Relativistic point dynamics and Einstein formula as a property of localized solutions of a nonlinear Klein-Gordon equation

Einstein's relation E=Mc^2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems which do not accelerate. By contrast, Newtonian approach to the mass is based on an accelerated motion. We study here a particular neoclassical field model of a particle governed by a nonlinear Klein-Gordon (KG) field equation. We prove that if a solution to the nonlinear KG equation and its energy density concentrate at a trajectory, then this trajectory and the energy must satisfy the relativistic version of Newton's law with the mass satisfying Einstein's relation. Therefore the internal energy of a localized wave affects its acceleration in an external field as the inertial mass does in Newtonian mechanics. We demonstrate that the "concentration" assumptions hold for a wide class of rectilinear accelerating motions

Linear superposition in nonlinear wave dynamics

We study nonlinear dispersive wave systems described by hyperbolic PDE's in R^{d} and difference equations on the lattice Z^{d}. The systems involve two small parameters: one is the ratio of the slow and the fast time scales, and another one is the ratio of the small and the large space scales. We show that a wide class of such systems, including nonlinear Schrodinger and Maxwell equations, Fermi-Pasta-Ulam model and many other not completely integrable systems, satisfy a superposition principle. The principle essentially states that if a nonlinear evolution of a wave starts initially as a sum of generic wavepackets (defined as almost monochromatic waves), then this wave with a high accuracy remains a sum of separate wavepacket waves undergoing independent nonlinear evolution. The time intervals for which the evolution is considered are long enough to observe fully developed nonlinear phenomena for involved wavepackets. In particular, our approach provides a simple justification for numerically observed effect of almost non-interaction of solitons passing through each other without any recourse to the complete integrability. Our analysis does not rely on any ansatz or common asymptotic expansions with respect to the two small parameters but it uses rather explicit and constructive representation for solutions as functions of the initial data in the form of functional analytic series.Comment: New introduction written, style changed, references added and typos correcte

Relativistic dynamics of accelerating particles derived from field equations

In relativistic mechanics the energy-momentum of a free point mass moving without acceleration forms a four-vector. Einstein's celebrated energy-mass relation E=mc^2 is commonly derived from that fact. By contrast, in Newtonian mechanics the mass is introduced for an accelerated motion as a measure of inertia. In this paper we rigorously derive the relativistic point mechanics and Einstein's energy-mass relation using our recently introduced neoclassical field theory where a charge is not a point but a distribution. We show that both the approaches to the definition of mass are complementary within the framework of our field theory. This theory also predicts a small difference between the electron rest mass relevant to the Penning trap experiments and its mass relevant to spectroscopic measurements.Comment: A few typos were correcte

Quantum theory of resonantly enhanced four-wave mixing: mean-field and exact numerical solutions

We present a full quantum analysis of resonant forward four-wave mixing based on electromagnetically induced transparency (EIT). In particular, we study the regime of efficient nonlinear conversion with low-intensity fields that has been predicted from a semiclassical analysis. We derive an effective nonlinear interaction Hamiltonian in the adiabatic limit. In contrast to conventional nonlinear optics this Hamiltonian does not have a power expansion in the fields and the conversion length increases with the input power. We analyze the stationary wave-mixing process in the forward scattering configuration using an exact numerical analysis for up to $10^3$ input photons and compare the results with a mean-field approach. Due to quantum effects, complete conversion from the two pump fields into the signal and idler modes is achieved only asymptotically for large coherent pump intensities or for pump fields in few-photon Fock states. The signal and idler fields are perfectly quantum correlated which has potential applications in quantum communication schemes. We also discuss the implementation of a single-photon phase gate for continuous quantum computation.Comment: 10 pages, 11 figure

Full quantum solutions to the resonant four-wave mixing of two single-photon wave packets

We analyze both analytically and numerically the resonant four-wave mixing of two co-propagating single-photon wave packets. We present analytic expressions for the two-photon wave function and show that soliton-type quantum solutions exist which display a shape-preserving oscillatory exchange of excitations between the modes. Potential applications including quantum information processing are discussed.Comment: 7 pages, 3 figure

Ecosystem function and particle flux dynamics across the Mackenzie Shelf (Beaufort Sea, Arctic Ocean): an integrative analysis of spatial variability and biophysical forcings

A. Forest et al. -- 78 pages, 18 figures, 6 tablesA better understanding of how environmental changes affect organic matter fluxes in Arctic marine ecosystems is sorely needed. Here, we combine mooring times-series, ship-based measurements and remote-sensing to assess the variability and forcing factors of vertical fluxes of particulate organic carbon (POC) across the Mackenzie Shelf in 2009. We developed a geospatial model of these fluxes to proceed to an integrative analysis of their biophysical determinants in summer. Flux data were obtained with sediment traps and via a regional empirical algorithm applied to particle size-distributions (17 classes from 0.08–4.2 mm) measured by an Underwater Vision Profiler 5. Redundancy analyses and forward selection of abiotic/biotic parameters, linear trends, and spatial structures (i.e. principal coordinates of neighbor matrices, PCNM), were conducted to partition the variation of POC flux size-classes. Flux variability was explained at 69.5 % by the addition of a linear temporal trend, 7 significant PCNM and 9 biophysical variables. The interaction of all these factors explained 27.8 % of the variability. The first PCNM canonical axis (44.4 % of spatial variance) reflected a shelf-basin gradient controlled by bottom depth and ice concentration (p < 0.01), but a complex assemblage of fine-to-broad scale patterns was also identified. Among biophysical parameters, bacterial production and northeasterly wind (upwelling-favorable) were the two strongest explanatory variables (r2 cum. = 0.37), suggesting that bacteria were associated with sinking material, which was itself partly linked to upwelling-induced productivity. The second most important spatial structure corresponded actually to the two areas where shelf break upwelling is known to occur under easterlies. Copepod biomass was negatively correlated (p < 0.05) with vertical POC fluxes, implying that metazoans played a significant role in the regulation of export fluxes. The low fractal dimension of settling particles (1.26) and the high contribution (~94 %) of fast-sinking small aggregates (<1 mm; 20–30 m d−1) to the mass fluxes suggested that settling material across the region was overall fluffy, porous, and likely resulting from the aggregation of marine detritus, gel-like substances and ballast minerals. Our study demonstrates that vertical POC fluxes in Arctic shelf systems are spatially complex, sensitive to environmental forcings, and determined by both physicochemical mechanisms and food web functioning. In conclusion, we hypothesize that the incorporation of terrestrial matter into the Beaufort Sea food web could be catalyzed by bacteria via the incorporation of dissolved terrestrial carbon liberated through the photo-cleavage and/or hydrolysis of land-derived POC interweaved with marine aggregatesThis work would not have been possible without the professional and enthusiastic assistance of the officers and crew members of the CCGS Amundsen. We express gratitude to L. Prieur and C. Marec for their help in the deployment of the CTD-rosette and for the onboard processing of UVP5 data. We thank J. Martin, J. Gagnon, A. Mignot and M. Gosselin for sharing the chlorophyll data in order to post-calibrate the fluorometer. 5 We thank P. Guillot for the validation of physical data. We thank M. Fortier, K. L´evesque and J. Ehn for the organization of the fieldwork, workshops and for support at sea. This study was conducted as part of the Malina Scientific Program funded by ANR (Agence nationale de la recherche), INSU-CNRS (Institut national des sciences de l’univers – Centre national de la recherche scientifique), CNES (Centre national d’e´tudes spatiales) and ESA (European Space Agency). Additional support from ArcticNet (a Network of Centres of Excellence of Canada) and from the ArcticNet-Imperial Oil Research Collaboration was welcomed and appreciated. The IAEA is grateful to the Government of the Principality of Monaco for the support provided to its Environment Laboratories. This work is a joint contribution to the Malina Project and to the research 15 programs of Que´bec-Oce´an, ArcticNet, the Takuvik Joint U. Laval/CNRS Laboratory, the Arctic in Rapid Transition (ART) Initiative, to the Canada Research Chair on the Response of Marine Arctic Ecosystems to ClimateWarming, and to the Canada Excellence Research Chair (CERC) in Remote Sensing of Canada’s New Arctic FrontierPeer reviewe

Self-trapped states and the related luminescence in PbCl2_2 crystals

We have comprehensively investigated localized states of photoinduced electron-hole pairs with electron-spin-resonance technique and photoluminescence (PL) in a wide temperature range of 5-200 K. At low temperatures below 70 K, holes localize on Pb$^{2+}$ ions and form self-trapping hole centers of Pb$^{3+}$. The holes transfer to other trapping centers above 70 K. On the other hand, electrons localize on two Pb$^{2+}$ ions at higher than 50 K and form self-trapping electron centers of Pb$_2$$^{3+}$. From the thermal stability of the localized states and PL, we clarify that blue-green PL band at 2.50 eV is closely related to the self-trapped holes.Comment: 8 pages (10 figures), ReVTEX; removal of one figure, Fig. 3 in the version

The fate of the homoctenids (Tentaculitoidea) during the Frasnian-Famennian mass extinction (Late Devonian)

The homoctenids (Tentaculitoidea) are small, conical-shelled marine animals which are amongst the most abundant and widespread of all Late Devonian fossils. They were a principal casualty of the Frasnian-Famennian (F-F, Late Devonian) mass extinction, and thus provide an insight into the extinction dynamics. Despite their abundance during the Late Devonian, they have been largely neglected by extinction studies. A number of Frasnian-Famennian boundary sections have been studied, in Poland, Germany, France, and the United States. These sections have yielded homoctenids, which allow precise recognition of the timing of the mass extinction. It is clear that the homoctenids almost disappear from the fossil record during the latest Frasnian “Upper Kellwasser Event”. The coincident extinction of this pelagic group, and the widespread development of intense marine anoxia within the water column, provides a causal link between anoxia and the F-F extinction. Most notable is the sudden demise of a group, which had been present in rock-forming densities, during this anoxic event. One new species, belonging to Homoctenus is described, but is not formally named here

Ontogenic changes in hematopoietic hierarchy determine pediatric specificity and disease phenotype in fusion oncogene-driven myeloid leukemia

Fusion oncogenes are prevalent in several pediatric cancers, yet little is known about the specific associations between age and phenotype. We observed that fusion oncogenes, such as ETO2–GLIS2, are associated with acute megakaryoblastic or other myeloid leukemia subtypes in an age-dependent manner. Analysis of a novel inducible transgenic mouse model showed that ETO2–GLIS2 expression in fetal hematopoietic stem cells induced rapid megakaryoblastic leukemia whereas expression in adult bone marrow hematopoietic stem cells resulted in a shift toward myeloid transformation with a strikingly delayed in vivo leukemogenic potential. Chromatin accessibility and single-cell transcriptome analyses indicate ontogeny-dependent intrinsic and ETO2–GLIS2-induced differences in the activities of key transcription factors, including ERG, SPI1, GATA1, and CEBPA. Importantly, switching off the fusion oncogene restored terminal differentiation of the leukemic blasts. Together, these data show that aggressiveness and phenotypes in pediatric acute myeloid leukemia result from an ontogeny-related differential susceptibility to transformation by fusion oncogenes. SIGNIFICANCE: This work demonstrates that the clinical phenotype of pediatric acute myeloid leukemia is determined by ontogeny-dependent susceptibility for transformation by oncogenic fusion genes. The phenotype is maintained by potentially reversible alteration of key transcription factors, indicating that targeting of the fusions may overcome the differentiation blockage and revert the leukemic state