Time of relaxation in dusty plasma model
Dust particles in plasma may have different values of average kinetic energy for
vertical and horizontal motion. The partial equilibrium of the subsystems and the relaxation
processes leading to this asymmetry are under consideration. A method for the relaxation time
estimation in nonideal dusty plasma is suggested. The characteristic relaxation times of vertical
and horizontal motion of dust particles in gas discharge are estimated by analytical approach and
by analysis of simulation results. These relaxation times for vertical and horizontal subsystems
appear to be different. A single hierarchy of relaxation times is proposed.
We analyzed theoretically localized charge relaxation in a double quantum dot (QD) system coupled with continuous spectrum states in the presence of localized electrons Coulomb interaction in a single QD. We have found that for a wide range of system parameters charge relaxation occurs through two stable regimes with significantly different relaxation rates. A peculiar time moment exists in the system at which rapid switching between stable regimes takes place. We consider this phenomenon to be applicable for creation of active elements in nano-electronics based on the fast transition effect between two stable states.
Wave processes occurring under the interaction of the Earth's magnetosphere with dusty plasma near the lunar surface are studied. Ion-acoustic waves are shown to be excited in some regions of the magnetosphere due to the development of a linear hydrodynamic instability. This results in the excitation of ion-acoustic turbulence in these regions. Dust-acoustic waves are demonstrated to be generated due to the development of linear kinetic instability in the entire region of magnetotail interaction with dusty plasma near the Moon. Correspondingly, dust-acoustic turbulence can be excited in the entire region of the interaction of the Earth's magnetosphere with dusty plasma near the lunar surface. We discuss magnetic reconnection processes, which are related to the development of plasma turbulence at the Moon.
A theory is developed which describes the processes of dust particle charging in the situation when dust particles are subjected to the action of a beam of electrons. It is shown that in this situation it is necessary to consider the electron field emission in addition to the influence of the electron beam on the dust particle. We calculate the current of the electron field emission modified by the Schottky effect and find the steady-state dust particle charge. We show that in the situation considered the electrostatic energy of the dust particle is much smaller than the electron energy in the beam.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
Let G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and P⊆G be a parabolic subgroup. Extending the results of Popov , we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.
I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables