Related papers: Multilayered folding with voids
We propose and solve a simple model describing secondary structure formation in random hetero-polymers. It describes monomers with a combination of one-dimensional short-range interactions (representing steric forces and hydrogen bonds) and…
In this work we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We find an equation that relates the foliation with the ambient manifold and apply it to investigate conditions for the leaves…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…
We study segregation and stratification of mixtures of grains differing in size, shape and material properties poured in two-dimensional silos using a microscopic lattice model for surface flows of grains. The model incorporates the…
The problem of partially hinged and partially free rectangular plate that aims to represent a suspension bridge subject to some external forces (for example the wind) is considered in order to model and simulate the unstable end behavior.…
Soft and biological matter come in a variety of shapes and geometries. When soft surfaces that do not fit into each other due to a mismatch in Gaussian curvatures form an interface, beautiful geometry-induced patterns emerge. In this paper,…
A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is…
We propose that several mechanisms contribute to friction in a polymer melt adsorbed at a structured surface. The first one is the well known disentanglement of bulk polymer chains from the surface layer. However, if the surface is ideal at…
We investigate equilibrium microstructures exhibited by diblock copolymers in confined 3D geometries. We perform Self-Consistent Field Theory (SCFT) simulations using a finite-element based computational framework (Ackerman et al. 2017),…
We consider the influence of elasticity and anisotropic surface energy on the energy-minimizing shape of a two-dimensional void under biaxial loading. In particular, we consider void shapes with corners for which the strain energy density…
Particles interacting with short-ranged potentials have attracted increasing interest, partly for their ability to model mesoscale systems such as colloids interacting via DNA or depletion. We consider the free energy landscape of such…
We simulate a two dimensional model of self-propelled particles confined by a deformable boundary. The particles tend to accumulate near the boundary and the shape of the boundary deforms upon the collisions. We find that there are two…
Recent work on the dynamics of monolayers on a metallic substrate attached to a quartz oscillator has provided interesting data on kinetic friction at the microscopic level. Sliding of the film relative to the substrate is often observed…
We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending…
The phase structure of self-avoiding polymerized membranes is studied by extensive Hybrid Monte Carlo simulations. Several folding transitions from the flat to a collapsed state are found. Using a suitable order parameter and finite size…
We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This features the coupling of elastic response and electrostatics by means of a capacitary term, which is naturally defined in…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
We characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or…
A geometric analysis of the global properties of the energy landscape of a minimalistic model of a polypeptide is presented, which is based on the relation between dynamical trajectories and geodesics of a suitable manifold, whose metric is…