Scale Geometry Research Articles

A Platform for Parameter Unlimited Molecular Geometry Imaging Obviously Enabling Life Saving Measures in ALS

This article deals with a molecular geometry imaging platform capable of mapping the spatial protein-colocalisation and anti-colocalisation code of large molecular systems at a time. The platform called molecular unlimited systems imaging cycler (MUSIC) robotics was applied to amyotrophic lateral sclerosis (ALS). The detection of ALS specific cells with a corresponding multimolecular geometry in the blood led to therapeutic depletion of these cells and to recovery of the treated patient, obviously because this therapy interferes with pathogenic invasion of these cells into the central nervous system, where they axotomize motor axons. Large scale geometry MUSIC robotics imaging of up to 4.5 × 10481 power of combinatorial molecular resolution is key to detect these cells and to control depletion therapy for clinical success. These data and new possibilities may argue for clinical application and for a systematic research in the field of molecular geometry of diseases to discover new mathematically defined insight.

Lipschitz structure and minimal metrics on topological groups

We discuss the problem of deciding when a metrisable topological group $G$ has a canonically defined local Lipschitz geometry. This naturally leads to the concept of minimal metrics on $G$, that we characterise intrinsically in terms of a linear growth condition on powers of group elements. Combining this with work on the large scale geometry of topological groups, we also identify the class of metrisable groups admitting a canonical global Lipschitz geometry. In turn, minimal metrics connect with Hilbert's fifth problem for completely metrisable groups and we show, assuming that the set of squares is sufficiently rich, that every element of some identity neighbourhood belongs to a $1$-parameter subgroup.

Shaking Table Test of a Half-Scale Geosynthetic-Reinforced Soil Bridge Abutment

This paper presents an experimental study on the dynamic response of a half-scale geosynthetic-reinforced soil (GRS) bridge abutment system using a shaking table. Experimental design of the model specimen followed established similitude relationships for shaking table tests on reduced-scale models in a 1-g gravitational field, including scaling of model geometry, geosynthetic-reinforcement stiffness, backfill soil modulus, bridge load, and characteristics of the earthquake motions. The 2.7-m-high GRS bridge abutment was constructed using well-graded sand backfill, modular facing blocks, and uniaxial geogrid reinforcements with a vertical spacing of 0.15 m in both the longitudinal and transverse directions. A bridge beam was placed on the GRS bridge abutment at one end and on a concrete support wall resting on a sliding platform off the shaking table at the other end. The GRS bridge abutment system was subjected to a series of input motions in the longitudinal direction. Results indicate that the testing system performed well, and that the GRS bridge abutment experienced small deformations. For two earthquake motions, the maximum incremental residual facing displacement in model scale was 1.0 mm, and the average incremental residual bridge seat settlement in model scale was 1.4 mm, which corresponds to a vertical strain of 0.7 %.

Modeling of flow stress size effect based on variation of dislocation substructure in micro-tension of pure nickel

Micro-forming is one promising technology for manufacturing micro metal parts. However, the traditional metal-forming theories fail to analyze the plastic deformation behavior in micro-scale due to the size effect arising from the part geometry scaling down from macro-scale to micro-scale. To reveal the mechanism of plastic deformation behavior size effect in micro-scale, the geometrical parameters and the induced variation of microstructure by them need to be integrated in the developed constitutive models considering the free surface effect. In this research, the variations of dislocation cell diameter with original grain size, strain and location (surface grain or inner grain) are derived according the previous research data. Then the overall flow stress of the micro specimen is determined by employing the surface layer model and the relationship between dislocation cell diameter and the flow stress. This new developed constitutive model considers the original grain size, geometrical dimension and strain simultaneously. The flow stresses in micro-tensile tests of thin sheets are compared with calculated results using the developed constitutive model. The calculated and experimental results match well. Thus the validity of the developed constitutive model is verified.

Hydrostatic Pressurization of Lung Surfactant Microbubbles: Observation of a Strain-Rate Dependent Elasticity.

The microbubble offers a unique platform to study lung surfactant mechanics at physiologically relevant geometry and length scale. In this study, we compared the response of microbubbles (∼15 μm initial radius) coated with pure dipalmitoyl-phosphatidylcholine (DPPC) versus naturally derived lung surfactant (SURVANTA) when subjected to linearly increasing hydrostatic pressure at different rates (0.5-2.3 kPa/s) at room temperature. The microbubbles contained perfluorobutane gas and were submerged in buffered saline saturated with perfluorobutane at atmospheric pressure. Bright-field microscopy showed that DPPC microbubbles compressed spherically and smoothly, whereas SURVANTA microbubbles exhibited wrinkling and smoothing cycles associated with buckling and collapse. Seismograph analysis showed that the SURVANTA collapse amplitude was constant, but the collapse rate increased with the pressurization rate. An analysis of the pressure-volume curves indicated that the dilatational elasticity increased during compression for both shell types. The initial dilatational elasticity for SURVANTA was nearly twice that of DPPC at higher pressurization rates (>1.5 kPa/s), producing a pressure drop of up to 60 kPa across the film prior to condensation of the perfluorobutane core. The strain-rate dependent stiffening of SURVANTA shells likely arises from their composition and microstructure, which provide enhanced in-plane monolayer rigidity and lateral repulsion from surface-associated collapse structures. Overall, these results provide new insights into lung surfactant mechanics and collapse behavior during compression.

Probing three-dimensional collective cancer invasion with DIGME

BackgroundMulticellular pattern formation plays an important role in developmental biology, cancer metastasis and wound healing. While many physical factors have been shown to regulate these multicellular processes, the role of ECM micro-to-meso scale geometry has been poorly understood in 3D collective cancer invasion.ResultsWe have developed a mechanical-based strategy, Diskoid In Geometrically Micropatterned ECM (DIGME). DIGME allows easy engineering of the shape of 3D tissue organoid, the mesoscale ECM heterogeneity, and the fiber alignment of collagen-based ECM all at the same time. We have employed DIGME to study the 3D invasion of MDA-MB-231 diskoids in engineered collagen matrix. We find that the collective cancer invasion is closely regulated by the micro-to-meso scale geometry of the ECM.ConclusionsWe conclude that DIGME provides a simple yet powerful tool to probe 3D dynamics of tissue organoids in physically patterned microenvironments.

Activation analysis for the HCPB blanket module in the European DEMO

The activity and decay heat inventories were assessed for the HCPB DEMO blankets making use of a code system that enables performing 3D activation calculations by linking the Monte Carlo transport code MCNP and the fusion inventory code FISPACT through an appropriate interface. The dedicated full scale geometry MCNP model of a 10° HCPB DEMO torus was adapted to the requirements for the coupled 3D neutron transport and activation calculations. The sensitivity analyses were performed to assess the effect of the homogenized geometry cells to the final results. The importance of the use of the impurities in the material definitions was pointed out and accounted for in the simulations. The activity of the HCPB blanket modules is dominated by the tungsten protecting layer up to one month after shutdown. After that it’s dominated by the breeding zone mixture of Eurofer, breeder ceramic and beryllium pebbles with impurities. The decay heat generation in blankets is especially high in the casing that requires intensive cooling efforts for their treatment after the shutdown. The accumulation of the poisoning 239Pu could make complicated the recycling of the beryllium pebbles extracted from the blankets.

A NOTE ON COMPUTING THE INTERSECTION OF SPHERES IN

Finding the intersection of $n$-dimensional spheres in $\mathbb{R}^{n}$ is an interesting problem with applications in trilateration, global positioning systems, multidimensional scaling and distance geometry. In this paper, we generalize some known results on finding the intersection of spheres, based on QR decomposition. Our main result describes the intersection of any number of $n$-dimensional spheres without the assumption that the centres of the spheres are affinely independent. A possible application in the interval distance geometry problem is also briefly discussed.

Flow of viscoelastic surfactants through porous media

We compare the flow behavior of viscoelastic surfactant (VES) solutions and Newtonian fluids through two different model porous media having similar permeability: (a) a 3D random packed bed and (b) a microchannel with a periodically spaced pillars. The former provides much larger flow resistance at the same apparent shear rate compared to the latter. The flow profile in the 3D packed bed cannot be observed since it is a closed system. However, visualization of the flow profile in the microchannel shows strong spatial and temporal flow instabilities in VES fluids appear above a critical shear rate. The onset of such elastic instabilities correlates to the flow rate where increased flow resistance is observed. The elastic instabilities are attributed to the formation of transient shear induced structures. The experiments provide a detailed insight into the complex interplay between the pore scale geometry and rheology of VES in the creeping flow regime. © 2017 American Institute of Chemical Engineers AIChE J, 64: 773–781, 2018

The effect of confinement and defects on the thermal stability of skyrmions

The stability of magnetic skyrmions against thermal fluctuations and external perturbations is investigated within the framework of harmonic transition state theory for magnetic degrees of freedom. The influence of confined geometry and atomic scale non-magnetic defects on the skyrmion lifetime is estimated. It is shown that a skyrmion on a track has lower activation energy for annihilation and higher energy for nucleation if the size of the skyrmion is comparable with the width of the track. Two mechanisms of skyrmion annihilation are considered: inside the track and escape through the boundary. For both mechanisms, the dependence of activation energy on the track width is calculated. Non-magnetic defects are found to localize skyrmions in their neighborhood and strongly decrease the activation energy for creation and annihilation. This is in agreement with experimental measurements that have found nucleation of skyrmions in presence of spin-polarized current preferably occurring near structural defects.

Holographic butterfly effect and diffusion in quantum critical region

We investigate the butterfly effect and charge diffusion near the quantum phase transition in holographic approach. We argue that their criticality is controlled by the holographic scaling geometry with deformations induced by a relevant operator at finite temperature. Specifically, in the quantum critical region controlled by a single fixed point, the butterfly velocity decreases when deviating from the critical point. While, in the non-critical region, the behavior of the butterfly velocity depends on the specific phase at low temperature. Moreover, in the holographic Berezinskii-Kosterlitz-Thouless transition, the universal behavior of the butterfly velocity is absent. Finally, the tendency of our holographic results matches with the numerical results of Bose-Hubbard model. A comparison between our result and that in the O(N ) nonlinear sigma model is also given.

Electronic components embedded in a single graphene nanoribbon

The use of graphene in electronic devices requires a band gap, which can be achieved by creating nanostructures such as graphene nanoribbons. A wide variety of atomically precise graphene nanoribbons can be prepared through on-surface synthesis, bringing the concept of graphene nanoribbon electronics closer to reality. For future applications it is beneficial to integrate contacts and more functionality directly into single ribbons by using heterostructures. Here, we use the on-surface synthesis approach to fabricate a metal-semiconductor junction and a tunnel barrier in a single graphene nanoribbon consisting of 5- and 7-atom wide segments. We characterize the atomic scale geometry and electronic structure by combined atomic force microscopy, scanning tunneling microscopy, and conductance measurements complemented by density functional theory and transport calculations. These junctions are relevant for developing contacts in all-graphene nanoribbon devices and creating diodes and transistors, and act as a first step toward complete electronic devices built into a single graphene nanoribbon.

Geometry of Molecular Motions in Dye Monolayers at Various Coverages

Molecular motion in monolayers is thought to influence the kinetics of charge transport and recombination in systems such as dye-sensitized solar cells (DSSCs). In this work, we use ab initio molecular dynamics to evaluate the geometry and time scale of such molecular motion in a D102 monolayer. D102, a dye that is routinely used in DSSCs, contains two chemical groups, namely, indoline and triphenylethylene, that are also present in many other dyes. We find that, at low surface coverage, the dye molecule exhibits two main tilting axes around which it heavily distorts within 10 ps. Further, the two benzene rings in the triphenylethylene group rotate with a 3–4-ps period. We observe that these large-amplitude movements are suppressed at full coverage, meaning that dye molecules in a monolayer are locked into place and undergo only minor conformational changes. Our observations indicate that, counterintuitively, charge diffusion across dye monolayers might be faster in the parts of the system that are charac...

Unified Compact Model for Nanowire Transistors Including Quantum Effects and Quasi-Ballistic Transport

We present a surface potential-based compact model for nanowire FETs, which considers 1-D electrostatics along with the effect of multiple energy subbands. The model is valid for any semiconductor material, cross-sectional geometry, and any channel length with transport regimes varying from drift-diffusive to quasi-ballistic. The model captures the phenomenon of quantum capacitance and the effect of temperature. We have validated it with numerical simulations and experimental data for Si, Ge, and InAs nanowires of different geometries. Circuit simulation has also been performed with the model. The physics-based model is accurate and can be used as a tool for analysis and prediction of the effects of geometry scaling, material dependence, and temperature variation on device and circuit characteristics. To the best of our knowledge, this is the first time a compact model for nanowire FETs is being presented, which includes multiple subbands along with geometry scaling while being valid for different degenerate and nondegenerate semiconductor materials.

Fractal and multifractal characterization of the scaling geometry of an urban bus-transport network

• A FD around D = 1.5 characterizes the fractal nature of the bus-transport network of Cordoba (Spain) for small spatial scales.

The response of a guyed transmission line system to boundary layer wind

The current study investigates the aeroelastic characteristics and structural response of a multiple-span guyed lattice transmission line system, through a simultaneous testing of four aeroelastic guyed lattice towers and conductors. The transmission line system simulated in the current study is a generic guyed transmission tower used by different hydro companies in North America and in different parts of the world. The aeroelastic model is designed for a geometry scale of 1:50 and tested in the Boundary Layer Wind Tunnel Laboratory at the University of Western Ontario, Canada. The model is tested using an open exposure wind profile. The aeroelastic test is performed for three different wind directions and for two configurations, with and without the transmission lines (conductors and ground-wires). Such aeroelastic model of guyed transmission line system with multiple-spans is not reported in literature. This represent a new contribution to the existing literature of the aeroelastic behaviour of transmission lines under wind actions. The study investigates the aeroelastic model response to boundary layer wind loading under different wind speeds and configurations. For the 37 wind speeds, two configurations, and three angles of attack used in the current aeroelastic test, no instabilities are observed for the tested transmission towers or lines. The measured natural frequencies of the aeroelastic model match those obtained by numerical modelling and those provided in the literature, and are affected by the value of the pretension force applied to the supporting guys. The results indicate that the multiple-span guyed transmission line system aeroelastic model responded in a quasi-static manner to boundary layer wind loads. Resonant dynamic response is less significant and becomes less distinguished by increasing the wind speeds. The results are used to understand the response of guyed transmission line systems to boundary layer wind loads.

Multi-Party, Whole-Body Interactions in Mathematical Activity

ABSTRACTThis study interrogates the contributions of multi-party, whole-body interactions to students' collaboration and negotiation of mathematics ideas in a task setting called walking scale geometry, where bodies in interaction became complex resources for students' emerging goals in problem solving. Whole bodies took up overlapping roles representing geometric objects, contributing to the communication and negotiation of problem-solving strategies and engaging as mathematical instruments for representation.

Computationally‐efficient surrogate‐assisted dimension scaling of compact dual‐band couplers

Reusing existing results in order to facilitate optimisation of structures for various sets of performance requirements such as operating frequencies is an attractive concept. When implemented properly, it can lead to considerable speedup of the microwave design process. In general, re-design of microwave structures is a challenging task, particularly for compact components where considerable electromagnetic (EM) cross-couplings make the relationships between geometry parameters and the structure responses complex. In this study, the authors address geometry scaling of miniaturised dual-band couplers by means of inverse surrogate modelling. It allows for fast estimation of the optimum values of structure dimensions corresponding to required operating frequencies, independently for each band. The inverse surrogate is constructed based on a set of reference designs obtained by optimising the equivalent circuit model of the coupler, and subsequently corrected using output space mapping to accommodate the discrepancies between the network model and the EM-simulation one. As demonstrated using a compact dual-band microstrip branch-line coupler example, geometry scaling is possible in a wide range of operating frequencies and at a very low cost of just a single EM simulation of the structure at hand. Numerical results are validated through physical measurements of fabricated coupler prototypes for several test cases.

Characterizing the transient geomorphic response to base‐level fall in the northeastern Tibetan Plateau

AbstractAnalysis of hillslope gradient, landscape relief, and channel steepness in the Daxia River basin provides evidence of a transient geomorphic response to base‐level fall on the northeastern Tibetan Plateau. Low‐gradient channels and gentle hillslopes of the upper watershed are separated from a steeper, high‐relief landscape by a series of convex knickzones along channel longitudinal profiles. Downstream projection of the “relict” portions of the profiles implies ~800–850 m of incision, consistent with geologic and geomorphic records of post ~1.7 Ma incision in the lower watershed. We combine optically stimulated luminescence dating of fluvial terrace deposits to constrain incision rates downstream of knickpoints with catchment‐averaged 10Be concentrations in modern sediment to estimate erosion rates in tributary basins both above and below knickpoints. Both sources of data imply landscape lowering rates of ~300 m Ma−1 below the knickpoint and ~50–100 m Ma−1 above. Field measurements of channel width (n = 48) and calculations of bankfull discharge (n = 9) allow determination of scaling relations among channel hydraulic geometry, discharge, and contributing area that we employ to estimate the patterns of basal shear stress, unit stream power, and bed load transport rate throughout the channel network. Our results imply a clear downstream increase of incision potential; this result would appear to be consistent with a detachment‐limited response to imposed base‐level fall, in which steepening of channels drives an increase in erosion rates. In contrast, however, we do not observe apparent narrowing of channels across the transition from slowly eroding to rapidly eroding portions of the watershed. Rather, the present‐day channel morphology as well as its scaling of hydraulic geometry imply that the river is primarily adjusted to transport its sediment load and suggest that channel morphology may not always reflect the presence of knickpoints and differences in landscape relief.

Beneficial aerodynamic effect of wing scales on the climbing flight of butterflies

It is hypothesized that butterfly wing scale geometry and surface patterning may function to improve aerodynamic efficiency. In order to investigate this hypothesis, a method to measure butterfly flapping kinematics optically over long uninhibited flapping sequences was developed. Statistical results for the climbing flight flapping kinematics of 11 butterflies, based on a total of 236 individual flights, both with and without their wing scales, are presented. Results show, that for each of the 11 butterflies, the mean climbing efficiency decreased after scales were removed. Data was reduced to a single set of differences of climbing efficiency using are paired t-test. Results show a mean decrease in climbing efficiency of 32.2% occurred with a 95% confidence interval of 45.6%–18.8%. Similar analysis showed that the flapping amplitude decreased by 7% while the flapping frequency did not show a significant difference. Results provide strong evidence that butterfly wing scale geometry and surface patterning improve butterfly climbing efficiency. The authors hypothesize that the wing scale’s effect in measured climbing efficiency may be due to an improved aerodynamic efficiency of the butterfly and could similarly be used on flapping wing micro air vehicles to potentially achieve similar gains in efficiency.