Angular Symmetry Breaking Induced by Electromagnetic Field

It is well known that velocities does not commute in presence of an electromagnetic field. This property implies that angular algebra symmetries, such as the sO(3) and Lorentz algebra symmetries, are broken. To restore these angular symmetries we show the necessity of adding the Poincare momentum M to the simple angular momentum L. These restorations performed succesively in a flat space and in a curved space lead in each cases to the generation of a Dirac magnetic monopole. In the particular case of the Lorentz algebra we consider an application of our theory to the gravitoelectromagnetism. In this last case we establish a qualitative relation giving the mass spectrum for dyons.Comment: 19 page

Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets

We analyze a timed Petri net model of an emergency call center which processes calls with different levels of priority. The counter variables of the Petri net represent the cumulated number of events as a function of time. We show that these variables are determined by a piecewise linear dynamical system. We also prove that computing the stationary regimes of the associated fluid dynamics reduces to solving a polynomial system over a tropical (min-plus) semifield of germs. This leads to explicit formul{\ae} expressing the throughput of the fluid system as a piecewise linear function of the resources, revealing the existence of different congestion phases. Numerical experiments show that the analysis of the fluid dynamics yields a good approximation of the real throughput.Comment: 21 pages, 4 figures. A shorter version can be found in the proceedings of the conference FORMATS 201

Effects of dietary l-arginine supplementation to gilts during early gestation on foetal survival, growth and myofiber formation

The effects of l-arginine on porcine foetal development and myogenesis were determined. Twenty Swiss Large White gilts were randomly allocated to either the control (C) or l-arginine treatment (A). In addition to the standard gestation diet, A-sows received 26 g l-arginine daily from days 14 to 28 of gestation. At day 75 of pregnancy, sows were sacrificed and the number and weight of foetuses were recorded. From each litter, the lightest, heaviest and the ones with an average foetal weight (FtW) were selected. Primary (P), secondary (S) and total myofiber number as well as S/P ratio were determined in the semitendinosus (ST) and rhomboideus (RH) muscles. In A-sows, the number of viable foetuses (13.0 v. 9.3) and total FtW (4925 v. 3729 g) was greater (P ⩽ 0.04) than in C-sows. Compared to C-sow foetuses, the ST of A-sow foetuses had 7% more (17 699 v. 16 477; P = 0.04) P myofibers and the S/P ratio in both muscles was lower (ST = 20.3 v. 21.5; RH = 24.1 v. 27.1; P ⩽ 0.07). Regardless of the maternal diet, the S myofiber number and the S/P ratio in both muscles were greater (P ⩽ 0.01) in foetuses with a high FtW compared to low FtW. These data suggest that l-arginine supplemented to gilts during early gestation enhanced foetal survival and in the ST positively affected the primary phase of myofiber formatio

Perelman's entropy for some families of canonical metrics

We numerically calculate Perelman’s entropy for a variety of canonical metrics on CP1-bundles over products of Fano Kähler-Einstein manifolds. The metrics investigated are Einstein metrics, Kähler-Ricci solitons and quasi-Einstein metrics. The calculation of the entropy allows a rough picture of how the Ricci flow behaves on each of the manifolds in question

From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics

In 1990, Dyson published a proof due to Feynman of the Maxwell equations assuming only the commutation relations between position and velocity. With this minimal assumption, Feynman never supposed the existence of Hamiltonian or Lagrangian formalism. In the present communication, we review the study of a relativistic particle using ``Feynman brackets.'' We show that Poincar\'e's magnetic angular momentum and Dirac magnetic monopole are the consequences of the structure of the Lorentz Lie algebra defined by the Feynman's brackets. Then, we extend these ideas to the dual momentum space by considering noncommutative quantum mechanics. In this context, we show that the noncommutativity of the coordinates is responsible for a new effect called the spin Hall effect. We also show its relation with the Berry phase notion. As a practical application, we found an unusual spin-orbit contribution of a nonrelativistic particle that could be experimentally tested. Another practical application is the Berry phase effect on the propagation of light in inhomogeneous media.Comment: Presented at the 3rd Feynman Festival (Collage Park, Maryland, U.S.A., August 2006

Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics

To build genuine generators of the rotations group in noncommutative quantum mechanics, we show that it is necessary to extend the noncommutative parameter $\theta$ to a field operator, which one proves to be only momentum dependent. We find consequently that this field must be obligatorily a dual Dirac monopole in momentum space. Recent experiments in the context of the anomalous Hall effect provide for a monopole in the crystal momentum space. We suggest a connection between the noncommutative field and the Berry curvature in momentum space which is at the origine of the anomalous Hall effect.Comment: 4 page

Spin Hall effect of Photons in a Static Gravitational Field

Starting from a Hamiltonian description of the photon within the set of Bargmann-Wigner equations we derive new semiclassical equations of motion for the photon propagating in static gravitational field. These equations which are obtained in the representation diagonalizing the Hamiltonian at the order $\hbar$, present the first order corrections to the geometrical optics. The photon Hamiltonian shows a new kind of helicity-magnetotorsion coupling. However, even for a torsionless space-time, photons do not follow the usual null geodesic as a consequence of an anomalous velocity term. This term is responsible for the gravitational birefringence phenomenon: photons with distinct helicity follow different geodesics in a static gravitational field.Comment: 6 page

Last passage percolation and traveling fronts

We consider a system of N particles with a stochastic dynamics introduced by Brunet and Derrida. The particles can be interpreted as last passage times in directed percolation on {1,...,N} of mean-field type. The particles remain grouped and move like a traveling wave, subject to discretization and driven by a random noise. As N increases, we obtain estimates for the speed of the front and its profile, for different laws of the driving noise. The Gumbel distribution plays a central role for the particle jumps, and we show that the scaling limit is a L\'evy process in this case. The case of bounded jumps yields a completely different behavior

Inverse problem and Bertrand's theorem

The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical equation. This permit a particulary compact and elegant proof of Bertrand's theorem.Comment: 11 pages, 3 figure