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

Satellite Evidence of Hurricane-Induced Phytoplankton Blooms in an Oceanic Desert

The physical effects of hurricanes include deepening of the mixed layer and decreasing of the sea surface temperature in response to entrainment, curl-induced upwelling, and increased upper ocean cooling. However, the biological effects of hurricanes remain relatively unexplored. In this paper, we examine the passages of 13 hurricanes through the Sargasso Sea region of the North Atlantic during the years 1998 through 2001. Remotely sensed ocean color shows increased concentrations of surface chlorophyll within the cool wakes of the hurricanes, apparently in response to the injection of nutrients and/or biogenic pigments into the oligotrophic surface waters. This increase in post-storm surface chlorophyll concentration usually lasted 2-3 weeks before it returned to its nominal pre-hurricane level

Ecosystem respiration: Drivers of daily variability and background respiration in lakes around the globe

We assembled data from a global network of automated lake observatories to test hypotheses regarding the drivers of ecosystem metabolism. We estimated daily rates of respiration and gross primary production (GPP) for up to a full year in each lake, via maximum likelihood fits of a free‐water metabolism model to continuous high‐frequency measurements of dissolved oxygen concentrations. Uncertainties were determined by a bootstrap analysis, allowing lake‐days with poorly constrained rate estimates to be down‐weighted in subsequent analyses. GPP and respiration varied considerably among lakes and at seasonal and daily timescales. Mean annual GPP and respiration ranged from 0.1 to 5.0 mg O2 L−1 d−1 and were positively related to total phosphorus but not dissolved organic carbon concentration. Within lakes, significant day‐to‐day differences in respiration were common despite large uncertainties in estimated rates on some lake‐days. Daily variation in GPP explained 5% to 85% of the daily variation in respiration after temperature correction. Respiration was tightly coupled to GPP at a daily scale in oligotrophic and dystrophic lakes, and more weakly coupled in mesotrophic and eutrophic lakes. Background respiration ranged from 0.017 to 2.1 mg O2 L−1 d−1 and was positively related to indicators of recalcitrant allochthonous and autochthonous organic matter loads, but was not clearly related to an indicator of the quality of allochthonous organic matter inputs

State-Selective Metabolic Labeling of Cellular Proteins

Transcriptional activity from a specified promoter can provide a useful marker for the physiological state of a cell. Here we introduce a method for selective tagging of proteins made in cells in which specified promoters are active. Tagged proteins can be modified with affinity reagents for enrichment or with fluorescent dyes for visualization. The method allows state-selective analysis of the proteome, whereby proteins synthesized in predetermined physiological states can be identified. The approach is demonstrated by proteome-wide labeling of bacterial proteins upon activation of the P_(BAD) promoter and the SoxRS regulon and provides a basis for analysis of more complex systems including spatially heterogeneous microbial cultures and biofilms

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

Thermodynamic Limit Of The Ginzburg-Landau Equations

We investigate the existence of a global semiflow for the complex Ginzburg-Landau equation on the space of bounded functions in unbounded domain. This semiflow is proven to exist in dimension 1 and 2 for any parameter values of the standard cubic Ginzburg-Landau equation. In dimension 3 we need some restrictions on the parameters but cover nevertheless some part of the Benjamin-Feijer unstable domain.Comment: uuencoded dvi file (email: [email protected]

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

Nonlinear multimode fiber optics: recent advances

We start by providing an overview of the emerging field of nonlinear optics in multimode optical fibers [1]. These fibers provide a simple testbed for observing complex wave propagation dynamics, in analogy with other fields of physics ranging from two-dimensional hydrodynamic turbulence and Bose-Einstein condensation. In addition, nonlinear multimode optical fibers enable new methods for achieving the ultrafast, light-activated control of temporal, spatial and spectral degrees of freedom of intense, pulsed light beams, for a range of different technological applications