Related papers: Matched Pair Analysis of Euler-Poincar\'{e} Flow o…
We explicitly establish a unitary correspondence between spherical irreducible tensor operators and cartesian tensor operators of any rank. That unitary relation is implemented by means of a basis of integer-spin wave functions that…
The fluid structure interaction of cylinders in tandem arrangement is used as validation basis of a multi-domain Lagrangian-Eulerian hybrid flow solver. In this hybrid combination, separate grids of limited width are defined around every…
A detailed analysis of electron-positron pair creation induced by a spatially nonuniform and static electric field from vacuum is presented. A typical example is provided by the Sauter potential. For this potential, we derive the analytic…
Work of Bezrukavnikov-Kazhdan-Varshavsky uses an equivariant system of trivial idempotents of Moy-Prasad groups to obtain an Euler-Poincar\'{e} formula for the r-depth Bernstein projector. Barbasch-Ciubotaru-Moy use depth-zero cuspidal…
We give a simple proof of Onsager's conjecture concerning energy conservation for weak solutions to the Euler equations on any compact Riemannian manifold, extending the results of Constantin-E-Titi and…
If for a vector space V of dimension g over a characteristic zero field we denote by $\wedge^iV$ its alternating powers, and by $V^\vee$ its linear dual, then there are natural Poincar\'e isomorphisms: $\wedge^i V^\vee \cong \wedge^{g-i}…
We study a class of 2-dimensional Hamiltonian systems $H(x,y,p_x,p_y)=\frac12(p_x^2+p_y^2) +V(x,y)$ in which the plane $x$=$p_x$=0 is invariant under the Hamiltonian flow, so that straight-line librations along the y axis exist, and we also…
We establish a quantum analogue of the classical metaplectic Howe duality involving the pair of Lie algebras $(\mathfrak{sp}_{2n},\mathfrak{sl}_2)$ in the case when $n=1$. Our results yield commuting representations of the pair of…
We present a general formulation of the theory for a non-minimally coupled perfect fluid in which both conformal and disformal couplings are present. We discuss how such non-minimal coupling is compatible with the assumptions of a perfect…
We consider two new classes of twisted D=4 quantum Poincar\'{e} symmetries described as the dual pairs of noncocommutative Hopf algebras. Firstly we investigate a two-parameter class of twisted Poincar\'{e} algebras which provide the…
We study a one-dimensional electron gas in a special antiferromagnetic environment made by two spin-1/2 Heisenberg chains and the one-dimensional two-channel Kondo-Heisenberg lattice away from half-filling. These models flow to an…
We show that the following three systems related to various hydrodynamical approximations: the Korteweg--de Vries equation, the Camassa--Holm equation, and the Hunter--Saxton equation, have the same symmetry group and similar bihamiltonian…
Predicting low-energy molecular conformations given a molecular graph is an important but challenging task in computational drug discovery. Existing state-of-the-art approaches either resort to large scale transformer-based models that…
Electroconvective flow between two infinitely long parallel electrodes is investigated via a multiphysics computational model. The model solves for spatiotemporal flow properties using two-relaxation-time Lattice Boltzmann Method for fluid…
We give two equivalent sets of invariants which classify pairs of coisotropic subspaces of finite-dimensional Poisson vector spaces. For this it is convenient to dualize; we work with pairs of isotropic subspaces of presymplectic vector…
In a basic framework of a complex Hilbert space equipped with a complex conjugation and an involution, linear operators can be real, quaternionic, symmetric or anti-symmetric, and orthogonal projections can furthermore be symplectic. This…
In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov…
This work establishes a multivariable Wold-type decomposition for left-inverse commuting $n$-tuples of bounded operators, built on the hypothesis that each component admits a Wold-type decomposition. For pairs of operators, we obtain a…
In this paper, we build the Hamiltonian system and the corresponding Lax pairs associated to a twisted connection in $\mathfrak{gl}_2(\mathbb{C})$ admitting an irregular and ramified pole at infinity of arbitrary degree, hence corresponding…
This paper investigates the global well-posedness and large-time behavior of solutions for a coupled fluid model in $\mathbb{R}^3$ consisting of the isothermal compressible Euler-Poisson system and incompressible Navier-Stokes equations…