Modulation Coefficient Research Articles

On Cohomology of Simple Modules for Modular Classical Lie Algebras

In this article, we obtain some cohomology of classical Lie algebras over an algebraically closed field of characteristic p>h, where h is a Coxeter number, with coefficients in simple modules. We assume that these classical Lie algebras are Lie algebras of semisimple and simply connected algebraic groups. To describe the cohomology of simple modules, we will use the properties of the connections between ordinary and restricted cohomology of restricted Lie algebras.

ОЦІНЮВАННЯ ВИМІРЮВАЛЬНИХ СИГНАЛІВ НА ОСНОВІ ТРИКУТНОЇ ЧАС-ІМПУЛЬСНОЇ МОДУЛЯЦІЇ ДЛЯ КОНТРОЛЮ ТЕХНІЧНОГО СТАНУ ЗАСОБІВ ЗВ’ЯЗКУ ТА ПЕРЕДАЧІ ДАНИХ

A method is proposed for triangular modulation of data on the temporal parameters of the carrier, followed by narrow-band filtering of measuring signals for monitoring the technical condition of communication and transmission facilities, which, compared with the binary modulation method, provides a decrease in the harmonic coefficient of the envelope at approximately the same, fairly small error in setting the amplitude modulation coefficient of the amplitude-modulated signal. The analysis of the obtained relations for the amplitude modulation coefficient of measuring signals with a triangular modulation law showed the following. Unipolar and bipolar carrier pulse sequences lead to the same values of the amplitude modulation coefficient of the generated amplitude-modulated signal, but with a bipolar carrier pulse sequence, the amplitude of the output signal doubles with the same amplitude of carrier pulses (without pulses). With phase modulation, the value of the amplitude modulation coefficient is much less than with width modulation. At the same time, two-way width modulation provides twice the value of the amplitude modulation coefficient than the modulation of the front or cutoff of the carrier pulses. This statement, however, is valid only for small values of the modulation coefficients proportional to the modulation coefficients of the temporal parameters of the carrier pulses with the corresponding numerical coefficients depending on the type of modulation. If the amplitude modulation coefficients are not small, then they are determined by more complex dependencies, but also more accurate, allowing to reduce the methodological error. In this case, for the required values of the amplitude modulation coefficient, the time modulation parameters can be calculated in advance or using the built-in microprocessor and stored in the memory of the measuring device (calibrator).

Математическая модель электромагнитного вибратора с источником питания на основе инвертора

Drives with electromagnetic vibration exciters (EMVE) occupy an important place among the vibration machines used in various industries owing to their having a simple design and ensuring high vibration intensity. Rational designing of such devices needs a theoretical justification. An electromagnetic vibrator was theoretically studied, as a result of which regularities interrelating its electrical, magnetic and mechanical subsystems have been established, and the dependence of coil inductance on the gap x that takes into account the inductance modulation coefficient has been determined. Correlations describing periodic solutions in the form of series in powers of a small parameter µ have been derived. Equations using which the stability of periodic solutions can be determined in a first approximation have been obtained. By using the small parameter method, relations for the current in the coil have been derived, and the power consumed by the electromagnet has been determined.

Two-stage digital differential atomic spin precession detection method

We propose and experimentally demonstrate a two-stage digital differential method for atomic spin precession detection. The first differential operation is carried out with a polarimeter module and subsequent digital differential. The second differential operation is achieved by orthogonally modulating the polarization direction of a linearly polarized probe light with a LiNbO3 electro-optic modulation module and by digitally demodulating the difference in the outputs corresponding to the positive and negative half periods of the modulation square-waves. This method is insensitive to the error of modulator and double sensitivity coefficient was obtained. The built detection system with the digital circuit was applied to a spin-exchange relaxation-free magnetometer, and the sensitivity coefficient, sensitivity, and bias instability were tested and compared with two other typical detection methods. The highest sensitivity and minimum bias instability and noise were achieved with the proposed method.

Evaluation of changes in laser Doppler flowmetry indices in patients with a combined subtype of rosacea under the influence of a course of complex phototherapy

BACKGROUND: The development of new methods for the treatment of rosacea, as well as a combination of various methods of physiotherapy, is of scientific and practical interest. In this work, the assessment of changes in microcirculation indices under complex phototherapy has been carried out.
 AIMS: Тo assess changes in microcirculation indices in patients with a combination of rosacea subtypes according to laser Doppler flowmetry under a course of complex phototherapy.
 MATERIAL AND METHODS: In 20172020 a randomized controlled study of 130 patients with a combination of rosacea subtypes. All patients were divided into 4 groups. In each separate group, laser therapy and 1% metronidazole cream were used (group I); phototherapy and 1% metronidazole cream (group II); complex photolaser therapy and 1% metronidazole cream (group III); in the comparison group (group IV), patients show only 1% metronidazole cream. The treatment, the duration of which was 3 months, included 6 sessions with an interval of 2 weeks. The effectiveness of therapy was assessed according to the data of laser Doppler flowmetry, reflecting changes in the hemodynamics of the microvasculature in the affected skin areas.
 RESULTS: The developed complex method, including exposure to intense pulsed light (intense pulsed light, IPL) 5201100 nm in combination with submillisecond neodymium laser radiation 1064 nm (submilisecond Nd: YAG laser 1064 nm) and daily application of 1% metronidazole cream showed the most pronounced improvement in the state of microcirculation according to laser Doppler flowmetry in comparison with the rest groups. Against the background of the course of complex phototherapy for all patients with the combined subtype of rosacea, statistically significant changes were in the volume of blood flow, modulation coefficients, coefficient of variation. On the contrary, no statistically significant changes were found in the ranges corresponding to active regulatory factors endothelial, neurogenic, myogenic, and passive respiratory and cardiac, as well as in the T index.
 CONCLUSION: After the course of complex phototherapy in the group of patients with a combination of rosacea subtypes, there was a decrease in the severity of clinical manifestations of diseases, as well as an improvement in the main indicators of microcirculation according to laser Doppler flowmetry.

Моделирование кристаллографической текстуры феррит / мартенситной стали при прокатке: уровень и анизотропия прочностных свойств

This paper presents the results of studies of the level and anisotropy of strength properties in ferritic / martensitic steel during warm rolling based on the data on crystallographic texture. The features of texture formation processes in the initial and UFG samples subjected to flat rolling are analyzed by the method of texture analysis and computer modeling. In particular, the analysis of the orientation distribution function (ODF) made it possible to establish the change in the main preferential orientations (Brass, Goss, Copper, Cube, TC, Y, Z and Rotated Cube) depending on the degree of reduction. It is shown that in flat rolling, a stable rolling texture is formed only after 70 % reduction, at which H {001}<011>, Goss {001}<110>, Cube {100}<001> and TC {255}<511> orientations become the main ones. At high degrees of flat rolling, the sharpness of the above textural maxima increases, which is accompanied by the activation of a smaller number of slip systems, and the misorientations between adjacent grains become predominantly high-angle ones. Within the framework of modeling of crystallographic textures, deformation mechanisms were established, two-dimensional projections of yield contours, Young's module and Lankford coefficients (r-value) were constructed. In particular, the results of computer simulation of the yield contours of steel after tempering the coarse-crystalline and UFG states showed that at low degrees of flat rolling reduction, an increased level of anisotropy of strength properties is associated with the residual crystallographic texture in the workpiece, and an increase in the degree of flat rolling leads to alignment of the strength anisotropy in sheets. It was found that the quantitative ratio of the main textural components of the type H {001}<011>, Goss {001}<110>, Cube {100}<001> and TC {255}<511> during rolling determine the anisotropy of the strength properties of steel.

Role of Second Harmonic in the Optimization of Microwave Conversion Efficiency From an Intense Relativistic Electron Beam

In this article, the effect of second harmonic (SH) on the microwave conversion efficiency in a klystron-like relativistic backward wave oscillator (RBWO) is investigated by the nonlinear theory, particle-in-cell (PIC) simulations, and experiments. The nonlinear theory of beam-wave interaction is developed with both the fundamental frequency and SH taken into account. The calculation results show that the optimized conversion efficiency is increased from 50% to 73% as the SH is included. The PIC simulations reveal that with the introduction of a dual-premodulation (DPM) cavity to increase the SH current and then the fundamental current modulation coefficient in a klystron-like RBWO, the conversion efficiency can be enhanced from 59% to 72%. In the klystron-like RBWO experiments, a significant efficiency increase from 58% for the device without the DPM cavity to 66% with the DPM cavity has been realized. As the electron beam power is 4 GW, the out powers of the fundamental frequency and SH are measured to be 2.6 GW and 100 MW, respectively. This provides helpful guidance to further increase the microwave conversion efficiency in high-power microwave sources driven by intense relativistic electron beams.

A Retroreflection Reduction Technique Based on the Wavefront Coded Imaging System

A novel anti-cat-eye effect imaging technique based on wavefront coding is proposed as a solution to the problem of previous anti-cat-eye effect imaging techniques where imaging quality was sacrificed to reduce the retroreflection from the photoelectric imaging equipment. With the application of the Fresnel–Kirchhoff diffraction theory, and the definition of generalized pupil function combining both phase modulation and defocus factors, the cat-eye echo formation of the wavefront coded imaging system is theoretically modeled. Based on the physical model, the diffracted spot profile distribution and the light intensity distribution on the observation plane are further simulated with the changes in the defocus parameter and the phase modulation coefficient. A verification test on the cat-eye laser echo power of the wavefront coded imaging system and that of the conventional imaging system at a 20 m distance are conducted, respectively. Simulations and experiment results show that compared with conventional imaging systems, the wavefront coding imaging system can reduce the retroreflection echo by two orders of magnitude while maintaining better imaging quality through defocusing.

Research on Maximum Power Tracking Control Method of 10MW MVSPMSG Based on Neutral Point Potential Balance

In order to meet safety and stability grid-connected requirementsof high-power offshore wind turbines, the 10 MW wind power generation system composed of medium voltage six phase permanent magnet synchronous generator (MVSPMSG) and distributed neutral point clamped (NPC) converter is adopted. On the basis, a maximum power point tracking control (MPPT) method of 10 MW MVSPMSG based on neutral point potential balance is studied in the paper.Firstly, the optimal reference torque of MVSPMSG is calculated according to speed feedback, and the double d-q current control loop of stator is designed based on the doubly fed decoupling. The MPPT of MVSPMSG is realized by the closed-loop combination of torque loop and double d-q current loop. Secondly, in order to suppress the fluctuation of DC neutral point potential, a midpoint potential balance coordinated control method based on modulation coefficients and vector group selection is proposed. The mid-point potential fluctuations is suppressed by adjusting the magnitude of the modulation coefficient in the normal range. The vector group selection method is collaboratively added to the midpoint potential balance control based on small vectors when the modulation coefficient exceeds the limit. Finally, the effectiveness of the proposed MPPT control strategy and midpoint potential balance strategy are verified, which provides a theoretical reference for the control of high-power permanent magnet wind turbine.

Experimental characterization of a novel configuration of thermoelectric refrigerator with integrated finned heat pipes

• A thermoelectric refrigerator is constructed and characterized in this work. • A performance analysis is performed including energy consumption, cooling time, temperatures and COP. • A mathematical model is developed to predict transient temperatures and cooling limit time. • Empirical equation for transient temperature prediction is settled. Thermoelectric refrigerating systems (TER) are environment-friendly technologies. They have several advantages such as low maintenance costs, are less cumbersome and long lifetime. However, these systems have low coefficient of performance and are limited in achieving low temperature levels. This study investigates a new configuration of TE refrigerator employing a novel arrangement of heat sinks with integrated flat and finned heat pipes. A mathematical model is firstly developed to predict transient temperatures and cooling limit time. An experimental characterization is then performed and it includes optimization of energy consumption, cooling time, temperature levels and TE refrigerator related COP. TE module coefficient of performance (COP TEC ) is evaluated at 0.74 while the hot and cold sides temperature difference ΔT is equal to 32.7 °C. The coefficient of performance of the TE refrigerator (COP TER ) is evaluated at 0.297 with an inside/outside temperature difference ΔT i/ o = 13 °C and an energy consumption rate of 42.7 Wh. Multiple experiment's results lead to a specific characterized chart adapted for this TE refrigerator. An empirical equation for transient temperature prediction is established and presents a novel contribution in this work.

Critical dynamics of an asymmetrically bidirectionally pumped optical microresonator

An optical ring resonator with third-order, or Kerr, nonlinearity will exhibit symmetry breaking between the two counterpropagating circulating powers when pumped with sufficient power in both the clockwise and counterclockwise directions. This is due to the effects of self- and cross-phase modulation on the resonance frequencies in the two directions. The critical point of this symmetry breaking exhibits universal behaviors including divergent responsivity to external perturbations, critical slowing down, and scaling invariance. Here we derive a model for the critical dynamics of this system, first for a symmetrically pumped resonator and then for the general case of asymmetric pumping conditions and self- and cross-phase modulation coefficients. This theory not only provides a detailed understanding of the dynamical response of critical-point-enhanced optical gyroscopes and near-field sensors, but is also applicable to nonlinear critical points in a wide range of systems.

Investigation of modulational instability in a coupled Kundu-Ekchaus equation in the presence of modified form of saturable nonlinearity

We study the impact of modified saturable nonlinearity on modulational instability (MI) criteria in a coupled birefringent fiber using pulse propagation technique. Based on the standard linear stability method, we enquire nonlinear self/cross phase modulation on MI in a coupled Kundu–Eckhaus (KE) equation in the absence of nonlinear four-wave mixing expression. Using the modified KE equation, we study the role of modified form of saturable nonlinearity on MI in a birefringent KE model with the adjustable self/cross phase modulation coefficients. In the case of KE without nonlinear saturation and four-wave mixing, we observed that the cross phase modulation (XPM) has less induced the instability region on MI in coupled birefringent fiber system as compared to self phase modulation (SPM) case as shown in Ref. Parasuraman (2021). But, in saturable KE model showed different characteristics of MI and growth rate of profile in a coupled birefringent fiber system in the presence of particular emphasis values of the nonlinear terms as depicted in Ref. Mohanraj (2021). This study shows the novel results of MI criterion in a coupled KE birefringent media with the help of modified type of saturable nonlinearity and both SPM/XPM values. From the above-detailed discussion, the modified form of saturable nonlinearity plays an important role for MI generation in a KE birefringent media. However, the modified nonlinear saturation KE model more helps to generate ultrashort pulses and soliton or solitary wave in a coupled nonlinear birefringent fiber with the help of 3D images.

Cohomology of simple modules for sl3(k) in characteristic 3

In this paper we calculate cohomology of a classical Lie algebra of type A2 over an algebraically field k of characteristic p = 3 with coefficients in simple modules. To describe their structure we will consider them as modules over an algebraic group SL3(k). In the case of characteristic p = 3, there are only two peculiar simple modules: a simple that module isomorphic to the quotient module of the adjoint module by the center, and a one-dimensional trivial module. The results on the cohomology of simple nontrivial module are used for calculating the cohomology of the adjoint module. We also calculate cohomology of the simple quotient algebra Lie of A2 by the center.

Holographic near-eye display based on complex amplitude modulation with band-limited zone plates.

A holographic near-eye display (NED) system based on complex amplitude modulation (CAM) with band-limited zone plates is proposed. The whole system mainly consists of a phase-only spatial light modulator (SLM), an Abbe-Porter filter system, an eyepiece, and an image combiner. The point source method based on band limited zone plates is used to accurately control the bandwidth of the target complex amplitude. The effects of intensity modulation coefficient γ in the frequency-filtering method on the intensity and the quality of reconstructed images are analyzed, which provide a judgment basis for selecting the appropriate value of γ. We also derive the expressions of the field of view (FOV) and exit pupil of the NED system. Since the holographic image is magnified in two steps in this system, the large FOV can be obtained. The optical experimental results show that the proposed system can provide a dynamic holographic three-dimensional (3D) augmented reality (AR) display with a 23.5° horizontal FOV.

Modulation instability analysis of a nonautonomous $$(3+1)$$-dimensional coupled nonlinear Schrödinger equation

We have investigated the modulation instability (MI) analysis of a nonautonomous \((3+1)\)-dimensional coupled nonlinear Schrödinger (NLS) equation with time-dependent dispersion and phase modulation coefficients. By employing standard linear stability analysis, we have obtained an explicit expression for the MI gain as a function of dispersion, phase modulation, perturbation wave numbers and an initial incidence power. A nonautonomous coupled NLS equation is found to be modulationally unstable for the same sign of dispersion and phase modulation coefficients. This equation is modulationally stable for zero dispersion and or phase modulation. For nonzero dispersion, the equation is found to be modulationally stable/unstable on distinct bandwidth of wave numbers. The trigonometric, exponential, algebraic functions of time and constant have been chosen as test functions for dispersion and phase modulation to study the effect on the MI analysis. The effect of focusing and defocusing medium on the MI analysis has also been investigated. The MI bandwidth in the focusing medium is found to be larger than defocusing medium. It is found that the MI of the equation can be managed by proper choice of the dispersion and phase modulation parameters.

Light delivery device modelling for homogenous irradiation distribution in photodynamic therapy of non-spherical hollow organs

SignificancePhotodynamic therapy (PDT) is a useful treatment for select cancers. Homogeneous illumination is a key factor in the successful application of PDT treatment of tumours in hollow organs. Over illumination may damage normal tissue while under illumination may not ablate the target. BackgroundThere have been many approaches to provide homogeneous irradiation for PDT treatment of hollow organs, including light-scattering medium and isotropic emitter to diffuse light, a balloon filled with solution to expand the organ wall, and shaped fibres. In most studies, the organ is assumed to be spherical. However, many hollow organs treated by PDT are non-spherical, and the uniformity of azimuthal irradiation remains an unsolved problem for cylindrical light sources. ObjectiveFind a design principle for homogeneous irradiation in a non-spherical cavity for PDT treatment. MethodA PDT light delivery device is modeled by a series of sub light sources placed along the longitudinal axis of an ellipsoid. In order to achieve a homogeneous azimuthal irradiation distribution on the elliptical arc, a cost function is solved by adding modulation coefficient to the emission profile. The coefficient of variation of uniformity (Ucov) describes the statistical dispersion of the variation in irradiation over the ellipsoid to the average value. Ucov is used to evaluate the homogeneity of the azimuthal irradiation distribution. ResultBy minimizing the cost function, we found that the truncated Gaussian function can be chosen as the emission profile to generate homogeneous irradiation profile within an ellipsoid cavity model. The emission profile can be tailored to generate Ucov of 96.7 %. Further discussion shows that the light distribution could be generated practically by a side-emitting optical fibre, a LED array, or moving an isotropic emitter successively. The impact of emission angle of light sub-source is analysed and the irradiation profile from discrete longitudinal emissions is calculated. ConclusionTheory analysis and simulation indicate that a cylindrical emitter with a non-uniform longitudinal emission profile (truncated Gaussian functions) results in an approximate homogeneous irradiance profile within an ellipsoidal cavity.

Diffraction of a Gaussian Beam with Limited cross Section by a Volume Phase Grating under Waveguide Mode Resonance.

In this work, the diffraction of a Gaussian beam on a volume phase grating was researched theoretically and numerically. The proposed method is based on rigorous coupled-wave analysis (RCWA) and Fourier transform. The Gaussian beam is decomposed into plane waves using the Fourier transform. The number of plane waves is determined using the sampling theorem. The complex reflected and transmitted amplitudes are calculated for each RCWA plane wave. The distribution of the fields along the grating for the reflected and transmitted waves is determined using inverse Fourier transform. The powers of the reflected and transmitted waves are determined based on these distributions. Our method shows that the energy conservation law is satisfied for the phase grating. That is, the power of the incident Gaussian beam is equal to the sum of the powers of the reflected and transmitted beams. It is demonstration of our approach correctness. The numerous studies have shown that the spatial shapes of the reflected and transmitted beams differ from the Gaussian beam under resonance. In additional, the waveguide mode appears also in the grating. The spatial forms of the reflected and transmitted beams are Gaussian in the absence of resonance. It was found that the width of the resonance curves is wider for the Gaussian beam than for the plane wave. However, the spectral and angular sensitivities are the same as for the plane wave. The resonant wavelengths are slightly different for the plane wave and the Gaussian beam. Numerical calculations for four refractive index modulation coefficients of the grating medium were carried out by the proposed method. The widths of the resonance curves decrease with the increasing in the refractive index modulation. Moreover, the reflection coefficient also increases.

Dispersion and phase managed optical soliton solutions of a nonautonomous (3+1)-dimensional coupled nonlinear Schrödinger equation

The complex amplitude ansatz method and He's semi-inverse method have been used to investigate the optical soliton solutions of a nonautonomous (3+1)-dimensional coupled non-linear Schrödinger (NLS) equation. The effect of the time-dependent dispersion (TD) and the phase modulation (PM) coefficients in the equation has been analyzed. The intensity profiles of the soliton solutions have been obtained by assigning different test functions to the coefficients and distinct values to the parameters, which help to understand the physical characteristics of the solutions. The intensities of two circularly polarized waves have bright, dark, parabolic, dark-bright, parabolic-bright, bright-singular, homoclinic and breather solitons that depend significantly on the dispersion and phase modulation. Some of the obtained soliton solutions are novel and did not exist in the earlier studies. It is found that the optical soliton velocity and frequency are dependent on wave numbers and dispersion of the medium but are free from the phase modulation. Moreover, the amplitude of the solitons are managed by dispersion and phase modulation both but the soliton width remains constant. The results in this study may be used for experimental investigation of transmission of dispersion and phase managed optical soliton in non-linear optical fiber.

A near-wall predictive model for passive scalars using minimal flow unit

In the present study, direct numerical simulations (DNSs) are performed to the passive scalar transport in minimal flow units (MFUs) at Reτ=1000, 2000, and 4000 and in a full-sized channel at Reτ=1000 for comparison. The molecular Prandtl number ranges from 0.2 to 2.0. At each Prandtl number, the scalar intensities in MFUs at different Reynolds numbers agree well with each other, and with those at MFU-contained scales in the full-sized channel. This suggests that scalar transport in MFUs is Reynolds number independent and is able to represent that at small scales in the full-sized channel. A near-wall predictive model for passive scalars based on MFU data is proposed in the framework of superposition and modulation of the outer large-scale motions. The modulation coefficients at different Prandtl numbers are collapsed together under the presently proposed transforming. Both the scalar intensities and the joint probability density functions of the predicted results agree well with those of the DNS results. Furthermore, a predictive model for wall scalar-flux based on MFU data and the quasi-steady hypothesis is put forward and validated against the DNS results.

Interactions between scales in wall turbulence: phase relationships, amplitude modulation and the importance of critical layers

Abstract