Related papers: An objective perspective for classic flow classifi…
Lagrangian motions of fluid particles in a general velocity field oscillating in time are studied with the use of the two-timing method. Our aims are: (i) to calculate systematically the most general and practically usable asymptotic…
The problem of classifying turbulent environments from partial observation is key for some theoretical and applied fields, from engineering to earth observation and astrophysics, e.g. to precondition searching of optimal control policies in…
We consider the evolution of hypersurfaces on the unit sphere $\mathbb{S}^{n+1}$ by smooth functions of the Weingarten map. We introduce the notion of `quasi-ancient' solutions for flows that do not admit non-trivial, convex, ancient…
Context. A universally accepted definition of what a vortex is has not yet been reached. Therefore, we lack an unambiguous and rigorous method for the identification of vortices in fluid flows. Such a method would be necessary to conduct…
Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type…
We introduce a new approach for analyzing ancient solutions and singularities of mean curvature flow that are locally modeled on a cylinder. Its key ingredient is a general mechanism, called the \emph{PDE--ODI principle}, which converts a…
Optical flow is a classical task that is important to the vision community. Classical optical flow estimation uses two frames as input, whilst some recent methods consider multiple frames to explicitly model long-range information. The…
This work studies Willmore flows of tori and their singularities via a dimension reduction approach. We introduce a Willmore flow that preserves the degenerate constraint of prescribed conformal class and, for rotationally symmetric initial…
The optical flow of natural scenes is a combination of the motion of the observer and the independent motion of objects. Existing algorithms typically focus on either recovering motion and structure under the assumption of a purely static…
Sparse trajectory data consist of a low number of trajectories such that the reconstruction of an underlying velocity field is not possible. Recently, approaches have been introduced to analyze flow behavior based on a single trajectory…
It has been broadly acknowledged that vortex detection algorithms, usually based on linear-algebraic properties of the velocity gradient tensor, can be plagued with severe shortcomings and may become, in practical terms, dependent on the…
For homogeneous metrics on the spaces of the title it is shown that the Ricci flow can move a metric of stricly positive sectional curvature to one with some negative sectional curvature and one of positive definite Ricci tensor to one with…
Robust velocity and position estimation is crucial for autonomous robot navigation. The optical flow based methods for autonomous navigation have been receiving increasing attentions in tandem with the development of micro unmanned aerial…
We study the transition to turbulence from the perspective of the velocity gradient tensor dynamics. Our work is motivated by the observation of nonlinear structures emerging during transition, as revealed by vortex identifiers such as the…
We present a direct derivation of the typical time derivatives used in a continuum description of complex fluid flows, harnessing the principles of the kinematics of line elements. The evolution of the microstructural conformation tensor in…
Existing optical flow methods make generic, spatially homogeneous, assumptions about the spatial structure of the flow. In reality, optical flow varies across an image depending on object class. Simply put, different objects move…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…
In this paper, we classify all noncollapsed singularities of the mean curvature flow in $\mathbb{R}^4$. Specifically, we prove that any ancient noncollapsed solution either is one of the classical historical examples (namely…
Optical flow is an indispensable building block for various important computer vision tasks, including motion estimation, object tracking, and disparity measurement. In this work, we propose TransFlow, a pure transformer architecture for…
Unsteadiness lies at the heart of turbulent fluid dynamics, eddy formation and instabilities in flows thus making it central to both understanding and controlling fluid systems. In this work, we present an objective measure for the…