On Solutions of Linear Ordinary Difference Equations in their Coefficient Field

We extend the notion of monomial extensions of differential fields, i.e. simple transcendental extensions in which the polynomials are closed under differentiation, to difference fields. The structure of such extensions provides an algebraic framework for solving generalized linear difference equations with coefficients in such fields. We then describe algorithms for finding the denominator of any solution of those equations in an important subclass of monomial extensions that includes transcendental indefinite sums and products. This reduces the general problem of finding the solutions of such equations in their coefficient fields to bounding their degrees. In the base case, this yields in particular a new algorithm for computing the rational solutions of q -difference equations with polynomial coefficients.     

Effective visualization of short routes

In this work we develop a new alternative to conventional maps for visualization of relatively short paths as they are frequently encountered in hotels, resorts or museums. Our approach is based on a warped rendering of a 3D model of the environment such that the visualized path appears to be straight even though it may contain several junctions. This has the advantage that the beholder of the image gains a realistic impression of the surroundings along the way which makes it easy to retrace the route in practice. We give an intuitive method for generation of such images and present results from user studies undertaken to evaluate the benefit of the warped images for orientation in unknown environments.     

Simulations of extensional flow in microrheometric devices

We present a detailed numerical study of the flow of a Newtonian fluid through microrheometric devices featuring a sudden contraction–expansion. This flow configuration is typically used to generate extensional deformations and high strain rates. The excess pressure drop resulting from the converging and diverging flow is an important dynamic measure to quantify if the device is intended to be used as a microfluidic extensional rheometer. To explore this idea, we examine the effect of the contraction length, aspect ratio and Reynolds number on the flow kinematics and resulting pressure field. Analysis of the computed velocity and pressure fields show that, for typical experimental conditions used in microfluidic devices, the steady flow is highly three-dimensional with open spiraling vortical structures in the stagnant corner regions. The numerical simulations of the local kinematics and global pressure drop are in good agreement with experimental results. The device aspect ratio is shown to have a strong impact on the flow and consequently on the excess pressure drop, which is quantified in terms of the dimensionless Couette and Bagley correction factors. We suggest an approach for calculating the Bagley correction which may be especially appropriate for planar microchannels. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Electrospinning hollow and core/sheath nanofibers using hydrodynamic fluid focusing

Hollow poly (vinylpyrrolidone) (PVP) + TiO₂ and polypyrrole (core)/PVP (sheath) nanofibers were successfully electrospun using hydrodynamic fluid focusing. Utilizing a two-dimensional fluid focusing technique previously applied to aqueous solutions, intersecting microchannels cast in (poly)dimethylsiloxane were utilized to dynamically center core fluids in immiscible sheath fluids prior to electrospinning at the channel outlet. Advantages of using microfluidic channel networks for the electrospinning of composite nanofibers include spatiotemporal control over input reagents, ease of fabrication and the ability to focus the core stream into sheath layer without the need of complex co-annular nozzles.     

Induction charge detector with multiple sensing stages

An induction charge detector yields the net charge and the time of flight of a particle. The unique ability to independently measure these two parameters sets apart this rather simple detection technique. The main shortcoming of this instrument is its high charge detection limit, resulting from the intrinsic noise of the detector electronics and the low signal associated with the charge to measure. The goal of the present work is to lower the detection limit of this detector. This article describes an induction charge detector whose main novelty is a sequence of aligned cylindrical electrodes for measuring the charge of a particle n times. In a time domain analysis, this feature reduces both the detection limit and the standard error of the charge measurement by factors of square root of 2 and square root of n. More importantly, sensing stages could be added to arbitrarily lower the detection limit in a frequency domain analysis.     

Guidelines for the incremental identification of aspects in requirements specifications

The desired principle of separation of concerns in software development can be jeopardized by the so-called crosscutting concerns, which tend to be scattered over (and tangled with) the functionality of the modular units of a system. The correct identification of such concerns (and their encapsulation into separate artifacts) is thereby considered a way to improve software understanding and evolution. Pursuing a proper management of concerns from the requirements engineering stage can greatly benefit the entire software life-cycle. In this paper, we propose conceptual guidelines on how to perform the identification of crosscutting concerns in the process of building requirements specifications. We argue that the identification must be carried out in an incremental way, to encapsulate apart the crosscutting concerns even if they have not emerged completely yet.

The equivalent elastic crack: 1. Load-Y equivalences

The use of crack growth resistance curves (R–a) to predict the behaviour of cracked specimens is a well established practice for ceramic and cementitious materials. When the cohesive crack model can be applied to these materials it is shown that the use of R–a curves is equivalent to setting up an elastic equivalence that greatly simplifies the computations. This equivalence has its drawbacks and limitations. This paper analyzes a class of equivalences—the load (P) versus another variable—between cracked cohesive materials and linear elastic ones, ascertaining its applicability to the interpretations of fracture data.     

Observation of the morphology of thin films of solid helium deposited from the fluid onto sapphire

Thin layers of solid helium were grown on sapphire single-crystal substrates at pressures from about 500 bar to 9 kbar. Grain boundaries can be observed in these layer crystals. The morphology of the grains depends on the crystal modification. In the hcp phase (below about 1.13 kbar) a system of parallel bands is observed, probably due to slip and twinning. In the fcc phase (above 1.13 kbar) a polygonal structure similar to a helium froth is found. Melting of this froth in the fcc phase shows grain boundary melting; fluid helium is wetting the fcc grains. Grain boundaries in the hcp phase are, in contrast, not wetted by fluid helium. Near the triple point at 1.13 kbar and 15.0 K one can deposit both crystalline phases side by side. In such structures, the transition fcc hcp⁴He can be observed during isothermal holding. The transition proceeds by the parallel motion of low-energy grain boundaries.     

Economic Costs of Sustaining Water Supplies: Findings from the Rio Grande

Water claims in many of the world??s arid basins exceed reliable supplies. Water demands for irrigation, urban use, the environment, and energy continue to grow, while supplies remain constrained by unsustainable use, drought and impacts of climate change. For example, policymakers in North America??s Upper Rio Grande Basin face the challenge of designing plans for allocating the basin??s water supplies efficiently and fairly to support current uses and current environments. Managers also seek resilient institutions that can ensure adequate supplies for future generations. This paper addresses those challenges by designing and applying an integrated basin-scale framework that accounts for the basin??s most important hydrologic, economic, and institutional constraints. Its unique contribution is a quantitative analysis of three policies for addressing long term goals for the basin??s reservoirs and aquifers: (1) no sustainability for water stocks, (2) sustaining water stocks, and (3) renewing water stocks. It identifies water use and allocation trajectories over time that result from each of these three plans. Findings show that it is hydrologically and institutionally feasible to manage the basin??s water supplies sustainably. The economic cost of protecting the sustainability of the basin??s water stocks can be achieved at 6?C11 percent of the basin??s average annual total economic value of water over a 20?year time horizon.