Related papers: Continuous and discrete Clebsch variational princi…
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…
Weakly conducting dielectric liquid drops suspended in another dielectric liquid and subject to an applied uniform electric field exhibit a wide range of dynamical behaviors contingent on field strength and material properties. These…
In this paper we study the general minimization vector problem (P), concerning a perturbation mapping, defined in locally convex Hausdorff topological vector spaces where the "WInf" stands for the weak infimum with respect to an ordering…
In this paper structure-preserving time-integrators for rigid body-type mechanical systems are derived from a discrete Hamilton-Pontryagin variational principle. From this principle one can derive a novel class of variational partitioned…
We extend the recently developed discrete geometric singular perturbation theory to the non-normally hyperbolic regime. Our primary tool is the Takens embedding theorem, which provides a means of approximating the dynamics of particular…
We present a simple and efficient variational finite difference method for simulating time-dependent Stokes flow in the presence of irregular free surfaces and moving solid boundaries. The method uses an embedded boundary approach on…
We re-express the quantum Calogero-Sutherland model for the Lie algebra E7 and the particular value of the coupling constant K=1 by using the fundamental irreducible characters of the algebra as dynamical variables. For that, we need to…
We present a novel structure-preserving semi-implicit finite volume method on vertex-based staggered meshes for the compatible discretization of first order systems of time-dependent partial differential equations (PDEs). The method…
This paper is concerned with long-time strong approximations of SDEs with non-globally Lipschitz coefficients.Under certain non-globally Lipschitz conditions, a long-time version of fundamental strong convergence theorem is established for…
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…
This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange-Dirac and…
A framework of finite-velocity model based Boltzmann equation has been developed for convection-diffusion equations. These velocities are kept flexible and adjusted to control numerical diffusion. A flux difference splitting based kinetic…
This paper develops a geometric mechanics framework for the reduction of general relativistic hydrodynamic variational principles, from the variation of worldlines approach in 4D spacetime to 3-dimensional Eulerian descriptions. We consider…
Many partial differential equations (PDEs) such as Navier--Stokes equations in fluid mechanics, inelastic deformation in solids, and transient parabolic and hyperbolic equations do not have an exact, primal variational structure. Recently,…
We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the…
We present some new Poisson bivectors that are invariants by the Clebsch system flow. Symplectic integrators on their symplectic leaves exactly preserve the corresponding Casimir functions, which have different physical meanings. The Kahan…
The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…
We present a pedagogical review of some of the methods employed in Eulerian computational fluid dynamics (CFD). Fluid mechanics is governed by the Euler equations, which are conservation laws for mass, momentum, and energy. The standard…
We theoretically explore the possibility of stabilizing the trapless polariton Bose-Einstein condensates (pBECs). Exploiting the variational method, we solve the associated nonlinear, complex Gross-Pitaevskii (cGP) equation and derive the…
In Willems' behavioral systems theory, a dynamical system is identified with the set of all trajectories compatible with its laws of motion. In the linear time-invariant setting this trajectory set is a linear subspace, and its algebraic…