Related papers: A pumping lemma for non-cooperative self-assembly
Silica nanoparticles trapped at air-water interface form a 2D solid state with amorphous order. We propose a theoretical model to describe how this solid-like state deforms under a shear strain ramp up to and beyond a yielding point which…
The production of sequence-specific copolymers using copolymer templates is fundamental to the synthesis of complex biological molecules and is a promising framework for the synthesis of synthetic chemical complexes. Unlike the…
Computationally, low-resolution coarse-grained models provide the most viable means for simulating the large length and time scales associated with mesoscopic phenomena. Moreover, since lyotropic phases in solution may contain high solvent…
We discuss the problem of counting certain LEGO structures, primarily those comprising parallel $w \times 1$ tiles. These can be combined, as a single LEGO structure, by interlocking the tiles. %Alternatively, if the interlocking condition…
This paper provides a bridge between the classical tiling theory and the complex neighborhood self-assembling situations that exist in practice. The neighborhood of a position in the plane is the set of coordinates which are considered…
Amorphous glassy materials of diverse nature -- concentrated emulsions, granular materials, pastes, molecular glasses -- display complex flow properties, intermediate between solid and liquid, which are at the root of their use in many…
We give an application of a topological dynamics version of multidimensional Brown's lemma to tiling theory: given a tiling of an Euclidean space and a finite geometric pattern of points $F$, one can find a patch such that, for each scale…
Ordered nanoarrays, i.e. regular patterns of quantum structures at the nanometre scale, have recently been synthesized in a wide range of systems. Here I explore a possible route to technological exploitation: assuming a simple form of…
We give new and rather general gluing theorems for anti-self-dual (ASD) conformal structures, following the method suggested by Floer. The main result is a gluing theorem for pairs of conformally ASD manifolds `joined' across a common piece…
In this paper, we introduce a novel design paradigm for modular architectured materials that allows for spatially nonuniform designs from a handful of building blocks, which can be robotically assembled for efficient and scalable…
Executing a control sequence requires computation. While this is a simple observation, developing a framework that relates a controller's required computation to its ability to successfully control a system (e.g. lower control cost) is…
The goal of inverse self-assembly is to design inter-particle interactions capable of assembling the units into a desired target structure. The effective assembly of complex structures often requires the use of multiple components, each new…
In this paper we present a mixed projection- and density-based topology optimization approach. The aim is to combine the benefits of both parametrizations: the explicit geometric representation provides specific controls on certain design…
In this paper we survey a number of recent results concerning the existence and moduli spaces of solutions of various geometric problems on noncompact manifolds. The three problems which we discuss in detail are: I. Complete properly…
3D printing enables the fabrication of complex architectures by automating long sequences of additive steps. The increasing sophistication of printers, materials, and generative design promises to make geometric complexity a non-issue in…
Despite substantial advances in the field, we still lack a predictive framework capable of guiding the discovery of new families of superconductors. While momentum-space approaches have advanced the microscopic understanding of…
We show both numerically and analytically that a chemically patterned active pore can act as a micro/nano-pump for fluids, even if it is fore-aft symmetric. This is possible due to a spontaneous symmetry breaking which occurs when advection…
A stable partitioned algorithm for fluid-structure interaction (FSI) problems that couple viscous incompressible flow with structural shells or beams is described. This added-mass partitioned (AMP) scheme uses Robin (mixed) interface…
Self-assembly is the autonomous organization of components into patterns or structures: an essential ingredient of biology and a desired route to complex organization. At equilibrium, the structure is encoded through specific interactions,…
Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…