Related papers: A Lagrangian perspective on nonautonomous advectio…
We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are…
Let $L_t:=\Delta_t+Z_t$ for a $C^{1,1}$-vector field $Z$ on a differential manifold $M$ with possible boundary $\partial M$, where $\Delta_t$ is the Laplacian induced by a time dependent metric $g_t$ differentiable in $t\in [0,T_c)$. We…
Lagrangian studies of the local temperature mixing and heat transport in turbulent Rayleigh-Benard convection are presented, based on three-dimensional direct numerical simulations. Contrary to vertical pair distances, the temporal growth…
We consider the infinite-dimensional Lie group $\mathfrak G$ which is the semidirect product of the group of compactly supported diffeomorphisms of a Riemannian manifold $X$ and the commutative multiplicative group of functions on $X$. The…
We establish the short-time asymptotic behaviour of the Markovian semigroups associated with strongly local Dirichlet forms under very general hypotheses. Our results apply to a wide class of strongly elliptic, subelliptic and degenerate…
Non-isothermal particles suspended in a fluid lead to complex interactions -- the particles respond to changes in the fluid flow, which in turn is modified by their temperature anomaly. Here, we perform a novel proof-of-concept numerical…
In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This results in a nonlocal Lagrangian partial differential…
We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…
Transport of the Brownian particles driven by L\'evy flights coexisting with subdiffusion in asymmetric periodic potentials is investigated in the absence of any external driving forces. Using the Langevin-type dynamics with subordination…
We report a numerical study of Rayleigh--B\'enard convection through random porous media using pore-scale modelling, focusing on the Lagrangian dynamics of fluid particles and heat transfer for varied porosities $\phi$. Due to the…
In this paper, we present a Lagrangian formalism for nonequilibrium thermodynamics. This formalism is an extension of the Hamilton principle in classical mechanics that allows the inclusion of irreversible phenomena in both discrete and…
We consider stochastic systems involving general -- non-Gaussian and asymmetric -- stable processes. The random quantities, either a stochastic force or a waiting time in a random walk process, explicitly depend on the position. A…
We study diffusions, variational principles and associated boundary value problems on directed graphs with natural weightings. Using random walks and exit times, we associate to certain subgraphs (domains) a pair of sequences, each of which…
Diffusion in nonhomogeneous media is described by a dynamical process driven by a general Levy noise and subordinated to a random time; the subordinator depends on the position. This problem is approximated by a multiplicative process…
We investigate the statistical properties of Lagrangian tracers transported by a time-correlated compressible renewing flow. We show that the preferential sampling of the phase space performed by tracers yields significant differences…
A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…
In this work, we propose a new semi-Lagrangian (SL) finite difference scheme for nonlinear advection-diffusion problems. To ensure conservation, which is fundamental for achieving physically consistent solutions, the governing equations are…
We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching we unveil a rich transport dynamics including…
Anomalous heat transport observed in low dimensional classical systems is associated to super-diffusive spreading of space-time correlation of the conserved fields in the system. This leads to non-local linear response relation between the…
Models describing transport and diffusion processes occurring along the edges of a graph and interlinked by its vertices have been recently receiving a considerable attention. In this paper we generalize such models and consider a network…