Related papers: Fiber bundle topology optimization for surface flo…

We introduce a new "subpixel-smoothed projection" (SSP) formulation for differentiable binarization in topology optimization (TopOpt) as a drop-in replacement for previous projection schemes, which suffer from near-non-differentiability and…

We provide some general theoretical results to guide the optimization of transverse hydrodynamic phenomena in superhydrophobic channels. Our focus is on the canonical micro- and nanofluidic geometry of a parallel-plate channel with an…

A formulation of the shallow water equations adapted to general complex terrains is proposed. Its derivation starts from the observation that the typical approach of depth integrating the Navier-Stokes equations along the direction of…

A fully coupled implicit finite-volume algorithm for incompressible viscoelastic interfacial flows is proposed, whereby the viscoelasticity of the flow is described by an upper-convected Maxwell constitutive model, including limited…

We propose a new condition $\aleph$ which enables to get new results on integrable geodesic flows on closed surfaces. This paper has two parts. In the first, we strengthen Kozlov's theorem on non-integrability on surfaces of higher genus.…

We propose conditioning field initialization for neural network based topology optimization. In this work, we focus on (1) improving upon existing neural network based topology optimization, (2) demonstrating that by using a prior initial…

We investigate the topological structure of flows on the Girl's surfaces which is one of two possible immersions of the projective plane in three-dimensional space with one triple point of the selfintersection. First, we describe the…

We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…

Topological photonic crystals (PCs) can support robust edge modes to transport electromagnetic energy in an efficient manner. Such edge modes are the eigenmodes of the PDE operator for a joint optical structure formed by connecting together…

We propose a two-fold approach to model reduction of fluid-structure interaction. The state equations for the fluid are solved with reduced basis methods. These are model reduction methods for parametric partial differential equations using…

Representing 3D surfaces as level sets of continuous functions over $\mathbb{R}^3$ is the common denominator of neural implicit representations, which recently enabled remarkable progress in geometric deep learning and computer vision…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…

In this paper, we generalize the minimum flow decomposition problem (MFD) to incorporate uncertain edge capacities and tackle it from the perspective of robust optimization. In the classical flow decomposition problem, a network flow is…

Tractography traces the peak directions extracted from fiber orientation distribution (FOD) suffering from ambiguous spatial correspondences between diffusion directions and fiber geometry, which is prone to producing erroneous tracks while…

Permitting multiple materials within a topology optimization setting increases the search space of the technique, which facilitates obtaining high-performing and efficient optimized designs. Structures with multiple materials involving…

Topology optimization techniques have been applied in integrated optics and nanophotonics for the inverse design of devices with shapes that cannot be conceived by human intuition. At optical frequencies, these techniques have only been…

In this paper a phase-field approach for structural topology optimization for a 3D-printing process which includes stress constraint and potentially multiple materials or multiscales is analyzed. First order necessary optimality conditions…

Controlling structural complexity, particularly the number of holes, remains a fundamental challenge in topology optimization, with significant implications for both theoretical analysis and manufacturability. Most existing approaches rely…

To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…

This work presents a mathematical model for the optimal control of thin-film flows over a flexible topography influenced by an external force. Our thin-film model allows for the rupture of films as well as the coalescence of bubbles. The…