Related papers: Looping Animations Using the Modular Flow and Elli…
Droplets moving in a microfluidic loop device exhibit both periodic and chaotic behaviors based on the inlet droplet spacing. We propose that the periodic behavior is an outcome of a dispersed phase conservation principle. This conservation…
Flow forming involves complicated tooling/workpiece interactions. Purely analytical models of the tool contact area are difficult to formulate, resulting in numerical approaches that are case-specific. Provided are the details of an…
Recent experiments and realistic flux-gradient-driven computer simulations provide evidence of plastic flow of flux lines in a superconductor. The striking videos of the onset of vortex motion vividly illustrate the existence of flowing…
We show that an observable fraction of the measured elliptic flow may originate in classical gluon fields at the initial stage of a peripheral high-energy nuclear collision. This mechanism complements the contribution of late stage…
Dynamical tide consists of various waves that can resonate with orbital motion. We test this coupling of dynamical tide and orbital motion using a simple two-dimensional shallow water model, which can be applied to a rocky planet covered…
We investigate a mechanism to manipulate wall-bounded flows whereby wave-like undulations of the wall topography drives the creation of bespoke longitudinal vortices. A resonant interaction between the ambient vorticity of the undisturbed…
The parabolic functions are introduced in analogy to the circular and hyperbolic cases. We discuss the relevant properties, the geometrical interpretation and touch on possible generalizations and their link with the modular elliptic…
Periodic lattices are natural generalizations of lattices, which arise naturally in diophantine approximations with rationals of bounded denominators. In this paper, we prove analogues of classical theorems in geometry of numbers for…
Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles,…
We study counting functions of planar polygons arising from homological mirror symmetry of elliptic curves. We first analyze the signature and rationality of the quadratic forms corresponding to the signed areas of planar polygons. Then we…
Optical flow, which captures motion information across frames, is exploited in recent video inpainting methods through propagating pixels along its trajectories. However, the hand-crafted flow-based processes in these methods are applied…
We present a theoretical and numerical study on the motion of isotropic helicoids in complex flows. These are particles whose motion is invariant under rotations but not under mirror reflections of the particle. This is the simplest, yet…
It is well known that a superfluid rotates by forming an array of quantized vortices. A relativistic formulation for superfluid vortex dynamics is required for a range of problems in astrophysics and cosmology, from neutron star interiors…
Caroline Series' [{\em The modular surface and continued fractions}, J. Lond. Math. Soc. (2), {\bf 31}, no.~1, (1985), 69--80] gives a clear framework linking, in a deceptively simple way, the dynamics of the geodesic flow on the modular…
Animated textures can be used to visualize the spatial structure and temporal evolution of vector fields at high spatial resolution. The animation requires two time-dependent vector fields. The first of these vector fields determines the…
In this talk we describe the recently discovered rich phenomenology of elliptic flow of electromagnetic probes of the hot matter created in relativistic heavy-ion collisions. Using a hydrodynamic model for the space-time dynamics of the…
This work advocates Eulerian motion representation learning over the current standard Lagrangian optical flow model. Eulerian motion is well captured by using phase, as obtained by decomposing the image through a complex-steerable pyramid.…
We study geometric modular flows in two-dimensional conformal field theories. We explore which states exhibit a geometric modular flow with respect to a causally complete subregion and, conversely, how to construct a state from a given…
We show that a general miraculous cancellation formula, the divisibility of certain characteristic numbers and some other topologiclal results are con- sequences of the modular invariance of elliptic operators on loop spaces. Previously we…
We study modular and integral flow polynomials of graphs by means of subgroup arrangements and lattice polytopes. We introduce an Eulerian equivalence relation on orientations, flow arrangements, and flow polytopes; and we apply the theory…