Person

Tudor Ratiu

Area preserving flows and metriplectic dynamics on an annulus

In this paper, we present metriplectic extensions of the Lie–Poisson dynamics of fluid flows over the unit annulus for both the Lebesgue [Formula: see text]-pairing and the Sobolev [Formula: see text]-pairing. Several examples are provided including 2D Nav ...

World Scientific Pub Co Pte Ltd2025

Cotangent Bundle Reduction

Tudor Ratiu

Elsevier2024

The Restricted Siegel Disc as Coadjoint Orbit

Tudor Ratiu

The restricted Siegel disc is a homogeneous space related to the con- nected component To(1) of the universal Teichmller space via the period mapping. In this paper, we show that it is a coadjoint orbit of the universal central extension of the restricted ...

Walter De Gruyter2024

Simultaneous local normal forms of dynamical systems with singular underlying geometric structures

Tudor Ratiu

The aim of this paper is to develop, for the first time, a general theory of simultaneous local normalisation of couples (X,G), where X is a dynamical system (vector field) and G is an underlying geometric structure preserved by X, even if both have singul ...

IOP Publishing Ltd2024

Stochastic Variational Principles for Dissipative Equations with Advected Quantities

Tudor Ratiu

This paper presents symmetry reduction for material stochastic Lagrangian systems with advected quantities whose configuration space is a Lie group. Such variational principles yield deterministic as well as stochastic constrained variational principles fo ...

2023

Symplectic induction, prequantum induction, and prequantum multiplicities

Tudor Ratiu

Frobenius reciprocity asserts that induction from a subgroup and restriction to it are adjoint functors in categories of unitary G-modules. In the 1980s, Guillemin and Sternberg established a parallel property of Hamiltonian G-spaces, which (as we show) un ...

WORLD SCIENTIFIC PUBL CO PTE LTD2022

On the Eringen model for nematic liquid crystals

Tudor Ratiu

We introduce the three-dimensional Eringen system of equations for the nematodynamics of liquid crystals, announce the short time existence and uniqueness of strong solutions for the one-dimensional problem in the periodic case, and show the continuous dep ...

centre Mersenne pour ldition scientifique ouverte2021

Wigner Measures and Coherent Quantum Control

Tudor Ratiu

We introduce Wigner measures for infinite-dimensional open quantum systems; important examples of such systems are encountered in quantum control theory. In addition, we propose an axiomatic definition of coherent quantum feedback. ...

2021

Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type

Tudor Ratiu

The geodesic flows are studied on real forms of complex semi-simple Lie groups with respect to a left-invariant (pseudo-)Riemannian metric of rigid body type. The Williamson types of the isolated relative equilibria on generic adjoint orbits are determined ...

SPRINGER INTERNATIONAL PUBLISHING AG2020

Quantum Anomalies via Differential Properties of Lebesgue-Feynman Generalized Measures

Tudor Ratiu

We address the problem concerning the origin of quantum anomalies, which has been the source of disagreement in the literature. Our approach is novel as it is based on the differentiability properties of families of generalized measures. To this end, we in ...

MAIK NAUKA/INTERPERIODICA/SPRINGER2020