Флуктуационно-диссипативная теорема и частотные моменты функций реакции плотной плазмы на электромагнитное поле

The fluctuation-dissipative theorem and frequency moments for quadratic functions of the reaction of a dense plasma in a constant magnetic field to an electromagnetic field are considered. The frequency moments of the corresponding correlation functions are studied. A model approach is proposed to calculate quadratic reaction functions that determine nonlinear phenomena caused by the quadratic interaction of electromagnetic waves in a dense charged medium (Coulomb systems, plasma) in a constant magnetic field. Keywords: dense plasma, nonlinear fluctuation-dissipative theorem, quadratic reaction functions, nonlinear phenomena.

Nonlinear vibrations of soil strata according to instrumental and numerical data

Исследования нелинейных явлений в грунтах, начатые в России почти 60 лет назад, явились стимулом современного развития исследований сейсмоаномальных явлений в комплексе геофизических показателей, наблюдающихся при сильных и разрушительных землетрясениях. Кроме чисто научных интересов большой интерес вызывает вопрос прогнозирования поведения грунтов и сооружений с точки зрения адекватности ожидаемому проявлению сейсмического воздействия. Адекватное изучение нелинейности, являющейся неотъемлемой характеристикой природных явлений, позволит приблизить соответствующее антисейсмические мероприятия к реальным особенностям проявлений сейсмического эффекта при сильных землетрясениях. Цельюработы являлось построение расчетной модели, описывающей явления, наблюдаемые в грунтовой среде при сильных сейсмических воздействиях и сопоставление расчетных данных с результатами инструментальных наблюдений. Методы. В работе анализируется иснтрументальная запись, полученная на слабых грунтах, на сонове вейвлет нанализа. Моделируются импульсы различной проолжитлеьности в среде с различной стпенью проявления нелинейных свойст (кртутизны нелиненйой заивисисмоти напряжение -деформация) методом конечных элементов. Результаты. В результате установлены различия в спектральном составе моделируемых импульсов. Сильное проявление нелинейных свойств характеризуется резкими изменениями фаз колебаний, в фазах высокой скорости нарастания амплитуд. В нелинейных спектрах происходит перераспределение энергии в более высокочастотную область, кратную основному пику, тем сильнее, чем сильнее нелинейность кривой наряжение-деформация. Studies of nonlinear phenomena in soils, which began in Russia almost 60 years ago, have stimulated the modern development of studies of seismically anomalous phenomena in the complex of geophysical indicators observed during strong and destructive earthquakes. In addition to scientific interests, the issue of forecasting the behavior of soils and structures from the point of view of adequacy to the expected manifestation of seismic impact is of great interest. An adequate study of nonlinearity, which is an integral characteristic of natural phenomena, will make it possible to bring the corresponding antiseismic measures closer to the real features of the manifestations of the seismic effect during strong earthquakes. Aim. The aim of the work was to build a computational model describing the phenomena observed in a soil medium under strong seismic effects and to compare the computed data with the results of instrumental observations. Methods.The paper analyzes an instrumental record obtained on soft soils using wavelet analysis. With the help of the finite element method pulses of different duration are modeled in a medium with different degrees of nonlinear properties manifestation (steepness of nonlinear stress-strain dependence). Results. As a result, differences in the spectral composition of the modeled pulses were determined. A strong manifestation of nonlinear properties is characterized by sharp changes in the phases of vibrations, in the phases of a high rate of amplitude rise. In nonlinear spectra, the energy is redistributed to a higher frequency region, which is a multiple of the main peak and the stronger the nonlinearity of the stress-strain curve is stronger.

A viscoelastic in-plane damage model for fibrous composite materials

This work presents a viscoelastic in-plane damage model for fibrous composites. The material behavior is modeled as linear viscoelastic, with brittle failure in the fiber-dominated direction, and progressive degradation of the matrix-dominated properties, when the composite is loaded perpendicularly to the fibers or in in-plane shear. An evaluation procedure has been performed by comparing computational stress-strain curves against tensile tests curves under three different displacement rates. In addition, a calibration of the viscoelastic properties, by means of the response surface methodology, is also presented. The proposed material model has shown reasonable performance up to the material reaching an experimentally-verified modulus transition zone. Besides, the viscoelastic calibration procedure has produced a good agreement with the experimental results, concerning maximum stresses. It was observed that the computational stress-strain curve has deviated from the experimental one for higher stress values, indicating that it is necessary to improve the assessment of the nonlinear phenomena, which occur within the material.

Dynamical Effects of Offset Terms on a Modified Chua’s Oscillator and Its Circuit Implementation

This paper addresses the effects of offset terms on the dynamics of a modified Chua’s oscillator. The mathematical model is derived using Kirchhoff’s laws. The model is analyzed with the help of the maximal Lyapunov exponent, bifurcation diagrams, phase portraits, and basins of attraction. The investigations show that the offset terms break the symmetry of the system, generating more complex nonlinear phenomena like coexisting asymmetric bifurcations, coexisting asymmetric attractors, asymmetric double-scroll chaotic attractors and asymmetric attraction basins. Also, a hidden attractor (period-1 limit cycle) is found when varying the initial conditions. More interestingly, this latter attractor coexists with all other self-excited ones. A microcontroller-based implementation of the circuit is carried out to verify the numerical investigations.

Chaos Control and Stabilization of a PID Controlled Buck Converter Using the Spotted Hyena Optimizer

The voltage controlled buck converter by constant-frequency pulse-width modulation in continuous conduction mode gives rise to a variety of nonlinear behaviors depending on the circuit parameters values, which complicate their analysis and control. In this paper, a description of the DC/DC buck converter and an overview of some of its chaotic dynamics is presented. A solution based on the optimized PID controller is suggested to eliminate the observed nonlinear phenomena and to enhance the dynamics of the converter. The parameters of the controller are optimized with the Spotted Hyena Optimizer (SHO) which uses the sum of the error between the reference voltage and the output voltage as well as the error between the values of the inductor current in every switch opening instant to determine the fitness of each solution. The simulations results in MATLAB proved the efficiency of the proposed solution.

Rogue and lump waves for the (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation in a liquid or lattice

Two-layer fluid models are used to depict some nonlinear phenomena in fluid mechanics, medical science and thermodynamics. In this paper, we investigate a (3[Formula: see text]1)-dimensional Yu-Toda-Sasa-Fukuyama equation for the interfacial waves in a two-layer liquid or elastic quasiplane waves in a lattice. Via the Kadomtsev-Petviashvili hierarchy reduction, we derive the rational solutions in the determinant forms and semi-rational solutions. The [Formula: see text]th-order lump waves and multi-lump waves are obtained, where [Formula: see text] is a positive integer. We observe the second-order lump waves: Two-lump waves interact with each other and separate into two new lump waves. Two-lump waves are observed: Overtaking interaction takes place between the two-lump waves; After the interaction, the two-lump waves propagate with their original velocities and amplitudes. Studying the semi-rational solutions, we show the fusion between a lump wave and a bell-type soliton and fission of a bell-type soliton. Interaction between a line rogue wave and a bell-type soliton is shown.

On Soliton Solutions of Perturbed Boussinesq and KdV-Caudery-Dodd-Gibbon Equations

Nonlinear science is a fundamental science frontier that includes research in the common properties of nonlinear phenomena. This article is devoted for the study of new extended hyperbolic function method (EHFM) to attain the exact soliton solutions of the perturbed Boussinesq equation (PBE) and KdV–Caudery–Dodd–Gibbon (KdV-CDG) equation. We can claim that these solutions are new and are not previously presented in the literature. In addition, 2d and 3d graphics are drawn to exhibit the physical behavior of obtained new exact solutions.

Metrics for Intercomparison of Remapping Algorithms (MIRA) applied to Earth System Models

Strongly coupled nonlinear phenomena such as those described by Earth System Models (ESM) are composed of multiple component models with independent mesh topologies and scalable numerical solvers. A common operation in ESM is to remap or interpolate results from one component's computational mesh to another, e.g., from the atmosphere to the ocean, during the temporal integration of the coupled system. Several remapping schemes are currently in use or available for ESM. However, a unified approach to compare the properties of these different schemes has not been attempted previously. We present a rigorous methodology for the evaluation and intercomparison of remapping methods through an independently implemented suite of metrics that measure the ability of a method to adhere to constraints such as grid independence, monotonicity, global conservation, and local extrema or feature preservation. A comprehensive set of numerical evaluations are conducted based on a progression of scalar fields from idealized and smooth to more general climate data with strong discontinuities and strict bounds. We examine four remapping algorithms with distinct design approaches, namely ESMF Regrid, TempestRemap, Generalized Moving-Least-Squares (GMLS) with post-processing filters, and Weighted-Least-Squares Essentially Non-oscillatory Remap (WLS-ENOR) method. By repeated iterative application of the high-order remapping methods to the test fields, we verify the accuracy of each scheme in terms of their observed convergence order for smooth data and determine the bounded error propagation using the challenging, realistic field data on both uniform and regionally refined mesh cases. In addition to retaining high-order accuracy under idealized conditions, the methods also demonstrate robust remapping performance when dealing with non-smooth data. There is a failure to maintain monotonicity in the traditional L2-minimization approaches used in ESMF and TempestRemap, in contrast to stable recovery through nonlinear filters used in both meshless (GMLS) and hybrid mesh-based (WLS-ENOR) schemes. Local feature preservation analysis indicates that high-order methods perform better than low-order dissipative schemes for all test cases. The behavior of these remappers remains consistent when applied on regionally refined meshes, indicating mesh invariant implementations. The MIRA intercomparison protocol proposed in this paper and the detailed comparison of the four algorithms demonstrate that the new schemes, namely GMLS and WLS-ENOR, are competitive compared to standard conservative minimization methods requiring computation of mesh intersections. The work presented in this paper provides a foundation that can be extended to include complex field definitions, realistic mesh topologies, and spectral element discretizations thereby allowing for a more complete analysis of production-ready remapping packages.

Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows

Axisymmetric viscoelastic pipe flow of Oldroyd-B fluids has been recently found to be linearly unstable by Garg et al. (Phys. Rev. Lett., vol. 121, 2018, 024502). From a nonlinear point of view, this means that the flow can transition to turbulence supercritically, in contrast to the subcritical Newtonian pipe flows. Experimental evidence of subcritical and supercritical bifurcations of viscoelastic pipe flows have been reported, but these nonlinear phenomena have not been examined theoretically. In this work, we study the weakly nonlinear stability of this flow by performing a multiple-scale expansion of the disturbance around linear critical conditions. The perturbed parameter is the Reynolds number with the others being unperturbed. A third-order Ginzburg–Landau equation is derived with its coefficient indicating the bifurcation type of the flow. After exploring a large parameter space, we found that polymer concentration plays an important role: at high polymer concentrations (or small solvent-to-solution viscosity ratio $\beta \lessapprox 0.785$ ), the nonlinearity stabilizes the flow, indicating that the flow will bifurcate supercritically, while at low polymer concentrations ( $\beta \gtrapprox 0.785$ ), the flow bifurcation is subcritical. The results agree qualitatively with experimental observations where critical $\beta \approx 0.855$ . The pipe flow of upper convected Maxwell fluids can be linearly unstable and its bifurcation type is also supercritical. At a fixed value of $\beta$ , the Landau coefficient scales with the inverse of the Weissenberg number ( $Wi$ ) when $Wi$ is sufficiently large. The present analysis provides a theoretical understanding of the recent studies on the supercritical and subcritical routes to the elasto-inertial turbulence in viscoelastic pipe flows.