Nonlinear Development of the E × B-Instability in the Adiabatic Approximation

Abstract

The nonlinear development of the E × B-instability in a weakly ionized plasma is governed by an infinite set of coupled ordinary nonlinear differential equations for the amplitudes of the modes of the system. The solution of these equations are investigated in the adiabatic approximation by setting the time derivative of linearly stable modes equal to zero. Approximate analytical solutions for the time development of the different modes, in good agreement with previous numerical results, have been obtained for control parameters fifteen times the critical value. The results clearly indicate the possible existence of a cascading process, where the amplitudes of the linearly most stable modes have the highest nonlinear growth rates.

The Mechanism of Fertilization in Metazoa

“…Results similar to those obtained by Borei with sea urchin and starfish eggs were reported earlier by Holter and Zeuthen (112) for unfertilized eggs of Ciona intestinalis. Results similar to those obtained by Borei with sea urchin and starfish eggs were reported earlier by Holter and Zeuthen (112) for unfertilized eggs of Ciona intestinalis.…”

“…The rate of respiration in fertilized sea urchin eggs (Fig. An exponential increase in respiration is also found in Chaetoptem (295) and Ciona ( 112). Lindahl (151) found that after the "exponential" period the curve arrives a t a plateau, but that shortly before the first sign of gastrulation the rate of respiration begins to increase again, although now as a linear function of time.…”

Low-frequency internal friction as express-method for identification of cryocrystals in pores of the solids

“…Direct evidence of hydrogen penetration into internal pores was obtained by Holter et.al [34][35][36][37][38] only. He studied a process of hydrogen saturation of metallic samples through temperature spectra of internal friction (at frequencies 200-300 Hz, i.e.…”

“…Fig.8. Comparison of temperature dependencies of Q -1 for hydrogen saturated sample and the basic (not saturated) one [34][35][36][37][38].…”

“…However, in bulk of the papers this influence was estimated using indirect results that can not give proper information concerning noticeable hydrogen content in pores of the sample. Direct evidence of hydrogen penetration into internal pores was obtained by Holter et.al [34][35][36][37][38] only. He studied a process of hydrogen saturation of metallic samples through temperature spectra of internal friction (at frequencies 200-300 Hz, i.e.…”