Related papers: Statistics of ambiguous rotations
It is shown that nonsymmetric microobjects orient while settling under gravity in a viscous fluid. To analyze this process, a simple shape is chosen: a non-deformable `chain'. The chain consists of two straight arms, made of touching solid…
Topological defects are an essential part of the structure and dynamics of all liquid crystals, and they are particularly important in experiments and simulations on active liquid crystals. In a recent paper, Vromans and Giomi [Soft Matter,…
Plasticity in amorphous solids is mediated by localized quadrupolar instabilities, but the mechanism by which an amorphous solid eventually fails or melts is debated. In this work we argue that these phenomena can be investigated in the…
An inversion transformation applied to an inertial observer is used to generate a nonstatic conformally flat geometry in spherical coordinates. A static observer in the new geometry is uniformly accelerating with respect to the inertial one…
We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the way we introduce a new class of combinatorial matroids and associated linear…
Graph maps that are homotopic to the identity and that permute the vertices are studied. Given a periodic point for such a map, a {\em rotation element} is defined in terms of the fundamental group. A number of results are proved about the…
In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this…
This paper presents a set of general strategies for the analysis of structure in amorphous materials and a general approach to assessing the utility of a selected structural description. Measures of structural diversity and utility are…
In many mathematical models for pattern formation, a regular hexagonal pattern is stable in an infinite region. However, laboratory and numerical experiments are carried out in finite domains, and this imposes certain constraints on the…
In uniaxial soft matter with a reorientational nonlinearity, such as nematic liquid crystals, a light beam in the extraordinary polarization walks off its wavevector due to birefringence, while it undergoes self-focusing via an increase in…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
In four-dimensional symplectic maps complex instability of periodic orbits is possible, which cannot occur in the two-dimensional case. We investigate the transition from stable to complex unstable dynamics of a fixed point under parameter…
The similarity renormalization group is used to transform a general Dirac Hamiltonian into diagonal form. The diagonal Dirac operator consists of the nonrelativistic term, the spin-orbit term, the dynamical term, and the relativistic…
In this paper we study the inverse of so-called unfair permutations, and explore various properties of them. Our investigation begins with comparing this class of permutations with uniformly random permutations, and showing that they behave…
We propose a simple mathematical model that describes the time evolution of a self-propelled object on a liquid surface using such variables as the object location, the surface concentration of active molecules and the hydrodynamic surface…
Modeling deformations of a real object is an important task in computer vision, biomedical engineering and biomechanics. In this paper, we focus on a situation where a three-dimensional object is rotationally deformed about a fixed axis,…
When dealing with an orbit determination problem, uncertainties naturally arise from intrinsic errors related to observation devices and approximation models. Following the least squares method and applying approximation schemes such as the…
For more than half a century, moments have attracted lot ot interest in the pattern recognition community.The moments of a distribution (an object) provide several of its characteristics as center of gravity, orientation, disparity, volume.…
Continuing the study of Hamiltonian pseudo-rotations of projective spaces, we focus on the conjecture that the fixed-point data set (the actions and the linearized flows at one-periodic orbits) of a pseudo-rotation exactly matches that data…
Suppose an interval is put on a horizontal line with random roughness. With probability one it is supported at two points, one from the left, and another from the right from its center. We compute probability distribution of support points…