Safe domain and elementary geometry

A classical problem of mechanics involves a projectile fired from a given point with a given velocity whose direction is varied. This results in a family of trajectories whose envelope defines the border of a 'safe' domain. In the simple cases of a constant force, harmonic potential and Kepler or Coulomb motion, the trajectories are conic curves whose envelope in a plane is another conic section which can be derived either by simple calculus or by geometrical considerations. The case of harmonic forces reveals a subtle property of the maximal sum of distances within an ellipse.Comment: Also available from http://democrite.in2p3.fr/democrite-0002317

Speculations in hadron spectroscopy

A selected survey is presented of the recent progress in hadron spectroscopy. This includes spin-singlet charmonium states, excitations of charmonium and open-charm mesons, double-charm baryons, and pentaquark candidates. Models proposing exotic bound states or resonances are reviewed. The sector of exotic mesons with two heavy quarks appears as particularly promising

Elusive multiquark spectroscopy

A review is presented of past and recent attempts to build multiquark states within current models already describing ordinary mesons and baryons. This includes: coherence in the chromomagnetic interaction, tetraquarks with two heavy quarks, Steiner-tree models of confinement, and hadronic molecules, in particular in the hidden-charm sector. Some emphasis is put on the difficulties encountered when extrapolating toward higher configurations the dynamics of confining forces, starting from the simple case of a quark and an antiquark, or three quarks in a colour singlet

Historical Survey of the Quasi-Nuclear Baryonium

We review ideas and speculations concerning possible bound states or resonances of the nucleon--antinucleon system.Comment: 12 pages, Talk at the Workshop on Hadron Spectroscopy, Frascati, Italy, march 199

Recent issues in hadron spectroscopy

A brief survey is presented of recently discovered hadrons, some of them presumably demonstrating a new kind of internal structure. This includes : spin-singlet quarkonium, mesons with unexpected mass or width, baryons with two heavy quarks, and pentaquark candidates. Flavour configurations with a combination of light and heavy quarks appear as particularly promising.Comment: Based on an invited talk at the session on Subnucleon degrees of freedo

Stability of multiquarks in a simple string model

A simple string model inspired by the strong-coupling regime of Quantum ChromoDynamics is used as a potential for studying the spectrum of multiquark systems with two quarks and two antiquarks, with a careful treatment of the four-body problem. It is found that the ground state is stable, lying below the threshold for dissociation into two isolated mesons.Comment: 4 pages, 2 figures, Refs. added, typos corrected, discussion improved, to appear in Phys. Rev.

Positivity domains for pairs of triples of spin observables

Positivity restrains the allowed domains for pairs or triples of spin observables in polarised reactions. Various domain shapes in ${1\over2}+{1\over2}\to{1\over2}+{1\over2}$ reactions are displayed. Some methods to determine these domains are mentioned and a new one based on the anticommutation between two observables is presented.Comment: Talk given by Xavier Artru at "DSPIN-07", XII Workshop on High-Energy Spin Physics, Dubna, Sept. 3-7, 2007, to appear in the Proceeding

Atomic hydrogen in the disturbed edge-on galaxy NGC 4631

We present WSRT HI observations of the nearby, disturbed, edge-on galaxy NGC 4631. A low-resolution (45 in. x 87 in.) map shows previously unknown tidal debris at large distances from the plane, and two dwarf companions. A high resolution (12 in. x 22 in.) map reveals a very disturbed gas layer in NGC 4631, with a wealth of small-scale structure. The most striking discovery is a supershell in the eastern half of the disk with a diameter of about 3 kpc, a mass of approximately 10 exp 8 solar mass and a tentative expansion velocity of 45 km/s. If the expansion is real, the energy which must have been injected by supernovae to explain the shell's current parameters is roughly 4 x 10(exp 55) ergs. Such a high energy requirement suggests an alternative formation mechanism, such as a collision with a small companion

Relation between Tcc,bbT_{cc,bb} and Xc,bX_{c,b} from QCD

We have studied, using double ratio of QCD (spectral) sum rules, the ratio between the masses of $T_{cc}$ and X(3872) assuming that they are respectively described by the $D-{D}^*$ and $D-\bar{D}^*$ molecular currents. We found (within our approximation) that the masses of these two states are almost degenerate. Since the pion exchange interaction between these mesons is exactly the same, we conclude that if the observed X(3872) meson is a $D\bar{D}^*+c.c.$ molecule, then the $DD^*$ molecule should also exist with approximately the same mass. An extension of the analysis to the $b$-quark case leads to the same conclusion. We also study the SU(3) breakings for the $T^s_{QQ}/T_{QQ}$ mass ratios. Motivated by the recent Belle observation of two $Z_b$ states, we revise our determination of $X_b$ by combining results from exponential and FESR sum rules.Comment: revised version to appear on Phys. Lett.

Graph Laplacians and Stabilization of Vehicle Formations

Control of vehicle formations has emerged as a topic of significant interest to the controls community. In this paper, we merge tools from graph theory and control theory to derive stability criteria for formation stabilization. The interconnection between vehicles (i.e., which vehicles are sensed by other vehicles) is modeled as a graph, and the eigenvalues of the Laplacian matrix of the graph are used in stating a Nyquist-like stability criterion for vehicle formations. The location of the Laplacian eigenvalues can be correlated to the graph structure, and therefore used to identify desirable and undesirable formation interconnection topologies