Search

We report superfluorescent (SF) emission in electrically pumped InGaN/InGaN QW lasers with saturable absorber. In particular, we observe a superlinear growth of the peak power of SF pulses with increasing amplitude of injected current pulses and attribute it to cooperative pairing of electron-hole (e-h) radiative recombinations. The phase transitions from amplified spontaneous emission to superfluorescence and then to lasing regime is confirmed by observing (i) abrupt peak power growth accompanied by spectral broadening, (ii) spectral shape with hyperbolic secant envelope and (iii) red shift of central wavelength of SF emission pulse. The observed red shift of SF emission is shown to be caused by the pairing of e-h pairs in an indirect cooperative X-transition., Comment: 18 pages, 7 figures

We study the level spacing distribution $P(S)$ of 2D real random matrices both symmetric as well as general, non-symmetric. In the general case we restrict ourselves to Gaussian distributed matrix elements, but different widths of the various matrix elements are admitted. The following results are obtained: An explicit exact formula for $P(S)$ is derived and its behaviour close to S=0 is studied analytically, showing that there is linear level repulsion, unless there are additional constraints for the probability distribution of the matrix elements. The constraint of having only positive or only negative but otherwise arbitrary non-diagonal elements leads to quadratic level repulsion with logarithmic corrections. These findings detail and extend our previous results already published in a preceding paper. For the {\em symmetric} real 2D matrices also other, non-Gaussian statistical distributions are considered. In this case we show for arbitrary statistical distribution of the diagonal and non-diagonal elements that the level repulsion exponent $\rho$ is always $\rho = 1$, provided the distribution function of the matrix elements is regular at zero value. If the distribution function of the matrix elements is a singular (but still integrable) power law near zero value of $S$, the level spacing distribution $P(S)$ is a fractional exponent pawer law at small $S$. The tail of $P(S)$ depends on further details of the matrix element statistics. We explicitly work out four cases: the constant (box) distribution, the Cauchy-Lorentz distribution, the exponential distribution and, as an example for a singular distribution, the power law distribution for $P(S)$ near zero value times an exponential tail., Comment: 21 pages, no figures, submitted to Zeitschrift fuer Naturforschung A

The phenomenon of irregular cessation and subsequent reversal of the large-scale circulation in turbulent Rayleigh-B\'enard convection is theoretically analysed. The force and thermal balance on a single plume detached from the thermal boundary layer yields a set of coupled nonlinear equations, whose dynamics is related to the Lorenz equations. For Prandtl and Rayleigh numbers in the range $10^{-2} \leq \Pr \leq 10^{3}$ and $10^{7} \leq \Ra \leq 10^{12}$, the model has the following features: (i) chaotic reversals may be exhibited at Ra $\geq 10^{7}$; (ii) the Reynolds number based on the root mean square velocity scales as $\Re_{rms} \sim \Ra^{[0.41 ... 0.47]}$ (depending on Pr), and as $\Re_{rms} \sim \Pr^{-[0.66 ... 0.76]}$ (depending on Ra); and (iii) the mean reversal frequency follows an effective scaling law $\omega / (\nu L^{-2}) \sim \Pr^{-(0.64 \pm 0.01)} \Ra^{0.44 \pm 0.01}$. The phase diagram of the model is sketched, and the observed transitions are discussed., Comment: 4 pages, 5 figures

Numerical simulations of fully developed turbulence driven by a modulated energy input rate or driving force are performed within two dynamical cascade models, the GOY shell model and a reduced wave vector set approximation of the Navier-Stokes equation (REWA). The frequency behavior of the system response is studied and compared with predictions from a variable range mean-field theory, which excludes turbulent fluctuations. In agreement with the mean-field approach we find a constant response amplitude for low driving frequencies and a 1/w-decay of the amplitude for high frequencies. In the mean-field theory, the finite cascade time scale had lead to an oscillating behavior of the response amplitude as a function of the driving frequency. In the simulations of both models we observe the main maximum. The higher maxima and minima are completely washed out by fluctuations., Comment: 12 pages, 10 figures, submitted to Phys.Rev. E

Isotropic and homogeneous turbulence driven by an energy input modulated in time is studied within a variable range mean-field theory. The response of the system, observed in the second order moment of the large-scale velocity difference D(L,t)=<<(\u(x+L)-\u(x))^2>>~Re(t)^2$, is calculated for varying modulation frequencies w and weak modulation amplitudes. For low frequencies the system follows the modulation of the driving with almost constant amplitude, whereas for higher driving frequencies the amplitude of the response decreases on average 1/w. In addition, at certain frequencies the amplitude of the response either almost vanishes or is strongly enhanced. These frequencies are connected with the frequency scale of the energy cascade and multiples thereof., Comment: 11 pages, 6 figures

We analyze the mechanism that determines the boundary of stability in Taylor-Couette flow. By simple physical argument we derive an analytic expression to approximate the stability line for all radius ratios and all speed ratios, for co- and counterrotating cylinders. The expression includes viscosity and so generalizes Rayleigh's criterion. We achieve agreement with linear stability theory and with experiments in the whole parameter space. Explicit formulae are given for limiting cases., Comment: 6 pages (LaTeX with REVTEX) including 4 figures (Postscript) Revised, discussion of two additional references. See also http://staff-www.uni-marburg.de/~esser