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Phyllotactic patterns, i.e. regular arrangements of leaves or seeds around a plant stem, are fascinating examples of complex structures encountered in Nature. In botany, their symmetries develop when a new primordium periodically grows in…
We determine the distribution of free ends and the monomer insertion potential in the strongly-stretched limit for regularly and statistically branched polymer brushes. We find that the end density flattens in the limit of very strong…
We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…
The work in this article is inspired by a classical problem: the statistical physical properties of a closed polymer loop that is wound around a rod. Historically the preserved topology of this system has been addressed through…
Polymers with active segments constitute prospective future materials and are used as a model for some biological systems such as chromatin. The directions of the active forces are typically introduced with temporal or spatial correlations…
Synchronization of mobile oscillators occurs in numerous contexts, including physical, chemical, biological and engineered systems. In vertebrate embryonic development, a segmental body structure is generated by a population of mobile…
The torsional elasticity of semiflexible polymers like DNA is of biological significance. A mathematical treatment of this problem was begun by Fuller using the relation between link, twist and writhe, but progress has been hindered by the…
The properties of a semiflexible polymer with fixed ends exposed to oscillatory shear flow are investigated by simulations. The two-dimensionally confined polymer is modeled as a linear bead-spring chain, and the interaction with the fluid…
We study the dynamics of a single chain polymer confined to a two dimensional cell. We introduce a kinetically constrained lattice gas model that preserves the connectivity of the chain, and we use this kinetically constrained model to…
Cells regulate gene expression in part by forming DNA-protein condensates in the nucleus. While existing theories describe the equilibrium size and stability of such condensates, their dynamics remain less understood. Here, we use…
A mesoscopic, mixed particle- and field-based Brownian dynamics methodology for the simulation of entangled polymer melts has been developed. Polymeric beads consist of several Kuhn segments, and their motion is dictated by the Helmholtz…
We investigate modifications of a stochastic polymer picture through a shift in the boundary between the system and an external environment. A conventional bead-and-spring model serving as the coarse-graining model is given by the Langevin…
We derive a coarse grained, free-energy functional which describes droplet configurations arising on nucleation of a product crystal within a parent. This involves a new `slow' vacancy mode that lives at the parent-product interface. A…
Here we study a driven lattice gas model for microtubule depolymerizing molecular motors, where traffic jams of motors induce stochastic switching between microtubule growth and shrinkage. We term this phenomenon \enquote{traffic dynamic…
While twist-bend nematic phases have been extensively studied, the experimental observation of two dimensional, oscillating splay-bend phases is recent. We consider two theoretical models that have been used to explain the formation of…
Phase separation within polymer networks plays a central role in shaping the structure and mechanics of both synthetic materials and living cells, including the formation of biomolecular condensates within cytoskeletal networks. Previous…
Charged (nano)particles confined in electrodynamic traps can evolve into strongly correlated Coulomb systems which are the subject of current investigation. Exciting physical phenomena associated to Coulomb systems are reported such as…
In this paper, we construct invariants of braids, knots and links by studying dynamics of points in $\R^{2}$ and applying the Ptolemy relation $ac+bd=xy$.
We propose a geometrically motivated mathematical model which reveals the key features of coastal and fluvial fragment shape evolution from the earliest stages of the abrasion. Our \textit{collisional polygon model} governs the evolution…
The emergence of spatially variable local dynamics, or dynamic heterogeneity, is common in multicomponent polymer systems. Although often attributed to differences in the intrinsic dynamics of each component, the molecular origin of their…