Related papers: A pumping lemma for non-cooperative self-assembly
We prove the unique assembly and unique shape verification problems, benchmark measures of self-assembly model power, are $\mathrm{coNP}^{\mathrm{NP}}$-hard and contained in $\mathrm{PSPACE}$ (and in $\mathrm{\Pi}^\mathrm{P}_{2s}$ for…
The thermodynamics of the O(N) nonlinear sigma model in 1+1 dimensions is studied. We calculate the finite temperature effective potential in leading order in the 1/N expansion and show that at this order the effective potential can be made…
There is evidence that the self-assembly of complex molecular systems often proceeds hierarchically, by first building subunits that later assemble in larger entities, in a process that can repeat multiple times. Yet, our understanding of…
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…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
The electric field grading of dielectric permittivity gradient devices is an effective way of enhancing their insulation properties. The in-situ electric field-driven assembly is an advanced method for the fabrication of insulation devices…
We present a mechanism and show two variants of a method where the average diameter of spontaneously (barrier-free) assembled single component unilamellar liposomes is intrinsic, in agreement with Helfrich's theory. It depends only on the…
We prove that by successively combining subassemblies, we can achieve sublinear construction times for "staged" assembly of micro-scale objects from a large number of tiny particles, for vast classes of shapes; this is a significant advance…
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,…
The study is devoted to the geometrically nonlinear simulation of fiber-reinforced composite structures. The applicability of the multiplicative approach to the simulation of viscoelastic properties of a composite material is assessed,…
It is broadly known that any parallelepiped tiles space by translating copies of itself along its edges. In earlier work relating to higher-dimensional sandpile groups, the second author discovered a novel construction which fragments the…
Using the numerical modular bootstrap, we constrain the space of 1+1d CFTs with a finite non-invertible global symmetry described by a fusion category $\mathcal{C}$. We derive universal and rigorous upper bounds on the lightest…
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 major goal in nanoscience and nanotechnology is the self-assembly of any desired complex structure with a system of particles interacting through simple potentials. To achieve this objective, intense experimental and theoretical efforts…
We use computer simulations to study a model, first proposed by Wales [1], for the reversible and monodisperse self-assembly of simple icosahedral virus capsid structures. The success and efficiency of assembly as a function of…
A challenge of molecular self-assembly is to understand how to design particles that self-assemble into a desired structure and not any of a potentially large number of undesired structures. Here we use simulation to show that a strategy of…
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…
Stripe patterns are ubiquitous in nature and everyday life. While the synthesis of these patterns has been thoroughly studied in the literature, their potential to control the mechanics of structured materials remains largely unexplored. In…
Equilibrium self-assembly and conventional materials processing techniques fall far short of mimicking dynamic self-actuating processes that are commonplace throughout biology. To bridge the gap between living and synthetic matter, we study…
Polypeptides can self-assemble into hierarchically organized fibrils consisting of a stack of individually folded polypeptides driven together by hydrophobic interaction. Using a coarse grained model, we systematically studied this…