Related papers: The Theory of Multiple Peeling
Piecewise constant image approximations of sequential number of segments or clusters of disconnected pixels are treated. The method of majorizing of optimal approximation sequence by hierarchical sequence of image approximations is…
We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…
A continuum model of crack propagation is presented and discussed. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic and viscoelastic effects are…
Given a set of $n$ labeled points in general position in the plane, we remove all of its points one by one. At each step, one point from the convex hull of the remaining set is erased. In how many ways can the process be carried out? The…
This paper investigates the flow of a solidifying liquid film on a solid surface subject to a complex kinematics, a process relevant to pancake making and surface coating. The flow is modeled using the lubrication approximation, with a…
Crumpling of a thin film leads to a unique stiff yet lightweight structure. The stiffness has been attributed to a complex interplay between four basic elements - smooth bends, sharp folds, localized points (developable cones), and…
A stack of coated conductors is a perspective configuration for various applications of high temperature superconductors. We present an efficient fast Fourier transform-based numerical method for magnetization problems for a stack of flat…
In this paper, we describe a multiscale model based on magneto-static traps of neutral atoms or ion traps. The idea is to levitate a magnetic spinning top in the air repelled by a base magnet. For such a problem, we have to deal with…
Filtration of feed containing multiple species of particles is a common process in the industrial setting. In this work we propose a model for filtration of a suspension containing an arbitrary number of particle species, each with…
Flaps can be detached from a thin film glued on a solid substrate by tearing and peeling. For flat substrates, it has been shown that these flaps spontaneously narrow and collapse in pointy triangular shapes. Here we show that various…
In this paper a theory of reflective X-ray multilayer structures with a graded (slowly varying) period based on the coupled waves method and quasi-classical asymptotic expansions is reported. A number of exact solutions of the coupled wave…
We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some…
An equilibrium phase diagram for the shape of compressively strained free-hanging films is developed by total strain energy minimization. For small strain gradients {\Delta}{\epsilon}, the film wrinkles, while for sufficiently large…
The lifted multicut problem is a combinatorial optimization problem whose feasible solutions relate one-to-one to the decompositions of a graph $G = (V, E)$. Given an augmentation $\widehat{G} = (V, E \cup F)$ of $G$ and given costs $c \in…
Interest in inverse dynamical, spectral and scattering problems for differential equations on graphs is motivated by possible applications to nano-electronics and quantum waveguides and by a variety of other classical and quantum…
A study of crack patterns in laponite films of different thickness is presented. Two cracking regimes are observed. The earlier with a higher rate of desiccation and shrinking has predominantly four-fold vertices in the crack network, while…
This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…
The dimer tiling problem asks in how many ways can the edges of a graph be covered by dimers so that each site is covered once. In the special case of a planar graph, this problem has a solution in terms of a free fermionic field theory. We…
We study experimentally the fracture dynamics during the peeling at a constant velocity of a roller adhesive tape mounted on a freely rotating pulley. Thanks to a high speed camera, we measure, in an intermediate range of peeling…
Since the turn of the millennium, capitalizing on modern advances in mathematics and computation, a slew of computational models have been proposed in the literature with the objective of describing the nucleation and propagation of…