Related papers: A flow-based approach to rough differential equati…
Finite-volume numerical method for study shallow water flows over an arbitrary bed profile in the presence of external force is proposed. This method uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with…
We introduce a gradient flow formulation of linear Boltzmann equations. Under a diffusive scaling we derive a diffusion equation by using the machinery of gradient flows.
We are concerned with a mixture of Boltzmann and McKean-Vlasov type equations, this means (in probabilistic terms) equations with coefficients depending on the law of the solution itself,and driven by a Poisson point measure with the…
With recently developed tools, we prove a homogenisation theorem for a random ODE with short and long-range dependent fractional noise. The effective dynamics are not necessarily diffusions, they are given by stochastic differential…
We consider rough differential equations whose coefficients contain path-dependent bounded variation terms and prove the existence and a priori estimate of solutions. These equations include classical path-dependent SDEs containing running…
To aid in prediction of turbulent boundary layer flows over rough surfaces, a new model is proposed to estimate hydrodynamic roughness based solely on geometric surface information. The model is based on a fluid-mechanics motivated…
We show that the fluctuations of the partial current in two dimensional diffusive systems are dominated by vortices leading to a different scaling from the one predicted by the hydrodynamic large deviation theory. This is supported by exact…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…
Weakly nonlinear analysis of a two dimensional sheared granular flow is carried out under the Lees-Edwards boundary condition. We derive the time dependent Ginzburg-Landau (TDGL) equation of a disturbance amplitude starting from a set of…
We develop the rough path counterpart of It\^o stochastic integration and - differential equations driven by general semimartingales. This significantly enlarges the classes of (It\^o / forward) stochastic differential equations treatable…
A continuous sequence of infinitesimal unitary transformations is used to diagonalize the quantum sine-Gordon model for \beta^2\in(2\pi,\infty). This approach can be understood as an extension of perturbative scaling theory since it links…
Diffusion-based models on continuous spaces have seen substantial recent progress through the mathematical framework of gradient flows, leveraging the Wasserstein-2 (${W}_2$) metric via the Jordan-Kinderlehrer-Otto (JKO) scheme. Despite the…
The dynamics of viscous thin-film particle-laden flows down inclined surfaces are commonly modeled with one of two approaches: a diffusive flux model or a suspension balance model. The diffusive flux model assumes that the particles migrate…
Hydrodynamic transport coefficients may be evaluated from first principles in a weakly coupled scalar field theory at arbitrary temperature. In a theory with cubic and quartic interactions, the infinite class of diagrams which contribute to…
We analyze common lifts of stochastic processes to rough paths/rough drivers-valued processes and give sufficient conditions for the cocycle property to hold for these lifts. We show that random rough differential equations driven by such…
We introduce a new sharp interface model for the flow of two immiscible, viscous, incompressible fluids. In contrast to classical models for two-phase flows we prescribe an evolution law for the interfaces that takes diffusional effects…
A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and…
Fluidisation is the process by which the weight of a bed of particles is supported by a gas flow passing through it from below. When fluidised materials flow down an incline, the dynamics of the motion differ from their non-fluidised…
We show that the flow approach of Duch [Duc21] can be adapted to prove local well-posedness for the generalized Kardar-Parisi-Zhang equation. The key step is to extend the flow approach so that it can accommodate semi-linear equations…
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector…