Without taking into account external friction, small transverse vibrations of a viscoelastic pipeline of unit length are described for nonnegative values of time in dimensionless variables by an ...integro-differential equation with hinged conditions at the ends and with initial conditions. The solution of this equation can be written in terms of an operator semigroup. In the present paper, we establish that this equation generates a semigroup that is analytic in some sector of the right half-plane.
The characteristics of acoustic-gravity waves (waveforms, time durations, amplitudes, azimuths and horizontal phase speeds) from the eruption of the Hunga-Tonga-Hunga-Hapai volcano detected at ...different infrasound stations of the Infrasound Monitoring System and at a network of low-frequency microbarographs in the Moscow region are studied. Using the correlation analysis of the signals at different locations, six arrivals of signals from the volcano, which made up to two revolutions around the Earth, were detected. The Lamb mode of acoustic gravity waves from the volcano eruption is identified and the effect of this mode on generation of tsunami waves and variation of aerosol concentration is studied. The energy released from an underwater volcano into the atmosphere is estimated from the parameters of the Lamb wave and compared with the energy released from the most powerful nuclear bomb of 58 Mt TNT.
An integrated approach is applied to reveal fine changes in the surface-normal structure of 1,2-dimyristoyl-sn-glycero-3-phospho-l-serine (DMPS) monolayers at the air–lipid–water interface occurring ...in a liquid expanded (LE)–liquid condensed (LC) transition. The combination of the Langmuir monolayer technique, X-ray reflectometry, and molecular dynamics (MD) modeling provides new insight into the molecular nature of electrostatic phenomena in different stages of lipid compression. A homemade setup with a laboratory X-ray source (λ = 1.54 Å) offers a nondestructive way to reveal the structural difference between the LE and LC phases of the lipid. The electron density profile in the direction normal to the interface is recovered from the X-ray reflectivity data with the use of both model-independent and model-based approaches. MD simulations of the DMPS monolayer are performed for several areas per lipid using the all-atom force field. Using the conventional theory of capillary waves, a comparison is made between the electron density profiles reconstructed from the X-ray data and those calculated directly from MD modeling, which demonstrates remarkable agreement between the experiment and simulations for all selected lipid densities. This confirms the validity of the simulations and allows an analysis of the contributions of the hydrophobic tails and hydrated polar groups to the electron density profile and to the dipole component of the electric field at the interface. According to the MD data, the dependence of the Volta potential on the area per lipid in the monolayer has a different molecular nature below and above the phase transition. In the LE state of the monolayer, the potential is determined mostly by the oriented water molecules in the polar region of the lipid. In the LE–LC transition, these molecules are displaced to the bulk, and their effect on the Volta potential becomes insignificant compared with the contribution of the hydrophobic tails. The hydrophobic tails are highly ordered in the state of the liquid crystal so that their dipole moments entirely determine the growth of the potential upon compression up to the monolayer collapse.
We consider an operator semigroup arising in the study of an integro-differential equation modeling small transverse vibrations of a viscoelastic pipeline with allowance for Kelvin–Voigt damping. The ...explicit form of the generator of this semigroup is established, its spectrum is studied, and the norm of its resolvent is estimated. Based on these results, the analyticity of this semigroup is proved with the use of well-known facts from the theory of semigroups.
In this paper we consider an operator function being a symbol of the abstract integro-differential equation describing the oscillations of a viscoelastic tube. The operator-function spectrum ...localization is determined in the paper and its resolvent norm is estimated in a domain free of spectral points.
The problem of attitude stabilization of a rigid body with the use of restoring and dissipative torques is studied. The possibility of implementing a control system in which the restoring torque ...tends to zero as time increases, and the only remaining control torque is a linear time-invariant dissipative one, is investigated. Both cases of linear and essentially nonlinear restoring torques are considered. With the aid of the Lyapunov direct method and the comparison method, conditions are derived under which we can guarantee stability or asymptotic stability of an equilibrium position of the body despite the vanishing of the restoring torque. A numerical simulation is provided to demonstrate the effectiveness of analytical results.
A satellite in a circular near-Earth orbit is under consideration. The three-axis stabilization of the satellite in the orbital coordinate system with the use of electrodynamic attitude control ...system is studied. No constraints are imposed on the Earth's magnetic field approximation. The gravity gradient disturbing torque acting on the satellite attitude dynamics is taken into account as the largest disturbing torque. With the use of the Lyapunov direct method, conditions under which electrodynamic control solves the problem are obtained. The restrictions on the control parameter values for which one can guarantee the asymptotic stability of the programmed satellite motion are found and represented in an explicit form. Comparison of the results of numerical simulation and analytical investigation demonstrate effectiveness of the proposed approach.
•Electromagnetic attitude control providing satellite stabilization is developed.•Asymptotic stability of the satellite program motion is proved.•No constraints are imposed on the Earth's magnetic field approximation.•Gravitational disturbing torque acting on satellite dynamics is taken into account.
The problem of attitude stabilization of a rigid body exposed to a nonstationary perturbing torque is investigated. The control torque consists of a restoring component and a dissipative one. Linear ...and nonlinear variants of restoring and perturbing torques are analyzed. Conditions of the asymptotic stability of the programmed orientation of the body are found with the use of the Lyapunov direct method and the averaging technique. The results of computer modeling, illustrating the conclusions obtained analytically, are presented.
The spectral properties of the correlation function of the heights of interlayer boundaries in a lamellar 1,2‑distearoyl-sn-glycero-3-phosphocholine film deposited on the surface of the hydrosol of ...amorphous silica nanoparticles are investigated within the scope of a model-independent approach based on the data of nonspecular X-ray scattering. The data analysis shows that the spectrum of interlayer roughnesses in a multilayer is qualitatively different from the prediction of the capillary wave theory in the entire considered interval of spatial frequencies.
This review considers the state-of-the-art on mechanisms and alternative pathways of electron transfer in photosynthetic electron transport chains of chloroplasts and cyanobacteria. The mechanisms of ...electron transport control between photosystems (PS) I and II and the Calvin–Benson cycle are considered. The redistribution of electron fluxes between the noncyclic, cyclic, and pseudocyclic pathways plays an important role in the regulation of photosynthesis. Mathematical modeling of light-induced electron transport processes is considered. Particular attention is given to the electron transfer reactions on the acceptor side of PS I and to interactions of PS I with exogenous acceptors, including molecular oxygen. A kinetic model of PS I and its interaction with exogenous electron acceptors has been developed. This model is based on experimental kinetics of charge recombination in isolated PS I. Kinetic and thermodynamic parameters of the electron transfer reactions in PS I are scrutinized. The free energies of electron transfer between quinone acceptors A
1A
/A
1B
in the symmetric redox cofactor branches of PS I and iron–sulfur clusters F
X
, F
A
, and F
B
have been estimated. The second-order rate constants of electron transfer from PS I to external acceptors have been determined. The data suggest that byproduct formation of superoxide radical in PS I due to the reduction of molecular oxygen in the A1 site (Mehler reaction) can exceed 0.3% of the total electron flux in PS I.
