Related papers: Transport f divergences
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,…
During the last decade Optimal Transport had a relevant role in the study of geometry of singular spaces that culminated with the Lott-Sturm-Villani theory. The latter is built on the characterisation of Ricci curvature lower bounds in…
We define and discuss the properties of a class of cost functions on the sphere which we term defective cost functions. We then discuss how to extend these definitions and some properties to cost functions defined on Euclidean space and on…
This work derives the Navier--Stokes hydrodynamic equations for a model of a confined, quasi-two-dimensional, $s$-component mixture of inelastic, smooth, hard spheres. Using the inelastic version of the revised Enskog theory, macroscopic…
We consider a class of convex optimization problems modelling temporal mass transport and mass change between two given mass distributions (the so-called dynamic formulation of unbalanced transport), where we focus on those models for which…
Transport surrounding is full of all kinds of fields, like particle potential, external potential. Under these conditions, how elements work and how position and momentum redistribute in the diffusion? For enriching the Fick law in…
The Maxwell approach from electrostatics is applied for calculation of transport coefficients in composites. The viscosity of a dilute emulsion is obtained as a function of the volume fraction of dispersed phase. The derived new formula is…
We study the transport properties of model networks such as scale-free and Erd\H{o}s-R\'{e}nyi networks as well as a real network. We consider the conductance $G$ between two arbitrarily chosen nodes where each link has the same unit…
We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus. We obtain for each order conditions for matrix…
Traffic flows are studied in terms of their noise of sound, which is an easily accessible experimental quantity. The sound noise data is studied making use of scaling properties of wavelet transforms and Hurst exponents are extracted. The…
In this chapter, we discuss urban mobility from a complexity science perspective. First, we give an overview of the datasets that enable this approach, such as mobile phone records, location-based social network traces, or GPS trajectories…
Dynamical systems often exhibit the emergence of long-lived coherent sets, which are regions in state space that keep their geometric integrity to a high extent and thus play an important role in transport. In this article, we provide a…
The structure of road networks impacts various urban dynamics, from traffic congestion to environmental sustainability and access to essential services. Recent studies reveal that most roads are underutilized, faster alternative routes are…
Given a function $F$ transforming a probability measure $\mu$ into another one $F(\mu)$, we study the existence and regularity of a transport representation of it. That is, we ask whether we can represent the image $F(\mu)$ of the input…
Gravitationally collapsed objects are known to be biased tracers of an underlying density contrast. Using symmetry arguments, generalised biasing schemes have recently been developed to relate the halo density contrast $\delta_h$ with the…
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…
Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…
From single vehicle data a number of new empirical results concerning the density-dependence of the velocity distribution and its moments as well as the characteristics of their temporal fluctuations have been determined. These are utilized…
We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…