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A new type of instability - electrokinetic instability - and an unusual transition to chaotic motion near a charge-selective surface was studied by numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear analysis near the threshold of instability. Two kinds of initial conditions were considered: (a) white noise initial conditions to mimic "room disturbances" and subsequent natural evolution of the solution; (b) an artificial monochromatic ion distribution with a fixed wave number to simulate regular wave patterns. The results were studied from the viewpoint of hydrodynamic stability and bifurcation theory. The threshold of electroconvective movement was found by the linear spectral stability theory, the results of which were confirmed by numerical simulation of the entire system. The following regimes, which replace each other as the potential drop between the selective surfaces increases, were obtained: one-dimensional steady solution; two-dimensional steady electroconvective vortices (stationary point in a proper phase space); unsteady vortices aperiodically changing their parameters (homoclinic contour); periodic motion (limit cycle); and chaotic motion. The transition to chaotic motion did not include Hopf bifurcation. Numerical resolution of the thin concentration polarization layer showed spike-like charge profiles along the surface, which could be, depending on the regime, either steady or aperiodically coalescent. The numerical investigation confirmed the experimentally observed absence of regular (near-sinusoidal) oscillations for the overlimiting regimes. There is a qualitative agreement of the experimental and the theoretical values of the threshold of instability, the dominant size of the observed coherent structures, and the experimental and theoretical volt-current characteristics., Comment: 34 pages, 12 figures (in color), 37 references

Some known analytical solutions for a cascade shower were used for determining the intensity of excess electrons' radio-emission. It is shown that the energy spectrum has a sharp decline in the region of high frequencies. At a usual root-mean-square radius of the disk within the Moon's regolith ~ 0.06m the maximum of the spectrum is in the region ~ 0.5-0.6 GHz while in the range 2-2.5 GHz the pulse's amplitude drops by 5-6 orders. This fact is a consequence of loss of coherence due to finite dimensions of the cascade disk and demands conducting a significant correction of "radio-frequency window" for measuring cosmic rays' flux with a radio telescope., Comment: 14 pages, 5 figures

The problem of infrared divergence of the effective electromagnetic field produced by elementary particles is revisited using the non-equilibrium model of an electron interacting with low-temperature photons. It is argued that the infrared singularity of the effective field can be interpreted as a thermalization of the electron. It is shown that this thermalization is negligible in actual field measurements as it is completely dominated by the usual quantum spreading., Comment: 8 pages, 3 figures

The problem of infrared divergence of the effective electromagnetic field at finite temperature (T) is revisited. A model of single spatially localized electron interacting with thermal photons is considered in the limit T to 0 using two different regularization schemes. The first is based on the shift i 0 to i varepsilon of the electron propagator pole in the complex energy plane, and is used to explicitly calculate the effective field in the one-loop approximation. We show that the matrix-valued imaginary part of the electron self-energy can be consistently related to the pole shift, and that the presence of the heat bath leads to appearance of an effective varepsilon sim T, thus providing a natural infrared regulator of the theory. We find that the one-loop effective Coulomb field calculated using this varepsilon vanishes. The other scheme combines an infrared momentum cutoff with smearing of the delta-functions in the interaction vertices. We prove that this regularization admits factorization of the infrared contributions in multi-loop diagrams, and sum the corresponding infinite series. The effective electromagnetic field is found to vanish in this case too. An essentially perturbative nature of this result is emphasized and discussed in connection with the long-range expansion of the effective field., Comment: 17 pages, 9 figures

The calculation of muon spectra from the decay of Lambda_c baryons was carried out on the basis of the description of recent data on charmed-baryon production in hadronic interactions. Data are described in the framework of Quark--Gluon String Model that allowes us to consider primary proton interactions of arbitrary high energy. MC code was built for charmed-baryon semileptonic decay in order to obtain the kinematical characteristics of resulting particles. It is predicted that the charge asymmetry between energy spectra of mu+ and mu- in laboratory system is clearly seen as the consequence of asymmetry between the spectra of charmed baryons and antibaryons.This extension of QGS Model can be useful to correct the calculations of muon and neutrino spectra in astrophysics., Comment: 10 pages, 4 epsfigures, ReVTeX, included in the Proceeding of QFHEP04, Peterhof, Russia, 2004; submitted to Phys. At. Nucl. (2005)

An expression for the Green function G(E;x_1,x_2) of the Schroedinger equation is obtained through the approximations of the path integral by n-fold multiple integrals. The approximations to Re{G(E;x,x)} on the real E-axis have peaks near the values of the energy levels E_{j}. The analytic and numerical examples for one-dimensional and multi-dimensional harmonic and anharmonic oscillators, and Poeschl-Teller potential wells, show that median values of these peaks for approximate G(E;0,0) corresponds with accuracy of order 10% to the exact values of even levels already in the lowest orders of approximation n=1 and n=2, i.e. when the path integral is replaced by a line or double integral. The weights of the peaks approximate the values of the squared modulus of the wave functions at x=0 with the same accuracy., Comment: 16 pages, 4 figures