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Bacterial genomes are partitioned into kilobases long domains that are topologically independent from each other, meaning that change of DNA superhelicity in one domain does not propagate to neighbours. This is made possible by proteins…
The effective surface dilatational viscosity is calculated of a flat interface separating two immiscible fluids laden with half-immersed monodisperse rigid spherical non-Brownian particles in the limit of high particle concentration. The…
Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…
In recent years the functionality of synthetic active microparticles has edged even closer to that of their biological counterparts. However, we still lack the understanding needed to recreate at the microscale key features of autonomous…
We study the problem of decomposing a volume bounded by a smooth surface into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled solution to this problem for generic smooth surfaces remained…
Connecting the collective behavior of disordered systems with local structure on the particle scale is an important challenge, for example in granular and glassy systems. Compounding complexity, in many scientific and industrial…
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of…
Discontinuous Galerkin (DG) schemes on unstructured meshes offer the advantages of compactness and the ability to handle complex computational domains. However, their robustness and reliability in solving hyperbolic conservation laws depend…
Cross-sections of cell shapes in a tissue monolayer typically resemble a tiling of convex polygons. Yet, examples exist where the polygons are not convex with curved cell-cell interfaces, as seen in the adaxial epidermis. To date,…
The packaging of genetic material within a protein shell, called the capsid, marks a pivotal step in the life cycle of numerous single-stranded RNA viruses. Understanding how hundreds, or even thousands, of proteins assemble around the…
To take full advantage of twisted bilayers of graphene or other two-dimensional materials, it is essential to precisely control the twist angle between the stacked layers, as this parameter determines the properties of the heterostructure.…
Consider a rational elliptic surface over a field $k$ with characteristic $0$ given by $\mathcal{E}: y^2 = x^3 + f(t)x + g(t)$, with $f,g\in k[t]$, $\text{deg}(f) \leq 4$ and $\text{deg}(g) \leq 6$. If all the bad fibres are irreducible,…
Bilayer graphene (BLG) has recently attracted a great deal of attention because of its electrically tunable energy gaps and its unusual electronic structure. In this Letter we present analytical and semi-analytical expressions, based on the…
Under the most common experimental conditions, the adsorption of proteins to solid surfaces is an spontaneous process that leads to a rather compact layer of randomly oriented molecules. Due to the importance of this process for the…
Although the auger-like 'swimming' motility of the African trypanosome was described upon its discovery over one hundred years ago, the precise biomechanical and biophysical properties of trypanosome flagellar motion has not been…
How can dense biological tissue maintain sharp boundaries between coexisting cell populations? We explore this question within a simple vertex model for cells, focusing on the role of topology and tissue surface tension. We show that the…
Twisted bilayer graphene (TBG) exhibits a wide range of intriguing physical properties, such as superconductivity, ferromagnetism, and superlubricity. Depending on the twist angle, periodic moir\'e superlattices form in twisted bilayer…
We develop coarse-grained models that describe the dynamic encapsidation of functionalized nanoparticles by viral capsid proteins. We find that some forms of cooperative interactions between protein subunits and nanoparticles can…
Living cells establish long-range orientational order through collective alignment, giving rise to topological defects whose functional relevance is increasingly recognized in tissue organization and morphogenesis. Engineered topographical…
Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity…