Related papers: Lagrangian versus Eulerian Methods for Toroidally-…
Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…
Two triangular factorizations of the deformation gradient tensor are studied. The first, termed the Lagrangian formulation, consists of an upper-triangular stretch premultiplied by a rotation tensor. The second, termed the Eulerian…
We analyze an axisymmetric magnetohydrodynamics configuration, describing the morphology of a purely differentially rotating thin plasma disk, in which linear and non-linear perturbations are triggered associated with microscopic magnetic…
We consider nodal-based Lagrangian interpolations for the finite element approximation of the Maxwell eigenvalue problem. The first approach introduced is a standard Galerkin method on Powell-Sabin meshes, which has recently been shown to…
In the early stages of a protoplanetary disk, when its mass is a significant fraction of its star's, turbulence generated by gravitational instability (GI) should feature significantly in the disk's evolution. At the same time, the disk may…
We present global 3D MHD simulations of geometrically thin but unstratified accretion disks in which a near Keplerian disk rotates between two bounding regions with initial rotation profiles that are stable to the MRI. The inner region…
Magnetized disk winds and wind-driven accretion are an essential and intensively studied dispersion mechanism of protoplanetary disks. However, the stability of these mechanisms has yet to be adequately examined. This paper employs…
Our understanding of the process through which magnetic fields reached their observed strengths in present-day galaxies remains incomplete. One of the advocated solutions is a turbulent dynamo mechanism that rapidly amplifies weak magnetic…
Hydrodynamic simulations of planet-disk interactions often show material accumulation near the co-orbital Lagrange points $L_4$ and $L_5$ -- features that may correspond to observed crescents in protoplanetary disks. Intriguingly, these…
The magnetorotational instability (MRI) is an important process in sufficiently ionized accretion disks, as it can create turbulence that acts as an effective viscosity, mediating angular momentum transport. Due to its local nature, it is…
The paper outlines novel variational technique for finding microstructures of optimal multimaterial composites, bounds of composites properties, and multimaterial optimal designs. The translation method that is used for the exact…
A Lagrangian numerical scheme for solving nonlinear degenerate Fokker-Planck equations in space dimensions $d\ge2$ is presented. It applies to a large class of nonlinear diffusion equations, whose dynamics are driven by internal energies…
We propose two closely--related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and…
Recently, we developed a pair of meshless finite-volume Lagrangian methods for hydrodynamics: the 'meshless finite mass' (MFM) and 'meshless finite volume' (MFV) methods. These capture advantages of both smoothed-particle hydrodynamics…
This review article summarizes two decades of laboratory research aimed at understanding the dynamics of accretion disks, with particular emphasis on magnetohydrodynamic experiments involving liquid metals and plasmas. First, the…
This paper presents numerical simulations of metal machining processes with Eulerian and Total Lagrangian Smoothed Particle Hydrodynamics (SPH). Being a mesh-free method, SPH can conveniently handle large deformation and material…
For integrable systems in the sense of multidimensional consistency (MDC) we can consider the Lagrangian as a form, which is closed on solutions of the equations of motion. For 2-dimensional systems, described by partial difference…
Global disk simulations provide a powerful tool for investigating accretion and the underlying magnetohydrodynamic turbulence driven by the magneto-rotational instability (MRI). Using them to predict accurately quantities such as stress,…
A unified, Bayesian inference of midplane electron temperature and density profiles using both Thompson scattering (TS) and interferometric data is presented. Beyond the Bayesian nature of the analysis, novel features of the inference are…
Mechanical contact between solids is almost exclusively modeled in Lagrangian frameworks. While these frameworks have been developed extensively and applied successfully to numerous contact problems, they generally require complex…