Shallow-water models for a vibrating fluid

We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency) free-surface waves. The first set of equations is obtained without assuming that the waves are long. These equations are as difficult to solve as the exact equations for irrotational water waves in a non-vibrating fluid. The other two models describe long waves. These models are obtained under two different assumptions about the amplitude of the vibration. Surprisingly, the governing equations have exactly the same form in both cases (up to interpretation of some constants). These equations reduce to the standard dispersionless shallow-water equations if the vibration is absent, and the vibration manifests itself via an additional term which makes the equations dispersive and, for small-amplitude waves, is similar to the term that would appear if surface tension were taken into account. We show that our dispersive shallow water equations have both solitary and periodic travelling wave solutions and discuss an analogy between these solutions and travelling capillary-gravity waves in a non-vibrating fluid

Theoretical prerequisites for substantiating the parameters of a rotary ripper for interrow potato cultivation

The article is devoted to the study of the process of interaction of the rotary ripper’s working bodies with the soil. The classification of rotary machines and implements according to the energy transmitted to the working body and the location of the rotation axis is outlined. The article notes that the main characteristics of the rotor work body motion are the trajectory type, the magnitude and direction of velocity of its most characteristic point, and in some cases, the magnitude and direction of acceleration. The article presents the results of theoretical research in the field of kinematics of interaction of rotary working tools with the soil. The design of the rotary ripper is presented and the description of the trajectory of its working bodies is made, the value of movement of the scraper plate in the contact area with the soil is established. We analyzed the segment of the path from the beginning of contact with the soil (the beginning of dragging the surface layer of soil) and the end of contact (the end of dragging the surface layer of soil), on the line of which weed combing, loosening and destruction of soil crust occurs

Electron and hole injection barriers between silicon substrate and RF magnetron sputtered In2O3 : Er films

In2O3 : Er films have been synthesized on silicon substrates by RF magnetron sputter deposition. The currents through the synthesized metal/oxide/semiconductor (MOS) structures (Si/In2O3 : Er/In-contact) have been measured for n and p type conductivity silicon substrates and described within the model of majority carrier thermoemission through the barrier, with bias voltage correction to the silicon potential drop. The electron and hole injection barriers between the silicon substrate and the film have been found to be 0.14 and 0.3 eV, respectively, by measuring the temperature dependence of the forward current at a low sub-barrier bias. The resulting low hole injection barrier is accounted for by the presence of defect state density spreading from the valence band edge into the In2O3 : Er band gap to form a hole conduction channel. The presence of defect state density in the In2O3 : Er band gap is confirmed by photoluminescence data in the respective energy range 1.55–3.0 eV. The band structure of the Si/In2O3 : Er heterojunction has been analyzed. The energy gap between the In2O3 : Er conduction band electrons and the band gap conduction channel holes has been estimated to be 1.56 eV

Theoretical prerequisites for substantiating the parameters of a rotary ripper for interrow potato cultivation

The article is devoted to the study of the process of interaction of the rotary ripper’s working bodies with the soil. The classification of rotary machines and implements according to the energy transmitted to the working body and the location of the rotation axis is outlined. The article notes that the main characteristics of the rotor work body motion are the trajectory type, the magnitude and direction of velocity of its most characteristic point, and in some cases, the magnitude and direction of acceleration. The article presents the results of theoretical research in the field of kinematics of interaction of rotary working tools with the soil. The design of the rotary ripper is presented and the description of the trajectory of its working bodies is made, the value of movement of the scraper plate in the contact area with the soil is established. We analyzed the segment of the path from the beginning of contact with the soil (the beginning of dragging the surface layer of soil) and the end of contact (the end of dragging the surface layer of soil), on the line of which weed combing, loosening and destruction of soil crust occurs

Electron and hole injection barriers between silicon substrate and RF magnetron sputtered In2O3 : Er films

In2O3 : Er films have been synthesized on silicon substrates by RF magnetron sputter deposition. The currents through the synthesized metal/oxide/semiconductor (MOS) structures (Si/In2O3 : Er/In-contact) have been measured for n and p type conductivity silicon substrates and described within the model of majority carrier thermoemission through the barrier, with bias voltage correction to the silicon potential drop. The electron and hole injection barriers between the silicon substrate and the film have been found to be 0.14 and 0.3 eV, respectively, by measuring the temperature dependence of the forward current at a low sub-barrier bias. The resulting low hole injection barrier is accounted for by the presence of defect state density spreading from the valence band edge into the In2O3 : Er band gap to form a hole conduction channel. The presence of defect state density in the In2O3 : Er band gap is confirmed by photoluminescence data in the respective energy range 1.55–3.0 eV. The band structure of the Si/In2O3 : Er heterojunction has been analyzed. The energy gap between the In2O3 : Er conduction band electrons and the band gap conduction channel holes has been estimated to be 1.56 eV