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

On Asymptotic Completeness of Scattering in the Nonlinear Lamb System, II

We establish the asymptotic completeness in the nonlinear Lamb system for hyperbolic stationary states. For the proof we construct a trajectory of a reduced equation (which is a nonlinear nonautonomous ODE) converging to a hyperbolic stationary point using the Inverse Function Theorem in a Banach space. We give the counterexamples showing nonexistence of such trajectories for nonhyperbolic stationary points

Giant Coulomb broadening and Raman lasing on ionic transitions

CW generation of anti-Stokes Raman laser on a number of blue-green argon-ion lines (4p-4s, 4p-3d) has been demonstrated with optical pumping from metastable levels 3d'^2G, 3d^4F. It is found, that the population transfer rate is increased by a factor of 3-5 (and hence, the output power of such Raman laser) owing to Coulomb diffusion in the velocity space. Measured are the excitation and relaxation rates for the metastable level. The Bennett hole on the metastable level has been recorded using the probe field technique. It has been shown that the Coulomb diffusion changes shape of the contour to exponential cusp profile while its width becomes 100 times the Lorentzian one and reaches values close to the Doppler width. Such a giant broadening is also confirmed by the shape of the absorption saturation curve.Comment: RevTex 18 pages, 5 figure

Random raman fiber laser based on a twin-core fiber with FBGs inscribed by femtosecond radiation

Narrowband Raman lasing in a polarization-maintaining two-core fiber (TCF) is demonstrated. Femtosecond point-by-point inscription of fiber Bragg gratings (FBGs) in individual cores produces a half-open cavity with random distributed feedback. The laser linewidth in the cavity with a single FBG inscribed in one core of the TCF reduced by ∼2 times with respect to the cavity with a fiber loop mirror. It is shown that the inscription of two FBGs in different cores leads to the formation of a Michelson-type interferometer, leading to the modulation of generation spectra near threshold. This technique offers new possibilities for spectral filtering or multi-wavelength generation

Electrodynamics of balanced charges

In this work we modify the wave-corpuscle mechanics for elementary charges introduced by us recently. This modification is designed to better describe electromagnetic (EM) phenomena at atomic scales. It includes a modification of the concept of the classical EM field and a new model for the elementary charge which we call a balanced charge (b-charge). A b-charge does not interact with itself electromagnetically, and every b-charge possesses its own elementary EM field. The EM energy is naturally partitioned as the interaction energy between pairs of different b-charges. We construct EM theory of b-charges (BEM) based on a relativistic Lagrangian with the following properties: (i) b-charges interact only through their elementary EM potentials and fields; (ii) the field equations for the elementary EM fields are exactly the Maxwell equations with proper currents; (iii) a free charge moves uniformly preserving up to the Lorentz contraction its shape; (iv) the Newton equations with the Lorentz forces hold approximately when charges are well separated and move with non-relativistic velocities. The BEM theory can be characterized as neoclassical one which covers the macroscopic as well as the atomic spatial scales, it describes EM phenomena at atomic scale differently than the classical EM theory. It yields in macroscopic regimes the Newton equations with Lorentz forces for centers of well separated charges moving with nonrelativistic velocities. Applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the same for the Schrodinger model with any desired accuracy.Comment: Manuscript was edited to improve the exposition and to remove noticed typo

Anisotropy and non-universality in scaling laws of the large scale energy spectrum in rotating turbulence

Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale $L_f$, it cascades towards smaller as well as larger scales. In this paper we analyze the flow in the \textit{inverse cascade} range at a small but fixed Rossby number, {$\mathcal{R}o_f \approx 0.05$}. Several {numerical simulations with} helical and non-helical forcing functions are considered in periodic boxes with unit aspect ratio. In order to resolve the inverse cascade range with {reasonably} large Reynolds number, the analysis is based on large eddy simulations which include the effect of helicity on eddy viscosity and eddy noise. Thus, we model the small scales and resolve explicitly the large scales. We show that the large-scale energy spectrum has at least two solutions: one that is consistent with Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of energy in two-dimensional (2D) turbulence with a {$\sim k_{\perp}^{-5/3}$} scaling, and the other that corresponds to a steeper {$\sim k_{\perp}^{-3}$} spectrum in which the three-dimensional (3D) modes release a substantial fraction of their energy per unit time to 2D modes. {The spectrum that} emerges {depends on} the anisotropy of the forcing function{,} the former solution prevailing for forcings in which more energy is injected into 2D modes while the latter prevails for isotropic forcing. {In the case of anisotropic forcing, whence the energy} goes from the 2D to the 3D modes at low wavenumbers, large-scale shear is created resulting in another time scale $\tau_{sh}$, associated with shear, {thereby producing} a $\sim k^{-1}$ spectrum for the {total energy} with the 2D modes still following a {$\sim k_{\perp}^{-5/3}$} scaling

Lasing on the D_2 line of sodium in helium atmosphere due to optical pumping on the D_1 line (up-conversion)

A new method is proposed to produce population inversion on transitions involving the ground state of atoms. The method is realized experimentally with sodium atoms. Lasing at the frequency corresponding to the sodium D_2 line is achieved in the presence of pump radiation resonant to the D_1 line with helium as a buffer gas.Comment: 4 pages, 4 figures, Late

Штучна вентиляція легень під час операції черезшкірної дилатаційної трахеостомії

The description of a reliable method of artificial lung ventilation (ALV) during controlled percutaneous dilative tracheostomy by the replacing of endotracheal tube to laryngeal mask. During artificial lung ventilation using a laryngeal mask eliminates a needful to find the placement of the tracheostoma by endoscopic control, help to improve the efficiency of artificial lung ventilation and the level of oxygen saturations.Висвітлено спосіб надійної штучної вентиляції легень (ШВЛ) під час виконання операції черезшкірної дилатаційної трахеостомії шляхом заміни перед операцією інтубаційної трубки на ларингеальну маску. При проведенні ШВЛ через ларингеальну маску відпадає необхідність ідентифікації місця формування трахеостомічного каналу за допомогою фібробронхоскопа, зростають ефективність ШВЛ і, відповідно, рівень забезпечення організму пацієнта киснем під час операційного втручання