Learning About ODEs Using Interactive Online Modules

This paper discusses the development and implementation of a set of online teaching and learning modules for the modeling and solution of simple linear Ordinary Differential Equations (ODEs). The paper describes how constructivist principles are used in the development of these modules and how in-built assessment has been used to enhance student learning. A discussion of the module structure is provided with particular emphasis on the concept of the module walk-through. Modules developed for the classical ODE problems of the simple pendulum and the mass on a spring are used to illustrate these module constructs. The paper concludes with a discussion of the effectiveness of these modules using data sourced from student questionnaires, focus groups and lab session evaluations

Learning a spin glass: determining Hamiltonians from metastable states

We study the problem of determining the Hamiltonian of a fully connected Ising Spin Glass of $N$ units from a set of measurements, whose sizes needs to be ${\cal O}(N^2)$ bits. The student-teacher scenario, used to study learning in feed-forward neural networks, is here extended to spin systems with arbitrary couplings. The set of measurements consists of data about the local minima of the rugged energy landscape. We compare simulations and analytical approximations for the resulting learning curves obtained by using different algorithms.Comment: 5 pages, 1 figure, to appear in Physica

Stability diagrams for bursting neurons modeled by three-variable maps

We study a simple map as a minimal model of excitable cells. The map has two fast variables which mimic the behavior of class I neurons, undergoing a sub-critical Hopf bifurcation. Adding a third slow variable allows the system to present bursts and other interesting biological behaviors. Bifurcation lines which locate the excitability region are obtained for different planes in parameter space.Comment: 7 pages, 3 figures, accepted for publicatio

Tectonic evolution of the Karakoram metamorphic complex (NW Himalayas) reflected in the 3D structures of spiral garnets: Insights from X-ray computed micro-tomography

We thank Pentti Hölttä and Syed Zahid Shah for many useful discussions. We thank the referees, F. George and an anonymous reviewer, for their constructive comments.Spiral garnet porphyroblasts are known to record lengthy periods of deformation and metamorphism by preserving single or multiple FIAs (Foliation Intersection Axis) formed normal to tectonic shortening directions. Thanks to technological advances in X-ray computed micro-tomography (XCMT), FIAs can now be readily determined in relatively large samples in contrast to previous methods that require the preparation of a set of radial vertical and horizontal thin sections of samples. XCMT scanning not only alleviates tedious thin section based procedures but also illuminates the complete internal architecture of a rock sample allowing three-dimensional (3D) quantitative shape analysis of an individual porphyroblast as well as precise measurement of FIAs. We applied the technique to a sample from the Hunza Valley in the Karakoram metamorphic complex (KMC), NW Himalayas, containing numerous garnet porphyroblasts with spiral-shaped inclusion trails. The XCMT imaging reveals an E-Wtrending FIA within the sample, which is consistent with orthogonal N-S collision of the India-Kohistan Island Arc with Asia. Garnet long axes (X-GT) have variable plunges that define a broad sub-vertical maximumand a small sub-horizontalmaximum. The X-GT principle maxima lie at N-090 and N-120. Smaller maxima lie at N-020 and N- 340. Geometric relationships between X-GT axes and FIA orientation in the sample suggest that porphyroblast shapes are controlled by the geometry of the lens-shaped microlithons in which they tend to nucleate and grow. The orientation of inclusion trails and matrix foliations in the sample are correlated with three discrete tectono-metamorphic events that respectively produced andalusite, sillimanite and kyanite in the KMC. Late staurolite growth in the sample reveals howthe rocks extruded to the surface via a significant role of roll-on tectonics, which can be correlated with the Central Himalayas

Modeling mass transfer in fracture flows with the time domain-random walk method

The time domain-random walk method was developed further for simulating mass transfer in fracture flows together with matrix diffusion in surrounding porous media. Specifically, a time domain-random walk scheme was developed for numerically approximating solutions of the advection-diffusion equation when the diffusion coefficient exhibits significant spatial variation or even discontinuities. The proposed scheme relies on second-order accurate, central-difference approximations of the advective and diffusive fluxes. The scheme was verified by comparing simulated results against analytical solutions in flow configurations involving a rectangular channel connected on one side with a porous matrix. Simulations with several flow rates, diffusion coefficients, and matrix porosities indicate good agreement between the numerical approximations and analytical solutions.Peer reviewe

Polyacrylonitrile-encapsulated amorphous zirconium phosphate composite adsorbent for Co, Nd and Dy separations

Recycled Nd and Dy from the end-of-life NdFeB permanent magnet is an important supplement for the increasing demand of rare-earth elements. Thus, there is an urgent need to develop an environmentally friendly recycling method. Amorphous zirconium phosphate exhibits selective separation properties towards the ternary Co-Nd-Dy system, however, its powdery form limits development of scaled-up applications. We present an efficient amorphous ZrP/Polyacrylonitrile (am-ZrP/PAN) composite ion exchanger for uptake and separation of Nd, Dy and Co. The am-ZrP/PAN composite was synthesized and its structural, morphologic and acidic properties were investigated by various methods. X-ray tomography revealed rather evenly distributed am-ZrP in the PAN polymer matrix. The selectivity and ion-exchange kinetics of the am-ZrP/PAN composite were determined in relation to the individual elements. Due to dimethylformide (DMF) intercalation into the interlayer of ZrP, the uptake of Co, Nd and Dy increased 50% compared with that of the pristine am-ZrP. Column separation of Co, Nd and Dy from the Co-Nd-Dy ternary system was assessed by varying the feed concentration, loading degree, temperature, running speed and elution agent (HNO3) concentration. Finally, gradient elution was employed for Co, Nd and Dy separation from a simulated ternary leachate. Fractions with 87.9% pure Co, 96.4% pure Nd and 40% pure Dy were collected through a single-column operation.Peer reviewe

Determining Crack Aperture Distribution in Rocks Using the C-14-PMMA Autoradiographic Method : Experiments and Simulations

Because cracks control the global mechanical and transport properties of crystalline rocks, it is of a crucial importance to suitably determine their aperture distribution, which evolves through alteration processes and rock weathering. Due to the high variability of crack networks in rocks, a multiscale approach is needed. The C-14-PMMA (polymethylmethacrylate) method was developed to determine crack apertures using a set of artificial crack samples with different controlled apertures and tilt angles and also using Monte Carlo simulations. The experiments and simulations show the same result: the estimation of apparent aperture w(A) was successful regardless of tilt angle, even if the estimates are less accurate for low tilt angles (Peer reviewe

Ichnogenus Trypanites in the Ordovician of Estonia (Baltica)

Trypanites is a common boring in Ordovician hardgrounds of Estonia (Baltica). The depth of the sedimentary basin and sedimentation rates controlled the distribution of Trypanites. The trace-makersâ community was diverse and changing over time. Three ichnospecies of Trypanites can be distinguished: T. sozialis, T. weisei and Trypanites isp. All three morphotypes can be recognized in the same hardground. It is impossible to distinguish between the different ichnospecies based only on the size of the boring aperture. The depth of early lithification of the seafloor determines the morphological variability seen in T. sozialis. The occurrence of elongated borings, such as T. weisei and Trypanites isp., is related to tropical environments, and their trace-makers strongly preferred substrates with a homogeneous and dense texture. The texture and available volume of hard substrate controls the ichnodiversity of Trypanites ichnospecies