Spin Waves as Metric in a Kinetic Space-Time

1) A wave equation is derived from the kinetic equations governing media with rotational as well as translational degrees of freedom. In this wave the fluctuating quantity is a vector, the bulk spin. The transmission is similar to compressive waves but propagation is possible even in the limit of incompressibility, where such disturbances could become dominant. 2) In this context a kinetic theory of space-time is introduced, in which hypothetical constituents of the space-time manifold possess such a rotational degree of freedom (spin). Physical fields (i.e. electromagnetic or gravitational) in such a theory are represented as moments of a statistical distribution of these constituents. The spin wave equation from 1) is treated as a candidate for governing light and metric. Such a theory duplicates to first order Maxwell's equations of electromagnetism, Schrodinger's equation for the electron, and the Lorentz transformations of special relativity. Slight deviations from the classical approach are predicted and should be experimentally verifiable.Comment: 13 pages + errat

Shell structure in the density profile of a rotating gas of spin-polarized fermions

We present analytical expressions and numerical illustrations for the ground-state density distribution of an ideal gas of spin-polarized fermions moving in two dimensions and driven to rotate in a harmonic well of circular or elliptical shape. We show that with suitable choices of the strength of the Lorentz force for charged fermions, or of the rotational frequency for neutral fermions, the density of states can be tuned as a function of the angular momentum so as to display a prominent shell structure in the spatial density profile of the gas. We also show how this feature of the density profile is revealed in the static structure factor determining the elastic light scattering spectrum of the gas.Comment: 12 pages, 6 figure

Semantic Segmentation of Earth Observation Data Using Multimodal and Multi-scale Deep Networks

International audienceThis work investigates the use of deep fully convolutional neural networks (DFCNN) for pixel-wise scene labeling of Earth Observation images. Especially, we train a variant of the SegNet architecture on remote sensing data over an urban area and study different strategies for performing accurate semantic segmentation. Our contributions are the following: 1) we transfer efficiently a DFCNN from generic everyday images to remote sensing images; 2) we introduce a multi-kernel convolutional layer for fast aggregation of predictions at multiple scales; 3) we perform data fusion from heterogeneous sensors (optical and laser) using residual correction. Our framework improves state-of-the-art accuracy on the ISPRS Vaihingen 2D Semantic Labeling dataset

Metafluid dynamics and Hamilton-Jacobi formalism

Metafluid dynamics was investigated within Hamilton-Jacobi formalism and the existence of the hidden gauge symmetry was analyzed. The obtained results are in agreement with those of Faddeev-Jackiw approach.Comment: 7 page

Kinetic theory of point vortices: diffusion coefficient and systematic drift

We develop a kinetic theory for point vortices in two-dimensional hydrodynamics. Using standard projection operator technics, we derive a Fokker-Planck equation describing the relaxation of a ``test'' vortex in a bath of ``field'' vortices at statistical equilibrium. The relaxation is due to the combined effect of a diffusion and a drift. The drift is shown to be responsible for the organization of point vortices at negative temperatures. A description that goes beyond the thermal bath approximation is attempted. A new kinetic equation is obtained which respects all conservation laws of the point vortex system and satisfies a H-theorem. Close to equilibrium this equation reduces to the ordinary Fokker-Planck equation.Comment: 50 pages. To appear in Phys. Rev.

Kinetic theory of Onsager's vortices in two-dimensional hydrodynamics

Starting from the Liouville equation, and using a BBGKY-like hierarchy, we derive a kinetic equation for the point vortex gas in two-dimensional (2D) hydrodynamics, taking two-body correlations and collective effects into account. This equation is valid at the order 1/N where N>>1 is the number of point vortices in the system (we assume that their individual circulation scales like \gamma ~ 1/N). It gives the first correction, due to graininess and correlation effects, to the 2D Euler equation that is obtained for $N\rightarrow +\infty$. For axisymmetric distributions, this kinetic equation does not relax towards the Boltzmann distribution of statistical equilibrium. This implies either that (i) the "collisional" (correlational) relaxation time is larger than Nt_D, where t_D is the dynamical time, so that three-body, four-body... correlations must be taken into account in the kinetic theory, or (ii) that the point vortex gas is non-ergodic (or does not mix well) and will never attain statistical equilibrium. Non-axisymmetric distributions may relax towards the Boltzmann distribution on a timescale of the order Nt_D due to the existence of additional resonances, but this is hard to prove from the kinetic theory. On the other hand, 2D Euler unstable vortex distributions can experience a process of "collisionless" (correlationless) violent relaxation towards a non-Boltzmannian quasistationary state (QSS) on a very short timescale of the order of a few dynamical times. This QSS is possibly described by the Miller-Robert-Sommeria (MRS) statistical theory which is the counterpart, in the context of two-dimensional hydrodynamics, of the Lynden-Bell statistical theory of violent relaxation in stellar dynamics