Related papers: Looping Animations Using the Modular Flow and Elli…
We look for elliptic curves featuring rational points whose coordinates form two arithmetic progressions, one for each coordinate. A constructive method for creating such curves is shown, for lengths up to 5.
Elliptical instability is due to a parametric resonance of two inertial modes in a fluid velocity field with elliptical streamlines. This flow is a simple model of the motion in a tidally deformed, rotating body. Elliptical instability…
Adapting Lindstr\"om's well-known construction, we consider a wide class of functions which are generated by flows in a planar acyclic directed graph whose vertices (or edges) take weights in an arbitrary commutative semiring. We give a…
We define generalizations of the multiple elliptic gamma functions and the multiple sine functions, associated to good rational cones. We explain how good cones are related to collections of $SL_r(\mathbb{Z})$-elements and prove that the…
A floating hemisphere under forced harmonic oscillation at very high and very low frequencies is considered. The problem is reduced to an elliptic one, that is, the Laplace operator in the exterior domain with standard Dirichlet and Neumann…
We study the behavior of orbits in two different galactic dynamical models, describing the motion in the central parts of a triaxial elliptical galaxy with a dense nucleus. Numerical experiments show that both models display regular motion…
We present elliptic-rogue wave solutions for integrable nonlinear soliton equations in theta functions. Unlike solutions generated on the plane wave background, these solutions depict rogue waves emerging on elliptic function backgrounds.…
The problem of the motion of a particle in an asymmetric double well is solved explicitly in terms of the Weierstrass and Jacobi elliptic functions. While the solution of the orbital motion is expressed simply in terms of the Weierstrass…
In this paper, we propose a method of fundamental solutions for the problems of two-dimensional potential flow past a doubly-periodic array of obstacles. The solutions of these problems involve doubly-periodic functions, and it is difficult…
An elliptic Newton flow is a dynamical system that can be interpreted as a continuous version of Newton's iteration method for finding the zeros of an elliptic function f. Previous work focusses on structurally stable flows (i.e., the phase…
The circular orbits and elliptical orbits of moving objects in a gravitational field are essential information in astronomy. There have been many methods developed in the literature and textbooks to describe these orbits. In this report, I…
Turbulent-laminar patterns near transition are simulated in plane Couette flow using an extension of the minimal flow unit methodology. Computational domains are of minimal size in two directions but large in the third. The long direction…
In this survey article, we summarise the known results towards the conjecture: elliptic curves over totally real number fields are modular. For understanding these recent results in the literature, we present some necessary background along…
Modular flow is a symmetry of the algebra of observables associated to spacetime regions. Being closely related to entanglement, it has played a key role in recent connections between information theory, QFT and gravity. However, little is…
Generative models for image generation are now commonly used for a wide variety of applications, ranging from guided image generation for entertainment to solving inverse problems. Nonetheless, training a generator is a non-trivial feat…
The space of elliptic modular forms of fixed weight and level can be identfied with a space of intertwining operators, from a holomorphic discrete series representation of SL2(R) to a space of automorphic forms. Moreover, multiplying…
We define matrix models that converge to the generating functions of a wide variety of loop models with fugacity taken in sets with an accumulation point. The latter can also be seen as moments of a non-commutative law on a subfactor planar…
In this paper we describe a method for modeling the dynamic behavior of splashing fluids. The model simulates the behavior of a fluid when objects impact or float on its surface. The forces generated by the objects create waves and splashes…
Flattened liquid drops poured on a very hot surface evaporate quite slowly and float on a film of their own vapour. In the cavities of a surface, an unusual type of vibrational motions occurs. Large vibrations take place and different forms…
The elliptical instability can take place in planetary cores and stars elliptically deformed by gravitational effects, where it generates large-scale three-dimensional flows assumed to be dynamo capable. In this work, we present the first…