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Motivated by the relevance of higher-order interactions in quantum physics and materials science at the nanoscale, recently a model has been introduced for new classes of networks that grow by the geometrically constrained aggregation of…
Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and…
Highly symmetric nano-shells are found in many biological systems, such as clathrin cages and viral shells. Several studies have shown that symmetric shells appear in nature as a result of the free energy minimization of a generic…
We report canonical and grand-canonical lattice Monte Carlo simulations of the self-assembly of addressable structures comprising hundreds of distinct component types. The nucleation behaviour, in the form of free-energy barriers to…
Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the framework of…
The design space for a self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. Using a…
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links,…
Understanding how highly symmetric, robust, monodisperse protein cages self-assemble can have major applications in various areas of bio-nanotechnology, such as drug delivery, biomedical imaging and gene therapy. We develop a model to…
Illumination of colloid sphere monolayers by circularly polarized beams enables the fabrication of concave patterns consisting of circular nanohole miniarrays that can be transferred into convex metal nanoparticle patterns via a lift-off…
Co-assembly of inorganic nanoparticles (NPs) and nanostructured polymer matrix represents an intricate interplay of enthalpic or entropic forces. Particle size largely affects the phase behavior of the nanocomposite. Theoretical studies…
Self-organized complex structures in nature, e.g. viral capsids, hierarchical biopolymers, and bacterial flagella, offer efficiency, adaptability, robustness, and multi-functionality. Can we program the self-assembly of three-dimensional…
We study structure, eigenvalue spectra and diffusion dynamics in a wide class of networks with subgraphs (modules) at mesoscopic scale. The networks are grown within the model with three parameters controlling the number of modules, their…
DNA nanoparticles with three-fold coordination have been observed to self-assemble in experiment into a network equivalent to the hexagonal (6.6.6) tiling, and a network equivalent to the 4.8.8 Archimedean tiling. Both networks are built…
We investigate simplicial complexes deterministically growing from a single vertex. In the first step, a vertex and an edge connecting it to the primordial vertex are added. The resulting simplicial complex has a 1-dimensional simplex and…
The fabrication of versatile building blocks that are reliably self-assemble into desired ordered and disordered phases is amongst the hottest topics in contemporary material science. To this end, microscopic units of varying complexity,…
Our work is concerned with simplicial complexes that describe higher-order interactions in real complex systems. This description allows to go beyond the pairwise node-to-node representation that simple networks provide and to capture a…
The design of large-scale colloidal quantum dots (QDs) assemblies and the investigation of their interaction with their close environment are of great interest for improving QD-based optoelectronic devices' performances. Understanding the…
Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations for many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree…
Lattice structures play a central role in spectral graph theory, offering analytical insight into diffusion, synchronization, and transport processes on regular discrete spaces. While their spectral properties are completely characterized…
In this study, we explore the interrelation between hypergraph symmetries represented by equivalence relations on the vertex set and the spectra of operators associated with the hypergraph. We introduce the idea of equivalence relation…