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In this paper we study the role of topology in DNA gel electrophoresis experiments via molecular dynamics simulations. The gel is modelled as a 3D array of obstacles from which half edges are removed at random with probability p, thereby…
We investigate with numerical simulations the molecular origin of viscosity in melts of flexible and semiflexible oligomer rings in comparison to corresponding systems with linear chains. The strong increase of viscosity with ring stiffness…
This paper considers the cohomology and bounded interpolation of nonstandard finite element complexes, e.g. Stokes, Hessian, Elasticity, divdiv. Compared to the standard finite element exterior calculus, the main challenge is the existence…
Helices are not generic outcomes of polymer collapse. Collapsed conformations of semiflexible polymers with isotropic attractions typically form globules, toroids, or rod-like structures, as seen in simulations and described by…
Filamentous cyanobacteria, forming long strands of connected cells, are one of the earliest and most successful forms of life on Earth. They exhibit self-organised behaviour, forming large-scale patterns in structures like biomats and…
Macrochains of topologically interlocked rings with unique physical properties have recently gained considerable interest in supramolecular chemistry, biology, and soft matter. Most of the work has been, so far, focused on linear chains and…
Helical structures are exciting and are utilized in numerous applications ranging from biotechnology to displays to medicine. Accurate description and understanding of resonance effects in helical structures provides crucial knowledge on…
The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows…
In this article, we introduce a framework to investigate the growth of nano-crystallites in a polymer matrix numerically. This framework combines the Flory theory of entropic elasticity with phase-field approaches commonly used to model…
We study the dynamics and patterning of polar contractile filaments on the surface of a cylindrical cell using active hydrodynamic equations that incorporate couplings between curvature and filament orientation. Cables and rings…
Self-shaping of curved structures, especially those involving flexible thin layers, has attracted increasing attention because of their broad potential applications in e.g. nanoelectromechanical/micro-electromechanical systems (NEMS/MEMS),…
The importance of nonlinearities in material constitutive relations has long been appreciated in the continuum mechanics of macroscopic rods. Although the moment (torque) response to bending is almost universally linear for small deflection…
Necking instabilities, in which tensile (extensional) deformation localizes into a small spatial region, are generic failure modes in elasto-viscoplastic materials. Materials in this very broad class --- including amorphous, crystalline,…
Helical structures are ubiquitous in nature and engineering, ranging from DNA molecules to plant tendrils, from sea snail shells to nanoribbons. While the helical shapes in natural and engineered systems often exhibit nearly uniform radius…
We study how the three-dimensional shape of rigid filaments determines the microscopic dynamics and macroscopic rheology of entangled semi-dilute Brownian suspensions. To control the filament shape we use bacterial flagella, which are…
Tangled active filaments are ubiquitous in nature, from chromosomal DNA and cilia carpets to root networks and worm blobs. How activity and elasticity facilitate collective topological transformations in living tangled matter is not well…
The unique properties of topological semimetals have strongly driven efforts to seek for new topological phases and related materials. Here, we identify a critical condition for the existence of linked nodal rings (LNRs) in symmorphic…
Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be…
We initiate the homotopical study of racks and quandles, two algebraic structures that govern knot theory and related braided structures in algebra and geometry. We prove analogs of Milnor's theorem on free groups for these theories and…
Shells, when confined, can deform in a broad assortment of shapes and patterns, often quite dissimilar to what is produced by their flat counterparts (plates). In this work we discuss the morphological landscape of shells deposited on a…