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Consider a deformable body immersed in an incompressible fluid that is randomly stirred. Sticking to physical situations in which the body departs only slightly from its spherical shape, we investigate the deformations of the body. The…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
We consider amplituhedron-like geometries which are defined in a similar way to the intrinsic definition of the amplituhedron but with non-maximal winding number. We propose that for the cases with minimal number of points the canonical…
We prove the well-definedness of some deformations of the fibred biset category in characteristic zero. The method is to realize the fibred biset category and the deformations as the invariant parts of some categories whose compositions are…
The time evolution of wave packets in a harmonic oscillator potential is studied. Some new results for the most general case are obtained. A natural number, called ``degree of rigidity'', is introduced to describe qualitatively how much the…
A sound source was proposed for acoustic measurements of physical models of the human vocal tract. The physical models are produced by Fast Prototyping, based on Magnetic Resonance Imaging during prolonged vowel production. The sound…
We consider practical aspects of reconstructing planar curves with prescribed Euclidean or affine curvatures. These curvatures are invariant under the special Euclidean group and the equi-affine groups, respectively, and play an important…
Inspired by biological systems, we introduce a general framework for quasi-static shape control of human-scale structures under slowly varying external actions or requirements. In this setting, shape control aims to traverse the stable…
A formulation for a non-trivial composition of two classical gauge structures is given: Two parent gauge structures of a common base space are synthesized so as to obtain a daughter structure which is fundamental by itself. The model is…
We present Shape-Haptics, an approach for designers to rapidly design and fabricate passive force feedback mechanisms for physical interfaces. Such mechanisms are used in everyday interfaces and tools, and they are challenging to design.…
A sharp bending scheme for the self-collimation of acoustic waves is proposed by simply truncating the sonic crystals. An all-angle and wide-band 90{\deg}-bending wave guide is demonstrated with nearly perfect transmissions for Gaussian…
Let X be a projective, equidimensional, singular scheme over an algebraically closed field. Then the existence of a geometric smoothing (i.e. a family of deformations of X over a smooth base curve whose generic fibre is smooth) implies the…
By the time of writing, quantum audio still is a very young area of study, even within the quantum signal processing community. This chapter introduces the state of the art in quantum audio and discusses methods for the quantum…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
Of all the characteristics of a violin, those that concern its shape are probably the most important ones, as the violin maker has complete control over them. Contemporary violin making, however, is still based more on tradition than…
The complete set of bounds for the technical constants of an elastic layer, plate or laminate is given. The bounds are valid in general, also for completely anisotropic bodies. They are obtained transforming the polar bounds previously…
Triaxial weaving is a handicraft technique that has long been used to create curved structures using initially straight and flat ribbons. Weavers typically introduce discrete topological defects to produce nonzero Gaussian curvature, albeit…
Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily…
Neural fields are receiving increased attention as a geometric representation due to their ability to compactly store detailed and smooth shapes and easily undergo topological changes. Compared to classic geometry representations, however,…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…