Related papers: Mass Generation from Embedding Geometry in Surface…
Induced by proteins within the cell membrane or by differential growth, heating, or swelling, spontaneous curvatures can drastically affect the morphology of thin bodies and induce mechanical instabilities. Yet, the interaction of…
Tailoring energy levels in quantum systems via Hamiltonian control parameters is essential for designing quantum thermodynamic devices and materials. However, conventional methods for manipulating finite-size systems, such as tuning…
These notes provide an introduction to the noncommutative matrix geometry which arises within matrix models of Yang-Mills type. Starting from basic examples of compact fuzzy spaces, a general notion of embedded noncommutative spaces…
This paper investigates the geometric consequences of equality in area-charge inequalities for spherical minimal surfaces and, more generally, for marginally outer trapped surfaces (MOTS), within the framework of the Einstein-Maxwell…
We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by "adiabatically" manipulating the environment with which it interacts. As…
It is proposed a new mechanism for the phenomenon of topological mass generation in three spacetime dimensions as the result of the interference of two opposite massless chiral modes. This mechanism, already used to produce the massive…
Curvature fundamentally alters the collective properties of soft, active, and biological materials. Here we study motility-induced phase separation (MIPS), a canonical non-equilibrium transition, and demonstrate that even weak and slowly…
We connect the theories of the deformation of elastic surfaces and phase surfaces arising in the description of almost periodic patterns. In particular, we show parallels between asymptotic expansions for the energy of elastic surfaces in…
Morphodynamic equations governing the behaviour of active nematic fluids on deformable curved surfaces are constructed in the large deformation limit. Emphasis is placed on the formulation of objective rates that account for normal…
Complex tissue flows in epithelia are driven by intra- and inter-cellular processes that generate, maintain, and coordinate mechanical forces. There has been growing evidence that cell shape anisotropy, manifested as nematic order, plays an…
Living cells respond to mechanical changes in the matrix surrounding them by applying contractile forces that are in turn transmitted to distant cells. We calculate the mechanical work that each cell performs in order to deform the matrix,…
We introduce Scan2Mesh, a novel data-driven generative approach which transforms an unstructured and potentially incomplete range scan into a structured 3D mesh representation. The main contribution of this work is a generative neural…
We describe Mosaic, a computational geometry method for constructing the surface mosaic induced when a Cartesian volume grid intersects a spherical shell. The motivating application is conservative coupling between data produced on…
We investigate the formation of trapped surfaces in cosmological spacetimes, using constant mean curvature slicing. Quantitative criteria for the formation of trapped surfaces demonstrate that cosmological regions enclosed by trapped…
We study geometrically-controlled twist transitions of a nematic confined between a sinusoidal grating and a flat substrate. In these cells the transition to the twisted state is driven by surface effects. We have identified the mechanisms…
Geometric momentum is the appropriate momentum for a particle constrained to move on a curved surface, which depends on the extrinsic curvature and leads to observable effects, and curvature-induced quantum potentials appear for a…
In this paper we investigate a mathematical model arising from volcanology describing surface deformation effects generated by a magma chamber embedded into Earth's interior and exerting on it a uniform hydrostatic pressure. The modeling…
Mapping a shape to some parametric domain is a fundamental tool in graphics and scientific computing. In practice, a map between two shapes is commonly represented by two meshes with same connectivity and different embedding. The standard…
The geometric effects of two-dimensional curved systems have been an interesting topic for a long time. A M\"{o}bius surface is specifically considered. For a relativistic particle confined to the nontrivial surface, we give the effective…
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…