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From ancient to modern times, acoustic structures have been used to control the propagation of acoustic waves. However, the design of the acoustic structures has remained widely a time-consuming and computational resource-consuming…
In various biomedical applications, precise focusing of nonlinear ultrasonic waves is crucial for efficiency and safety of the involved procedures. This work analyzes a class of shape optimization problems constrained by general…
Canonical quantization has taught us great things. A common example is that of the harmonic oscillator, which is like swinging a ball on a string back and forth. However, the half-harmonic oscillator blocks the ball at the bottom and then…
Discretization of curves is an ancient topic. Even discretization of curves with an eye toward differential geometry is over a century old. However there is no general theory or methodology in the literature, despite the ubiquitous use of…
Many different proteins self-aggregate into insoluble fibrils growing apically by reversible addition of elementary building blocks. But beyond this common principle, the modalities of fibril formation are very disparate, with various…
We introduce ART, Articulated Reconstruction Transformer -- a category-agnostic, feed-forward model that reconstructs complete 3D articulated objects from only sparse, multi-state RGB images. Previous methods for articulated object…
We investigate an idealized model for the size reduction and smoothing of a polygonal rock due to repeated chipping at corners. Each chip is sufficiently small so that only a single corner and a fraction of its two adjacent sides are cut…
Trimming is a core technique in geometric modeling. Unfortunately, the resulting objects do not take the requirements of numerical simulations into account and yield various problems. This paper outlines principal issues of trimmed models…
Artificial gauge fields are currently realized in a wide range of physical settings. This includes solid-state devices but also engineered systems, such as photonic crystals, ultracold gases and mechanical setups. It is the aim of this…
The optical geometric phase encoded by the in-plane spatial orientation of microstructures has promoted the rapid development of numerous new-type optical meta-devices. However, pushing the concept of the geometric phase toward the acoustic…
The alignment of shapes has been a crucial step in statistical shape analysis, for example, in calculating mean shape, detecting locational differences between two shape populations, and classification. Procrustes alignment is the most…
For any classical field configuration or mechanical system with a finite number of degrees of freedom we introduce the concept of topological spectrum. It is based upon the assumption that for any classical configuration there exists a…
Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict…
Soft, amorphous solids such as tissues, foams, and emulsions are composed of deformable particles. However, the effect of single-particle deformability on the collective behavior of soft solids is still poorly understood. We perform…
We propose a simple method to measure acoustic responses using any sounds by converting them suitable for measurement. This method enables us to use music pieces for measuring acoustic conditions. It is advantageous to measure such…
Working over imperfect fields, we give a comprehensive classification of genus-one curves that are regular but not geometrically regular, extending the known case of geometrically reduced curves. The description is given intrinsically, in…
Shape calculus concerns the calculation of directional derivatives of some quantity of interest, typically expressed as an integral. This article introduces a type of shape calculus based on localized dilation of boundary faces through…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
The definition of the complement of a fuzzy subset is algebraic in nature and when it is used in the context of fuzzy topological spaces it does not share any similarity with the usual property of topological spaces that the complement of…
We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility.