Related papers: Flows of Calogero-Moser Systems
We study electric polarization and nonlinear optical effects in spin systems with broken inversion symmetry. We apply strong coupling expansion to the underlying electronic Hamiltonians, and systematically derive expressions for electric…
This paper describes the results of our theoretical and numerical studies of hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls, under creeping-flow conditions. We propose a novel…
We study the integrability of a two-dimensional Hamiltonian system with a gyroscopic term and a non-homogeneous potential composed of two homogeneous components of different degrees. The model describes the motion of a particle in a plane…
We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The algorithm discretizes partial derivatives at scattered points using radial basis functions as…
We develop a block-structured solver for high-fidelity simulation of flows in complex geometries, based on overlapping (Chimera) meshes. The key components of the algorithm are a baseline dissipation-free central discretization and…
We investigate the topological properties of dynamical states evolving on periodic oriented graphs. This evolution, that encodes the scattering processes occurring at the nodes of the graph, is described by a single-step global operator, in…
General relativity uses curved space-time to describe accelerating frames. The movement of particles in different curved space-times can be regarded as equivalent physical processes based on the covariant transformation between different…
A hallmark of meso-scale interfacial fluids is the multi-faceted, scale-dependent interfacial energy, which often manifests different characteristics across the molecular and continuum scale. The multi-scale nature imposes a challenge to…
A moving parallel frame method is applied to geometric non-stretching curve flows in the Hermitian symmetric space Sp(n)/U(n) to derive new integrable systems with unitary invariance. These systems consist of a bi-Hamiltonian modified…
We consider a Hamiltonian system which has its origin in a generalization of exact renormalization group flow of matrix scalar field theory and describes a non-linear generalization of the shock-wave equation that is known to be integrable.…
A Lagrangian-type numerical scheme called the "comoving mesh method" or CMM is developed for numerically solving certain classes of moving boundary problems which include, for example, the classical Hele-Shaw flow problem and the well-known…
A 3D fluid-structure interaction solver based on an improved weakly-compressible moving particle simulation (WC-MPS) method and a geometrically nonlinear shell structural model is developed and applied to hydro-elastic free-surface flows.…
A universal algorithm to construct N-particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum…
In this article we review the perfect-fluid hydrodynamics with spin framework proposed recently. This framework generalises the standard relativistic hydrodynamics framework to include spin degrees of freedom and provides a natural method…
This paper provides a unified framework connecting dynamical systems with tools from topological data analysis and geometric topology and inspires new interactions among dynamical systems, topology, and nonlinear analysis. To this end, we…
In our recent works we have used meromorphic differentials on Riemann surfaces all of whose periods are real to study the geometry of the moduli spaces of Riemann surfaces. In this paper we survey the relevant constructions and show how…
The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite 2D channel.…
We discuss a new Monte Carlo algorithm for the simulation of complex fluids. This algorithm employs geometric operations to identify clusters of particles that can be moved in a rejection-free way. It is demonstrated that this geometric…
Starting from a homogeneous polynomial in momenta of arbitrary order we extract multi-component hydrodynamic-type systems which describe 2-dimensional geodesic flows admitting the initial polynomial as integral. All these hydrodynamic-type…
Generalized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in the study of spectral curves and…