Giulio Soliani

Vortices and invariant surfaces generated by symmetries for the 3D Navier–Stokes equations

We show that certain infinitesimal operators of the Lie-point symmetries of the incompressible 3D Navier–Stokes equations give rise to vortex solutions with different characteristics. This approach allows an algebraic classification of vortices and throws light on the alignment mechanism between the vorticity ω and the vortex stretching vector Sω, where S is the strain matrix. The symmetry algebra associated with the Navier–Stokes equations turns out to be infinite-dimensional. New vortical structures, generalizing in some cases well-known configurations such as, for example, the Burgers and Lundgren solutions, are obtained and discussed in relation to the value of the dynamic angle φ=arctan|ω→∧Sω→|/ω→·Sω→. A systematic treatment of the boundary conditions invariant under the symmetry group of the equations under study is also performed, and the corresponding invariant surfaces are recognized.

A group analysis of the 2D Navier–Stokes–Fourier equations

We study a (2+1)-dimensional model of an incompressible thermoconducting fluid named Navier–Stokes–Fourier system. We apply a group-theoretical analysis. In correspondence of the generators of the symmetry group allowed by this model, exact solutions are found. Some of them show possible interesting physical interpretations. In our first exploration, this feature is illustrated by dealing with simple special cases.

Generalized measurement of the non-normal two-boson operator

We address the generalized measurement of the two-boson operator

A class of nonlinear wave equations containing the continuous Toda case

Z_\gamma= a_1 + \gamma a_2^\dag

Equations of the reaction-diffusion type with a loop algebra structure

which, for

A NOTE ON THE LOSS OF COHERENCE IN WAVE PACKETS SQUEEZED SYSTEMS

|\gamma|^2 \neq 1

On certain canonoid transformations and invariants for the parametric oscillator

, is not normal and cannot be detected by a joint measurement of quadratures on the two bosons. We explicitly construct the minimal Naimark extension, which involves a single additional bosonic system, and present its decomposition in terms of two-boson linear SU(2) interactions. The statistics of the measurement and the added noise are analyzed in details. Results are exploited to revisit the Caves-Shapiro concept of generalized phase observable based on heterodyne detection.

Temperature behaviour of vortices of a 3D thermoconducting viscous fluid

We consider a nonlinear field equation which can be derived from a binomial lattice as a continuous limit. This equation, containing a perturbative friction-like term and a free parameter , reproduces the Toda case (in the absence of the friction-like term) and other equations of physical interest, by choosing particular values of . We apply the symmetry and the approximate-symmetry approach, and the prolongation technique. Our main aim is to check the limits of validity of different analytical methods in the study of nonlinear field equations. We show that the equation under investigation with the friction-like term is characterized by a finite-dimensional Lie algebra admitting a realization in terms of boson annhilation and creation operators. In the absence of the friction-like term, the equation is linearized and connected with Bessel-type equations. Examples of exact solutions are displayed, and the algebraic structure of the equation is discussed.

Continuous approximation of binomial lattices

A system of equations of the reaction-diffusion type is studied in the framework of both the direct and the inverse prolongation structure. We find that this system allows an incomplete prolongation Lie algebra, which is used to find the spectral problem and a whole class of nonlinear field equations containing the original ones as a special case.

Properties of equations of the continuous Toda type

Time-dependent dynamical systems with a particular emphasis on models attaining the minimum value of uncertainty formula are considered. The role of the Bogolubov coefficients, in general and in the context of the loss of minimum uncertainty, is analyzed. Different fluctuation values on squeezed states are performed. The decoherence energy is parametrized by an angle ϕ and turns out to vanish whenever ϕ=π. An application to the Paul trap theory is discussed.