Related papers: A pumping lemma for non-cooperative self-assembly
Although common in nature, the self-assembly of small molecules at sold-liquid interfaces is difficult to control in artificial systems. The high mobility of dissolved small molecules limits their residence at the interface, typically…
The pseudomode method for open quantum systems, also known as the mesoscopic leads approach, consists in replacing a structured environment by a set of auxiliary "pseudomodes" subject to local damping that approximate the environment's…
Cyclomatic complexity is an incompletely specified but mathematically principled software metric that can be usefully applied to both source and binary code. We consider the application of path homology as a stronger analogue of cyclomatic…
We provide a detailed derivation of the mode-coupling equations for a colloidal liquid confined by two parallel smooth walls. We introduce irreducible memory kernels for the different relaxation channels thereby extending the projection…
The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to…
Let n be a positive integer, and let R be a finitely presented (but not necessarily finite dimensional) associative algebra over a computable field. We examine algorithmic tests for deciding (1) if every n-dimensional representation of R is…
The traditional goal of inverse self-assembly is to design interactions that drive particles toward a desired target structure. However, achieving successful self-assembly also requires tuning the thermodynamic conditions under which the…
It is demonstrated that any almost-tilting module over a gentle algebra is indeed partial-tilting, meaning it can be completed as a tilting module. Furthermore, such a module has at most $2n$ possible complements, thereby confirming a…
The conflict between stiffness and toughness is a fundamental problem in engineering materials design. However, the systematic discovery of microstructured composites with optimal stiffness-toughness trade-offs has never been demonstrated,…
The interaction between thin structures and incompressible Newtonian fluids is ubiquitous both in nature and in industrial applications. In this paper we present an isogeometric formulation of such problems which exploits a boundary…
A commonly held view in the turbomachinery community is that finite element methods are not well-suited for very large-scale thermomechanical simulations. We seek to dispel this notion by presenting performance data for a collection of…
We present a minimal model for simulating dynamics of assorted lipid assemblies in a computationally efficient manner. Our model is particle-based and consists of coarse-grained beads put together on a modular platform to give generic…
This paper considers the shape formation problem within the 3D hybrid model, where a single agent with a strictly limited viewing range and the computational capacity of a deterministic finite automaton manipulates passive tiles through…
Self-assembly kinetics is usually described by approaches which assume that the shape of the aggregates has a definite form (e.g., spherical, cylindrical, cubic, etc), however that is unlikely to be the case in many finite-sized…
We say that a tile is $\sigma$-morphic if it tiles the plane in exactly $\aleph_0$ many noncongruent ways (up to an isometry). It is an unsolved problem of whether a $\sigma$-morphic tile exist in the plane. In this note we present a…
In geometrically frustrated assemblies, equilibrium self-limitation manifests in the form of a minimum in the free energy per subunit at a finite, multi-subunit size which results from the competition between the elastic costs of…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
Rational design strategies for self-assembly require a detailed understanding of both the equilibrium state and the assembly kinetics. While the former is starting to be well understood, the latter remains a major theoretical challenge,…
In micro- and nano-scale systems, particles can be moved by using an external force like gravity or a magnetic field. In the presence of adhesive particles that can attach to each other, the challenge is to decide whether a shape is…
We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making `analytic' connected sums. In…