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Bound states of two interacting particles moving on a lattice can exhibit remarkable features that are not captured by the underlying single-particle picture. Inspired by this phenomenon, we introduce a novel framework by which genuine…
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…
One of the most important problems in development is how epigenetic domains can be first established, and then maintained, within cells. To address this question, we propose a framework which couples 3D chromatin folding dynamics, to a…
Helices are the quintessential geometric motif of the microscale, from alpha-helices in proteins to double helices in DNA. Assembly of the helical geometry of biopolymers is a foundational step in a hierarchy of structure that eventually…
A new discrete cohesive zone model (DCZM) is presented for modeling the interface behavior of adhesive-bonded thin laminates and sandwich panels. The proposed model treats the interface as a spring element and the adherent as a beam…
A statistical mechanical distance constraint model (DCM) is presented that explicitly accounts for network rigidity among constraints present within a system. Constraints are characterized by local microscopic free energy functions.…
Interlayer coupling in two-dimensional (2D) layered nanomaterials can provide us novel strategies to evoke their superior properties, such as the exotic flat bands and unconventional superconductivity of twisted layers, the formation of…
We propose that protein loops can be interpreted as topological domain-wall solitons. They interpolate between ground states that are the secondary structures like alpha-helices and beta-strands. Entire proteins can then be folded simply by…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
We study the topological properties of a kagome plasmonic metasurface, modelled with a coupled dipole method which naturally includes retarded long range interactions. We demonstrate the system supports an obstructed atomic limit phase…
We present a symmetry-based exhaustive approach to explore the structural and compositional richness of two-dimensional materials. We use a ``combinatorial engine'' that constructs potential compounds by occupying all possible Wyckoff…
We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…
The presence of nanoparticles in a diblock copolymer leads to changes in the morphology and properties of the matrix and can produce highly organized hybrid materials. The resulting material properties depend not only on the polymer…
By means of extensive replica-exchange simulations of generic coarse-grained models for helical polymers, we systematically investigate the structural transitions into all possible helical phases for flexible and semiflexible elastic…
A reduced model, which can fold both helix and sheet structures, is proposed to study the problem of protein folding. The goal of this model is to find an unbiased effective potential that has included the effects of water and at the same…
We propose and solve a simple model describing secondary structure formation in random hetero-polymers. It describes monomers with a combination of one-dimensional short-range interactions (representing steric forces and hydrogen bonds) and…
In systems characterized by a rough potential energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
The design of specified nonlinear mechanical responses into a structure or material is a highly sought after capability, which would have a significant impact in areas such as wave tailoring in metamaterials, impact mitigation, soft…
The microscopic structure of several amorphous substances often reveals complex patterns such as medium- or long-range order, spatial heterogeneity, and even local polycrystallinity. To capture all these features, models usually incorporate…