Related papers: Reducing Tile Complexity for Self-Assembly Through…
Self-assembly materials are traditionally designed so that molecular or meso-scale components form a single kind of large structure. Here, we propose a scheme to create "multifarious assembly mixtures", which self-assemble many different…
Parallel tempering Monte Carlo has proven to be an efficient method in optimization and sampling applications. Having an optimized temperature set enhances the efficiency of the algorithm through more-frequent replica visits to the…
We give a stochastic optimization algorithm that solves a dense $n\times n$ real-valued linear system $Ax=b$, returning $\tilde x$ such that $\|A\tilde x-b\|\leq \epsilon\|b\|$ in time: $$\tilde O((n^2+nk^{\omega-1})\log1/\epsilon),$$ where…
An entangled multipartite system coupled to a zero-temperature bath undergoes rapid disentanglement in many realistic scenarios, due to local, symmetry-breaking, differences in the particle-bath couplings. We show that locally controlled…
We develop an optimization-based approach to the problem of reconstructing temperature-dependent material properties in complex thermo-fluid systems described by the equations for the conservation of mass, momentum and energy. Our goal is…
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…
Tasks such as classification of data and determining the groundstate of a Hamiltonian cannot be carried out through purely unitary quantum evolution. Instead, the inherent non-unitarity of the measurement process must be harnessed.…
Microstructural geometry plays a critical role in the response of heterogeneous materials. Consequently, methods for generating microstructural samples are increasingly crucial to advanced numerical analyses. We extend Sonon et al.'s…
We consider the thermodynamically driven self-assembly of spheres onto the surface of a central sphere. This assembly process forms self-limiting, or terminal, anisotropic clusters (N-clusters) with well defined structures. We use Brownian…
Molecular building blocks interacting at the nanoscale organize spontaneously into stable mono- layers that display intriguing long-range ordering motifs on the surface of atomic substrates. The patterning process, if appropriately…
High temperatures have dramatic negative effects on interconnect performance and, hence, numerous techniques have been proposed to reduce the power consumption of on-chip buses. However, existing methods fall short of fully addressing the…
In this paper we propose a research programme for getting structural characterisations for 2-dimensional languages generated by self-assembling tiles. This is part of a larger programme on getting a formal foundation of parallel,…
We propose a general framework for solving inverse self-assembly problems, i.e. designing interactions between elementary units such that they assemble spontaneously into a predetermined structure. Our approach uses patchy particles as…
Both biological and artificial self-assembly processes can take place by a range of different schemes, from the successive addition of identical building blocks, to hierarchical sequences of intermediates, all the way to the fully…
We introduce a partial decidability protocol for the Wang tiling problem (which is the prototype of undecidable problems in combinatorics and statistical physics) by constructing a suitable mapping from tilings of finite squares of…
Linear scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These…
We present an active tile assembly model which extends Winfree's abstract tile assembly model to tiles that are capable of transmitting and receiving binding site activation signals. In addition, we introduce a mathematical framework to…
Self-assembly via nanoscale phase-separation offers an elegant route to fabricate nanocomposites with physical properties unattainable in single-component systems. One important class of nanocomposites are optical metamaterials which…
We study O(N) symmetric supersymmetric models in three dimensions at finite temperature. These models are known to have an interesting phase structures. In particular, in the limit $N \to \infty$ one finds spontaneous breaking of scale…
In the task of unitarily cooling a quantum system with access to a larger quantum system, known as the machine or reservoir, how does the structure of the machine impact an agent's ability to cool and the complexity of their cooling…