Related papers: Geometry of interactions in complex bodies
No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depends on the size of the probe used to observe it. As a consequence rough interfaces are abundant in nature. Here the old, but still active field…
The near-field interaction of an atom with a dielectric surface is inversely proportional to the cube to the distance to the surface, and its coupling strength depends on a dielectric image coefficient. This coefficient, simply given in a…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
We show that the detection of geometric intersection in an arbitrary representation of the mapping class group of surface implies the injectivity of that representation up to center, and vice versa. As an application, we discuss the…
Biological membranes often exhibit heterogeneous protein patterns, which cells control. Strong patterns, like the polarity spot in budding yeast, can be described as surface condensates, formed by physical interactions between constituents.…
Tribological phenomena are governed by combined effects of material properties, topology and surface-chemistry. We study the interplay of multiscale surface structures with molecular-scale interactions towards interpreting static frictional…
Fluid interfaces, such as soap films, liquid droplets or lipid membranes, are known to give rise to several special geometries, whose complexity and beauty continue to fascinate us, as observers of the natural world, and challenge us as…
The effective transport properties of heterogeneous nanoscale materials and structures are affected by several geometrical and physical factors. Among them the presence of imperfect interfaces plays a central role being often at the origin…
Fundamental biological and biomimetic processes, from tissue morphogenesis to soft robotics, rely on the propagation of chemical and mechanical surface waves to signal and coordinate active force generation. The complex interplay between…
The behavior of perturbations is studied in cosmological models which consist of two different homogeneous regions connected in a spherical shell boundary. The junction conditions for the metric perturbations and the displacements of the…
We consider a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss mean curvature flow scaled with a term that depends on a quantity…
Dense suspensions of fine particles are significant in numerous biological, industrial, and natural phenomena. They also provide an ideal tool to develop statistical mechanics description for out-of-equilibrium systems. Predicting the bulk…
Purely real space versions of the differential equations describing the kinematics of a dislocated crystalline medium are considered. The differential geometric structures associated with them are revealed.
In dense biological tissues, cell types performing different roles remain segregated by maintaining sharp interfaces. To better understand the mechanisms for such sharp compartmentalization, we study the effect of an imposed heterotypic…
In the present note we describe geometrically the homology classes in the total space of a surface bundle over a surface in terms of the holonomy map. We treat the cases where the base surface is closed or has one boundary component. We…
Invariants underlying shape inference are elusive: a variety of shapes can give rise to the same image, and a variety of images can be rendered from the same shape. The occluding contour is a rare exception: it has both image salience, in…
We study the properties of mode-mode interactions for waves propagating in nonlinear disordered one-dimensional systems. We focus on i) the localization volume of a mode which defines the number of interacting partner modes, ii) the overlap…
We combine standard persistent homology with image persistent homology to define a novel way of characterizing shapes and interactions between them. In particular, we introduce: (1) a mixup barcode, which captures geometric-topological…
Wetting phenomena, molecular protrusions of lipid bilayers and membrane stacks under lateral tension provide physical examples for interacting surfaces with tension. Such surfaces are studied theoretically using functional renormalization…
Pattern dynamics on curved surfaces are found everywhere in nature. The geometry of surfaces have been shown to influence dynamics and play a functional role, yet a comprehensive understanding is still elusive. Here, we report for the first…