Related papers: Earthquakes on the once-punctured torus
This review explores recent advances in the theory of $T\bar{T}$ deformation, an irrelevant yet solvable deformation of quantum field theories defined via the quadratic form of the energy-momentum tensor. It addresses classical and quantum…
We develop here a concept of deformed algebras through three examples and an application. Deformed algebras are obtained from a fixed algebra by deformation along a family of indexes, through formal series. We show how the example of…
We study the topology associated with physical vector and scalar fields. A mathematical object, e.g., a ball, can be continuously deformed, without tearing or gluing, to make other topologically equivalent objects, e.g., a cube or a solid…
We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of "chaoticity". The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the…
A class of Hamiltonian deformations of plane curves is defined and studied. Hamiltonian deformations of conics and cubics are considered as illustrative examples. These deformations are described by systems of hydrodynamical type equations.…
In this article, we first investigate the kinematics of specific geodesic flows on two dimensional media with constant curvature, by explicitly solving the evolution (Raychaudhuri) equations for the expansion, shear and rotation along the…
The traction evolution is a fundamental ingredient to model the dynamics of an earthquake rupture which ultimately controls, during the coseismic phase, the energy release, the stress redistribution and the consequent excitation of seismic…
The purpose of this article is to give an explicit formula for all curves of constant torsion $\tau$ in the unit two-sphere $S^2(1)$. These curves and their basic properties have been known since the 1890's, and some of these properties are…
The number of earthquakes as a function of magnitude decays as a power law. This trend is usually justified using spring-block models, where slips with the appropriate global statistics have been numerically observed. However, prominent…
We study several exotic systems, including the X-cube model, on a flat three-torus with a twist in the $xy$-plane. The ground state degeneracy turns out to be a sensitive function of various geometrical parameters. Starting from a lattice,…
We describe in elementary geometrical terms Teichm\" uller spaces of decorated and holed surfaces. We construct explicit global coordinates on them as well as on the spaces of measured laminations with compact and closed support…
Kashaev algebra associated to a surface is a noncommutative deformation of the algebra of rational functions of Kashaev coordinates. For two arbitrary complex numbers, there is a generalized Kashaev algebra. The relationship between the…
In a previous paper, the authors extended Mirzakhani's (almost-everywhere defined) measurable conjugacy between the earthquake and horocycle flows to a measurable bijection. In this one, we analyze the continuity properties of this map and…
We study the regularity of stationary and time-dependent solutions to strong perturbations of the free Schr\"odinger equation on two-dimensional flat tori. This is achieved by performing a second microlocalization related to the size of the…
We study a class of continuous deformations of branched complex projective structures on closed surfaces of genus $g\geq 2$, which preserve the holonomy representation of the structure and the order of the branch points. In the case of…
In this paper we study the effect of a torus topology on Loop Quantum Cosmology. We first derive the Teichmueller space parametrizing all possible tori using Thurston's theorem and construct a Hamiltonian describing the dynamics of these…
We investigate topology change in (1+1) dimensions by analyzing the scalar-curvature action $1/2 \int R dV$ at the points of metric-degeneration that (with minor exceptions) any nontrivial Lorentzian cobordism necessarily possesses. In two…
We analyze the optical resonances of a dielectric sphere whose surface has been slightly deformed in an arbitrary way. Setting up a perturbation series up to second order, we derive both the frequency shifts and modified linewidths. Our…
We describe the deformation space of a solid torus with boundary modelled on convex ideal hyperbolic polyhedra. This deformation space is given by natural Gauss--Bonnet type inequalities on the dihedral angles. The result extends to solid…
If we assume that earthquakes are chaotic, and influenced locally then chaos theory suggests that there should be a temporal association between earthquakes in a local region that should be revealed with statistical examination. To date no…