Related papers: Rheological modeling with GENERIC and with the Ons…
The Euler system in fluid dynamics is a model of a compressible inviscid fluid incorporating the three basic physical principles: Conservation of mass, momentum, and energy. We show that the Cauchy problem is basically ill-posed for the…
Dirac-Frenkel instantaneous residual minimization evolves nonlinear parametrizations of PDE solutions in time, but ill-conditioning can render the parameter dynamics non-unique. We interpret this non-uniqueness as a gauge freedom: nullspace…
When a polymer solution is uniaxially stretched and held fixed at both ends, the solution quickly separates into droplets connected by strings and takes the beads-on-string structure. The string then becomes thinner by capillary forces.…
We study the thermodynamics of open systems weakly driven out-of-equilibrium by nonconservative and time-dependent forces using the linear regime of stochastic thermodynamics. We make use of conservation laws to identify the potential and…
Metriplectic systems are state space formulations that have become well-known under the acronym GENERIC. In this work we present a GENERIC based state space formulation in an operator setting that encodes a weak-formulation of the field…
We propose several linear, fully decoupled numerical schemes with first- and second-order temporal accuracy for a novel Q-tensor-based two-phase hydrodynamic model describing the coupling of active nematic liquid crystal solutions with…
The relativistic hydrodynamic model is applied to describe the expansion of the dense matter formed in relativistic heavy-ion collisions. The hydrodynamic expansion of the fluid, supplemented with the statistical emission of hadrons at…
In this work, we develop a modelling framework for granular flows based on the shallow water moment equations on inclined planes. Under the assumption of a polynomial expansion of the velocity field, the model extends the classical shallow…
We here present two simplified models aimed at describing the long-term, irregular behaviours observed in the rheological response of certain complex fluids, such as periodic oscillations or chaotic-like variations. Both models exploit the…
An inviscid two-dimensional fluid model with nonlinear dispersion that arises simultaneously in coarse-grained descriptions of the dynamics of the Euler equation and in the description of non-Newtonian fluids of second grade is considered.…
The ability to model mechanics of soft materials under flowing conditions is key in designing and engineering processes and materials with targeted properties. This generally requires solution of internal stress tensor, related to the…
We propose a new reduced model for gravity-driven free-surface flows of shallow elastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for elastic fluids. The viscosity is assumed small (of order…
In this paper, we are interested in the dynamics of charged particles interacting with the incompressible viscous flow. More precisely, we consider the Vlasov-Poisson or Vlasov-Poisson-Fokker-Planck equation coupled with the incompressible…
In a recent paper, Phys. Rev E 81, 041137 (2010), the author attempts to derive ten necessary conditions for stability of dissipative fluids and plasmas. Assuming the validity of the local equilibrium principle, these criteria have been…
Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…
In this paper, we introduce a new approach to solving the porous medium equation using a moving mesh finite element method that leverages the Onsager variational principle as an approximation tool. Both the continuous and discrete problems…
We propose a unified approach to the formal long-wave reduction of several fluid models for thin-layer incompressible homogeneous flows driven by a constant external force like gravity. The procedure is based on a mathematical coherence…
We show that the incompressible Euler equations in three spatial dimensions can be expressed in terms of an abelian gauge theory with a topological BF term. A crucial part of the theory is a 3-form field strength, which is dual to a…
We study the motion of a rigid body within a compressible, isentropic, and viscous fluid contained in a fixed bounded domain $\Omega \subset \mathbb{R}^3$. The fluid's behavior is described by the Navier-Stokes equations, while the motion…
A general set of fluid equations that allow for energy-conserving momentum transport by gyroscopic motion of fluid elements is obtained. The equations are produced by a class of action principles that yield a large subset of the known fluid…