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Blends of polymers of different topologies, such as ring and supercoiled, naturally occur in biology and often exhibit emergent viscoelastic properties coveted in industry. However, due to their complexity, along with the difficulty of…
We develop a mathematical model for the energy landscape of polyhedral supramolecular cages recently synthesized by self-assembly [Sun et al., Science 2010]. Our model includes two essential features of the experiment: (i) geometry of the…
Athermal models of disordered fibrous networks are highly useful for studying the mechanics of elastic networks composed of stiff biopolymers. The underlying network architecture is a key aspect that can affect the elastic properties of…
While superconductors are conventionally established by attractive interactions, higher-temperature mechanisms for emergent electronic pairing from strong repulsive electron-electron interactions remain under considerable scrutiny. Here, we…
Two-state cooperativity is an important characteristic in protein folding. It is defined by a depletion of states lying energetically between folded and unfolded conformations. While there are different ways to test for two-state…
A core challenge in the interpretation of deep neural networks is identifying commonalities between the underlying algorithms implemented by distinct networks trained for the same task. Motivated by this problem, we introduce DYNAMO, an…
The success of topological insulators (TI) in creating devices with unique functionalities is directly connected to the ability of coupling their helical spin states to well defined perturbations. However, up to now, TI-based…
Molecular self-assembly plays a very important role in various aspects of technology as well as in biological systems. Governed by the covalent, hydrogen or van der Waals interactions - self-assembly of alike molecules results in a large…
Latent space models are frequently used for modeling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well-developed for more complex…
The 2-fold degeneracy of the ground state of a quasi-one-dimensional system allows it to support topological excitations such as solitons. We study the combined effects of Coulomb interactions and confinement due to interchain coupling on…
We study the many-body phases of bosonic atoms with $N$ internal states confined to a 1D optical lattice under the influence of a synthetic magnetic field and strong repulsive interactions. The $N$ internal states of the atoms are coupled…
Biological molecules can form hydrogen bonds between nearby residues, leading to helical secondary structures. The associated reduction of configurational entropy leads to a temperature dependence of this effect: the "helix-coil…
The coupling interactions between deformable structures and unsteady fluid flows occur across a wide range of spatial and temporal scales in many engineering applications. These fluid-structure interactions (FSI) pose significant challenges…
Building structures with hierarchical order through the self-assembly of smaller blocks is not only a prerogative of nature, but also a strategy to design artificial materials with tailored functions. We explore in simulation the…
The ability to manipulate two-dimensional (2D) electrons with external electric fields provides a route to synthetic band engineering. By imposing artificially designed and spatially periodic superlattice (SL) potentials, 2D electronic…
Scaffold proteins organize cellular processes by bringing signaling molecules into interaction, sometimes by forming large signalosomes. Several of these scaffolds are known to polymerize. Their assemblies should therefore not be understood…
We introduce two partially overlapping classes of pathwise dualities between interacting particle systems that are based on commutative monoids (semigroups with a neutral element) and semirings, respectively. For interacting particle…
We present the results of analytic calculations and numerical simulations of the behaviour of a new class of chain molecules which we call thick polymers. The concept of the thickness of such a polymer, viewed as a tube, is encapsulated by…
In this work, a new class of vector-valued phase field models is presented, where the values of the phase parameters are constrained by a convex set. The generated phase fields feature the partition of the domain into patches of distinct…
While intersections of convex sets are convex, their unions have rather complicated behavior. Some natural contexts where they appear include duality arguments involving boundaries of convex sets and valuations, which have an Euler…