Related papers: Pebbles, graphs and equilibria: higher order shape…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
Topology and geometry of a sphere create constraints for particles that lie on its surface which they otherwise do not experience in Euclidean space. Notably, the number of particles and the size of the system can be varied separately,…
We use Stein characterizations to obtain new moment-type estimators for the parameters of three classical spherical distributions (namely the Fisher-Bingham, the von Mises-Fisher, and the Watson distributions) in the i.i.d. case. This leads…
In this work we obtain a new criterion to establish ergodicity and non-uniform hyperbolicity of smooth measures of diffeomorphisms. This method allows us to give a more accurate description of certain ergodic components. The use of this…
As the usage of 3D models increases, so does the importance of developing accurate 3D shape retrieval algorithms. A common approach is to calculate a shape descriptor for each object, which can then be compared to determine two objects'…
Two-dimensional random surfaces are studied numerically by the dynamical triangulation method. In order to generate various kinds of random surfaces, two higher derivative terms are added to the action. The phases of surfaces in the…
Understanding of sedimentation dynamics of particles in bounded fluids is of crucial importance for a wide variety of processes. While there is profound knowledge base regarding the sedimentation of rigid solid particles, the fundamental…
Structure-property relationships in ordered materials have long been a core principle in materials design. However, the intentional introduction of disorder into materials provides structural flexibility and thus access to material…
In this work model-based methods are employed along with machine learning techniques to classify sediments in oceanic environments based on the geoacoustic properties of a two-layer seabed. Two different scenarios are investigated. First, a…
The statistical objects characterizing turbulence in real turbulent flows differ from those of the ideal homogeneous isotropic model.They containcontributions from various 2d and 3d aspects, and from the superposition ofinhomogeneous and…
Unlike molecular crystals, soft self-assembled fibres, micelles, vesicles, etc., exhibit a certain order in the arrangement of their constitutive monomers, but also high structural dynamicity and variability. Defects and disordered local…
In this paper, we present a conceptual design of a novel gesture-based instruction/input device using wave detection. The device recogonizes/detects gestures from a person and based on which to give the specific orders/inputs to the…
Establishing character shape correspondence is a critical and fundamental task in computer vision and graphics, with diverse applications including re-topology, attribute transfer, and shape interpolation. Current dominant functional map…
High-order accurate summation-by-parts (SBP) finite difference (FD) methods constitute efficient numerical methods for simulating large-scale hyperbolic wave propagation problems. Traditional SBP FD operators that approximate first-order…
Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…
Local M-smoothers are interesting and important signal and image processing techniques with many connections to other methods. In our paper we derive a family of partial differential equations (PDEs) that result in one, two, and three…
We use an extended laser Doppler technique to track optically the velocity of individual particles in a high Reynolds number turbulent flow. The particle sizes are of the order of the Kolmogorov scale and the time resolution, 30…
A first-order transition is numerically found in a spherical surface model with skeletons, which are linked to each other at junctions. The shape of the triangulated surfaces is maintained by skeletons, which have a one-dimensional bending…
Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…
A multi-scale method for the hyperbolic systems governing sediment transport in subcritical case is developed. The scale separation of this problem is due to the fact that the sediment transport is much slower than flow velocity. We first…