Existence and Non-Existence of Fisher-KPP Transition Fronts

We consider Fisher-KPP-type reaction–diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-front-type global-in-time solutions while creating a global-in-time bump-like solution. This is the first example of a medium in which no reaction–diffusion transition front exists. A weaker localized inhomogeneity leads to the existence of transition fronts, but only in a finite range of speeds. These results are in contrast with both Fisher-KPP reactions in homogeneous media as well as ignition-type reactions in inhomogeneous media.     

Stable isotope compositions of CO(2) in background air and at polluted sites in Hungary

CO(2) samples were collected from air at three sites in Hungary for comparison of polluted and background areas. In order to reduce the uncertainties caused by the varying amount of N(2)O, a gas chromatography (GC)-based vacuum separation was applied. The reliability of the procedure was demonstrated by careful standardization and comparison with global network data. The stable isotope data show complex diurnal and seasonal variations that can be explained by fractionations during photosynthesis and respiration. The isotopic characteristics of pollution-derived (anthropogenic) and biogenic CO(2) appear to be indistinguishable at the study sites. However, the sites at unpolluted areas reveal a seasonal variation in the carbon isotope composition of biogenic CO(2) that may be related to changes in soil biogenic activities. The atmospheric background CO(2) shows constant delta(13)C in the region. Finally, the study demonstrates the need for careful standardization of sampling in order to make the data obtained from different sampling systems comparable.     

Effect of the symmetry of H2 molecules on their rotations around an OCS molecule in superfluid 4He droplets

The infrared spectra of OCS-(H2)(n) clusters in cold (0.15 K) superfluid 4He droplets coated with 3He exhibit resolved rotational bands for each n up to n=8 para-H2 (pH(2)) or ortho-D2 (oD(2)) molecules. An analysis of the different Q-branch intensities based on the different spin symmetries of pH(2) and oD(2) indicates the formation of symmetric 5- or 6-membered rings around the linear carbonyl sulfide (OCS) chromophore. The rings of distinguishable oD(2) are found to undergo axial rotations, whereas for 6 pH(2) molecules the symmetry-allowed rotational levels lie too high to be excited at the 0.15 K droplet temperatures.     

Synchronization of active mechanical oscillators by an inertial load

Motivated by the operation of myogenic (self-oscillatory) insect flight muscle, we study a model consisting of a large number of identical oscillatory contractile elements joined in a chain, whose end is attached to a damped mass-spring oscillator. When the inertial load is small, the serial coupling favors an antisynchronous state in which the extension of one oscillator is compensated by the contraction of another, in order to preserve the total length. However, a sufficiently massive load can synchronize the oscillators and can even induce oscillation in situations where isolated elements would be stable. The system has a complex phase diagram displaying quiescent, synchronous and antisynchronous phases, as well as an unusual asynchronous phase in which the total length of the chain oscillates at a different frequency from the individual active elements.     

Luminescence-spectrum and strength properties of rhodamine 6G-doped silica gel films

Silica gel films dyed with rhodamine 6G in the sol stage are prepared and investigated. It is shown that the host matrix of the film loosens structurally as a result of intensification of the formation of dye molecular associates, lowering of the luminescence photon yield, and enhancement of the luminescence spectral sensitivity of such films to vapors of highly volatile organic solvents. Fiz. Tverd. Tela (St. Petersburg) 40, 466–471 (March 1998)     

Large sets in intuitionistic set theory

We consider properties of sets in an intuitionistic setting corresponding to large cardinals in classical set theory. Adding such ‘large set axioms’ to intuitionistic ZF set theory does not violate well-know metamathematical properties of intuitionistic systems. Moreover, we consider statements in constructive analysis equivalent to the consistency of such ‘large set axioms’.