Related papers: A low-frequency variational model for energetic pa…
We develop a new Lagrangian approach --- flow dynamic approach to effectively capture the interface in the Allen-Cahn type equations. The underlying principle of this approach is the Energetic Variational Approach (EnVarA), motivated by…
A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom the Poincar\'e map provides a splitting of the phase space into regions where…
General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…
This work investigates variational frameworks for modeling stochastic dynamics in incompressible fluids, focusing on large-scale fluid behavior alongside small-scale stochastic processes. The authors aim to develop a coupled system of…
Recent theoretical work has developed the Hamilton's-principle analog of Lie-Poisson Hamiltonian systems defined on semidirect products. The main theoretical results are twofold: (1) Euler-Poincar\'e equations (the Lagrangian analog of…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
A new fully kinetic system is proposed for modeling collisionless magnetic reconnection. The formulation relies on fundamental principles in Lagrangian dynamics, in which the inertia of the electron mean flow is neglected in the expression…
Turbulent flows laden with small bubbles are ubiquitous in many natural and industrial environments. From the point of view of numerical modeling, to be able to handle a very large number of small bubbles in direct numerical simulations,…
A meshfree Lagrangian method for the fluctuating hydrodynamic equations (FHEs) with fluid-structure interactions is presented. Brownian motion of the particle is investigated by direct numerical simulation of the fluctuating hydrodynamic…
A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which…
Suspensions with fiber-like particles in the low Reynolds number regime are modeled by two different approaches that both use a Lagrangian representation of individual particles. The first method is the well-established formulation based on…
A class of generally nonlinear dynamical systems is considered, for which the Lagrangian is represented as a sum of homogeneous functions of the displacements and their derivatives. It is shown that an energy partition as a single relation…
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…
For a large system of identical particles interacting by means of a potential, we find that a strong large scale flow velocity can induce motions in the inertial range via the potential coupling. This forcing lies in special bundles in the…
We study the geometric particle-in-cell methods for an electrostatic hybrid plasma model. In this model, ions are described by the fully kinetic equations, electron density is determined by the Boltzmann relation, and space-charge effects…
A model for the pseudo-turbulent Reynolds stress tensor in compressible flows through monodisperse particle clouds is developed based on data from particle resolved numerical simulations. This model extends previous models for the…
Homogenisation theory has seen recent applications in deriving stochastic transport models for fluid dynamics. In this work, we first derive the stochastic Lagrange-to-Euler map that underpins stochastic transport noise in fluid dynamics as…
We present an analysis and discuss consequences of the strong correlations of the configurational parts of pressure and energy in their equilibrium fluctuations at fixed volume reported for simulations of several liquids in the companion…
We present a novel partitioned iterative formulation for modeling of fluid-structure interaction in two-phase flows. The variational formulation consists of a stable and robust integration of three blocks of differential equations, viz.,…
Modeling the chemical, electric, and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolution within a material in an electronic device setting involves the solution of partial differential…