Combined pitching and yawing motion of airplanes

This report treats the following problems: The beginning of the investigated motions is always a setting of the lateral controls, i.e., the rudder or the ailerons. Now, the first interesting question is how the motion would proceed if these settings were kept unchanged for some time; and particularly, what upward motion would set in, how soon, and for how long, since therein lie the dangers of yawing. Two different motions ensue with a high rate of turn and a steep down slope of flight path in both but a marked difference in angle of attack and consequently different character in the resultant aerodynamic forces: one, the "corkscrew" dive at normal angle, and the other, the "spin" at high angle

Cohomogeneity one manifolds and selfmaps of nontrivial degree

We construct natural selfmaps of compact cohomgeneity one manifolds with finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds with simple cohomology rings this yields in certain cases relations between the order of the Weyl group and the Euler characteristic of a principal orbit. We apply our construction to the compact Lie group SU(3) where we extend identity and transposition to an infinite family of selfmaps of every odd degree. The compositions of these selfmaps with the power maps realize all possible degrees of selfmaps of SU(3).Comment: v2, v3: minor improvement

Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation

In this paper we classify Weingarten surfaces integrable in the sense of soliton theory. The criterion is that the associated Gauss equation possesses an sl(2)-valued zero curvature representation with a nonremovable parameter. Under certain restrictions on the jet order, the answer is given by a third order ordinary differential equation to govern the functional dependence of the principal curvatures. Employing the scaling and translation (offsetting) symmetry, we give a general solution of the governing equation in terms of elliptic integrals. We show that the instances when the elliptic integrals degenerate to elementary functions were known to nineteenth century geometers. Finally, we characterize the associated normal congruences

Quasi-Gaussian Statistics of Hydrodynamic Turbulence in 3/4+\epsilon dimensions

The statistics of 2-dimensional turbulence exhibit a riddle: the scaling exponents in the regime of inverse energy cascade agree with the K41 theory of turbulence far from equilibrium, but the probability distribution functions are close to Gaussian like in equilibrium. The skewness \C S \equiv S_3(R)/S^{3/2}_2(R) was measured as \C S_{\text{exp}}\approx 0.03. This contradiction is lifted by understanding that 2-dimensional turbulence is not far from a situation with equi-partition of enstrophy, which exist as true thermodynamic equilibrium with K41 exponents in space dimension of $d=4/3$. We evaluate theoretically the skewness \C S(d) in dimensions ${4/3}\le d\le 2$, show that \C S(d)=0 at $d=4/3$, and that it remains as small as \C S_{\text{exp}} in 2-dimensions.Comment: PRL, submitted, REVTeX 4, 4 page

Statistical properties of Lorenz like flows, recent developments and perspectives

We comment on mathematical results about the statistical behavior of Lorenz equations an its attractor, and more generally to the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statisitcal behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated to the existence of physical measures: \emph{in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure}. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors.Comment: 40 pages; 10 figures; Keywords: sensitive dependence on initial conditions, physical measure, singular-hyperbolicity, expansiveness, robust attractor, robust chaotic flow, positive Lyapunov exponent, large deviations, hitting and recurrence times. Minor typos corrected and precise acknowledgments of financial support added. To appear in Int J of Bif and Chaos in App Sciences and Engineerin

Effect of frequency detuning on pulse propagation in one-dimensional photonic crystal with a dense resonant medium: application to optical logic

We consider propagation of light pulses detuned from the atomic resonance in a dense two-level medium and photonic structures with it. The large density of the medium is important to decrease spatial scale of such nonlinear effects as pulse compression, though it does not provide any fundamentally new phenomena as compared to dilute media. Frequency detuning decreases the effectivity of such nonlinear phenomena as pulse compression and dispersion spreading compensation as well. We propose simple logic gates based on interaction between two pulses in one-dimensional nonlinear photonic crystal. It turned out, that frequency detuning is necessary to obtain ultrafast AND gate, while OR and NOT gates can be realized in the system without detuning.Comment: 7 pages, 6 figure

Metal and oxidative potential exposure through particle inhalation and oxidative stress biomarkers: a 2-week pilot prospective study among Parisian subway workers.

In this pilot study on subway workers, we explored the relationships between particle exposure and oxidative stress biomarkers in exhaled breath condensate (EBC) and urine to identify the most relevant biomarkers for a large-scale study in this field. We constructed a comprehensive occupational exposure assessment among subway workers in three distinct jobs over 10 working days, measuring daily concentrations of particulate matter (PM), their metal content and oxidative potential (OP). Individual pre- and post-shift EBC and urine samples were collected daily. Three oxidative stress biomarkers were measured in these matrices: malondialdehyde (MDA), 8-hydroxy-2'deoxyguanosine (8-OHdG) and 8-isoprostane. The association between each effect biomarker and exposure variables was estimated by multivariable multilevel mixed-effect models with and without lag times. The OP was positively associated with Fe and Mn, but not associated with any effect biomarkers. Concentration changes of effect biomarkers in EBC and urine were associated with transition metals in PM (Cu and Zn) and furthermore with specific metals in EBC (Ba, Co, Cr and Mn) and in urine (Ba, Cu, Co, Mo, Ni, Ti and Zn). The direction of these associations was both metal- and time-dependent. Associations between Cu or Zn and MDA <sub>EBC</sub> generally reached statistical significance after a delayed time of 12 or 24 h after exposure. Changes in metal concentrations in EBC and urine were associated with MDA and 8-OHdG concentrations the same day. Associations between MDA in both EBC and urine gave opposite response for subway particles containing Zn versus Cu. This diverting Zn and Cu pattern was also observed for 8-OHdG and urinary concentrations of these two metals. Overall, MDA and 8-OHdG responses were sensitive for same-day metal exposures in both matrices. We recommend MDA and 8-OHdG in large field studies to account for oxidative stress originating from metals in inhaled particulate matter

Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L^{p,q}_{x,t}$-norm of the velocity with $3/p+2/q\leq 2$, $1\leq q\leq \infty$, or the $L^{p,q}_{x,t}$-norm of the vorticity with $3/p+2/q\leq 3$, $1 \leq q < \infty$, or the $L^{p,q}_{x,t}$-norm of the gradient of the vorticity with $3/p+2/q\leq 4$, $1 \leq q$, $1 \leq p$, is sufficiently small near $z$