Related papers: Geometry Selects Highly Designable Structures
Long range order and symmetry in heterogeneous materials architected on crystal lattices lead to elastic and inelastic anisotropies and thus limit mechanical functionalities in particular crystallographic directions. Here, we present a…
The aim of this paper is to rigorously study dynamics of Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called hubs, are very well connected while most nodes interact…
We present Monte Carlo simulation results for a two-dimensional Ising model with ferromagnetic nearest-neighbor couplings and a competing long-range dipolar interaction on a honeycomb lattice. Both structural and thermodynamic properties…
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…
From the complex motions of robots to the oxygen binding of hemoglobin, the function of many mechanical systems depends on large, coordinated movements of their components. Such movements arise from a network of physical interactions in the…
Folding channels and free-energy landscapes of hydrophobic-polar heteropolymers are discussed on the basis of a minimalistic off-lattice coarse-grained model. We investigate how rearrangements of hydrophobic and polar monomers in a…
Computational methods for designing interactions between colloidal particles that induce self-assembly have received much attention for their promise to discover tailored materials. However, it often remains a challenge to translate…
Designing complex engineered systems requires managing tightly coupled trade-offs between subsystem capabilities and resource requirements. Monotone co-design provides a compositional language for such problems, but its generality does not…
Geometrical properties of protein ground states are studied using an algebraic approach. It is shown that independent from inter-monomer interactions, the collection of ground state candidates for any folded protein is unexpectedly small:…
In the realm of functional materials, the production of two-dimensional structures with tuneable porosity is of paramount relevance for many practical applications: surfaces with regular arrays of pores can be used for selective adsorption…
Wang-Landau sampling has been applied to investigate the thermodynamics and structural properties of a lattice hydrophobic-polar heteropolymer (the HP protein model) interacting with an attractive substrate. For simplicity, we consider a…
Proteins are an example of heteropolymers able to self-assemble in specific target structures. The self-assembly of designed artificial heteropolymers is still, to the best of our knowledge, not possible with control over the single chain…
Adaptive transport networks in biological and physical systems exhibit hierarchical organization, characteristic channel spacing, and robust scaling relations. Existing adaptive network models, formulated on a lattice, successfully…
We study conformational transitions of simple coarse-grained models for protein-like heteropolymers on the simple cubic lattice and off-lattice, respectively, by means of multicanonical sampling algorithms. The effective hydrophobic/polar…
Correlation of interacting particles is studied in their dynamics and localization in ideal and disordered lattice systems with the help of numerical tools. Both 1D and 2D systems are considered. In 1D lattices with long-range hopping,…
We present some properties of hyperkahler torsion (or heterotic) geometry in four dimensions that make it even more tractable than its hyperkahler counterpart. We show that in $d=4$ hypercomplex structures and weak torsion hyperkahler…
Self-assembly in the laboratory can now yield `information-rich' nanostructures in which each component is of a distinct type and has a defined spatial position. Ensuring the thermodynamic stability of such structures requires…
We perform off-lattice, canonical ensemble molecular dynamics simulations of the self-assembly of long segmented copolymers consisting of alternating, tunably attractive and hydrophobic {\em binder} domains, connected by hydrophilic {\em…
Characterization of medium-range order in amorphous materials and its relation to short-range order is discussed. A new topological approach is presented here to extract a hierarchical structure of amorphous materials, which is robust…
The algebraic structure of the attractors in a dynamical system determine much of its global dynamics. The collection of all attractors has a natural lattice structure, and this structure can be detected through attracting neighborhoods,…