相关论文: Kirchhoff-Love shell theory based on tangential di…

Inspired by recent results on self-avoiding inextensible curves, we propose and experimentally investigate a numerical method for simulating isometric plate bending without self-intersections. We consider a nonlinear two-dimensional…

We present a theoretical and computational framework based on fractional calculus for the analysis of the nonlocal static response of cylindrical shell panels. The differ-integral nature of fractional derivatives allows an efficient and…

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…

In this PhD thesis, we give a new geometric approach to higher Teichm\"uller theory. In particular we construct a geometric structure on surfaces, generalizing the complex structure, and we explore its link to Hitchin components. The…

We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have…

This paper addresses the question: What is the de Rham theory for general differentiable spaces? We identify two potential answers and study them. In the first part, we show that the de Rham cohomology calculated using (the completion of)…

We discuss in this paper the lattice discretizations of all topological defect lines (TDLs) for diagonal, minimal CFTs, using integrable restricted solid-on-solid (RSOS) models. For these CFTs, the TDLs can be labeled by the Kac labels. In…

Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires…

We present a new hybrid discrete exterior calculus (DEC) and finite difference (FD) method to simulate fully three-dimensional Boussinesq convection in spherical shells subject to internal heating and basal heating, relevant in the…

Helical configurations of inhomogeneous symmetric rods with non-constant bending and twisting stiffness are studied within the framework of the Kirchhoff rod model. From the static Kirchhoff equations, we obtain a set of differential…

We perform a dimension reduction analysis for a coupled rate-dependent/rate-independent adhesive-contact model in the setting of visco-elastodynamic plates. We work with a weak solvability notion inspired by the theory of (purely)…

Discrete exterior calculus offers a coordinate--free discretization of exterior calculus especially suited for computations on meshes over curved manifolds. The discretization of the wedge product, that would be compatible with discrete…

While shape optimization using isogeometric shells exhibits appealing features by integrating design geometries and analysis models, challenges arise when addressing computer-aided design (CAD) geometries comprised of multiple non-uniform…

We present a method for comparing the classical and quantum calculations of the electric quadrupolar Love number $k_2$ and show that our previous derivation of the quantum Love number of a quantum blackhole matches exactly the classical…

We present an open-source Python framework for the shape optimization of complex shell structures using isogeometric analysis (IGA). IGA seamlessly integrates computer-aided design (CAD) and analysis models by employing non-uniform rational…

Tidal Love numbers of anti-de Sitter black holes are understood as linear response coefficients governing how the holographically dual plasma polarizes when the geometry of the space, in which the plasma lives, is deformed. So far, this…

Tropical Differential Algebraic Geometry considers difficult or even intractable problems in Differential Equations and tries to extract information on their solutions from a restricted structure of the input. The Fundamental Theorem of…

A central problem of geometry is the tiling of space with simple structures. The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp…

The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…

In this paper we derive, by means of $\Gamma$-convergence, the shallow shell models starting from non linear three dimensional elasticity. We use the approach analogous to the one for shells and plates. We start from the minimization…