Conceptual thinking and metrology concepts

In introducing the term ‘concept’, the authors of the 2008 International vocabulary of metrology ‘Basic and general concepts and associated terms’ (VIM, 2008) recognize that in order to operationalize a globally accepted set of metrology terms, one requires to deal with a higher level of abstraction. Concepts are obviously not specific to metrology–handling complex tasks in any domain of knowledge that requires conceptual thinking abilities. In this short white paper, we discuss how to assess and develop conceptual thinking of professionals in service, business, and industrial environments. The approach builds on a proven methodology called MERLO that has been developed in the last 15 years by experts in psychology and education with adaptation to new interactive technologies such as clickers and internet-based formative assessments. MERLO pedagogy can be used to assess individuals’ inherent conceptual thinking abilities and train them to enhance their competence in analyzing complex conceptual situations. This is pertinent to the education of metrology, quality, and statistical thinking. We suggest that MERLO can be considered as a complementary enabler to VIM, so that this fundamental work can enhance its impact and applicability.     

A metering rotary nanopump for microfluidic systems

We describe the design, fabrication, and testing of a microfabricated metering rotary nanopump for the purpose of driving fluid flow in microfluidic devices. The miniature peristaltic pump is composed of a set of microfluidic channels wrapped in a helix around a central camshaft in which a non-cylindrical cam rotates. The cam compresses the helical channels to induce peristaltic flow as it is rotated. The polydimethylsiloxane (PDMS) nanopump design is able to produce intermittent delivery or removal of several nanolitres of fluid per revolution as well as consistent continuous flow rates ranging from as low as 15 nL min(-1) to above 1.0 μL min(-1). At back pressures encountered in typical microfluidic devices, the pump acts as a high impedance flow source. The durability, biocompatibility, ease of integration with soft-lithographic fabrication, the use of a simple rotary motor instead of multiple synchronized pneumatic or mechanical actuators, and the absence of power consumption or fluidic conductance in the resting state all contribute to a compact pump with a low cost of fabrication and versatile implementation. This suggests that the pump design may be useful for a wide variety of biological experiments and point of care devices.     

Computation of determinant expansion coefficients within the graphically contracted function method

Most electronic structure methods express the wavefunction as an expansion of N‐electron basis functions that are chosen to be either Slater determinants or configuration state functions. Although the expansion coefficient of a single determinant may be readily computed from configuration state function coefficients for small wavefunction expansions, traditional algorithms are impractical for systems with a large number of electrons and spatial orbitals. In this work, we describe an efficient algorithm for the evaluation of a single determinant expansion coefficient for wavefunctions expanded as a linear combination of graphically contracted functions. Each graphically contracted function has significant multiconfigurational character and depends on a relatively small number of variational parameters called arc factors. Because the graphically contracted function approach expresses the configuration state function coefficients as products of arc factors, a determinant expansion coefficient may be computed recursively more efficiently than with traditional configuration interaction methods. Although the cost of computing determinant coefficients scales exponentially with the number of spatial orbitals for traditional methods, the algorithm presented here exploits two levels of recursion and scales polynomially with system size. Hence, as demonstrated through applications to systems with hundreds of electrons and orbitals, it may readily be applied to very large systems. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Rapid estimation of trace organophosphonate used as a scale inhibitor in aqueous systems by reactive pyrolysis-gas chromatography/mass spectrometry

The determination of trace organophosphonates which are used in cooling towers as a scale inhibitor usually involves extraction and/or concentration of the target components prior to analysis. The extracts are analyzed using chromatographic or spectroscopic methods. This methodology is not only cumbersome but also results in poor data quality. This work presents a novel approach for the rapid and sensitive determination of trace amounts of an organophosphonate: 1-hydroxyethylidene-1,1-diphosphonic acid (HEDP) in aqueous solution. This method is based upon reactive pyrolysis-GC/MS in the presence of tetramethyl ammonium hydroxide (TMAH). Approximately 10 μL of the aqueous sample containing a trace amount of HEDP and 1 μL of 25% a methanol TMAH solution was placed in the sample cup. The cup was then dropped into the furnace which was at 350 °C. The heat initiated the hydrolysis of the organophosphonate followed by the methylation of the hydrolysates. Trimethylphosphate (TMP) was detected by GC/MS. The level of TMP is related to the level of the phosphonate, HEDP in the aqueous sample. Using an external standard calibration curve, it was possible to make a rapid estimation of mg/L levels of organophosphate.     

The modularity of K3 surfaces with non-symplectic group actions

We consider complex K3 surfaces with a non-symplectic group acting trivially on the algebraic cycles. Vorontsov and Kondō classified those K3 surfaces with transcendental lattice of minimal rank. The purpose of this note is to study the Galois representations associated to these K3 surfaces. The rank of the transcendental lattices is even and varies from 2 to 20, excluding 8 and 14. We show that these K3 surfaces are dominated by Fermat surfaces, and hence they are all of CM type. We will establish the modularity of the Galois representations associated to them. Also we discuss mirror symmetry for these K3 surfaces in the sense of Dolgachev, and show that a mirror K3 surface exists with one exception.     

Possible Worlds of Doubt

A prominent contemporary anti-skeptical strategy, most famously articulated by Keith DeRose, aims to cage the skeptic′s doubts by contextualizing subjunctive conditional accounts of knowledge through a conversational rule of sensitivity. This strategy, I argue, courts charges of circularity by selectively invoking heavy counterfactual machinery. The reason: such invocation threatens to utilize a metric for modal comparison that is implicitly informed by judgments of epistemic sameness. This gives us reason to fear that said modal metric is selectively cherry-picked in advance to support the very anti-skeptical conclusion for which the contextualist longs.     

A Gelfand model for wreath products

A Gelafand model for wreath products ℤ _r ≀ S _n is constructed. The proof relies on a combinatorial interpretation of the characters of the model, extending a classical result of Frobenius and Schur.     

Phase Transitions in Gravitational Allocation

Given a Poisson point process of unit masses (“stars”) in dimension d ≥ 3, Newtonian gravity partitions space into domains of attraction (cells) of equal volume. In earlier work, we showed the diameters of these cells have exponential tails. Here we analyze the quantitative geometry of the cells and show that their large deviations occur at the stretched-exponential scale. More precisely, the probability that mass exp(−R ^γ ) in a cell travels distance R decays like exp(-R^f_d(g)){\left(-R^{f_d(\gamma)}\right)} where we identify the functions f _d (·) exactly. These functions are piecewise smooth and the discontinuities of f^￠_d{f^{\prime}_d} represent phase transitions. In dimension d = 3, the large deviation is due to a “distant attracting galaxy” but a phase transition occurs when f ₃(γ) = 1 (at that point, the fluctuations due to individual stars dominate). When d ≥ 5, the large deviation is due to a thin tube (a “wormhole”) along which the star density increases monotonically, until the point f _d (γ) = 1 (where again fluctuations due to individual stars dominate). In dimension 4 we find a double phase transition, where the transition between low-dimensional behavior (attracting galaxy) and highdimensional behavior (wormhole) occurs at γ = 4/3.     

Geometrical dependence of optical negative index meta-materials at 1.55 μm

We have studied the geometry dependency of fishnet-like negative refractive index meta-materials (NIMs), and developed a process to fabricate such NIMs using nanoimprint lithography (NIL) in a controlled way for it to achieve negative refractive index in the desired frequency range. As an example, we fabricated a fishnet structure with a minimum negative refractive index of −1.7 at 1560 nm, which was only 10 nm off the targeted wavelength of 1550 nm.