Related papers: Conformal Mapping on Rough Boundaries II: Applicat…
The morphology of a growing crystal surface is studied in the case of an unstable two-dimensional step flow. Competition between bunching and meandering of steps leads to a variety of patterns characterized by their respective instability…
Direct numerical simulations are conducted to study the receptivity and transition mechanisms in a solitary wave boundary layer developing over randomly organized wave-like bottom topography. The boundary layer flow shows a selective…
We use PDE methods as developed for the Liouville equation to study the existence of conformal metrics with prescribed singularities on surfaces with boundary, the boundary condition being constant geodesic curvature. Our first result shows…
When discretizing symmetric stress tensors in variational problems arising in continuum mechanics, one has to choose how to enforce the symmetry of the stress tensor: (i) strongly by requiring the discrete tensors to be pointwise symmetric…
We study dual conformal transformations of minimal area surfaces in $AdS_5 \times S^5$ corresponding to holographic smooth Wilson loops and some other related observables. To act with dual conformal transformations we map the string…
Finite element methods are used to study non-adhesive, frictionless contact between elastic solids with self-affine surfaces. We find that the total contact area rises linearly with load at small loads. The mean pressure in the contact…
The application of stress to multiphase solid-liquid systems often results in morphological instabilities. Here we propose a solid-solid phase transformation model for roughening instability in the interface between two porous materials…
Many solid mechanics problems on complex geometries are conventionally solved using discrete boundary methods. However, such an approach can be cumbersome for problems involving evolving domain boundaries due to the need to track boundaries…
Tube-like surfaces are widely encountered in geometry processing, engineering structures, and medical anatomy, yet their intrinsic longitudinal and circumferential topology is not well preserved by conventional planar annular or rectangular…
The stressed state of flattened thin elastic sheet, as well as that of translationally symmetric 3D solids, are effectively 2D problems. This paper study equilibrium state-of-stress in metrically-incompatible 2D elastic materials. The…
The load-area relation of rough surfaces is of great interest in tribology. For elastic-plastic solids with strain hardening, an incremental model is adopted to analyze the contact of rough surfaces, in which the contact is modeled by…
Superhydrophobic surfaces demonstrate promising potential for skin friction reduction in naval and hydrodynamic applications. Recent developments of superhydrophobic surfaces aiming for scalable applications use random distribution of…
A nonlinear inverse problem of antiplane elasticity for a multiply connected domain is examined. It is required to determine the profile of $n$ uniformly stressed inclusions when the surrounding infinite body is subjected to antiplane…
We consider several ways to test for topology directly in harmonic space by comparing the measured a_lm with the expected correlation matrices. Two tests are of a frequentist nature while we compute the Bayesian evidence as the third test.…
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…
Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace's equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in…
In this work, we introduce a novel computational framework for solving the two-dimensional Hele-Shaw free boundary problem with surface tension. The moving boundary is represented by point clouds, eliminating the need for a global…
In this paper we introduce conformal heat flow of (extrinsic) biharmonic maps on $4$-manifold, simply called bi-conformal heat flow (bi-CHF), and study its properties. Similar to other CHF of harmonic maps and regularized $n$-harmonic maps,…
The purpose of this paper is to analyze a mixed method for linear elasticity eigenvalue problem, which approximates numerically the stress, displacement, and rotation, by piecewise $(k+1)$, $k$ and $(k+1)$-th degree polynomial functions…
We study eigenvibrations for inhomogeneous string consisting of two parts with strongly contrasting stiffness and mass density. In this work we treat a critical case for the high frequency approximations, namely the case when the order of…