Related papers: Intrinsic universality in tile self-assembly requi…
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,…
Assembly Theory (AT) and its central measure, the assembly index (Ai), represent an invaluable opportunity to address some of the most persistent and widespread conflations and misconceptions about computability and complexity theory in…
Multi-component self-assembly mixtures offer the possibility of encoding multiple target structures with the same set of interacting components. Selective retrieval of one of the stored structures has been attempted by preparing an initial…
The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's…
We consider generalized quantum Ising models, including those which could describe disordered materials or quantum annealers, and we prove that for all temperatures above a system-size independent threshold the path integral Monte Carlo…
Multifarious assembly models consider multiple structures assembled from a shared set of components, reflecting the efficient usage of components in biological self-assembly. These models are subject to a high-dimensional parameter space,…
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
In contrast to most self-assembling synthetic materials, which undergo unbounded growth, many biological self-assembly processes are self-limited. That is, the assembled structures have one or more finite dimensions that are much larger…
The impact of confinement on self-assembly of particles interacting with short-range attraction and long-range repulsion (SALR) potential is studied for thermodynamic states corresponding to local ordering of clusters or layers in the bulk.…
We present a unified perspective on nonequilibrium heat engines by generalizing nonlinear irreversible thermodynamics. For tight-coupling heat engines, a generic constitutive relation of nonlinear response accurate up to the quadratic order…
Controlling the topology of structures self-assembled from a set of heterogeneous building blocks is highly desirable for many applications, but is poorly understood theoretically. Here we show that the thermodynamic theory of self-assembly…
Numerous tasks at the core of statistics, learning and vision areas are specific cases of ill-posed inverse problems. Recently, learning-based (e.g., deep) iterative methods have been empirically shown to be useful for these problems.…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
A hallmark of living systems is the ability to employ a common set of versatile building blocks that can self-organize into a multitude of different structures, in a way that can be controlled with minimal cost. This capability can only be…
We introduce a general-purpose framework for interconnecting scientific simulation programs using a homogeneous, unified interface. Our framework is intrinsically parallel, and conveniently separates all component numerical modules in…
Let $Y$ denote a $D$-class symmetric association scheme with $D \geq 3$, and suppose $Y$ is almost-bipartite P- and Q-polynomial. Let $x$ denote a vertex of $Y$ and let $T=T(x)$ denote the corresponding Terwilliger algebra. We prove that…
We address three problems faced by effective interfacial Hamiltonian models of wetting based on a single collective coordinate \ell representing the position of the unbinding fluid interface. Problems (P1) and (P2) refer to the predictions…
Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…
We introduce a computational framework to statistically infer thermophysical properties of any given wall from in-situ measurements of air temperature and surface heat fluxes. The proposed framework uses these measurements, within a…
Most large engineering structures are described as assemblies of plates and shells and they are computed as such using adhoc Finite Element packages. In fact their computation in 3D would be much too costly. In this framework, the…