Understanding the effect of seams on the aerodynamics of an association football

The aerodynamic properties of an association football were measured using a wind tunnel arrangement. A third scale model of a generic football (with seams) was used in addition to a 'mini-football'. As the wind speed was increased, the drag coefficient decreased from 0.5 to 0.2, suggesting a transition from laminar to turbulent behaviour in the boundary layer. For spinning footballs, the Magnus effect was observed and it was found that reverse Magnus effects were possible at low Reynolds numbers. Measurements on spinning smooth spheres found that laminar behaviour led to a high drag coefficient for a large range of Reynolds numbers, and Magnus effects were inconsistent, but generally showed reverse Magnus behaviour at high Reynolds number and spin parameter. Trajectory simulations of free kicks demonstrated that a football that is struck in the centre will follow a near straight trajectory, dipping slightly before reaching the goal, whereas a football that is struck off centre will bend before reaching the goal, but will have a significantly longer flight time. The curving kick simulation was repeated for a smooth ball, which resulted in a longer flight time, due to increased drag, and the ball curving in the opposite direction, due to reverse Magnus effects. The presence of seams was found to encourage turbulent behaviour, resulting in reduced drag and more predictable Magnus behaviour for a conventional football, compared with a smooth ball. © IMechE 2005

Complete solution of a constrained tropical optimization problem with application to location analysis

We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective function defined on vectors over an idempotent semifield by means of a conjugate transposition operator, subject to constraints in the form of linear vector inequalities. A complete direct solution to the problem under fairly general assumptions is given in a compact vector form suitable for both further analysis and practical implementation. We apply the result to solve a multidimensional minimax single facility location problem with Chebyshev distance and with inequality constraints imposed on the feasible location area.Comment: 20 pages, 3 figure

Bond breaking in vibrationally excited methane on transition metal catalysts

The role of vibrational excitation of a single mode in the scattering of methane is studied by wave packet simulations of oriented CH4 and CD4 molecules from a flat surface. All nine internal vibrations are included. In the translational energy range from 32 up to 128 kJ/mol we find that initial vibrational excitations enhance the transfer of translational energy towards vibrational energy and increase the accessibility of the entrance channel for dissociation. Our simulations predict that initial vibrational excitations of the asymmetrical stretch (nu_3) and especially the symmetrical stretch (nu_1) modes will give the highest enhancement of the dissociation probability of methane.Comment: 4 pages REVTeX, 2 figures (eps), to be published in Phys. Rev. B. (See also arXiv:physics.chem-ph/0003031). Journal version at http://publish.aps.org/abstract/PRB/v61/p1565

Spectrally resolved multi-channel contributions to the harmonic emission in N 2

International audienceWhen generated in molecules, high-order harmonics can be emitted through different ionization channels. The coherent and ultrafast electron dynamics occurring in the ion during the generation process is directly imprinted in the harmonic signal, i.e. in its amplitude and spectral phase. In aligned N2 molecules, we find evidence for a fast variation of this phase as a function of the harmonic order when varying the driving laser intensity. Basing our analysis on a three-step model, we find that this phase variation is a signature of transitions from a single- to a multi-channel regime. In particular, we show that significant nuclear dynamics may occur in the ionization channels on the attosecond timescale, affecting both the amplitude and the phase of the harmonic signal

Molecular orbital tomography from multi-channel harmonic emission in N2

International audienceHigh-order harmonic generation in aligned molecules can be used as an ultrafast probe of molecular structure and dynamics. By characterizing the emitted signal , one can retrieve information about electronic and nuclear dynamics occurring in the molecule at the attosecond timescale. In this paper , we discuss the theoretical and experimental aspects of molecular orbital tomography in N 2 and investigate the influence of multi-channel ionization on the orbital imaging. By analyzing the spectral phase of the harmonic emission as a function of the driving laser intensity , we address two distinct cases , which in principle allow the orbital reconstruction. First , the contributions from two molecular orbitals could be disentangled in the real and imaginary parts of the measured dipole , making it possible to reconstruct both orbitals. Second , by decreasing the driving laser intensity , the transition from a multi-channel to a single-channel ionization regime is shown. The highest occupied molecular orbital may then be selected as the only one contributing efficiently to the harmonic emission. The latter approach paves the way towards the generalization of tomography to more complex systems

Semiring and semimodule issues in MV-algebras

In this paper we propose a semiring-theoretic approach to MV-algebras based on the connection between such algebras and idempotent semirings - such an approach naturally imposing the introduction and study of a suitable corresponding class of semimodules, called MV-semimodules. We present several results addressed toward a semiring theory for MV-algebras. In particular we show a representation of MV-algebras as a subsemiring of the endomorphism semiring of a semilattice, the construction of the Grothendieck group of a semiring and its functorial nature, and the effect of Mundici categorical equivalence between MV-algebras and lattice-ordered Abelian groups with a distinguished strong order unit upon the relationship between MV-semimodules and semimodules over idempotent semifields.Comment: This version contains some corrections to some results at the end of Section

Asymptotics of Selberg-like integrals: The unitary case and Newton's interpolation formula

We investigate the asymptotic behavior of the Selberg-like integral $$\frac1{N!}\int_{[0,1]^N}x_1^p\prod_{i<j}(x_i-x_j)^2\prod_ix_i^{a-1}(1-x_i)^{b-1}dx_i$$, as $N\to\infty$ for different scalings of the parameters $a$ and $b$ with $N$. Integrals of this type arise in the random matrix theory of electronic scattering in chaotic cavities supporting $N$ channels in the two attached leads. Making use of Newton's interpolation formula, we show that an asymptotic limit exists and we compute it explicitly