Maria Kiseleva

Line mixing and collision induced absorption in the oxygen A-band using cavity ring-down spectroscopy

This paper reports on the absorption of molecular oxygen in the region of the A-band near 760 nm under atmospheric conditions relevant for satellite retrieval studies. We use pulsed laser cavity ring-down spectroscopy with a narrow bandwidth laser and use pressure scans to increase the accuracy of the measured oxygen extinction coefficients. Absolute binary absorption coefficients in minima between absorption lines of the A-band spectrum have been measured and tabulated. We use the so-called adjustable branch coupling model including line mixing to calculate the magnetic dipole absorption in order to determine the contribution of collision induced absorption. The line mixing model has been optimized such that the collision induced absorption spectrum is smooth.

Hidden and self-excited attractors in Chua circuit: synchronization and SPICE simulation

Graphical Abstract Two symmetric hidden chaotic attractors (blue), trajectories (red) from unstable manifolds of two saddle points are either attracted to locally stable zero equilibrium, or tend to infinity; trajectories (black) from stable manifolds tend to equilibria. Abstract Nowadays various chaotic secure communication systems based on synchronization of chaotic circuits are widely studied. To achieve synchronization, the control signal proportional to the difference between the circuits signals, adjust the state of one circuit. In this paper the synchronization of two Chua circuits is simulated in Simulation Programs with Integrated Circuit Emphasis. It is shown that the choice of control signal is not straightforward, especially in the case of multistability and hidden attractors.

Hidden Oscillations in Electromechanical Systems

In this paper an electromechanical system with two different types of motor is considered. It is shown that during the spin-up, the system with DC motor may experience unwanted vibration—the Sommerfeld effect. This is a well-known effect when the motor of electromechanical system gets stuck near the resonance zone instead of reaching its nominal power. The absence of this effect is demonstrated in the system with synchronous motor. Nowadays, there are many works devoted to the study of this effect in various systems. Here we discuss the Sommerfeld effect from the point of view of localization of the so-called hidden oscillations.

Hidden oscillations in drilling system actuated by induction motor

Abstract Study of drilling systems is a topical problem in drilling industry due to the amount of failures which lead to considerable cost and time loses for mining companies. This paper presents mathematical model of drilling system actuated by induction motor. The model consists of two discs connected by a no-mass string. The upper disc is actuated by the rotor of the motor and the lower disc is connected with a brake device which causes friction torque. Set-valued force laws are used in order to model the friction. The obtained model is described by system of ordinary differential equations (ODEs) with discontinuous right-hand side. A bifurcation analysis of the model is done. Presence of so-called hidden oscillations (represented by stick-slip stable vibrations) along with stable equilibrium is demonstrated. Such system requires accurate numerical modeling in the neighborhood of the discontinuous surface. Here the method of modeling such systems based on Filippov definition of solution for systems of ODEs with discontinuous right-hand side is used for analysis of dynamics of the model.

The temperature dependence of intensity and the function of the transition dipole moment for the induced optical absorption bands of oxygen in the region of the Herzberg photodissociation continuum (200–230 nm)

The values of the binary absorption coefficient μ11 of oxygen in the region of the Herzberg photo-dissociation continuum (200–230 nm) at temperatures from 200 to 110 K are obtained for the first time. It is shown that the induced optical absorption spectrum of oxygen in the region from 200 to 230 nm is composed of two bands with significantly different temperature dependences of μ11: the binary absorption coefficient of the Herzberg III band increases by approximately 50% on cooling from room temperature to 110 K, while the other band shows no pronounced temperature dependence of μ11 in this temperature range. The μ11(T) dependences are calculated theoretically using different functions M(r) of the induced transition dipole moment, namely, a function exponentially dependent on the intermolecular distance and a more complicated function accounting for both the short-range interaction and the long-range interaction due to quadrupole moments averaged over wave functions of various electronic states. It is found that the latter function M(r) better describes the temperature dependence of the Herzberg III oxygen absorption band in the whole temperature range studied and gives a physically justified value for the parameter r0 in the exponential part of the function.

On the temperature dependence of the intensity of the induced absorption of oxygen in a region of the herzberg photodissociation continuum in binary mixtures of oxygen with argon and nitrogen

Values of the binary absorption coefficient μ12 in the induced Herzberg III band of oxygen for O2-Ar and O2-N2 pairs have been obtained for the first time in the range 200–215 nm and in the temperature interval 295–120 K. It has been found that, as the temperature decreases, the binary absorption coefficient increases continuously: for O2-Ar pairs, a marked increase in μ12 starts immediately from room temperature, and, for O2-N2 pairs, it begins at temperatures below 180 K. As the temperature decreases from room temperature to 120 K, μ12 increases roughly by 40 and 35% for O2-Ar and O2-N2 pairs, respectively. For each type of pairs, the dependence μ12(T) has been calculated with the use of the dipole moment function of the induced transition, taking into account both short-and long-range interactions, as well as the multiparametric isotropic potential of intermolecular interactions. It is shown that it is possible to select such parameters of the dipole moment function of the transition that the theoretical curve μ12(T) describes satisfactorily the experimental data on the temperature dependence of μ12 in the Herzberg III band for O2-Ar and O2-N2 pairs in the whole temperature range under study.

Theory of Differential Inclusions and Its Application in Mechanics

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work, three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load chande is studied. Analytical methods of investigation of systems with such asymmetrical friction, based on the use of Lyapunov functions, are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems.

Collision-induced absorption of mixture of oxygen with argon in the region of the Herzberg photodissociation continuum

The values of the binary absorption coefficient μ12 for an O2 - Ar pair in the region of the Herzberg photodissociation continuum (200 - 230 nm) have been measured in the temperature range 295 - 120 K. It was found that for the temperatures from 295 K to 160 K the values of μ12 demonstrate rather weak temperature dependence, while as the temperature decreases from 160 K to 120 K, the values of μ12 increase by ~ 15%. Transition dipole moment function of exponential type was proposed to describe the observed temperature dependence of the values of the binary absorption coefficient μ12 for an O2 - Ar pair in the Herzberg III band of oxygen. Comparison of the temperature dependences of the binary absorption coefficients for an O2 - Ar pair and for an O2 - O2 pair was carried out.

Collision-Induced Absorption of Gaseous Oxygen in the Herzberg Continuum

The values of the binary absorption coefficient for gaseous molecular oxygen in the region of the Herzberg photodissociation continuum (200–230 nm) have been measured in the temperature range 110–295 K. The induced absorption of oxygen in the 200–220 nm spectral region was found to result from two bands with quite different temperature dependence of their intensity: for the Herzberg III band the values of the binary absorption coefficient increase by ~ 50% as the temperature decreases from 295 to 110 K, while for the other band no distinct temperature dependence of the binary absorption coefficient was observed. A transition dipole moment function including both short-range term (overlap of the electron shells of interacting molecules) and long-range term (interaction of the transient quadrupole moments) is proposed to describe the temperature dependence of the binary absorption coefficients in the Herzberg III band.