Hidden geometries in networks arising from cooperative self-assembly

Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and compatibility of the building blocks are decisive factors in each phase of growth. Therefore, a comprehensive understanding of these processes is essential for the design of large assemblies of desired properties. Here, we introduce a computational model for cooperative self-assembly with simultaneous attachment of structured groups of particles, which can be described by simplexes (connected pairs, triangles, tetrahedrons and higher order cliques) to a growing network, starting from a small seed. The model incorporates geometric rules that provide suitable nesting spaces for the new group and the chemical affinity $\nu$ of the system to accepting an excess number of particles. For varying chemical affinity, we grow different classes of assemblies by binding the cliques of distributed sizes. Furthermore, to characterise the emergent large-scale structures, we use the metrics of graph theory and algebraic topology of graphs, and 4-point test for the intrinsic hyperbolicity of the networks. Our results show that higher Q-connectedness of the appearing simplicial complexes can arise due to only geometrical factors, i.e., for $\nu = 0$, and that it can be effectively modulated by changing the chemical potential and the polydispersity of the size of binding simplexes. For certain parameters in the model we obtain networks of mono-dispersed clicks, triangles and tetrahedrons, which represent the geometrical descriptors that are relevant in quantum physics and frequently occurring chemical clusters.Comment: 9 pages, 8 figure

An assembly oriented design framework for product structure engineering and assembly sequence planning

The paper describes a novel framework for an assembly-oriented design (AOD) approach as a new functional product lifecycle management (PLM) strategy, by considering product design and assembly sequence planning phases concurrently. Integration issues of product life cycle into the product development process have received much attention over the last two decades, especially at the detailed design stage. The main objective of the research is to define assembly sequence into preliminary design stages by introducing and applying assembly process knowledge in order to provide an assembly context knowledge to support life-oriented product development process, particularly for product structuring. The proposed framework highlights a novel algorithm based on a mathematical model integrating boundary conditions related to DFA rules, engineering decisions for assembly sequence and the product structure definition. This framework has been implemented in a new system called PEGASUS considered as an AOD module for a PLM system. A case study of applying the framework to a catalytic-converter and diesel particulate filter sub-system, belonging to an exhaust system from an industrial automotive supplier, is introduced to illustrate the efficiency of the proposed AOD methodology

A CSP model for simple non-reversible and parallel repair plans

Thiswork presents a constraint satisfaction problem (CSP) model for the planning and scheduling of disassembly and assembly tasks when repairing or substituting faulty parts. The problem involves not only the ordering of assembly and disassembly tasks, but also the selection of them from a set of alternatives. The goal of the plan is the minimization of the total repairing time, and the model considers, apart from the durations and resources used for the assembly and disassembly tasks, the necessary delays due to the change of configuration in the machines, and to the transportation of intermediate subassemblies between different machines. The problem considers that sub-assemblies that do not contain the faulty part are nor further disassembled, but allows non-reversible and parallel repair plans. The set of all feasible repair plans are represented by an extended And/Or graph. This extended representation embodies all of the constraints of the problem, such as temporal and resource constraints and those related to the selection of tasks for obtaining a correct plan.Ministerio de Educación y Ciencia DIP2006-15476-C02-0

Noncooperative algorithms in self-assembly

We show the first non-trivial positive algorithmic results (i.e. programs whose output is larger than their size), in a model of self-assembly that has so far resisted many attempts of formal analysis or programming: the planar non-cooperative variant of Winfree's abstract Tile Assembly Model. This model has been the center of several open problems and conjectures in the last fifteen years, and the first fully general results on its computational power were only proven recently (SODA 2014). These results, as well as ours, exemplify the intricate connections between computation and geometry that can occur in self-assembly. In this model, tiles can stick to an existing assembly as soon as one of their sides matches the existing assembly. This feature contrasts with the general cooperative model, where it can be required that tiles match on \emph{several} of their sides in order to bind. In order to describe our algorithms, we also introduce a generalization of regular expressions called Baggins expressions. Finally, we compare this model to other automata-theoretic models.Comment: A few bug fixes and typo correction

Review of research in feature-based design

Research in feature-based design is reviewed. Feature-based design is regarded as a key factor towards CAD/CAPP integration from a process planning point of view. From a design point of view, feature-based design offers possibilities for supporting the design process better than current CAD systems do. The evolution of feature definitions is briefly discussed. Features and their role in the design process and as representatives of design-objects and design-object knowledge are discussed. The main research issues related to feature-based design are outlined. These are: feature representation, features and tolerances, feature validation, multiple viewpoints towards features, features and standardization, and features and languages. An overview of some academic feature-based design systems is provided. Future research issues in feature-based design are outlined. The conclusion is that feature-based design is still in its infancy, and that more research is needed for a better support of the design process and better integration with manufacturing, although major advances have already been made