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We consider conjugation action of symmetric group on the semigroup of all partial functions and develop a machinery to investigate character formulas and multiplicities. In particular, we determine nilpotent matrices whose orbit under…
We discuss and analyze the properties of Casimir forces acting between nonreciprocal objects in thermal equilibrium. By starting from the fluctuation-dissipation theorem and splitting the force into those arising from individual sources, we…
The concept of inverse energy cascades has played a central role in the development of turbulence theory, with applications in two-dimensional and quasi-two-dimensional flows. We examine the presence or absence of inverse energy cascades in…
We consider an anisotropic inhomogeneous model to simulate measured vertical-seismic-profile traveltimes. In this model, we assume that velocity increases linearly with depth and anisotropy is the result of elliptical velocity dependence.…
The quantum rotor represents, after the harmonic oscillator, the next obvious quantum system to study the complementary pair of variables: the angular momentum and the unitary shift operator in angular momentum. Proper quantification of…
Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a…
High-resolution imaging provides dense trajectories of migrating cells, flocking animals, and synthetic active particles, from which interaction laws can be determined with a wide variety of methods. Yet, distinguishing whether front-back…
Geometric structures underlying commutative and non commutative integrable dynamics are analyzed. They lead to a new characterization of noncommutative integrability in terms of spectral properties and of Nijenhuis torsion of an invariant…
In this effort we show that the Legendre reciprocity relations,thermodynamic's essential formal feature, are respected by any entropic functional, even if it is NOT of trace-form nature, as Shannon's is. Further, with reference to the…
The rotational dynamics of anisotropic particles advected in a turbulent fluid flow are important in many industrial and natural setting. Particle rotations are controlled by small scale properties of turbulence that are nearly universal,…
Using representation theory techniques we prove that various spaces of derivations or one-sided multipliers over certain operator algebras are reflexive. A sample result: any bounded local derivation (local left multiplier) on an…
The theory of fully developed turbulence is usually considered in an idealized homogeneous and isotropic state. Real turbulent flows exhibit the effects of anisotropic forcing. The analysis of correlation functions and structure functions…
The influence of the basic rotation on anisotropic and inhomogeneous turbulence is discussed in the context of differential rotation theory. An improved representation for the original turbulence leads to a $\Lam$-effect which complies with…
The construction of field theories with space-time symmetries, including tensorial charges (i.e. of M-theory type), initiated in hep-th/9907011, is extended to include interaction. For SO(2,2) gravity in a tensorial space-time, with…
This is a survey paper about reciprocal processes. The bridges of a Markov process are also Markov. But an arbitrary mixture of these bridges fails to be Markov in general. However, it still enjoys the interesting properties of a reciprocal…
This paper initiates the systematic study of thermal field theory for generic equilibrium density matrices, which feature arbitrary values not only of temperature and chemical potentials, but also of average angular momentum. The focus here…
Employing a simple ideal magnetohydrodynamic model in spherical geometry,we show that the presence of either rotation or finite magnetic helicity is sufficient to induce dynamical reversals of the magnetic dipole moment. The statistical…
This work investigates the theory behind a thought experiment that intends to measure momentum and angular momentum of matter exposed to `isotropic radiative noise'. Radiative momentum has been a controversial subject for decades. The…
We derive multipolar equations of motion for gravitational theories with general nonminimal coupling in spacetimes admitting torsion. Our very general findings allow for the systematic testing of whole classes of theories by means of…
A quantum-mechanical framework is set up to describe the full counting statistics of particles flowing between reservoirs in an open system under time-dependent driving. A symmetry relation is obtained which is the consequence of…