相关论文: Rotation, Embedding and Topology for the Szekeres …

Ordered states of matter are typically categorized by their broken symmetries. With the ordering of spins in a ferromagnet or the freezing of a liquid into a solid, the loss of symmetry distinguishes the ordered state from the disordered…

We broaden the investigation of the dynamical properties of tidally perturbed, rotating star clusters by relaxing the traditional assumptions of coplanarity, alignment, and synchronicity between the internal and orbital angular velocity…

After introducing the Szekeres and Lema\^{\i}tre--Tolman cosmological models, the real-time cosmology program is briefly mentioned. Then, a few widespread misconceptions about the cosmological models are pointed out and corrected.…

Shell models provide a simplified mathematical framework that captures essential features of incompressible fluid turbulence, such as the energy cascade and scaling of the fluid observables. We perform a precision analysis of the direct and…

We show that model molecules with particular rotational symmetries can self-assemble into network structures equivalent to rhombus tilings. This assembly happens in an emergent way, in the sense that molecules spontaneously select irregular…

A new numerical framework, based on the use of a simple first order strongly hyperbolic evolution equations, is introduced and tested in case of 4-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that…

In this paper we consider two topological transforms that are popular in applied topology: the Persistent Homology Transform (PHT) and the Euler Characteristic Transform (ECT). Both of these transforms are of interest for their mathematical…

Classical Heisenberg spins in the continuum limit (i.e. the nonlinear sigma-model) are studied on an elastic cylinder section with homogeneous boundary conditions. The latter may serve as a physical realization of magnetically coated…

Inhomogeneous cosmological models are able to fit cosmological observations without dark energy under the assumption that we live close to the "center" of a very large-scale under-dense region. Most studies fitting observations by means of…

Spatial symmetries can enrich the topological classification of interacting quantum matter and endow systems with non-trivial strong topological invariants (protected by internal symmetries) with additional "weak" topological indices. In…

We follow our general model in Ref. [3] and analyze the formation of retinotopic projections for the biologically relevant situation of spherical geometries. To this end we elaborate both a linear and a nonlinear synergetic analysis which…

We consider three-dimensional Einstein gravity in Euclidean signature with a finite boundary of torus topology endowed with an induced metric of fixed conformal class and a constant trace of extrinsic curvature $K$. For vanishing, positive,…

See http://youtu.be/Mf4IE8gWcJs for a YouTube video showing part of the results in this paper. We consider helicoidal immersions in the Euclidean space whose axis of symmetry is the z-axis that are solutions of the equation 2 H=\Lambda_0-a…

Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects -- from atoms to the macroscopic scale -- transform under the action of rigid rotations. Equivariant models of…

Accurate rotation estimation is at the heart of robot perception tasks such as visual odometry and object pose estimation. Deep neural networks have provided a new way to perform these tasks, and the choice of rotation representation is an…

It is fairly well known that rotation in three dimensions can be expressed as a quadratic in a skew symmetric matrix via the Euler-Rodrigues formula. A generalized Euler-Rodrigues polynomial of degree 2n in a skew symmetric generating…

Mercury is entrapped in a 3:2 resonance: it rotates on its axis three times for every two revolutions it makes around the Sun. It is generally accepted that this is due to the large value of the eccentricity of its orbit. However, the…

The edge of torn elastic sheets and growing leaves often form a hierarchical buckling pattern. Within non-Euclidean plate theory this complex morphology can be understood as low bending energy isometric immersions of hyperbolic Riemannian…

Direct linkages between regular or irregular isometric embeddings of surfaces and steady compressible or incompressible fluid dynamics are investigated in this paper. For a surface $(M,g)$ isometrically embedded in $\mathbb{R}^3$, we…

We study the statistical properties of helicity in direct numerical simulations of fully developed homogeneous and isotropic turbulence and in a class of turbulence shell models. We consider correlation functions based on combinations of…