Related papers: On Exponents of Thickness in Geometry Rigidity Ine…
Theory and numerical simulations of the thinning of liquid threads at high superficial concentration of surfactants suggest the existence of an asymptotic regime where surface tension balances surface viscous stresses, leading to an…
Adhesion control at the interface of two surfaces is crucial in various applications, including the design of micro- and nanodevices such as microfluidic devices, triboelectric nanogenerators, biochips, and electronic sensors. Several…
For two different scenarios regarding thin elastic structures, described by 2d-F\"oppl-von K\'arm\'an plate models, we obtain energy scaling laws. Firstly, assuming the reference geometry being that of a singular excess-cone, we obtain…
We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells. In flat membranes with a shear modulus, thermal fluctuations increase the bending rigidity and reduce the in-plane elastic moduli in a…
We report experimental and computational observations of dynamic contact networks for colloidal suspensions undergoing shear thickening. The dense suspensions are comprised of sterically stabilized poly(methyl methacrylate) hard sphere…
We consider a perturbation $f$ of a hyperbolic toral automorphism $L$. We study rigidity related to exceptional properties of the strong and weak stable foliations for $f$. If the strong foliation is mapped to the linear one by the…
We investigate the interaction between two cracks propagating in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. We find that two tears converge along self-similar paths…
I consider the shape of a deformed elastic shell. Using the fact that the lowest-energy, small deformations are along infinitesimal isometries of the shell's mid-surface, I describe a class of weakly-stretching deformations for thin shells…
We establish a rigidity theorem for Brendle and Hung's recent systolic inequality, which involves Gromov's notion of \(T^{\rtimes}\)-stabilized scalar curvature. Our primary technique is the construction of foliations by free boundary…
The fracture toughness of Al/SiC nanolaminates with different layer thicknesses (in the range 10 to 100 nm) was measured by means of micropillar splitting and bending of a notched beam. The crack plane was perpendicular to the layers in the…
We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long time numerical simulations makes this system extremely valuable for wave turbulence studies.…
We show how rigidity emerges in experiments of sheared frictional granular materials by using generalizations of two methods for identifying rigid structures. Both approaches, the force-based dynamical matrix and the topology-based rigidity…
We contrast analytical results of a variety of growth models involving subdiffusion, thermal noise and quenched disorder with simulations of these models, concluding that the assumed self-affinity property is more an exception than a rule.…
The roughness exponent is reported in numerical simulations with a three-dimensional elastic beam lattice. Two different types of disorder have been used to generate the breaking thresholds, i.e., distributions with a tail towards either…
We discuss several issues regarding material homogeneity and strain compatibility for materially uniform thin elastic shells from the viewpoint of a 3-dimensional theory, with small thickness, as well as a 2-dimensional Cosserat theory. A…
We report a theoretical and numerical investigation of the linear and nonlinear dynamics of a thin liquid film of viscosity $\mu$ sandwiched between a solid substrate and an unbounded liquid bath of viscosity $\lambda \mu$. In the limit of…
This work is motivated by two central questions in the birational geometry of moduli spaces of curves -- Fulton's conjecture and the effective cone of $\bar M_g$. We study the algebro-geometric aspect of Teichmuller curves parameterizing…
The fatigue fracture surfaces of a metallic alloy, and the stress corrosion fracture surfaces of glass are investigated as a function of crack velocity. It is shown that in both cases, there are two fracture regimes, which have a well…
In this paper, we give some new characterizations of umbilic hypersurfaces in general warped product manifolds, which can be viewed as generalizations of the work in \cite{KLP18} and \cite{WX14}. Firstly, we prove the rigidity for…
We prove rigidity for hypersurfaces with boundary in the unit $(n+1)$-sphere with scalar curvature bounded below by $n(n-1)$. Under appropriate boundary conditions, the hypersurfaces are shown to be part of the equatorial spheres. The lower…