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…
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 terms of the gauged nonlinear $\sigma$-models, we describe some results and implications of solving the following problem: Given a smooth symplectic manifold as target space with a quasi-free Hamiltonian group action, perform the…
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…
A one-dimensional model of inertial pumping is introduced and solved. The pump is driven by a high-pressure vapor bubble generated by a microheater positioned asymmetrically in a microchannel. The bubble is approximated as a short-term…
The simulated self-assembly of molecular building blocks into functional complexes is a key area of study in computational biology and materials science. Self-assembly simulations of proteins using physically-motivated potentials for…
We present fast simulation methods for the self-assembly of complex shapes in two dimensions. The shapes are modeled via a general boundary curve and interact via a standard volume term promoting overlap and an interpenetration penalty. To…
Topological photonics was initially inspired by the quantum-optical analogy between the Schr\"odinger equation for an electron wavefunction and the paraxial equation for a light beam. Here, we reveal an unexpected phenomenon in topological…
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…
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…
Probabilistic models of directed polymers in random environment have received considerable attention in recent years. Much of this attention has focused on integrable models. In this paper, we introduce some new computational tools that do…
Existing computationally efficient methods for penalized likelihood GAM fitting employ iterative smoothness selection on working linear models (or working mixed models). Such schemes fail to converge for a non-negligible proportion of…
An aperiodic tile set was first constructed by R.Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics ranging from logic (the Entscheidungsproblem) to physics…
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…
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…
Many remarkably robust, rapid and spontaneous self-assembly phenomena in nature can be modeled geometrically starting from a collection of rigid bunches of spheres. This paper highlights the role of symmetry in sphere-based assembly…
We investigate general properties of non-deterministic self-assembly with asymmetric interactions, using a computational model and DNA tile assembly experiments. By contrasting symmetric and asymmetric interactions we show that the latter…
Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow…
Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of…
Self-assembly plays an essential role in many natural processes, involving the formation and evolution of living or non-living structures, and shows potential applications in many emerging domains. In existing research and practice, there…