On the fundamental solution of linear delay differential equations with multiple delays

For a class of linear autonomous delay differential equations with parameter $\alpha$ we give upper bounds for the integral \int_{0}^{\infty}\left|X\left(t,\alpha\right)\right|\mbox{d}t of the fundamental solution $X\left(\cdot,\alpha\right)$. The asymptotic estimations are sharp at a critical value $\alpha_{0}$ where $x=0$ loses stability. We use these results to study the stability properties of perturbed equations

Local stability implies global stability for the 2-dimensional Ricker map

Consider the difference equation $x_{k+1}=x_k e^{\alpha-x_{n-d}}$ where $\alpha$ is a positive parameter and d is a non-negative integer. The case d = 0 was introduced by W.E. Ricker in 1954. For the delayed version d >= 1 of the equation S. Levin and R. May conjectured in 1976 that local stability of the nontrivial equilibrium implies its global stability. Based on rigorous, computer aided calculations and analytical tools, we prove the conjecture for d = 1.Comment: for associated C++ program, mathematica worksheet and output, see http://www.math.u-szeged.hu/~krisztin/ricke

Experimental energy levels and partition function of the 12^{12}C2_2 molecule

The carbon dimer, the $^{12}$C$_2$ molecule, is ubiquitous in astronomical environments. Experimental-quality rovibronic energy levels are reported for $^{12}$C$_2$, based on rovibronic transitions measured for and among its singlet, triplet, and quintet electronic states, reported in 42 publications. The determination utilizes the Measured Active Rotational-Vibrational Energy Levels (MARVEL) technique. The 23,343 transitions measured experimentally and validated within this study determine 5,699 rovibronic energy levels, 1,325, 4,309, and 65 levels for the singlet, triplet, and quintet states investigated, respectively. The MARVEL analysis provides rovibronic energies for six singlet, six triplet, and two quintet electronic states. For example, the lowest measurable energy level of the \astate\ state, corresponding to the $J=2$ total angular momentum quantum number and the $F_1$ spin-multiplet component, is 603.817(5) \cm. This well-determined energy difference should facilitate observations of singlet--triplet intercombination lines which are thought to occur in the interstellar medium and comets. The large number of highly accurate and clearly labeled transitions that can be derived by combining MARVEL energy levels with computed temperature-dependent intensities should help a number of astrophysical observations as well as corresponding laboratory measurements. The experimental rovibronic energy levels, augmented, where needed, with {\it ab initio} variational ones based on empirically adjusted and spin-orbit coupled potential energy curves obtained using the \Duo\ code, are used to obtain a highly accurate partition function, and related thermodynamic data, for $^{12}$C$_2$ up to 4,000 K.Comment: ApJ Supplements (in press), 48 page

Detection of ionospheric signatures from GPS-derived total electron content maps

The processing of measurement data from satellite constellations such as Global Navigation Satellite Systems (GNSS), including the well-known Global Positioning System (GPS), have been successfully applied to virtually all areas of geophysical sciences. In this work, a method is described where Geographical Information Systems (GIS) are employed to build hourly ionospheric Total Electron Content (TEC) maps for 2011 over the southern Iberian Peninsula. The maps used GPS-derived geometryfree linear combinations attained from station data from the Algarve, Alentejo (Portugal), Andalusia, Murcia and Valencia (Spain) regions. Following the construction of the ionospheric maps, it was possible to relate these results to natural phenomena. The observed phenomena included diurnal and seasonal variations: daytime TEC maxima, nighttime TEC peaks, summer TEC value decreases, and spring and fall TEC maxima. After validation of these periodic phenomena, detection of non-periodic changes, such as solar flares and tectonic interactions with the ionosphere were attempted. The results showed a TEC increase following a selected solar flare event and a potential TEC build-up prior to the 2011 Lorca earthquake. Further studies could open up the possibility of building early warning systems. The presented methods, based on available software packages, are also of value in monitoring the effect of the ionosphere on radio signals, satellite and mobile communication, power grids, and for accurate GNSS navigation

Molecular Spiders with Memory

Synthetic bio-molecular spiders with "legs" made of single-stranded segments of DNA can move on a surface which is also covered by single-stranded segments of DNA complementary to the leg DNA. In experimental realizations, when a leg detaches from a segment of the surface for the first time it alters that segment, and legs subsequently bound to these altered segments more weakly. Inspired by these experiments we investigate spiders moving along a one-dimensional substrate, whose legs leave newly visited sites at a slower rate than revisited sites. For a random walk (one-leg spider) the slowdown does not effect the long time behavior. For a bipedal spider, however, the slowdown generates an effective bias towards unvisited sites, and the spider behaves similarly to the excited walk. Surprisingly, the slowing down of the spider at new sites increases the diffusion coefficient and accelerates the growth of the number of visited sites.Comment: 10 pages, 3 figure

A betonok fagy- és olvasztósóállóság-vizsgálati hámlásának lassulási folyamata

A betonok fagy-, illetve fagy- és olvasztósóállóság-vizsgálati hámlása időben lejátszódó folyamat, amely lassuló vagy gyorsuló jellegének korábban nem túl sok figyelmet szenteltünk. A hámlasztásos fagyasztási lassulás is viszonylag új fogalomnak tekinthető, amely fogalom ilyen elnevezésének a nemzetközi irodalomban sem találtuk a nyomát. E cikkben – amelyet az NVKP 16-1-2016-0019 pályázati támogatásból dolgoztuk ki – a hámlasztásos fagyasztási lassulási feltételt tartalmazó szabványoknak a lassulási feltétellel kapcsolatos intézkedéseit, valamint a lassulási feltétel e szabványokon túlmenő továbbfejlesztésének lehetőségét mutatjuk be

Distribution of Electric Currents in Solar Active Regions

There has been a long-lasting debate on the question of whether or not electric currents in solar active regions are neutralized. That is, whether or not the main (or direct) coronal currents connecting the active region polarities are surrounded by shielding (or return) currents of equal total value and opposite direction. Both theory and observations are not yet fully conclusive regarding this question, and numerical simulations have, surprisingly, barely been used to address it. Here we quantify the evolution of electric currents during the formation of a bipolar active region by considering a three-dimensional magnetohydrodynamic simulation of the emergence of a sub-photospheric, current-neutralized magnetic flux rope into the solar atmosphere. We find that a strong deviation from current neutralization develops simultaneously with the onset of significant flux emergence into the corona, accompanied by the development of substantial magnetic shear along the active region's polarity inversion line. After the region has formed and flux emergence has ceased, the strong magnetic fields in the region's center are connected solely by direct currents, and the total direct current is several times larger than the total return current. These results suggest that active regions, the main sources of coronal mass ejections and flares, are born with substantial net currents, in agreement with recent observations. Furthermore, they support eruption models that employ pre-eruption magnetic fields containing such currents.Comment: 6 pages, 5 figures, to appear in Astrophysical Journal Letter