Probabilistic Analysis of Self-assembly

Probabilistic Analysis of Self-assembl

Powers and Behaviors of Directed Self-assembly

In nature there are a variety of self-assembling systems occurring at varying scales which give rise to incredibly complex behaviors. Theoretical models of self-assembly allow us to gain insight into the fundamental nature of self-assembly independent of the specific physical implementation. In Winfree\u27s abstract tile assembly model (aTAM), the atomic components are unit square tiles which have glues on their four sides. Beginning from a seed assembly, these tiles attach one at a time during the assembly process in an asynchronous and nondeterministic manner. We can gain valuable insights into the nature of self-assembly by comparing different models of self-assembly which use fundamentally different mechanisms for local interactions. A powerful notion which allows us to compare models of self-assembly is simulation. The first result of this thesis examines the role of non-determinism in simulation. It shows that the universal simulation of directed aTAM systems requires undirectedness. A tile assembly model is said to be directed if it always assembles the same final assembly. We distinguish between two types of aTAM systems: cooperative systems and non-cooperative systems. In cooperative aTAM systems, we are able to enforce that in order for a tile to attach to an assembly, the glues of a tile must match two or more glues of neighboring tiles. On the other hand, in non-cooperative aTAM systems, tiles are able to attach to an assembly provided that one of the tile\u27s glues match an exposed glue on the assembly. It is well known that the cooperative aTAM is computationally universal, and it is conjectured that the non-cooperative aTAM is not computationally universal. For our second result, we show that if we allow tiles to be polygons with six or more sides, then the class of non-cooperative systems is capable of universal computation. On the other hand, we show that the class of systems consisting of polygons with six or less sides is not capable of computing using any of the currently known methods

An aesthetics of touch: investigating the language of design relating to form

How well can designers communicate qualities of touch? This paper presents evidence that they have some capability to do so, much of which appears to have been learned, but at present make limited use of such language. Interviews with graduate designer-makers suggest that they are aware of and value the importance of touch and materiality in their work, but lack a vocabulary to fully relate to their detailed explanations of other aspects such as their intent or selection of materials. We believe that more attention should be paid to the verbal dialogue that happens in the design process, particularly as other researchers show that even making-based learning also has a strong verbal element to it. However, verbal language alone does not appear to be adequate for a comprehensive language of touch. Graduate designers-makers’ descriptive practices combined non-verbal manipulation within verbal accounts. We thus argue that haptic vocabularies do not simply describe material qualities, but rather are situated competences that physically demonstrate the presence of haptic qualities. Such competencies are more important than groups of verbal vocabularies in isolation. Design support for developing and extending haptic competences must take this wide range of considerations into account to comprehensively improve designers’ capabilities

The Evolution of 3D Printing in AEC: From Experimental to Consolidated Techniques

The chapter leads the reader through the historical development of additive manufacturing (AM) techniques until the most recent developments. A tentative taxonomy is added to the historical perspective, in order to better understand the main lines of development and the potential cross-fertilization opportunities. Some case studies are analyzed in order to provide a clearer picture of the practical applications of AM in architecture engineering and construction (AEC), with a particular attention to the use of AM for final products rather than just prototypes. Eventually, some thoughts are shared as to the impact of AM on AEC beyond the mere cost-effectiveness and well into the potential change of paradigms in how architecture can be thought of and further developed embracing the new world of opportunities brought by AM

The Need for Seed (in the abstract Tile Assembly Model)

In the abstract Tile Assembly Model (aTAM) square tiles self-assemble, autonomously binding via glues on their edges, to form structures. Algorithmic aTAM systems can be designed in which the patterns of tile attachments are forced to follow the execution of targeted algorithms. Such systems have been proven to be computationally universal as well as intrinsically universal (IU), a notion borrowed and adapted from cellular automata showing that a single tile set exists which is capable of simulating all aTAM systems (FOCS 2012). The input to an algorithmic aTAM system can be provided in a variety of ways, with a common method being via the "seed" assembly, which is a pre-formed assembly from which all growth propagates. In this paper we present a series of results which investigate the the trade-offs of using seeds consisting of a single tile, versus those containing multiple tiles. We show that arbitrary systems with multi-tile seeds cannot be converted to functionally equivalent systems with single-tile seeds without using a scale factor > 1. We prove tight bounds on the scale factor required, and also present a construction which uses a large scale factor but an optimal number of unique tile types. That construction is then used to develop a construction that performs simultaneous simulation of all aTAM systems in parallel, as well as to display a connection to other tile-based self-assembly models via the notion of intrinsic universality.Comment: To appear in the SODA 2023 proceeding

A framework towards the design of more sustainable concrete structures

Includes bibliographical references.The main contribution of this study is the development of a novel framework for the design of reinforced concrete (RC) structures which aims at ensuring that future RC structures have the lowest possible carbon footprint, energy use and impact on the environment. The key focus of the study is on structural design where there is a lack of grasp of materials aspects, and environmental aspects of construction. In the proposed framework, a set of quantifiable design parameters and variables (binder type, concrete grade, diffusivity, concrete cover depth, area of steel in the structural component) are selected with respect to a set of performance measures which cover the functionality and availability of the structure to the user during its service life. The outputs generated from the framework are optimised material types and properties which not only meet the design performance requirements but also lead to minimised life-cycle environmental impacts. Two case studies are used to demonstrate the proposed design methodology. These include a reinforced concrete frame building and a post-tensioned box girder. The application of the framework for design in the material specifications showed a reduced volume of materials in construction compared to the current materials and structures design practice