Related papers: Building a monostable tetrahedron
We construct the first dynamically stable ergostars (equilibrium neutron stars that contain an ergoregion) for a compressible, causal equation of state. We demonstrate their stability by evolving both strict and perturbed equilibrium…
The aim of this paper is to study all the natural first steps of the minimal model program for the moduli space of stable pointed curves. We prove that they admit a modular interpretation and we study their geometric properties. As a…
We build a model structure from the simple point of departure of a structured interval in a monoidal category - more generally, a structured cylinder and a structured co-cylinder in a category.
We introduce multi-soliton sets in the two-dimensional medium with the second-harmonic-generating nonlinearity subject to spatial modulation in the form of a triangle of singular peaks. Various families of symmetric and asymmetric sets are…
If the four triangular facets of a tetrahedron can be partitioned into pairs having the same area, then the triangles in each pair must be congruent to one another. A Heron-style formula is then derived for the volume of a tetrahedron…
Let M be an o-minimal structure with elimination of imaginaries, N an unstable structure definable in M. Then there exists X, interpretable in N, such that X with all the structure induced from N is o-minimal. In particular X is linearly…
When Morris and Thorne first proposed the possible existence of traversable wormholes, they adopted the following strategy: maintain complete control over the geometry, thereby leaving open the determination of the stress-energy tensor. In…
Until recently, the simplest known flexible polyhedron was Steffen's polyhedron on nine vertices. However, in 2024, an embedded flexible polyhedron on eight vertices was announced. It attains the known lower bound for the number of…
In this article a multi-segmented planar tensegrity mechanism was presented. This mechanism has a three-segment structure with each segment residing on top of another. The size of the segments may decrease proportionally from base to top,…
We produce the first regular unimodular triangulation of an arbitrary matroid base polytope. We then extend our triangulation to integral generalized permutahedra. Prior to this work it was unknown whether each matroid base polytope…
This paper constructs a Riemann surface associated to the icosahedron and discusses the geodesics associated to a flat metric on this surface. Because of the icosahedral symmetry, this is a distinguished special case of the example treated…
A system of a metastable phase with several sorts of heterogeneous centers is considered. An analytical theory for the process of decay in such a system has been constructed. The free energy of formation of a critical embryo is assumed to…
We consider a thin and narrow rectangular plate where the two short edges are hinged whereas the two long edges are free. This plate aims to represent the deck of a bridge, either a footbridge or a suspension bridge. We study a nonlocal…
We construct a model in which stable magnetic monopoles have magnetic charges that are identical to the electric charges on leptons and quarks and the colored monopoles are confined by strings in color singlets.
In this paper we introduce the notion of a patient first-mean stable system. Such systems are switched systems that are first-mean stable meaning that they converge to a globally attracting fixed point on average. They are also patient so…
These notes are a self-contained short proof of the stability of persistence diagrams.
In this survey results on the behavior of simple closed geodesics on regular tetrahedra in three-dimensional spaces of constant curvature are presented.
A novel self-assembly strategy for polypeptide nanostructure design was presented in [Design of a single-chain polypeptide tetrahedron assembled from coiled-coil segments, Nature Chemical Biology 9 (2013) 362--366]. The first mathematical…
The three-dimensional cranking model is used to investigate the microscopic aspects of the rotation of nuclei with the tetrahedral symmetry. Two classes of rotation axes are studied corresponding to two different discrete symmetries of the…
The one-dimensional toy models proposed for the three-dimensional electron magnetohydrodynamics in our previous work share some similarities with the original dynamics under certain symmetry. We continue to study the well-posedness issue…