Complex-valued Burgers and KdV-Burgers equations

Spatially periodic complex-valued solutions of the Burgers and KdV-Burgers equations are studied in this paper. It is shown that for any sufficiently large time T, there exists an explicit initial data such that its corresponding solution of the Burgers equation blows up at T. In addition, the global convergence and regularity of series solutions is established for initial data satisfying mild conditions

Phase Diagram of a Superconducting and Antiferromagnetic System with SO(5) Symmetry

Temperature vs. chemical-potential phase diagrams of an SO(5) model for high-(T_c) cuprates are calculated by Monte Carlo simulation. There is a bicritical point where the second-order antiferromagnetism (AF) and superconductivity transition lines merge tangentially into a first-order line, and the SO(5) symmetry is achieved. In an external magnetic field, the AF ordering is first order in the region where the first-order melting line of flux lattice joins in. There is a tricritical point on the AF transition line from which the AF ordering becomes second order.Comment: 6 pages, 5 postscript figures, RevTe

Statistical mechanics of temporal association in neural networks with transmission delays

We study the representation of static patterns and temporal sequences in neural networks with signal delays and a stochastic parallel dynamics. For a wide class of delay distributions, the asymptotic network behavior can be described by a generalized Gibbs distribution, generated by a novel Lyapunov functional for the determination dynamics. We extend techniques of equilibrium statistical mechanics so as to deal with time-dependent phenomena, derive analytic results for both retrieval quality and storage capacity, and compare them with numerical simulations

De Sitter and Schwarzschild-De Sitter According to Schwarzschild and De Sitter

When de Sitter first introduced his celebrated spacetime, he claimed, following Schwarzschild, that its spatial sections have the topology of the real projective space RP^3 (that is, the topology of the group manifold SO(3)) rather than, as is almost universally assumed today, that of the sphere S^3. (In modern language, Schwarzschild was disturbed by the non-local correlations enforced by S^3 geometry.) Thus, what we today call "de Sitter space" would not have been accepted as such by de Sitter. There is no real basis within classical cosmology for preferring S^3 to RP^3, but the general feeling appears to be that the distinction is in any case of little importance. We wish to argue that, in the light of current concerns about the nature of de Sitter space, this is a mistake. In particular, we argue that the difference between "dS(S^3)" and "dS(RP^3)" may be very important in attacking the problem of understanding horizon entropies. In the approach to de Sitter entropy via Schwarzschild-de Sitter spacetime, we find that the apparently trivial difference between RP^3 and S^3 actually leads to very different perspectives on this major question of quantum cosmology.Comment: 26 pages, 8 figures, typos fixed, references added, equation numbers finally fixed, JHEP versio

An intermittent extreme BL Lac: MWL study of 1ES 2344+514 in an enhanced state

Extreme high-frequency BL Lacs (EHBL) feature their synchrotron peak of the broad-band spectral energy distribution (SED) at vs ≥ 1017 Hz. The BL Lac object 1ES 2344+514 was included in the EHBL family because of its impressive shift of the synchrotron peak in 1996. During the following years, the source appeared to be in a low state without showing any extreme behaviours. In 2016 August, 1ES 2344+514 was detected with the groundbased γ -ray telescope FACT during a high γ -ray state, triggering multiwavelength (MWL) observations. We studied the MWL light curves of 1ES 2344+514 during the 2016 flaring state, using data from radio to very-high-energy (VHE) γ -rays taken with OVRO, KAIT, KVA, NOT, some telescopes of the GASP-WEBT collaboration at the Teide, Crimean, and St. Petersburg observatories, Swift-UVOT, Swift-XRT, Fermi-LAT, FACT, and MAGIC. With simultaneous observations of the flare, we built the broad-band SED and studied it in the framework of a leptonic and a hadronic model. The VHE γ -ray observations show a flux level of 55 per cent of the Crab Nebula flux above 300 GeV, similar to the historical maximum of 1995. The combination of MAGIC and Fermi-LAT spectra provides an unprecedented characterization of the inverse-Compton peak for this object during a flaring episode. The _ index of the intrinsic spectrum in the VHE γ -ray band is 2.04 ± 0.12stat ± 0.15sys.We find the source in an extreme state with a shift of the position of the synchrotron peak to frequencies above or equal to 1018 Hz.The financial support of the German BMBF and MPG, the Italian INFN and INAF, the Swiss National Fund SNF, the ERDF under the Spanish MINECO (FPA2017-87859-P, FPA2017-85668-P, FPA2017-82729-C6-2-R, FPA2017-82729-C6-6-R, FPA2017-82729-C6-5-R, AYA2015-71042-P, AYA2016-76012-C3-1-P, ESP2017-87055-C2-2-P, and FPA2017-90566-REDC), the Indian Department of Atomic Energy, the Japanese JSPS and MEXT, the Bulgarian Ministry of Education and Science, National RI Roadmap Project DO1-153/28.08.2018, and the Academy of Finland grant no. 320045 is gratefully acknowledged. This work was also supported by the Spanish Centro de Excelencia ‘Severo Ochoa’ SEV-2016-0588 and SEV-2015-0548, and Unidad de Excelencia ‘María de Maeztu’ MDM-2014-0369, by the Croatian Science Foundation (HrZZ) Project IP-2016-06-9782 and the University of Rijeka Project 13.12.1.3.02, by the DFG Collaborative Research Centers SFB823/C4 and SFB876/C3, the Polish National Research Centre grant UMO-2016/22/M/ST9/00382 and by the Brazilian MCTIC, CNPq, and FAPERJ. The FACT collaboration acknowledges the important contributions from ETH Zurich grants ETH-10.08-2 and ETH-27.12-1 as well as the funding by the Swiss SNF and the German BMBF (Verbundforschung Astro- und Astroteilchenphysik) and HAP (Helmoltz Alliance for Astroparticle Physics) are gratefully acknowledged. Part of this work is supported by Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Center SFB 876 ‘Providing Information by Resource-Constrained Analysis’, project C3

Detailed spectral and morphological analysis of the shell type SNR RCW 86

Aims: We aim for an understanding of the morphological and spectral properties of the supernova remnant RCW~86 and for insights into the production mechanism leading to the RCW~86 very high-energy gamma-ray emission. Methods: We analyzed High Energy Spectroscopic System data that had increased sensitivity compared to the observations presented in the RCW~86 H.E.S.S. discovery publication. Studies of the morphological correlation between the 0.5-1~keV X-ray band, the 2-5~keV X-ray band, radio, and gamma-ray emissions have been performed as well as broadband modeling of the spectral energy distribution with two different emission models. Results:We present the first conclusive evidence that the TeV gamma-ray emission region is shell-like based on our morphological studies. The comparison with 2-5~keV X-ray data reveals a correlation with the 0.4-50~TeV gamma-ray emission.The spectrum of RCW~86 is best described by a power law with an exponential cutoff at $E_{cut}=(3.5\pm 1.2_{stat})$ TeV and a spectral index of $\Gamma$~$1.6\pm 0.2$. A static leptonic one-zone model adequately describes the measured spectral energy distribution of RCW~86, with the resultant total kinetic energy of the electrons above 1 GeV being equivalent to $\sim$0.1\% of the initial kinetic energy of a Type I a supernova explosion. When using a hadronic model, a magnetic field of $B$~100$\mu$G is needed to represent the measured data. Although this is comparable to formerly published estimates, a standard E$^{-2}$ spectrum for the proton distribution cannot describe the gamma-ray data. Instead, a spectral index of $\Gamma_p$~1.7 would be required, which implies that ~$7\times 10^{49}/n_{cm^{-3}}$erg has been transferred into high-energy protons with the effective density $n_{cm^{-3}}=n/ 1$ cm^-3. This is about 10\% of the kinetic energy of a typical Type Ia supernova under the assumption of a density of 1~cm^-3.Comment: accepted for publication by A&

Detection of variable VHE gamma-ray emission from the extra-galactic gamma-ray binary LMC P3

Context. Recently, the high-energy (HE, 0.1-100 GeV) $\gamma$-ray emission from the object LMC P3 in the Large Magellanic Cloud (LMC) has been discovered to be modulated with a 10.3-day period, making it the first extra-galactic $\gamma$-ray binary. Aims. This work aims at the detection of very-high-energy (VHE, >100 GeV) $\gamma$-ray emission and the search for modulation of the VHE signal with the orbital period of the binary system. Methods. LMC P3 has been observed with the High Energy Stereoscopic System (H.E.S.S.); the acceptance-corrected exposure time is 100 h. The data set has been folded with the known orbital period of the system in order to test for variability of the emission. Energy spectra are obtained for the orbit-averaged data set, and for the orbital phase bin around the VHE maximum. Results. VHE $\gamma$-ray emission is detected with a statistical significance of 6.4 $\sigma$. The data clearly show variability which is phase-locked to the orbital period of the system. Periodicity cannot be deduced from the H.E.S.S. data set alone. The orbit-averaged luminosity in the $1-10$ TeV energy range is $(1.4 \pm 0.2) \times 10^{35}$ erg/s. A luminosity of $(5 \pm 1) \times 10^{35}$ erg/s is reached during 20% of the orbit. HE and VHE $\gamma$-ray emissions are anti-correlated. LMC P3 is the most luminous $\gamma$-ray binary known so far.Comment: 5 pages, 3 figures, 1 table, accepted for publication in A&

Characterizing the gamma-ray long-term variability of PKS 2155-304 with H.E.S.S. and Fermi-LAT

Studying the temporal variability of BL Lac objects at the highest energies provides unique insights into the extreme physical processes occurring in relativistic jets and in the vicinity of super-massive black holes. To this end, the long-term variability of the BL Lac object PKS 2155-304 is analyzed in the high (HE, 100 MeV 200 GeV) gamma-ray domain. Over the course of ~9 yr of H.E.S.S observations the VHE light curve in the quiescent state is consistent with a log-normal behavior. The VHE variability in this state is well described by flicker noise (power-spectral-density index {\ss}_VHE = 1.10 +0.10 -0.13) on time scales larger than one day. An analysis of 5.5 yr of HE Fermi LAT data gives consistent results ({\ss}_HE = 1.20 +0.21 -0.23, on time scales larger than 10 days) compatible with the VHE findings. The HE and VHE power spectral densities show a scale invariance across the probed time ranges. A direct linear correlation between the VHE and HE fluxes could neither be excluded nor firmly established. These long-term-variability properties are discussed and compared to the red noise behavior ({\ss} ~ 2) seen on shorter time scales during VHE-flaring states. The difference in power spectral noise behavior at VHE energies during quiescent and flaring states provides evidence that these states are influenced by different physical processes, while the compatibility of the HE and VHE long-term results is suggestive of a common physical link as it might be introduced by an underlying jet-disk connection.Comment: 11 pages, 16 figure

Bioelectrical signals and ion channels in the modeling of multicellular patterns and cancer biophysics

Bioelectrical signals and ion channels are central to spatial patterns in cell ensembles, a problem of fundamental interest in positional information and cancer processes. We propose a model for electrically connected cells based on simple biological concepts: i) the membrane potential of a single cell characterizes its electrical state; ii) the long-range electrical coupling of the multicellular ensemble is realized by a network of gap junction channels between neighboring cells; and iii) the spatial distribution of an external biochemical agent can modify the conductances of the ion channels in a cell membrane and the multicellular electrical state. We focus on electrical effects in small multicellular ensembles, ignoring slow diffusional processes. The spatio-temporal patterns obtained for the local map of cell electric potentials illustrate the normalization of regions with abnormal cell electrical states. The effects of intercellular coupling and blocking of specific channels on the electrical patterns are described. These patterns can regulate the electrically-induced redistribution of charged nanoparticles over small regions of a model tissue. The inclusion of bioelectrical signals provides new insights for the modeling of cancer biophysics because collective multicellular states show electrical coupling mechanisms that are not readily deduced from biochemical descriptions at the individual cell level

New Hard-TeV Extreme Blazars Detected with the MAGIC Telescopes

Extreme high-frequency-peaked BL Lac objects (EHBLs) are blazars that exhibit extremely energetic synchrotron emission. They also feature nonthermal gamma-ray emission whose peak lies in the very high-energy (VHE, E > 100 GeV) range, and in some sources exceeds 1 TeV: this is the case for hard-TeV EHBLs such as 1ES 0229+200. With the aim of increasing the EHBL population, 10 targets were observed with the MAGIC telescopes from 2010 to 2017, for a total of 265 hr of good-quality data. The data were complemented by coordinated Swift observations. The X-ray data analysis confirms that all but two sources are EHBLs. The sources show only a modest variability and a harder-when-brighter behavior, typical for this class of objects. At VHE gamma-rays, three new sources were detected and a hint of a signal was found for another new source. In each case, the intrinsic spectrum is compatible with the hypothesis of a hard-TeV nature of these EHBLs. The broadband spectral energy distributions (SEDs) of all sources are built and modeled in the framework of a single-zone, purely leptonic model. The VHE gamma-ray-detected sources were also interpreted with a spine-layer model and a proton synchrotron model. The three models provide a good description of the SEDs. However, the resulting parameters differ substantially in the three scenarios, in particular the magnetization parameter. This work presents the first mini catalog of VHE gamma-ray and multiwavelength observations of EHBLs