Atmospheric chemistry of diazomethane – an experimental and theoretical study

The kinetics of the O₃, OH and NO₃ radical reactions with diazomethane were studied in smog chamber experiments employing long-path FTIR and PTR-ToF-MS detection. The rate coefficients were determined to be k _CH2NN+O3?=?(3.2?±?0.4)?×?10^?17 and k _CH2NN+OH?=?(1.68?±?0.12)?×?10^?10 cm³ molecule^?1 s^?1 at 295?±?3?K and 1013?±?30 hPa, whereas the CH₂NN?+?NO₃ reaction was too fast to be determined in the static smog chamber experiments. Formaldehyde was the sole product observed in all the reactions. The experimental results are supported by CCSD(T*)-F12a/aug-cc-pVTZ//M062X/aug-cc-pVTZ calculations showing the reactions to proceed exclusively via addition to the carbon atom. The atmospheric fate of diazomethane is discussed.     

Mode competition and control in higher-power gyrotron oscillators

One of the most important problems in the design of high-power millimeter-wave sources such as gyrotron oscillators is insuring that the device operates in the desired mode. For high-power and short-wavelength devices the effective mode density is high, in that the current is above threshold for many modes. One then is led to ask whether operation in a single mode is possible and what steps must be taken to maximize the electronic efficiency of the device while ensuring single-mode operation. The answer to the first question has been determined to be yes. Provided that certain conditions are met, single-mode operation is stable. The present results emphasize time-dependent multimode simulations showing how these stable states can be accessed. In particular, the accessibility to the stable single mode with maximum efficiency is studied. Regions of parameter space for which stable single-mode operation is possible are plotted for an annular beam for a closed-cavity gyrotron operating at a high-order whispering-gallery mode (TE_80.4). These results also apply to the quasioptical gyrotron with a pencil electron beam     

Relativistic Sturmian basis functions

The properties of relativistic one-electron Sturmian basis sets are discussed using Goscinski's definition of Sturmians rather than Rotenberg's. The potential-weighted orthonormality relations obeyed by the members of such a set are discussed. Weighted orthonormality relations in momentum space are also derived and used to construct a Sturmian expansion of the kernel of the momentum-space Dirac equation. The special case of spherical symmetry is discussed, and, as an illustrative example, relativistic Coulomb Sturmian basis sets are used to obtain solutions to the Dirac equation for an electron moving in a non-Coulomb potential. This revised version was published online in July 2006 with corrections to the Cover Date.     

Wigner–Weyl–Moyal Formalism on Algebraic Structures

We first introduce theWigner–Weyl–Moyal formalism for a theorywhose phase space is an arbitrary Lie algebra. We alsogeneralize to quantum Lie algebras and to supersymmetrictheories. It turns out that the noncommutativity leads to a deformation ofthe classical phase space: instead of being a vectorspace, it becomes a manifold, the topology of which isgiven by the commutator relations. It is shown in fact that the classical phase space, for asemisimple Lie algebra, becomes a homogeneous symplecticmanifold. The symplectic product is also deformed. Wefinally make some comments on how to generalise to C*-algebras and other operator algebras,too.     

Space-Time Topology (II)—Causality, the Fourth Stiefel–Whitney Class and Space-Time as a Boundary

We show that stable causality is related to the vanishing of the top Stiefel–Whitney class of a space-time manifold M, and that if M is a stably causal space-time manifold, then it is the boundary of a five-dimensional space-time. We then propose a scheme for making it both a necessary and sufficient condition.     

Regions of stability of high-power gyrotron oscillators

The problem of mode competition in a high-power gyrotron oscillator is considered. The regions of parameter space in which a preexisting large-amplitude mode is able to suppress competing satellites are determined for cases in which the coupling coefficients and cavity quality factors for the operating and satellite modes are different. In addition, the effect of beam quality on the regimes of stable single-mode operation is investigated. Generally speaking, the requirement of stable operation favors devices whose interaction length measured by the parameter μ is not too large. It is found that for μ near 10 the operation is relatively stable and μ near 17 is not     

Comment on "Long time evolution of phase oscillator systems" [Chaos 19, 023117 (2009)

In a recent paper by Ott and Antonsen [Chaos 19, 023117 (2009)], it was shown for the case of Lorentzian distributions of oscillator frequencies that the dynamics of a very general class of large systems of coupled phase oscillators time-asymptotes to a particular simplified form given by Ott and Antonsen [Chaos 18, 037113 (2008)]. This comment extends this previous result to a broad class of oscillator distribution functions.     

Lagrangian chaos and the effect of drag on the enstrophy cascade in two-dimensional turbulence

We investigate the effect of drag force on the enstrophy cascade of two-dimensional Navier-Stokes turbulence. We find a power law decrease of the energy wave number (k) spectrum that is faster than the classical (no-drag) prediction of k(-3). It is shown that the enstrophy cascade with drag can be analyzed by making use of a previous theory for finite lifetime passive scalars advected by a Lagrangian chaotic fluid flow. Using this we relate the power law exponent of the energy wave number spectrum to the distribution of finite time Lyapunov exponents and the drag coefficient.