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When two solids are squeezed together they will in general not make atomic contact everywhere within the nominal (or apparent) contact area. This fact has huge practical implications and must be considered in many technological…
We present a physical model for turbulent friction on rough surfaces with regularly distributed roughness elements. Wall shear stresses are expressed as functions of physical quantities. Surfaces with varying roughness densities and…
We extend the mathematical theory of rigidity of frameworks (graphs embedded in $d$-dimensional space) to consider nonlocal rigidity and flexibility properties. We provide conditions on a framework under which (I) as the framework flexes…
Natural images can be viewed as patchworks of different textures, where the local image statistics is roughly stationary within a small neighborhood but otherwise varies from region to region. In order to model this variability, we first…
Geometric phases play a crucial role in diverse fields. In chemistry they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wavefunction experiences quantum-mechanical…
A remarkable feature of static granular matter is the distribution of force along intricate networks. Even regular inter-particle contact networks produce wildly inhomogeneous force networks where certain "chains" of particles carry forces…
Two dimensional simulations of non-cohesive granular matter in a biaxial shear tester are discussed. The effect of particle elasticity on the mechanical behavior is investigated using two complementary distinct element methods (DEM): Soft…
We introduce an approximate model for predicting the net contact wrench between nominally rigid objects for use in simulation, control, and state estimation. The model combines and generalizes two ideas: a bed of springs (an "elastic…
The paper introduces a finite element method for the incompressible Navier--Stokes equations posed on a closed surface $\Gamma\subset\R^3$. The method needs a shape regular tetrahedra mesh in $\mathbb{R}^3$ to discretize equations on the…
In this paper we calculate the Casimir-Polder force density (force per unit area acting on the elements of the surface) on a metallic plate placed in front of a neutral atom. To obtain the force density we use the quantum operator…
Perturbative corrections to the Casimir free energy due to macroscopic roughness of dielectric interfaces are obtained in the framework of an effective low-energy field theory. It describes the interaction of electromagnetic fields with…
In both nature and engineering, loosely packed granular materials are often compacted inside confined geometries. Here, we explore such behaviour in a quasi-two dimensional geometry, where parallel rigid walls provide the confinement. We…
The adhesive contact between elastic solids with randomly rough, self affine fractal surfaces is studied by molecular dynamics (MD) simulations. The interfacial binding energy obtained from the simulations of nominally flat and curved…
Soft-bubble tactile sensors have the potential to capture dense contact and force information across a large contact surface. However, it is difficult to extract contact forces directly from observing the bubble surface because local…
A stress equilibration procedure for hyperelastic material models is proposed andanalyzed in this paper. Based on the displacement-pressure approximation computed with a stable finite element pair, it constructs, in a vertex-patch-wise…
Competing pinning effects on a D-dimensional interface by weak impurity disorder and a periodic potential of the underlying crystal lattice are analyzed for $2<D<4$. We use both the Gaussian variational method (GVM) and the functional…
We study an atomistic model that describes the microscopic formation of material voids inside elastically stressed solids under an additional curvature regularization at the discrete level. Using a discrete-to-continuum analysis, by means…
The motion-induced drag force acting on a particle moving parallel to an arrangement of $N$ objects is analyzed. Particular focus is placed on the nonequilibrium statistics of the interaction and on the interplay between the system's…
This paper presents an intuitive, geometrical derivation of the relativistic addition of velocities, and of the electromagnetic interaction between two uniformly moving charged particles, based on 2 spatial + 1 temporal dimensional…
This paper presents the Virtual Element Method (VEM) for the modeling of crack propagation in 2D within the context of linear elastic fracture mechanics (LEFM). By exploiting the advantage of mesh flexibility in the VEM, we establish an…