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Active matter agents consume internal energy or extract energy from the environment for locomotion and force generation. Already rather generic models, such as ensembles of active Brownian particles, exhibit phenomena, which are absent at…
We present simulation results for single a-thermal chain polymers in finite volumes. For this we use a recently proposed recursive implementation of the enrichment method. In 3 dimensions it allows the simulation of extremely long chains…
Matter agglomeration mesoscopic phenomena of irreversible type are well described by nonequilibrium thermodynamics formalism. The description assumes that the thermodynamic (internal) state variables are in local equilibrium, and uses the…
Implicit in the RNA world hypothesis is that prebiotic RNA synthesis, despite occurring in an environment without biochemical catalysts, produced the long RNA polymers which are essential to the formation of life. In order to investigate…
We write exact equations for the thermodynamic properties of a linear polymer molecule confined to walk on a lattice of finite size. The dimension of the space in which the lattice resides can be arbitrary. We also calculate polymer…
Polymer association at liquid-liquid interfaces is a promising way to spontaneously obtain soft self-healing membranes. In the case of reversible bonding between two polymers, the macromolecules are mobile everywhere within the membrane and…
We investigate the motion of two overlapping polymers with self-avoidance confined in a narrow 2d box. A statistical model is constructed using blob free-energy arguments. We find spontaneous segregation under the condition: $L > R_{//}$,…
In the first chapter of Shannon's "A Mathematical Theory of Communication," it is shown that the maximum entropy rate of an input process of a constrained system is limited by the combinatorial capacity of the system. Shannon considers…
A computational framework that leverages data from self-consistent field theory simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. This is a substantial two-dimensional…
Computing equilibrium concentrations of molecular complexes is generally analytically intractable and requires numerical approaches. In this work we focus on the polymer-monomer level, where indivisible molecules (monomers) combine to form…
We construct $n$-node graphs on which any $O(n)$-size spanner has additive error at least $+\Omega(n^{3/17})$, improving on the previous best lower bound of $\Omega(n^{1/7})$ [Bodwin-Hoppenworth FOCS '22]. Our construction completes the…
We investigate the copolymerization behavior of a two-component system into quasi-linear self-assemblies under conditions that interspecies binding is favored over identical species binding. The theoretical framework is based on a…
We present the exact solutions of various directed walk models of polymers confined to a slit and interacting with the walls of the slit via an attractive potential. We consider three geometric constraints on the ends of the polymer and…
Probabilistic models of directed polymers in random environment have received considerable attention in recent years. Much of this attention has focused on integrable models. In this paper, we introduce some new computational tools that do…
We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence is equivalent to asymptotic independence…
We present experimental evidence that the effective medium approximation (EMA), developed by D.C. Morse [Phys. Rev. E {\bf 63}, 031502, (2001)], provides the correct scaling law of the macroscopic plateau modulus…
The interplay of topological constraints, excluded volume interactions, persistence length and dynamical entanglement length in solutions and melts of linear chains and ring polymers is investigated by means of kinetic Monte Carlo…
Natural systems, such as tendons and spider silk, demonstrate how the combination of strength and stretchability can be effectively achieved by integrating stiff and flexible network structures. Inspired by these systems, we developed a…
The generation of molecules with Artificial Intelligence (AI) is poised to revolutionize materials discovery. Potential applications range from development of potent drugs to efficient carbon capture and separation technologies. However,…
A lattice model is presented for the simulation of dynamics in polymeric systems. Each polymer is represented as a chain of monomers, residing on a sequence of nearest-neighbor sites of a face-centered-cubic lattice. The polymers are self-…