On gradient flows with obstacles and Euler’s elastica

Pedestrian Flows in Bounded Domains with Obstacles

In this paper we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space occupancy by pedestrians is described via a sequence of Radon positive measures generated by a push-forward recursive relation. We assume that two fundamental aspect...

Elastica with Hinges

Large deviations and gradient flows.

In recent work we uncovered intriguing connections between Otto's characterization of diffusion as an entropic gradient flow on the one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other. In this paper, we sketch this connection, show how it generalizes to a wider class of systems and comment on consequences and implications. Specifically, we c...

Completely Integrable Gradient Flows

In this paper we exhibit the Toda lattice equations in a double bracket form which shows they are gradient flow equations (on their isospectral set) on an adjoint orbit of a compact Lie group. Representations for the flows are given and a convexity result associated with a momentum map is proved. Some general properties of the double bracket equations are demonstrated, including a discussion of...

Gradient Flows and Geometric Active Contour Models Gradient Flows and Geometric Active Contour Models

In this note, we analyze the geometric active contour models proposed in 10, 31] from a curve evolution point of view and propose some modiications based on gradient ows relative to certain new metrics. This leads to a novel snake paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus the snake is attracted very naturally and eeciently to the ...