arXiv subjects

Joanna Furno

Publications and source records attributed to Joanna Furno.

5 recordsLinked to original sources

arXiv2020

Bounded remainder sets for rotations on higher dimensional adelic tori

In this paper we give a simple, explicit construction of polytopal bounded remainder sets of all possible volumes, for any irrational rotation on the $d$ dimensional adelic torus $\mathbb{A}^d/\mathbb{Q}^d$. Our construction involves ideas from dynamical systems and harmonic analysis on the adeles, as well as a geometric argument that reduces the existence argument to the case of an irrational rotation on the torus $\mathbb{R}^d/\mathbb{Q}^d$.

math.NT↗

arXiv2019

Bounded remainder sets for rotations on the adelic torus

In this paper we give an explicit construction of bounded remainder sets of all possible volumes, for any irrational rotation on the adelic torus $\mathbb A/\mathbb Q$. Our construction involves ideas from dynamical systems and harmonic analysis on the adeles, as well as a geometric argument which originated in the study of deformation properties of mathematical quasicrystals.

math.DS↗

arXiv2016

Everywhere divergence of the one-sided ergodic Hilbert transform and Liouville numbers

We prove some results on the behavior of infinite sums of the form $Σf\circ T^n(x)\frac{1}{n}$, where $T:S^1\to S^1$ is an irrational circle rotation and $f$ is a mean-zero function on $S^1$. In particular, we show that for a certain class of functions $f$, there are Liouville $α$ for which this sum diverges everywhere. We also show that there are Liouville $α$ for which the sum converges everywhere.

math.DS↗

arXiv2007

Apparatus for real-time acoustic imaging of Rayleigh-Benard convection

We have designed and built an apparatus for real-time acoustic imaging of convective flow patterns in optically opaque fluids. This apparatus takes advantage of recent advances in two-dimensional ultrasound transducer array technology; it employs a modified version of a commercially available ultrasound camera, similar to those employed in non-destructive testing of solids. Images of convection patterns are generated by observing the lateral variation of the temperature dependent speed of sound via refraction of acoustic plane waves passing vertically through the fluid layer. The apparatus has been validated by observing convection rolls in both silicone oil and ferrofluid.

cond-mat.mtrl-sci↗

arXiv2007

Tidal pattern instabilities on multi-moon planets

The equilibrium tide-generating forces in the lunar orbital plane of a planet of radius R are calculated for the case of N moons of mass M_i orbiting the planet at instantaneous polar coordinates (D_i, α_i). For the case of a single moon, there are only two high tides. For the case of two moons, it is found that there can exist a critical lunar orbital distance at which two high tides become unstable with respect to formation of three high tides. Bifurcation diagrams are presented which depict how the angular positions of the high and low tides on the planet vary with the lunar distances and lunar separation angle. Tidal stability diagrams, which illustrate the stability regions for various tidal patterns as a function of lunar distances and lunar separation angle, are presented for various values of D_2/D_1 and M_2/M_1. Generally speaking, the aforementioned tidal instability, and hence the propensity for formation of three high tides on a two-moon planet, exists over a significant range of lunar distances and separation angles provided that M_2/M_1 \sim (D_2/D_1)^3. For the case of N>2 moons, the tidal stability diagram becomes more complex, revealing a diversity of potential tidal patterns.

physics.ao-ph↗