Distinguishing Resonant from Non-Resonant Nonlinear Optical Processes Using Intensity–Intensity Correlation Analyses

Three-color coherent anti-Stokes Raman scattering (CARS) represents non-degenerate four wave mixing that includes both non-resonant and resonant processes, the contributions of which depend upon how the molecular vibrational modes are being excited by the input laser pulses. The scattering signal due to resonant processes builds up progressively. An advanced analytical tool to reveal this deferred resonant signal buildup phenomenon is in need. In this work, we adapt a quantitative analytical tool by introducing one-dimensional and two-dimensional intensity–intensity correlation functions in terms of a new variable (probe pulse delay) and a new perturbation parameter (probe pulse linewidth). In particular, discrete diagonal directional sums are defined here as a tool to reduce both synchronous and asynchronous two-dimensional correlation spectroscopy (2D-COS) maps down to one-dimensional plots while maintaining the valuable analytical information. Detailed analyses using the all-Gaussian coherent Raman scattering closed-form solutions and the representative experimental data for resonant and non-resonant processes are presented and compared. The present work holds a promising potential for industrial application, e.g., by extractive industries to distinguish hydrocarbons (chemically resonant substance) from water (non-resonant contaminant) by utilizing the one- and two-dimensional correlation analyses.

A dark state of Chern bands: Designing flat bands with higher Chern number

We introduce a scheme by which flat bands with higher Chern number \vert C\vert>1|C|>1 can be designed in ultracold gases through a coherent manipulation of Bloch bands. Inspired by quantum-optics methods, our approach consists in creating a ``dark Bloch band" by coupling a set of source bands through resonant processes. Considering a \LambdaΛ system of three bands, the Chern number of the dark band is found to follow a simple sum rule in terms of the Chern numbers of the source bands: C_D\!=\!C_1+C_2-C_3CD=C1+C2−C3. Altogether, our dark-state scheme realizes a nearly flat Bloch band with predictable and tunable Chern number C_DCD. We illustrate our method based on a \LambdaΛ system, formed of the bands of the Harper-Hofstadter model, which leads to a nearly flat Chern band with C_D\!=\!2CD=2. We explore a realistic sequence to load atoms into the dark Chern band, as well as a probing scheme based on Hall drift measurements. Dark Chern bands offer a practical platform where exotic fractional quantum Hall states could be realized in ultracold gases.

On Developing the Theory of Resonant Processes in Power Transformer Windings. Part 2. Frequency Responses of a Circuit with Four PI Sections

In the first part of the article, the results from theoretical studies of frequency responses in a homogeneous chain circuit containing two PI sections were presented, and conclusions about the voltage resonance occurrence conditions were drawn. A circuit with two PI sections has a single independent node and one natural frequency, whereas transformer windings are more complex oscillatory circuits and have a much larger number of natural oscillation frequencies. The second part of the article presents the results from studies of frequency responses in a homogeneous chain circuit containing four PI sections, three independent nodes, and three natural oscillation frequencies. Analytical expressions for the admittances of the equivalent circuit individual parts and the voltages at the intermediate nodes, as well as expressions for the natural frequencies are obtained. Using an analysis of the frequency dependences of the admittances of the equivalent circuit parts, the conditions and frequency ranges under which voltage resonance may occur at the first, second, and third natural frequencies, are shown. It has been demonstrated that for the considered resonant circuits there is a critical frequency above which the conditions for voltage resonance are not satisfied. Formulas for impedances and voltages at intermediate nodes of a chain circuit with an arbitrary number of PI sections are given.

On Developing the Theory of Resonant Processes in Power Transformer Windings. Part 1. Frequency Responses of a Circuit with Two PI Sections

The windings of power transformers are complex oscillatory circuits. Their natural oscillation frequencies range from a few to hundreds of kHz, and under unfavorable conditions they can coincide with the frequencies of transient voltage oscillations in electrical networks caused by switching operations and short circuit faults in cable lines. The development of electrical networks and the technical solutions that have come in wide use in recent years give rise to a situation in which the cases of damage to the insulation of power transformer windings resulting from resonant overvoltages are increasingly more frequently encountered during operation. An attempt is made in the article to develop the theory of resonant processes in the windings of power transformers. The frequency responses of voltages and currents in a simplified equivalent circuit of the power transformer winding are considered. Analytical expressions are obtained for the admittances of individual parts of equivalent circuits and the voltages at intermediate nodes, as well as expressions for the natural frequencies of the equivalent circuits considered. It is shown that the resonant growth of voltage in the transformer windings results from the voltage resonance caused by the presence of the winding’s own inductance and capacitance with respect to ground. By analyzing the frequency dependences of the admittances of equivalent circuit individual parts, the conditions and frequency ranges in which voltage resonance may occur are shown.

MULTI-POINTED FIELD-EMISSION CATHODE AS A GENERATOR OF HIGHFREQUENCY OSCILLATIONS

Semiconductor field-emission cathodes have gained considerable popularity in modern radio electronics and electronic optics due to the high-power generation of the electron beam in the external electric field at temperatures close to the room ones. However, their wide application is restricted by the high dependence of the electron emission current on the value of the applied field and geometrical parameters of the cathode. This study aimed to examine the effect of resonance processes on amplifying the field emission of the multi-pointed semiconductor cathode. Modeling the behavior of resonant tunneling of electrons from semiconductors to vacuum was simulated by solving the one-dimensional Schrodinger’s equation, and the amplification due to resonant processes was estimated. The modeling results showed that as the electric field increases, the resonance conditions shift towards low energy levels. With the increase in the width of the barrier for the electron inside the solid body, the resonance conditions shift towards higher energies. It has been established that in onedimensional semiconductors with electrons of low conductivity width, the resonant energy coincides with the Fermi level. These cathode properties are optimal for amplifying the emission current and reducing failures of vacuum electronic devices based on semiconductive field cathodes. The proposed technique can be used to study the regularities of emission amplification due to resonant processes in multipoint semiconductor cathodes with multilayered structure and with metal tips.

Andreev conductance through a triangular-shaped quantum dot structure hosting Majorana bound states

The Andreev conductance in [Formula: see text]-shaped quantum dots (QDs) system coupled with Majorana bound states (MBSs) is studied and resulting conductance spectrum displays resonant and non-resonant processes. These fluctuated resonances render features like insulating band, bonding (antibonding) in the low-bias region due to non-trivial role of interdot coupling [Formula: see text] and dots-MBSs coupling [Formula: see text]. On comparing QD levels [Formula: see text], and the coupling between the MBSs, coherent oscillating dynamics of an electron between the nanowire and the QDs can be portrayed. The insulating band is robust against [Formula: see text], but highly sensitive to [Formula: see text], which causes to increase (decrease) the conductance. We can claim that under finite bias voltage, transport can facilitate the researchers to expose the essential features of the Majorana fermion in such closed systems composed of MBSs.

DEVELOPMENT OF THE NUMERICAL METHODOLOGY FOR THE ESTIMATION OF RESONANT PROCESSES AT GASTURBINE ENGINE FLOW DUCT

Ensuring safety of flights is the most important task that is being solved in the process of designing an aircraft engine and aircraft. The most complex are the physical processes occurring inside the aircraft engine, especially in its gas generator: combustion chamber, high-pressure compressor and high-pressure turbine. The unsteady flow of gas in the flow duct of the aircraft engine is very complex, it is difficult to model, because the flow is characterized by a wide range of time and space scales. Unsteady flow in a high-pressure compressor can cause surge and breakdown of the compressor and the entire engine as a whole. Along with the detachment flows causing the surge, in the flow duct there can be resonant phenomena associated with the propagation of powerful sound waves along the flow duct of the engine, which, when a direct and reflected wave is imposed, create a very powerful standing wave that affects the structure. With a certain combination of conditions, the coincidence of the natural frequencies of the oscillations of the air volume and the solid body, such resonant processes in the flow duct of the gas turbine engine can lead to serious breakdowns, such as breakage of rotor blades and guide vanes, destruction of the aeroengine framework and other. The main difficulty is that it is problematic to identify such processes at the design and debugging stage, since there are no suitable mathematical models, and for experimental verification it is required to withstand the specific operating conditions of the node that are not known in advance. This work is devoted to the creation of a calculation technique that will allow in the future to diagnose resonance phenomena at the design stage and thereby significantly reduce the costs for the design, testing and manufacture of an aircraft engine. The proposed technique is based on the nonstationary Navier-Stokes equations for a compressible gas.

Dynamics of inhomogeneous elastic half-space under moving load

Wave processes in an elastic half-space covered with an elastic layer and (or) a thin elastic plate are considered in the paper. External load moves along the free surface. In the stationary statement, the waveguide properties of the system are determined. The multiple roots of the dispersion equations are revealed and the critical load velocities, leading to the initiation of resonant processes, are determined. In the case when the load moves with the velocity of the Rayleigh wave, additional resonances determined by the structure can be realized in the structure under consideration. It is revealed that Rayleigh resonance exists for long waves only. Numerical solutions are obtained that make it possible to trace the development of resonant excitations. The models of simple structures that have dispersive properties in the medium wave zone are analyzed, such as a thin plate on an elastic base; a model with an attached inertial medium. Analytical solutions have been obtained for these models. Computer simulations conducted simultaneously allow us to analyze the quantitative features of process throughout the entire time period of the load effect. The numerical and asymptotic solutions are compared.