Nondispersive solutions to the L2-critical half-wave equation

We consider the focusing $L^2$-critical half-wave equation in one space dimension $$i \partial_t u = D u - |u|^2 u,$$ where $D$ denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold $M_* > 0$ such that all $H^{1/2}$ solutions with $\| u \|_{L^2} < M_*$ extend globally in time, while solutions with $\| u \|_{L^2} \geq M_*$ may develop singularities in finite time. In this paper, we first prove the existence of a family of traveling waves with subcritical arbitrarily small mass. We then give a second example of nondispersive dynamics and show the existence of finite-time blowup solutions with minimal mass $\| u_0 \|_{L^2} = M_*$. More precisely, we construct a family of minimal mass blowup solutions that are parametrized by the energy $E_0 >0$ and the linear momentum $P_0 \in \R$. In particular, our main result (and its proof) can be seen as a model scenario of minimal mass blowup for $L^2$-critical nonlinear PDE with nonlocal dispersion.Comment: 51 page

Correlations of the elements of the neutrino mass matrix

Assuming Majorana nature of neutrinos, we re-investigate, in the light of the recent measurement of the reactor mixing angle, the allowed ranges for the absolute values of the elements of the neutrino mass matrix in the basis where the charged-lepton mass matrix is diagonal. Apart from the derivation of upper and lower bounds on the values of the matrix elements, we also study their correlations. Moreover, we analyse the sensitivity of bounds and correlations to the global fit results of the neutrino oscillation parameters which are available in the literature.Comment: 37 pages, 146 figures, minor corrections, 17 additional figures, version for publication in JHE

A rare case of a natural contact zone in Morocco between an autopolyploid and an allopolyploid of Centaurea aspera with sterile tetraploid hybrids

This is the accepted version of the following article: Garmendia, A., Ferriol, M., Juarez, J., Zając, A., Kałużny, K., Merle, H. (2015), A rare case of a natural contact zone in Morocco between an autopolyploid and an allopolyploid of Centaurea aspera with sterile tetraploid hybrids. Plant Biology, 17: 746–757, which has been published in final form at http://dx.doi.org/10.1111/plb.12284A new contact zone between Centaurea aspera and Centaurea seridis was found in Morocco. Chromosome counts and flow cytometry showed that both taxa were tetra- ploid (4 x = 44). A literature review and morphometric analysis established that C. aspera corresponds to the autopolyploid C. aspera subsp. gentilii and C. seridis corresponds to the allopolyploid C. seridis var. auriculata. This contact area was compared with the homologous contact zones in Spain formed by the diploid C. aspera subsp. stenophylla and the tetraploid C. seridis subsp. maritima. Natural hybrids between parental species were frequent in both areas. In Spain, hybrids were triploid (from reduced gametes A and gamete AB), highly sterile and exerted a triploid block . In Morocco, cytometry showed that hybrids were tetraploid and, therefore, probably fertile, but all the capitula lacked achenes. It is likely that the resulting genome of the new tetraploid hybrid (AAAB), through the fusion of reduced gametes AA (from subsp. gentilii) and AB (from var. auriculata), could explain irregularities in meiosis through formation of aneuploid gametes and, therefore, infertility of the hybrid. Moroccan sterile tetraploid hybrids develop, but have the identical irregularities to Spanish triploids, probably due to the odd number of homologous chromosomes. The new hybrid is first described as C. x subdecurrens nothosubsp. paucispinus. In addition, distribution and ecological traits are analysedGarmendia, A.; Ferriol Molina, M.; Juarez, J.; Zajac, A.; Kaluzny, K.; Merle Farinós, HB. (2015). A rare case of a natural contact zone in Morocco between an autopolyploid and an allopolyploid of Centaurea aspera with sterile tetraploid hybrids. Plant Biology. 17(3):746-757. doi:10.1111/plb.12284S746757173Abbott, R., Albach, D., Ansell, S., Arntzen, J. W., Baird, S. J. E., Bierne, N., … Zinner, D. (2013). Hybridization and speciation. Journal of Evolutionary Biology, 26(2), 229-246. doi:10.1111/j.1420-9101.2012.02599.xAleza, P., Juárez, J., Ollitrault, P., & Navarro, L. (2009). Production of tetraploid plants of non apomictic citrus genotypes. Plant Cell Reports, 28(12), 1837-1846. doi:10.1007/s00299-009-0783-2Ball, J. (1878). Spicilegium Florae Maroccanae-Part III. Containing descriptions of Genera and Species. Umbelliferae to Gentianeae. 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Morphological and ploidy level variation ofCentaurea phrygia agg. (Asteraceae) in the Czech Republic, Slovakia and Ukraine. Folia Geobotanica, 42(1), 77-102. doi:10.1007/bf02835103Koutecký, P. (2012). A diploid drop in the tetraploid ocean: hybridization and long-term survival of a singular population of Centaurea weldeniana Rchb. (Asteraceae), a taxon new to Austria. Plant Systematics and Evolution, 298(7), 1349-1360. doi:10.1007/s00606-012-0641-5KOUTECKÝ, P., BAĎUROVÁ, T., ŠTECH, M., KOŠNAR, J., & KARÁSEK, J. (2011). Hybridization between diploidCentaurea pseudophrygiaand tetraploidC. jacea(Asteraceae): the role of mixed pollination, unreduced gametes, and mentor effects. Biological Journal of the Linnean Society, 104(1), 93-106. doi:10.1111/j.1095-8312.2011.01707.xMadlung, A. (2012). Polyploidy and its effect on evolutionary success: old questions revisited with new tools. Heredity, 110(2), 99-104. doi:10.1038/hdy.2012.79Marks, G. E. (1966). The Origin and Significance of Intraspecific Polyploidy: Experimental Evidence from Solanum chacoense. Evolution, 20(4), 552. doi:10.2307/2406589Médail, F., & Quézel, P. (1999). Plant Ecology, 140(2), 221-244. doi:10.1023/a:1009775327616Mlinarec, J., Šatović, Z., Mihelj, D., Malenica, N., & Besendorfer, V. (2011). Cytogenetic and phylogenetic studies of diploid and polyploid members of Tribe Anemoninae (Ranunculaceae). Plant Biology, 14(3), 525-536. doi:10.1111/j.1438-8677.2011.00519.xMráz, P., Garcia-Jacas, N., Gex-Fabry, E., Susanna, A., Barres, L., & Müller-Schärer, H. (2012). Allopolyploid origin of highly invasive Centaurea stoebe s.l. (Asteraceae). Molecular Phylogenetics and Evolution, 62(2), 612-623. doi:10.1016/j.ympev.2011.11.006Otto, S. P. (2007). The Evolutionary Consequences of Polyploidy. Cell, 131(3), 452-462. doi:10.1016/j.cell.2007.10.022Parisod, C., Holderegger, R., & Brochmann, C. (2010). Evolutionary consequences of autopolyploidy. 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Trends in Ecology & Evolution, 16(7), 351-358. doi:10.1016/s0169-5347(01)02187-5ROMASCHENKO, K., ERTUǦRUL, K., SUSANNA, A., GARCIA-JACAS, N., UYSAL, T., & ARSLAN, E. (2004). New chromosome counts in the Centaurea Jacea group (Asteraceae, Cardueae) and some related taxa. Botanical Journal of the Linnean Society, 145(3), 345-352. doi:10.1111/j.1095-8339.2004.00292.xSatina, S., Blakeslee, A. F., & Avery, A. G. (1938). Chromosome Behavior in Triploid Datura. III. The Seed. American Journal of Botany, 25(8), 595. doi:10.2307/2436519Scheiner, S. M. (1993). Genetics and Evolution of Phenotypic Plasticity. Annual Review of Ecology and Systematics, 24(1), 35-68. doi:10.1146/annurev.es.24.110193.000343Siljak-Yakovlev, S., Solic, M. E., Catrice, O., Brown, S. C., & Papes, D. (2005). Nuclear DNA Content and Chromosome Number in Some Diploid and Tetraploid Centaurea (Asteraceae: Cardueae) from the Dalmatia Region. Plant Biology, 7(4), 397-404. doi:10.1055/s-2005-865693Soltis, P. S., & Soltis, D. 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A Centre-Stable Manifold for the Focussing Cubic NLS in R1+3R^{1+3}

Consider the focussing cubic nonlinear Schr\"odinger equation in $R^3$: $$i\psi_t+\Delta\psi = -|\psi|^2 \psi.$$ It admits special solutions of the form $e^{it\alpha}\phi$, where $\phi$ is a Schwartz function and a positive ($\phi>0$) solution of $$-\Delta \phi + \alpha\phi = \phi^3.$$ The space of all such solutions, together with those obtained from them by rescaling and applying phase and Galilean coordinate changes, called standing waves, is the eight-dimensional manifold that consists of functions of the form $e^{i(v \cdot + \Gamma)} \phi(\cdot - y, \alpha)$. We prove that any solution starting sufficiently close to a standing wave in the $\Sigma = W^{1, 2}(R^3) \cap |x|^{-1}L^2(R^3)$ norm and situated on a certain codimension-one local Lipschitz manifold exists globally in time and converges to a point on the manifold of standing waves. Furthermore, we show that \mc N is invariant under the Hamiltonian flow, locally in time, and is a centre-stable manifold in the sense of Bates, Jones. The proof is based on the modulation method introduced by Soffer and Weinstein for the $L^2$-subcritical case and adapted by Schlag to the $L^2$-supercritical case. An important part of the proof is the Keel-Tao endpoint Strichartz estimate in $R^3$ for the nonselfadjoint Schr\"odinger operator obtained by linearizing around a standing wave solution.Comment: 56 page

Hyperbolic quenching problem with damping in the micro-electro mechanical system device

[[abstract]]We study the initial boundary value problem for the damped hyperbolic equation arising in the micro-electro mechanical system device with local or nonlocal singular nonlinearity. For both cases, we provide some criteria for quenching and global existence of the solution. We also derive the existence of the quenching curve for the corresponding Cauchy problem with local source[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[countrycodes]]US

Reactor Neutrino Experiments with a Large Liquid Scintillator Detector

We discuss several new ideas for reactor neutrino oscillation experiments with a Large Liquid Scintillator Detector. We consider two different scenarios for a measurement of the small mixing angle $\theta_{13}$ with a mobile $\bar{\nu}_e$ source: a nuclear-powered ship, such as a submarine or an icebreaker, and a land-based scenario with a mobile reactor. The former setup can achieve a sensitivity to $\sin^2 2\theta_{13} \lesssim 0.003$ at the 90% confidence level, while the latter performs only slightly better than Double Chooz. Furthermore, we study the precision that can be achieved for the solar parameters, $\sin^2 2\theta_{12}$ and $\Delta m_{21}^2$, with a mobile reactor and with a conventional power station. With the mobile reactor, a precision slightly better than from current global fit data is possible, while with a power reactor, the accuracy can be reduced to less than 1%. Such a precision is crucial for testing theoretical models, e.g. quark-lepton complementarity.Comment: 18 pages, 3 figures, 2 tables, revised version, to appear in JHEP, Fig. 1 extended, Formula added, minor changes, results unchange

Cover Crop Effect on Subsequent Wheat Yield in the Central Great Plains

Crop production systems in the water-limited environment of the semiarid central Great Plains may not have potential to profitably use cover crops because of lowered subsequent wheat (Triticum asestivum L.) yields following the cover crop. Mixtures have reportedly shown less yield-reducing effects on subsequent crops than single-species plantings. This study was conducted to determine winter wheat yields following both mixtures and single-species plantings of spring-planted cover crops. The study was conducted at Akron, CO, and Sidney, NE, during the 2012–2013 and 2013–2014 wheat growing seasons under both rainfed and irrigated conditions. Precipitation storage efficiency before wheat planting, wheat water use, biomass, and yield were measured and water use efficiency and harvest index were calculated for wheat following four single-species cover crops (flax [Linum usitatissimum L.], oat [Avena sativa L.], pea [Pisum sativum ssp. arvense L. Poir], rapeseed [Brassica napus L.]), a 10-species mixture, and a fallow treatment with proso millet (Panicum miliaceum L.) residue. There was an average 10% reduction in wheat yield following a cover crop compared with following fallow, regardless of whether the cover crop was grown in a mixture or in a single-species planting. Yield reductions were greater under drier conditions. The slope of the wheat water use–yield relationship was not significantly different for wheat following the mixture (11.80 kg ha–1 mm–1) than for wheat following single-species plantings (12.32–13.57 kg ha–1 mm–1). The greater expense associated with a cover crop mixture compared with a single species is not justified

Effectiveness of a stand-alone, smartphone-based virtual reality exposure app to reduce fear of heights in real-life: a randomized trial

Smartphone-based virtual reality (VR) applications (apps) might help to counter low utilization rates of available treatments for fear of heights. Demonstration of effectiveness in real-life situations of such apps is crucial, but lacking so far. Objective of this study was to develop a stand-alone, smartphone-based VR exposure app-Easy Heights-and to test its effectiveness in a real-life situation. We performed a single-blind, parallel group, randomized controlled trial. We recruited 70 participants with fear of heights, aged 18-60 years. Primary outcome was performance in a real-life Behavioral Avoidance Test (BAT) on a lookout tower after a single 1-h app use (phase 1) and after additional repeated (6 × 30 min) app use at home (phase 2). After phase 2, but not phase 1, participants in the Easy Heights condition showed significantly higher BAT scores compared to participants in the control condition (Cohen's d = 1.3, p = 0.0001). Repeated use of our stand-alone, smartphone-based VR exposure app reduces avoidance behavior and fear, providing a low-threshold treatment for fear of heights

On the Quantitative Impact of the Schechter-Valle Theorem

We evaluate the Schechter-Valle (Black Box) theorem quantitatively by considering the most general Lorentz invariant Lagrangian consisting of point-like operators for neutrinoless double beta decay. It is well known that the Black Box operators induce Majorana neutrino masses at four-loop level. This warrants the statement that an observation of neutrinoless double beta decay guarantees the Majorana nature of neutrinos. We calculate these radiatively generated masses and find that they are many orders of magnitude smaller than the observed neutrino masses and splittings. Thus, some lepton number violating New Physics (which may at tree-level not be related to neutrino masses) may induce Black Box operators which can explain an observed rate of neutrinoless double beta decay. Although these operators guarantee finite Majorana neutrino masses, the smallness of the Black Box contributions implies that other neutrino mass terms (Dirac or Majorana) must exist. If neutrino masses have a significant Majorana contribution then this will become the dominant part of the Black Box operator. However, neutrinos might also be predominantly Dirac particles, while other lepton number violating New Physics dominates neutrinoless double beta decay. Translating an observed rate of neutrinoless double beta decay into neutrino masses would then be completely misleading. Although the principal statement of the Schechter-Valle theorem remains valid, we conclude that the Black Box diagram itself generates radiatively only mass terms which are many orders of magnitude too small to explain neutrino masses. Therefore, other operators must give the leading contributions to neutrino masses, which could be of Dirac or Majorana nature.Comment: 18 pages, 4 figures; v2: minor corrections, reference added, matches journal version; v3: typo corrected, physics result and conclusions unchange

Separated cross sections in \pi^0 electroproduction at threshold at Q^2 = 0.05 GeV^2/c^2

The differential cross sections \sigma_0=\sigma_T+\epsilon \sigma_L, \sigma_{LT}, and \sigma_{TT} of \pi^0 electroproduction from the proton were measured from threshold up to an additional center of mass energy of 40 MeV, at a value of the photon four-momentum transfer of Q^2= 0.05 GeV^2/c^2 and a center of mass angle of \theta=90^\circ. By an additional out-of-plane measurement with polarized electrons \sigma_{LT'} was determined. This showed for the first time the cusp effect above the \pi^+ threshold in the imaginary part of the s-wave. The predictions of Heavy Baryon Chiral Perturbation Theory are in disagreement with these data. On the other hand, the data are somewhat better predicted by the MAID phenomenological model and are in good agreement with the dynamical model DMT.Comment: 6 pages, 4 figure