Parallelisation with Space-Filling Curves

Bäder, Michael

doi:10.1007/978-3-642-31046-1_10

Cited by 7 publications

(10 citation statements)

References 209 publications

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“…A scale factor equal to r/w is also defined, which is independent of arc angle. 19 This horseshoe pattern is a modified version of the traditional unit Peano curve 20 shown in Figure 1a. In this study, a horseshoe pattern repeated in one direction describes a first-order Peano curve, to which uniaxial strains can be applied while conductivity is maintained (Figure 1c).…”

Section: Design and Fabricationmentioning

confidence: 99%

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confidence: 99%

“…[15][16][17][18][19] In the work of Rogers et al, 16 a fractal-inspired space-filling curve, or Peano curve, 20 is investigated in order to support biaxial and radial strains while allowing for a range of conductor topologies that can be tailored to a given application. The traditional unit Peano curve is shown in Figure 1a, 20 along with the modified unit Peano curve having rounded corners in Figure 1b. 16 We expand on the investigation of Peano curves and similar patterns 15,[17][18][19] for use in stretchable electronics by fabricating a large set of repeated firstorder Peano curve structures and systematically testing the effect of z E-mail: dan.hilbich@gmail.com geometric parameter variation on stretchability, which is defined here as the ability to maintain conductivity under an applied strain.…”

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Characterization of Stretchable Interconnects Fabricated Using a Low Cost Metallization Transfer Process onto PDMS

Hilbich

Gray

et al. 2015

ECS J. Solid State Sci. Technol.

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The growing number of applications requiring conformal electronic devices incorporated into unconventional and dynamic surfaces has led to an increase in the development of stretchable electronics. Together with novel materials and fabrication processes, innovative conductive patterns are being developed in order to meet the needs of modern applications. Here, we present the design, fabrication, and characterization of first-order curved Peano structures fabricated using a newly developed thick film copper metallization transfer process onto PDMS. In order to maximize the stretchability of these structures, we present a characterization and analysis of the relationship between relative resistance and tensile strain in fabricated devices while systematically varying the geometric parameters of various curve designs. The response of the structures to cyclic failure and recovery is also characterized. These results demonstrate that the newly developed transfer process can be used to fabricate stretchable Peano curves and provide insight into the geometric optimization of these curves in stretchable electronics applications. Stretchable electronics is an emerging technology enabling new devices that cannot be fabricated using traditionally rigid substrates. The particular advantages of stretchable devices over their rigid counterparts are the ability to conform to a curved surface (for example, the human body), the ability to be folded within a constrained volume, and the ability to otherwise be physically flexed or stretched without failing. Example applications are particularly prevalent in biomedicine and include wearable monitoring devices, 1,2 implantable neural or muscular stimulators, 3 implantable drug delivery systems, 4 fluid control systems, 4 flexible sensors and actuators, 5-7 and flexible integrated circuit technology. 8 In an effort to further the development of these devices, there are two primary areas of improvement; the first area is in fabrication process technologies, and the second is in investigating new geometries that enable more effective stretchable structures.With respect to fabrication technologies, there are several existing processes suitable for the development of stretchable electronics, including the direct metallization of polymers, nanocomposite polymer (NCP) fabrication, 9 fabrication using conductive polymers, 10 and inkjet printing of conductive inks.11 While many of these methods can produce impressive flexible features, the conductivity of non-metallic structures is generally poorer than deposited pure metals. Therefore, the metallization of polymers is commonly used due to high electrical performance and relatively low cost. In previous work, 12 we have shown a new process for low-cost, large-scale, thick-film metallization of PDMS; in this work, we demonstrate the application of this process to stretchable electronics.Using a given process, stretchable metal patterns on polymers can generally be achieved with pre-stressed, thin-film, metal conductors that form stretchable m...

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Section: Design and Fabricationmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Characterization of Stretchable Interconnects Fabricated Using a Low Cost Metallization Transfer Process onto PDMS

Hilbich

Gray

et al. 2015

ECS J. Solid State Sci. Technol.

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“…A space-filling curve is a single onedimensional curve that tours around an entire 2 or more dimensional space and recursively fills up all points when the number of iterations approaches infinity [23,24]. Because Giuseppe Peano (1858-1932) was the first to discover one of the filling curve constructions, space-filling curves in 2-dimensional planes are sometimes called Peano curves.…”

Section: Space-filling Curvementioning

confidence: 99%

“…Because Giuseppe Peano (1858-1932) was the first to discover one of the filling curve constructions, space-filling curves in 2-dimensional planes are sometimes called Peano curves. Some of the most celebrated are the Hilbert curve and the Sierpiński curve [23]. Space-filling curves are used in many fields.…”

Section: Space-filling Curvementioning

confidence: 99%

An Energy Balancing Strategy Based on Hilbert Curve and Genetic Algorithm for Wireless Sensor Networks

Kong

Pan

Sung

et al. 2017

Wireless Communications and Mobile Computing

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A wireless sensor network is a sensing system composed of a few or thousands of sensor nodes. These nodes, however, are powered by internal batteries, which cannot be recharged or replaced, and have a limited lifespan. Traditional two-tier networks with one sink node are thus vulnerable to communication gaps caused by nodes dying when their battery power is depleted. In such cases, some nodes are disconnected with the sink node because intermediary nodes on the transmission path are dead. Energy load balancing is a technique for extending the lifespan of node batteries, thus preventing communication gaps and extending the network lifespan. However, while energy conservation is important, strategies that make the best use of available energy are also important. To decrease transmission energy cost and prolong network lifespan, a three-tier wireless sensor network is proposed, in which the first level is the sink node and the third-level nodes communicate with the sink node via the service sites on the second level. Moreover, this study aims to minimize the number of service sites to decrease the construction cost. Statistical evaluation criteria are used as benchmarks to compare traditional methods and the proposed method in the simulations.

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Non-equidistant scanning path generation for the evaluation of surface curvature in metrological scanning probe microscopes

2021

Meas. Sci. Technol.

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In this paper, we present a novel geometry information-based adaptive step (non-equidistance) scanning path generation method for metrological scanning probe microscopes. This method reduces the total amount of required data and enables faster surface scanning speed for large industrial workpieces while preserving adequate geometric information for performance evaluation after surface reconstruction. The grid points are generated iteratively while gaining knowledge of the surface geometry step by step. We focus on the curvature properties and then propose a metric for the curvature information based on the triangulated surface geometry. With certain convergence criteria on the curvature measure variation, the proposed methods promise better surface reconstruction completeness and performance evaluation correctness. Simulations on the algorithm are performed on a typical parametric surface. A brief comparison to height-based scanning algorithm is performed to show the adaptability of the novel method on curvature evaluation. Experimental verifications are conducted to show the efficiency of the proposed algorithm.

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Parallelisation with Space-Filling Curves

Cited by 7 publications

References 209 publications

Characterization of Stretchable Interconnects Fabricated Using a Low Cost Metallization Transfer Process onto PDMS

Characterization of Stretchable Interconnects Fabricated Using a Low Cost Metallization Transfer Process onto PDMS

An Energy Balancing Strategy Based on Hilbert Curve and Genetic Algorithm for Wireless Sensor Networks

Non-equidistant scanning path generation for the evaluation of surface curvature in metrological scanning probe microscopes

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