Aeroelastic instability of rectangular cylinders in a heaving mode

This paper deals with wind tunnel experiments on the aeroelastic instability in a heaving mode of two-dimensional rectangular cylinders in a uniform two-dimensional flow. Both the free oscillation method and the forced oscillation method are employed for the experiments. Emphasis is placed on finding the effect of the ratio $\text{c}\text{d}$, which is the ratio of the lengths of the sides of the rectangle, to the aeroelastic instability phenomena in the vicinity of the resonance speed. Emphasis is also placed on finding possible limitations in the application of the quasi-steady aerodynamic theory to the analysis of the aeroelastic characteristics.     

Theory of the spin depolarisation rate of μ+ SR in pure Fe

The diffusion constant (D) and the spin depolarisation rate (λ_S) of the positive muon in the ferromagnetic b.c.c. lattices such as Fe have been calculated on the basis of the small polaron (SP) model with particular attention to the hopping and the coherent motions. They have been obtained in the forms: $\text{D=}\text{d}{}^2\text{w}{}_{\mathrm{D}}\text{6}$ and $\text{λ}{}_{\mathrm{S}}\text{=}\text{4γ}{}^2{}_{\mathrm{\mu }}\text{H}{}^2{}_{\mathrm{d}}\text{3w}{}_{\mathrm{S}}$, where d is a jump length, and H_d is a magnitude of internal dipolar field. At high temperatures, the activated-type hopping motion gives a dominant contribution to w_D, and w_S coincides with w_D. With decreasing temperature, w_D turns to be increasing owing to the coherent motion. Whereas w_S deviates from w_D, after passing the minimum, to have a maximum, and then decreases in inverse proportion to a lifetime (_B) of the SP band states. Because of the cell periodicity of the internal fields, the spin in an SP band state feels a definite magnetic field corresponding to the state, and sees various fields if scattered to other states. These scattering processes succeeding in a time shorter than (γ_μH_d)^-1 result in the motional narrowing of the spectra, with λ_{S ?} γ²_μH_d_B.     

Statistical properties of aggregation with injection

We study a generalized aggregation process in which charged particles diffuse and coalesce randomly on a lattice. For one-dimensional and mean-field models, we show that there exists a statistically-invariant steady state when randomly charged particles are continuously injected. The steady-state charge distribution obeys a power law with the exponent depending both on the type of the injection and on the spatial dimension. The response of the system to a perturbation (i.e., relaxation) is characterized by either a power law decay (t ^– ,1) or a compressed exponential decay [exp(–t ),>1].     

Localization transition of <Emphasis Type="Italic">d</Emphasis>-friendly walkers

 Friendly walkers is a stochastic model obtained from independent one-dimensional simple random walks {S ^k _j } _j≥0 , k=1,2,…,d by introducing ``non-crossing condition': and ``reward for collisions' characterized by parameters . Here, the reward for collisions is described as follows. If, at a given time n, a site in ℤ is occupied by exactly m≥2 walkers, then the site increases the probabilistic weight for the walkers by multiplicative factor exp (β _m )≥1. We study the localization transition of this model in terms of the positivity of the free energy and describe the location and the shape of the critical surface in the (d−1)-dimensional space for the parameters . Received: 13 June 2002 / Revised version: 24 August 2002 Published online: 28 March 2003 Mathematics Subject Classification (2000): 82B41, 82B26, 82D60, 60G50 Key words or phrases: Random walks – Random surfaces – Lattice animals – Phase transitions – Polymers – Random walks     

Classical solutions of higher-dimensional nonlinear sigma models on spheres

We construct several classical solutions of higher-dimensional nonlinear sigma models on spheres. These solutions are characterized by typical topological maps, in particular, four famous Hopf maps and the universal maps of theK-theory.Dedicated to the late Professor Shichiro Oka.     

A study on the effect of filling factor for laser action in dielectric random media

In a random system composed of dielectric materials, laser action is expected to occur from the light localization caused by multiple scattering and interference effect. The wavelengths at which the laser oscillation occurs in random media depend on the mean free path of continuous scattering. Since the mean free path of continuous scattering is dependent on the filling factor, it is important to investigate systematically the effect of the filling factor for the laser action. In the present study, we calculate the Poynting vectors of the light emitted from two-dimensional random media consisting of dielectric rods with population inversion modeled by the negative imaginary part of relative permittivity. The spectra of the radiated Poynting vectors from the two-dimensional random media are shown for several different filling factors and for various values of population inversion. We try to find laser generation which occurs at low population inversion and discuss about the threshold of laser action occurring in dielectric structures with different filling factors. We also study the spacial distribution of the electric field amplitude in several frequency regions where light strongly amplifies.     

Investigation of the center intensity of first- and second-order Laguerre-Gaussian beams with linear and circular polarization

The vectorial Debye integral shows that tightly focused Laguerre-Gaussian (LG) beams have a residual intensity at the focal point for linear polarization, for a topological charge of m=1 and 2. We measured the shapes of linearly and circularly polarized LG beams and found that a central intensity appeared at m=1 and 2 for linear and right-handed circular polarization, however, it is completely canceled for left-handed circular polarization. In general, when the orbital angular momentum of the LG beam is parallel to the spin angular momentum of the photons, zero intensity is always achieved at the focus.     

Lidar measurement of constituents of microparticles in air by laser-induced breakdown spectroscopy using femtosecond terawatt laser pulses

We experimentally demonstrated remote sensing of the constituents of microparticles in air by combining laser-induced breakdown spectroscopy (LIBS) and lidar, using femtosecond terawatt laser pulses. Laser pulses of 70 fs duration and 130 mJ energy generated filaments when focused at a focal length of 20 m and the pulses irradiated artificial saltwater aerosols in air at a 10 Hz pulse repetition rate. Na fluorescence was observed remotely at a distance of 16 m using a 318 mm diameter Newtonian telescope, a spectrometer, and an intensified CCD camera. These results show the possibility of remote measurement of the constituents of atmospheric particles, such as aerosols, clouds, and toxic materials, by LIBS-lidar using femtosecond terawatt laser pulses.