Wallpaper group kirigami

Kirigami, the art of paper cutting, has become a paradigm for mechanical metamaterials in recent years. The basic building blocks of any kirigami structures are repetitive deployable patterns that derive inspiration from geometric art forms and simple planar tilings. Here, we complement these approaches by directly linking kirigami patterns to the symmetry associated with the set of 17 repeating patterns that fully characterize the space of periodic tilings of the plane. We start by showing how to construct deployable kirigami patterns using any of the wallpaper groups, and then design symmetry-preserving cut patterns to achieve arbitrary size changes via deployment. We further prove that different symmetry changes can be achieved by controlling the shape and connectivity of the tiles and connect these results to the underlying kirigami-based lattice structures. All together, our work provides a systematic approach for creating a broad range of kirigami-based deployable structures with any prescribed size and symmetry properties.

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Similarity in Symmetry Groups of Ornaments as a Measure for Cultural Interactions in Medieval Times

10.20944/preprints202008.0031.v2 ◽

2020 ◽

Author(s):

Mehmet Erbudak ◽

Selim Onat

Keyword(s):

Systematic Approach ◽

Symmetry Groups ◽

Two Dimensional ◽

Mathematical Methods ◽

Symmetry Properties ◽

Art Practices ◽

Euclidean Distances ◽

Similarities And Differences ◽

Wallpaper Groups ◽

Cultural Interactions

The symmetry properties of an ornament contain information about its civilisation and its interactions with other cultural sources. Two-dimensional periodic ornaments can be strictly classified into a limited set of 17 mathematical symmetry groups, also known as wallpaper groups. The collection of ornaments thus classified for a civilisation is characteristic of the cultural group and serves as a fingerprint to identify that group. If the distribution of wallpaper groups is available for several societies, mathematical methods can be applied to determine similarities and differences between the art practices of these communities. This method allows a systematic approach to the general ornamental practices within a culture and their interactions in the form of similarity of fingerprints. We test the feasibility of the method on examples of medieval Armenians, Byzantium, Seljuks first in Persia and then in Anatolia and among Arabs in the Middle East. For this purpose we present the distribution of the planar ornaments and calculate the Euclidean distances in pairs. We tested to what extend geographical and religious factors could account for the observed similarity of ornamental groups between cultures. The results suggest an intensive interaction between the Seljuk Turks and Arab craftsmen who produced the ornaments. Therefore the cultural interactions are religiously motivated.

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Similarity in Symmetry Groups of Ornaments as a Measure for Cultural Interactions in Medieval Times

10.20944/preprints202008.0031.v1 ◽

2020 ◽

Author(s):

Mehmet Erbudak ◽

Selim Onat

Keyword(s):

Systematic Approach ◽

Pearson Correlation ◽

Correlation Coefficients ◽

Symmetry Groups ◽

Dimensional Scaling ◽

Symmetry Properties ◽

Art Practices ◽

Scaling Algorithms ◽

Multi Dimensional Scaling ◽

Wallpaper Groups

The symmetry properties of an ornament contain information about its civilisation and its interactions with other cultural sources. Two-dimensional periodic ornaments can be strictly classified into mathematical wallpaper groups. The collection of ornaments thus classified for a civilisation is characteristic of the cultural group and serves as a fingerprint to identify that group. If the distribution of wallpaper groups is available for several societies, multi-dimensional scaling algorithms can be applied to determine similarities and differences between the art practices of these communities. This method allows a systematic approach to the general ornamental practices within a culture and their interactions in the form of similarity of fingerprints. We test the feasibility of the method on examples of medieval Armenians, Byzantium, Seljuks first in Persia and then in Anatolia and among Arabs in the Middle East. For this purpose we present the distribution of the planar ornaments and calculate the corresponding Pearson correlation coefficients in pairs. The results suggest an intense interaction between the Seljuk Turks and Arab craftsmen, as well as between Armenian and Byzantine artisans who made the ornaments.

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Axially Chiral Bis(α-amino Acid)s and Their Deamino Analogues. Synthesis and Configurational Assignment

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19980211 ◽

1998 ◽

Vol 63 (2) ◽

pp. 211-221 ◽

Cited By ~ 5

Author(s):

Miloš Tichý ◽

Luděk Ridvan ◽

Miloš Buděšínský ◽

Jiří Závada ◽

Jaroslav Podlaha ◽

...

Keyword(s):

Amino Acid ◽

Nmr Spectra ◽

Building Blocks ◽

X Ray Diffraction ◽

Amino Groups ◽

X Ray ◽

Configurational Assignment ◽

Symmetry Properties ◽

Axially Chiral ◽

Polymeric Structures

The axially chiral bis(α-amino acid)s cis-2 and trans-2 as possible building blocks for polymeric structures of novel type of helicity were prepared. Their configuration has been determined by NMR spectroscopy and, in the case of the trans-isomer, confirmed by single-crystal X-ray diffraction. Analogous pair of stereoisomeric diacids cis-3 and trans-3, devoid of the amino groups, was also prepared and their configuration assigned. The observed differences in the NMR spectra of cis- and trans-isomers of 2 and 3 are discussed from the viewpoint of their different symmetry properties.

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Mechanically axially chiral catenanes and noncanonical mechanically axially chiral rotaxanes

10.21203/rs.3.rs-1161933/v1 ◽

2022 ◽

Author(s):

Stephen Goldup ◽

John Maynard ◽

Peter Gallagher ◽

David Lozano ◽

Patrick Butler

Keyword(s):

Building Blocks ◽

Biological Properties ◽

Mirror Image ◽

Symmetry Properties ◽

Covalently Bonded ◽

Axially Chiral ◽

Mechanical Bond ◽

A Chain ◽

Lord Kelvin ◽

Molecular Rings

Abstract The term chiral was introduced by Lord Kelvin over a century ago to describe objects that are distinct from their own mirror image. Chirality is relevant in many scientific areas, but particularly chemistry because different mirror image forms of a molecule famously have different biological properties. Chirality typically arises in molecules due to a rigidly chiral arrangement of covalently bonded atoms. Less generally appreciated is that molecular chirality can arise when molecules are threaded through one another to create a mechanical bond. For example, when two molecular rings with chemically distinct faces are joined like links in a chain the resulting structure is chiral even when the rings themselves are not. We re-examined the symmetry properties of such mechanically axially chiral catenanes and in doing so identified a straightforward route to these molecules from simple building blocks. This also led to the discovery of a previously overlooked mechanical stereogenic unit that can arise when such a ring encircles a dumbbell-shaped axle to generate a rotaxane. These insights allowed us to produce the first highly enantioenriched axially chiral catenane and the same approach gave access to a molecule containing the newly identified noncanonical axially chiral rotaxane motif. With methods to access these structures in hand, the process of exploring their properties and applications can now begin.

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WAVE ANALYSIS OF A L-BEAM STRUCTURE WITH A BLOCKING MASS

Proceedings of the International Conference on Emerging Trends in Engineering & Technology (IConETech-2020) ◽

10.47412/ewgf2313 ◽

2020 ◽

Author(s):

Johnny Tiu ◽

Richard Bachoo

Keyword(s):

Systematic Approach ◽

Building Blocks ◽

Element Model ◽

Structural Systems ◽

Structural Elements ◽

Wave Analysis ◽

Beam Structure ◽

Reflection Matrix ◽

Geometric Changes ◽

Transmission And Reflection

The wave vibration approach regards the vibrations present within a structure as waves, whereby each wave flows along a structural member and upon meeting a discontinuity; portions of the incident wave are reflected and transmitted across the discontinuity. The reflected, transmitted and propagating wave transformations are represented mathematically by matrices, which are used to develop a set of wave relation equations at each discontinuity that can be used to describe the frequency response of the system holistically. This method creates a systematic approach of analysing structures by utilizing common cases as building blocks for a specific structure. The L-joint, described as two beams meeting at right angles; is a ubiquitous case for spatial portal and structural frames, which may become geometrically complex. Such structures are well suited to a wave vibration approach due to the large number of geometric changes and the prevalence as well as recurrence of specific cases. In this paper, the L-joint expanded to include a blocking mass, typically employed in structural systems and allows for the isolation and reflection of vibration away from contiguous structural elements. Included are; variance of transmission and reflection matrix components as the size of the blocking mass increases, numerical examples and comparison to a Finite Element Model developed in ANSYS.

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A Sequential Two-Step Design Framework for Deformable Mechanical Metamaterials

Volume 12: Mechanics of Solids, Structures, and Fluids ◽

10.1115/imece2020-24270 ◽

2020 ◽

Author(s):

Sree Kalyan Patiballa ◽

Girish Krishnan

Keyword(s):

Shape Change ◽

Building Blocks ◽

Load Flow ◽

Stretchable Electronics ◽

Design Framework ◽

Shape Morphing ◽

Mechanical Metamaterials ◽

Global Deformation ◽

Deformation Patterns

Abstract Deformable metamaterials are materials that are made up of several repeating elastic building blocks whose geometries can be tailored to obtain a specified global shape change or stiffness behavior. They are deemed useful in soft robotics, shape morphing mechanisms, stretchable electronics, wearable devices, and devices that adapt according to their environment. This paper presents a two-step sequential design framework for the synthesis of deformable mechanical metamaterials where (a) topology optimization is used to map global deformation requirement to local elasticity matrix, followed by (b) a selection of building block microstructure geometry from a database and refining it to match the elasticity requirement. The first step is accomplished through a unique parameterization scheme that enables the classification of the planar orthotropic elasticity matrix into four distinct classes. The second step uses a kinetostatic framework known as load flow visualization to populate candidate microstructure geometries within these four classes. Finally, the framework is validated for the design of a cantilever beam with a specified lateral stiffness requirement and the design of planar sheets that exhibit sinusoidal deformation patterns.

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Trust in the Value-Creation Chain of Multimedia Goods

Handbook of Research on Secure Multimedia Distribution ◽

10.4018/978-1-60566-262-6.ch021 ◽

2011 ◽

pp. 403-424

Author(s):

Andreas U. Schmidt ◽

Nicolai Kuntze

Keyword(s):

Value Creation ◽

Systematic Approach ◽

Trusted Computing ◽

Digital Rights Management ◽

Building Blocks ◽

Use Case ◽

Computing Technology ◽

Digital Rights ◽

Rights Management ◽

Computing Platforms

Security in the value creation chain hinges on many single components and their interrelations. Trusted Platforms open ways to fulfil the pertinent requirements. This chapter gives a systematic approach to the utilisation of trusted computing platforms over the whole lifecycle of multimedia products. This spans production, aggregation, (re)distribution, consumption, and charging. Trusted Computing technology as specified by the Trusted Computing Group provides modular building blocks which can be utilized at many points in the multimedia lifecycle. We propose an according research roadmap beyond the conventional Digital Rights Management use case. Selected technical concepts illustrate the principles of Trusted Computing applications in the multimedia context.

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Kinematics of the RRR, RRT (Passive) and RRRR, RRRT (Active) Linkage-Mechanism Building Blocks With Applications and Reporting of New Findings

Journal of Mechanisms and Robotics ◽

10.1115/1.4044546 ◽

2019 ◽

Vol 11 (6) ◽

Author(s):

P. A. Simionescu

Keyword(s):

Closed Form ◽

Building Blocks ◽

Linkage Mechanism ◽

Deployable Structures ◽

Optimum Synthesis ◽

New Findings

Abstract Closed-form equations for the analyses of the RRR and RRT (passive) and of the RRRR and RRRT (active) kinematic building blocks are presented in the paper. Implementations of these equations in computer subroutine are then discussed. Applications chosen to illustrate the usefulness of these subroutines include optimum synthesis of a function-generating mechanism, deployable structures, radial engines, a tire-curing press, and the concomitant simulation of four-bar and crank-slider coupler cognates. For the latter, properties not yet reported have been revealed through numerical experimentations.

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A SYSTEMATIC APPROACH TO GENERATING N-SCROLL ATTRACTORS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127402006230 ◽

2002 ◽

Vol 12 (12) ◽

pp. 2907-2915 ◽

Cited By ~ 74

Author(s):

GUO-QUN ZHONG ◽

KIM-FUNG MAN ◽

GUANRONG CHEN

Keyword(s):

Systematic Approach ◽

Building Blocks ◽

Chaotic Attractors ◽

Chua’S Circuit ◽

Chua's Circuit ◽

Nonlinear Resistor ◽

Construction Scheme ◽

Break Points ◽

Set Up

A new circuitry design based on Chua's circuit for generating n-scroll attractors (n = 1, 2, 3, …) is proposed. In this design, the nonlinear resistor in Chua's circuit is constructed via a systematical procedure using basic building blocks. With the proposed construction scheme, the slopes and break points of the v–i characteristic of the circuit can be tuned independently, and chaotic attractors with an even or an odd number of scrolls can be easily generated. Distinct attractors with n-scrolls (n = 5, 6, 7, 8, 9, 10) obtained with this simple experimental set-up are demonstrated.

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