#### Pregled bibliografske jedinice broj: 1011251

## On Calculating the Packing Efficiency for Embedding Hexagonal and Dodecagonal Sensors in a Circular Container

On Calculating the Packing Efficiency for Embedding Hexagonal and Dodecagonal Sensors in a Circular Container

*// Mathematical problems in engineering,*

**2019**(2019), 1-16 doi:10.1155/2019/9624751 (međunarodna recenzija, članak, znanstveni)

CROSBI ID: **1011251**
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**Naslov**

On Calculating the Packing Efficiency for Embedding Hexagonal and
Dodecagonal Sensors in a Circular Container

**Autori**

Marina Prvan ; Julije Ožegović ; Arijana Burazin Mišura

**Izvornik**

Mathematical problems in engineering (1024-123X) **2019**
(2019);
1-16

**Vrsta, podvrsta i kategorija rada**

Radovi u časopisima, članak, znanstveni

**Ključne riječi**

Hexagon ; Packing Efficiency ; Sensors ; Tessellation

**Sažetak**

In this paper, a problem of packing hexagonal and dodecagonal sensors in a circular container is considered. We concentrate on the sensor manufacturing application, where sensors need to be produced from a circular wafer with maximal silicon efficiency (SE) and minimal number of sensor cuts. Also, a specific application is considered when produced sensors need to cover the circular area of interest with the largest packing efficiency (PE). Even though packing problems are common in many fields of research, not many authors concentrate on packing polygons of known dimensions into a circular shape to optimize a certain objective. We revisit this problem by using some well- known formulations concerning regular hexagons. We provide mathematical expressions to formulate the difference in efficiency between regular and semiregular tessellations. It is well- known that semiregular tessellation will cause larger silicon waste, but it is important to formulate the ratio between the two, as it affects the sensor production cost. The reason why we have replaced the “perfect” regular tessellation with semiregular one is the need to provide spacings at the sensor vertices for placing mechanical apertures in the design of the new CMS detector. Archimedean semiregular tessellation and its more flexible variants with irregular dodecagons can provide these triangular spacings but with larger number of sensor cuts. Hence, we construct an irregular convex hexagon that is semiregularly tessellating the targeted area. It enables the sensor to remain symmetric and hexagonal in shape, even though irregular, and produced with minimal number of cuts with respect to dodecagons. Efficiency remains satisfactory, as we show that, by producing the proposed irregular hexagon sensors from the same wafer as a regular hexagon, we can obtain almost the same SE.

**Izvorni jezik**

Engleski

**Znanstvena područja**

Elektrotehnika, Računarstvo, Interdisciplinarne tehničke znanosti

**POVEZANOST RADA**

**Ustanove**

Fakultet elektrotehnike, strojarstva i brodogradnje, Split,

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#### Citiraj ovu publikaciju

#### Časopis indeksira:

- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus