Related papers: General theory for packing icosahedral shells into…
Recently low-temperature structural transition has been reported for complex cubic compounds Cd6M (M=Ca, Yb, Y, rare earth) and it is believed that the transition is due to orientational ordering of an atomic shell in the icosahedral…
We apply Landau theory of crystallization to explain and to classify the capsid structures of small viruses with spherical topology and icosahedral symmetry. We develop an explicit method which predicts the positions of centers of mass for…
A general method is described for detecting and analysing galaxy systems. The multivariate geometrical structure of the sample is studied by using an extension of the method which we introduced in a previous paper. The method is based on an…
We develop a general theory for estimating the probability that a galaxy cluster of a given shape exists. The theory is based on the observed result that the distribution of galaxies is very close to quasi-equilibrium, in both its linear…
For a three dimensional system we answer two questions, how simple a particle system might be to show the quasicrystal order and, what system features are the most important for quasicrystal formation? One-component system of particles with…
One emerging approach for the fabrication of complex architectures on the nanoscale is to utilize particles customized to intrinsically self-assemble into a desired structure. Inverse methods of statistical mechanics have proven…
We present a universal method for the large-scale prediction of the atomic structure of clusters. Our algorithm performs the joint evolutionary search for all clusters in a given area of the compositional space and takes advantage of…
There is a growing interest in cylindrical structures of hard and soft particles. A promising new method to assemble such structures has recently been introduced by Lee et al. [T. Lee, K. Gizynski, and B. Grzybowski, Adv. Mater. 29, 1704274…
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,…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
The mechanical, optical, and chemical properties of a wide variety of soft materials are enabled and constrained by their bulk structure. How this structure emerges at small system sizes during self-assembly has been the subject of decades…
Spherical nanoclusters and nanoparticles are rising materials whose functional design provides many useful applications ranging from catalysis, molecular sensing, gas storage to drug targeting and delivery. Here, we develop phenomenological…
We present a new theoretical framework for modelling the cluster growing process. Starting from the initial tetrahedral cluster configuration, adding new atoms to the system and absorbing its energy at each step, we find cluster growing…
Hard helices can be regarded as a paradigmatic elementary model for a number of natural and synthetic soft matter systems, all featuring the helix as their basic structural unit: from natural polynucleotides and polypeptides to synthetic…
Let $S$ be a surface, $G$ a simply-connected classical group, and $G'$ the associated adjoint form of the group. In \cite{FG1}, it was shown that the moduli spaces of framed local systems $\X_{G',S}$ and $\A_{G,S}$ have the structure of…
High-throughput computational materials searches generate large databases of locally-stable structures. Conventionally, the needle-in-a-haystack search for the few experimentally-synthesizable compounds is performed using a convex hull…
The kinetics of aggregation in a monolayer of magnetic particles are studied using stochastic dynamics computer simulations. At low densities (<8% coverage) the equilibrium structure is made up of chains and rings; the primary mechanisms by…
Many biological and synthetic materials self-assemble into helical or twisted aggregates. The shape is determined by a complex interplay between elastic forces and the orientation and chirality of the constituent molecules. We study this…
Two typical morphology of two-dimensional aggregates are considered: compact crystalline clusters and string-like non-compact conformations. Simulated trajectories of both types of aggregates are analysed with fine spatial resolution. While…
We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical…