, testing, and application of a microfluidic device and associated optical system for simultaneous measurement of platelet aggregation at multiple initial shear rates within four stenotic channels in label-free whole blood. Following computational design, requisite shear rates were achieved in the device by micro- surface milling a mold and subsequent PDMS casting. We applied the microfluidic system to measure platelet aggregation in whole porcine blood for shear rates spanning physiological to pathological flow conditions (500-13000 s(-1)). Real-time, non-contact, label-free, microscope-free measurements of platelet aggregation were acquired using an optical system comprising a 650 nm diode laser and a linear CCD. We observed fully occlusive platelet aggregation in less than 20 min above a threshold initial shear rate of 4000 s(-1), and no occlusive platelet aggregation below 1500 s(-1) (N = 86 trials). Accumulation of thrombus was consistent between laser intensity, light microscopy, histology, and mass flow rate measurements. The amount of blood volumes producing occlusion were dependent on shear rate. Times to occlusion were not found to be dependent on shear rate above the threshold level of 4000 s(-1). This microfluidic system enables measurement of the entire process of occlusive platelet thrombosis in whole, unlabeled blood, in vitro, at multiple shear rates. Such a system may be useful as a point-of-care diagnostic tool for studying anti-platelet therapies in individual blood samples from high-risk patients.     

Stirring unmagnetized plasma

A new concept for spinning unmagnetized plasma is demonstrated experimentally. Plasma is confined by an axisymmetric multicusp magnetic field and biased cathodes are used to drive currents and impart a torque in the magnetized edge. Measurements show that flow viscously couples momentum from the magnetized edge (where the plasma viscosity is small) into the unmagnetized core (where the viscosity is large) and that the core rotates as a solid body. To be effective, collisional viscosity must overcome the ion-neutral drag due to charge-exchange collisions.