Related papers: Deviation equations in spaces with a transport alo…

Mixing and transport of passive particles are studied in a simple kinematic model of a meandering jet flow motivated by the problem of lateral mixing and transport in the Gulf Stream. We briefly discuss a model streamfunction, Hamiltonian…

Different observations of a relation between inputs ("sources") and outputs ("targets") are often reported in terms of histograms (discretizations of the source and the target densities). Transporting these densities to each other provides…

Structures such as waves, jets, and vortices have a dramatic impact on the transport properties of a flow. Passive tracer transport in incompressible two-dimensional flows is described by Hamiltonian dynamics, and, for idealized structures,…

It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\to X$ of…

Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…

We develop a differential geometric framework for parallel transport over path spaces and a corresponding discrete theory, an integrated version of the continuum theory, using a category-theoretic framework.

Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…

Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…

To estimate the displacements of physical state variables, the physics principles that govern the state variables must be considered. Technically, for a certain class of state variables, each state variable is associated to a tensor field.…

Here we consider a perturbation of continuous mappings on Banach spaces and investigate their image under various conditions. Consequently, we study the solvability of some classes of equations and inclusions. For these, we start by the…

We define a class of divergences to measure differences between probability density functions in one-dimensional sample space. The construction is based on the convex function with the Jacobi operator of mapping function that pushforwards…

We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…

We introduce an alternative formalization of curved spaces in which the concept of a pointwise affine space, as defined here, replaces that of a manifold. New or modified definitions of familiar notions from differential geometry such as…

We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from the symmetry argument for three kinds of variables. One is a…

Coincidences of maps between smooth manifolds are studied via a geometric approach which involves (nonstabilized) normal bordism theory and pathspaces.

In this paper we consider a manifold with a dynamical vector field and inquire about the possible tangent bundle structures which would turn the starting vector field into a second order one. The analysis is restricted to manifolds which…

A self-contained introduction is presented of the notion of the (abstract) differentiable manifold and its tangent vector fields. The way in which elementary topological ideas stimulated the passage from Euclidean (vector) spaces and linear…

We consider a linear perturbation in the velocity field of the transport equation. We investigate solutions in the space of bounded Radon measures and show that they are differentiable with respect to the perturbation parameter in a proper…

We define an evolution of multiple particles on a discrete manifold $G$. Each particle alone moves on geodesics and particles can interact if they are on the same facet. They move deterministically and reversibly on the frame bundle $P$ of…

We consider the path space of a curved manifold on which a point particle is introduced in a conservative physical system with constant total energy to formulate its action functional and geodesic equation together with breaks on the path.…