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In addition to novel surface states, topological insulators can also exhibit robust gapless states at crystalline defects. Step edges constitute a class of common defects on the surface of crystals. In this work we establish the topological…
We give an elementary new method for obtaining rigorous lower bounds on the connective constant for self-avoiding walks on the hypercubic lattice $Z^d$. The method is based on loop erasure and restoration, and does not require exact…
Previous efforts in complex networks research focused mainly on the topological features of such networks, but now also encompass the dynamics. In this Letter we discuss the relationship between structure and dynamics, with an emphasis on…
The structural and bonding properties of small neutral alkali-halide clusters (AX)n, with n less than or equal to 10, A=Li, Na, K, Rb and X=F, Cl, Br, I, are studied using the ab initio Perturbed Ion (aiPI) model and a restricted structural…
Phase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative way. In recent years, a number of novel topological metrics for microstructures…
Species interaction networks are a powerful tool for describing ecological communities; they typically contain nodes representing species, and edges representing interactions between those species. For the purposes of drawing abstract…
We simulate a model of repulsively interacting colloids on a commensurate two-dimensional triangular pinning substrate where the amount of heterogeneous motion that appears at melting can be controlled systematically by turning off a…
We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results established in [2]. First of all the random walk is transient in dimension at least three. Focusing on dimension two,…
We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40…
We reconsider the problem of even-visiting random walks in one dimension. This problem is mapped onto a non-Hermitian Anderson model with binary disorder. We develop very efficient numerical tools to enumerate and characterize even-visiting…
Hydrodynamic interactions driven by particle activity are ubiquitous in active colloidal systems. Although these interactions are strongly influenced by the interfacial actuation mechanism and geometry of the swimming particles, theoretical…
The work develops the structure-dynamic approach in nanoionics for detailed description of non-stationary ion-transport processes in irregular potential relief (direct problem) and interpretation of ionic properties and characteristics of…
Turn the set of permutations of $n$ objects into a graph $G_n$ by connecting two permutations that differ by one transposition, and let $\sigma_t$ be the simple random walk on this graph. In a previous paper, Berestycki and Durrett [In…
In this study, we performed comprehensive morphological investigations of the spontaneous formations of effective network structures among elements in coupled logistic maps, specifically with a delayed connection change. Our proposed model…
Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random…
Isomorphs are curves in the thermodynamic phase diagram of invariant excess entropy, structure, and dynamics, while pseudoisomorphs are curves of invariant structure and dynamics, but not of the excess entropy. The latter curves have been…
We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N; its mean…
Thermal transport properties at the metal/MoS2 interfaces are analyzed by using an atomistic phonon transport model based on the Landauer formalism and first-principles calculations. The considered structures include chemisorbed…
Analyzing the magnetic structure factor of a field demagnetized artificial square ice, qualitative deviations from what would predict the square ice model are observed. Combining micromagnetic and Monte Carlo simulations, we demonstrate…
Step edges of topological crystalline insulators can be viewed as predecessors of higher-order topology, as they embody one-dimensional edge channels embedded in an effective three-dimensional electronic vacuum emanating from the…