Intense Energy Exchange Research Articles

Numerical study of the effects of vegetation stem thickness on the flow characteristics of curved channels

ABSTRACT A curved channel is a common flow form in nature, often hosting aquatic vegetation along rivers. The stem thickness of this vegetation affects its resistance to flow and subsequently influences flow characteristics. To explore the impact of stem thickness on river flow in curved channels, we developed a Reynolds stress model based on real river flow conditions and vegetation data. The flow characteristics were analyzed in terms of flow velocity, Reynolds stress and turbulence intensity by varying the stem thickness of the vegetation in the vegetated area. The results of the study reveal that: (1) Water velocity in the vegetated area is significantly reduced compared to the non-vegetated area, with a greater reduction observed for thicker stems. Increasing the vegetation diameter by 3 mm resulted in a velocity decrease of 2.31–26.55%. (2) Thicker vegetation stems lead to more intense energy exchange in water flow. A 3 mm increase in vegetation diameter increased Reynolds stress by 91.81–139.70%. (3) Turbulent kinetic energy in the vegetated area is significantly higher than in the non-vegetated area, with greater turbulence intensity observed for thicker vegetation stems. Increasing the vegetation diameter by 3 mm resulted in a turbulent kinetic energy increase of 115.19–218.55%.

Mechanism of multiphase coupling transport evolution of free sink vortex

In the evolution of confluence sink vortex with a free surface, there exists some physical processes , such as multiphase coupling, mass transfer, and intensive energy exchange. Here, the transport mechanism of multiphase coupling is a complex dynamic problem with highly nonlinear characteristics. The mechanical modeling and numerical solution of multiphase viscous coupled transport are facing a significant challenge. To address the above problem, a method of modeling and solving multiphase coupling transport of the free sink vortex is proposed. Based on the coupled level set and volume-of-fluid (CLSVOF) method, a multiphase coupling transport model of the free sink vortex is set up with a continuous surface tension model and a realizable (<i>k</i>-<i>ε</i>) turbulence model. By using an effective volumetric correction scheme, the high-speed rotating flow is calculated, and the mass conservation of flow field and the velocity field without divergence are ensured. Then, an interphase coupling solution approach accurately traces the multiphase fluid distribution and multiphase interface. The multiphase coupling interface and cross-scale vortex cluster transport laws are obtained according to the multi-characteristic physical variables. The interaction mechanism between the multiphase coupling transport process and the pressure pulsation characteristics is revealed. The results show that the multiphase coupling transport is the critical state of the fluid medium transition. The vortex microclusters are subjected to different spatiotemporal disturbance modes and form the layered threaded waveforms at the interface. With the increase of the nozzle sizes, the multiphase coupling process is strengthened, and the coupling energy shock causes nonlinear pressure pulsation. This study can offer valuable references to the researches of the vortex transport mechanism, cross-scale solution of vortex cluster, and flow pattern tracking.

The onset timing of plate tectonics: Controversies,progress, and prospects

<p indent="0mm">Plate tectonics is widely accepted as a fundamental theory in Earth science and is hailed as an important scientific discovery of the 20th century. However, the major challenge of this theory since its foundation for half a century now is the debate over when Earth first developed plate tectonics—4 billion years ago vs. later than 1 billion years ago—an uncertainty which spans nearly three-quarters of Earth history. At present, most researchers view the “earliest evidence of subduction” as the timing of onset of plate tectonics. However, it is debated which phenomena could be viewed as the “oldest evidence”. In this study, we argued that local subduction itself cannot be equated with plate tectonics, but rather, a global subduction network is the essence of plate tectonics. We first conducted comprehensive geological observations along the northern margin of the North China Craton. We recognized key information supporting significant horizontal movement and subduction of an oceanic plate at a convergent tectonic boundary nearly 2 billion years ago, and reconstructed the accurate position of North China in the Earth’s first supercontinent based on its iconic subduction record. According to the prediction of the new proposed geological model, there should be a relic of a subduction interface preserved beneath the North China Craton at the depth of the crust-mantle boundary. We then carried out a high-resolution seismic survey across the northern North China. The seismic profile indeed revealed the geophysical interface preserved by the ancient continental convergence. These features identified are identical to the surface and deep structure of the modern Himalayan orogenic belt, indicating that North China underwent a similar geological process at 2 billion years ago. Because we have assessed the geology and geophysics of the ancient Tethyan Realm, and concluded that subduction has been the main driver of plate motion over the last 500 million years, accordingly, the plate tectonics should work as a subduction network that was driven by subducting plates. Following this knowledge, we finally put the key findings from China in a global context, and proposed that Earth gave birth to its global plate subduction network 2 billion years ago, leading to the formation of Earth’s earliest supercontinent due to the pulling forces of subduction. Therefore, the supercontinent is the result of the global plate subduction network, which can be used as the signpost to identify the onset of plate tectonics. Only after the onset of the global tectonic network did the Earth start the cyclic assembly and breakup of supercontinents. Such active plate margins led to intensive mass and energy exchange between Earth’s surface and interior, which was an important driving force for maintaining and even enhancing planetary habitability. The onset of plate tectonics signifies the contrasting evolutionary paths among Earth and other planets. Future research involves quantitative analysis on why the plates can be subducted continuously. Innovative systems of data- and model-driven scientific research can help us better understand the Earth’s past and consequently predict its future.

Efficiency of using the formula of feed additives based on local raw materials for heifers in the conditions of Yakutia

The article presents the results of experience in using the formulation of feed additives based on local raw materials for heifers. The positive effect of using the formulation of feed additives from local raw materials in the diets of heifers on the digestibility and absorption of nutrients has been proven. Full-fledged feeding of Simmental heifers, using the recipe for feed additives No. 1, ensured normal development and made it possible to increase the digestibility of feed nutrients. The digestibility of dry matter ranged from 67.01 to 72.08%, crude protein - from 50.28 to 60.61%, fiber - from 60.22 to 64.22%. Good absorption of calcium and phosphorus was noted in all groups. The features of feed consumption, feed digestibility and energy use of Simmental heifers have been studied. Thus, the experimental animals of the control group consumed gross energy less by 3.0 and 3.5 MJ, and also digested less energy by 0.3 and 2.6 MJ with the same digestibility. In this regard, with comparatively equal energy losses, the yield of exchangeable energy in heifers of the I-experimental group was higher by 2.8 and 3.3 MJ in comparison with their peers. This indicates a more intensive energy exchange in heifers of the I-experimental group, which contributed to the absorption of nutrients and the containment of microbiological imbalances.

Influence of kinetic effects on long wavelength gradient-drift instability in high-frequency range in Hall thruster

A typical for Hall thruster discharges strong inhomogeneity of plasma parameters is a source of various types of instabilities. Some types of such instabilities (long high-frequency waves, in particular) are assumed to contribute to anomalous electron conductivity, which is essential to understand for the development of a reliable modelling tool for Hall thrusters. In this paper, the results of an analytical study of the influence of kinetic effects on dispersion properties of high-frequency perturbations in Hall thruster plasmas are presented, including the effect of the gradient magnetic electron drift on the long wavelength high-frequency instability. It was shown that when the long waves with phase velocity on the order of the unperturbed electron drift motion occur, the electron guiding center deviates significantly from the electric field equipotential line. The observed phenomenon leads to a self-sustained cycle of an intensive energy exchange between the waves and the electrons and a long-wavelength high-frequency instability inciting each other.

Flow structures and kinetic-potential exchange in forced rotating stratified turbulence

Flow structures and the kinetic-potential energy exchange in rotating stratified turbulence are studied by simulations. Differences of cyclonic and anticyclonic vortices are shown. The intense kinetic-potential energy exchange is found to be associated with the cyclonic structures.

Nonlinear waves and instabilities leading to secondary reconnection in reconnection outflows

Reconnection outflows have been under intense recent scrutiny, from in situ observations and from simulations. These regions are host to a variety of instabilities and intense energy exchanges, often even superior to the main reconnection site. We report here a number of results drawn from an investigation of simulations. First, the outflows are observed to become unstable to drift instabilities. Second, these instabilities lead to the formation of secondary reconnection sites. Third, the secondary processes are responsible for large energy exchanges and particle energization. Finally, the particle distribution function are modified to become non-Maxwellian and include multiple interpenetrating populations.

Nonconventional synchronization and energy localization in weakly coupled autogenerators.

The present work follows our previous study dealing with a new type of synchronization in a system of two weakly coupled generalized van der Pol-Duffing autogenerators. The essence of the effect revealed is that the synchronized oscillations are not stationary but accompanied by the most intensive energy exchange between the oscillators. The phase shift between the generators remains constant most of the time, except for vanishingly small transitional intervals. The current analysis deals with a generalized model in order to clarify the frequency detuning effect. We found that varying the frequency detuning, nonlinearity, and dissipation parameters can lead to structural changes in phase diagrams of the energy exchange dynamics, with important transitions from the intensive energy exchange to its localization on one of the two oscillators. The main conclusion is that stationary and nonstationary synchronizations associate with nonlinear normal and local modes, respectively. The analysis uses phase plane diagrams, including the concept of limiting phase trajectories, whose role in nonstationary synchronization appears to be similar to the role of nonlinear normal modes in conventional stationary states.

Nonlinear dynamics of hidden modes in a system with internal symmetry

We consider a discrete dynamical system with internal degrees of freedom (DOF). Due to the symmetry between the internal DOFs, certain internal modes cannot be excited by external forcing (in a case of linear interactions) and thus are considered “hidden”. If such a system is weakly asymmetric, the internal modes remain approximately “hidden” from the external excitation, given that small damping is taken into account. However, already in the case of weak cubic nonlinearity, these hidden modes can be excited, even as the exact symmetry is preserved. This excitation occurs through parametric resonance. Floquet analysis reveals instability patterns for the explored modes. To perform this analysis with the required accuracy, we suggest a special method for obtaining the Fourier series of the unperturbed solution for the nonlinear normal mode. This method does not require explicit integration of the arising quadratures. Instead, it employs expansion of the solution at the stage of the implicit quadrature in terms of Chebyshev polynomials. The emerging implicit equations are solved by using a fixed-point iteration scheme. Poincaré sections help to clarify the correspondence between the loss of stability of the modes and the global structure of the dynamical flow. In particular, the conditions for intensive energy exchange in the system are characterized.

Nonlinear optical vibrations of single-walled carbon nanotubes. 1. Energy exchange and localization of low-frequency oscillations

We present the results of analytical study and molecular dynamics simulation of low energy nonlinear non-stationary dynamics of single-walled carbon nanotubes (CNTs). New phenomena of intense energy exchange between different parts of CNT and weak energy localization in the excited part of CNT are analytically predicted in the framework of the continuum shell theory. Their origin is clarified by means of the concept of Limiting Phase Trajectory, and the analytical results are confirmed by the molecular dynamics simulation of simply supported CNTs.

Limiting Phase Trajectories as an Alternative to Nonlinear Normal Modes

We discuss a recently developed concept of limiting phase trajectories (LPTs) allowing a unified description of resonance, highly non-stationary processes for a wide range of classical and quantum dynamical systems with constant and varying parameters. This concept provides a far going extension and adequate mathematical description of the well-known linear beating phenomenon to a diverse variety of nonlinear systems ranging from classical multi-particle models to nonlinear quantum tunneling. While stationary (and non-stationary, but non-resonant) oscllations can be described in the framework of non-linear normal modes (NNMs) concept, it is not so in the considered case of resonant non-stationary processes. In the latter case which is characterized by intense energy exchange between different parts of a system, an additiional slow time scale appears. The energy exchange proceeds in this time scale and can be identified as strong modulation of the fast oscillations. The aforementioned resonant non-staionary prcesses include, e.g., targeted energy transfer, non-stationary vibrations of carbon nanotubes, quantum tunneling, auto-resonance and non-conventional synchronization. Besides the non-linear beating, the LPT concept allows one to find the conditions of transition from intense energy exchange to strongly localized (e.g. breather-like) excitations. A special mathematical technique based on the non- smooth temporal transformations leads to the clear and simple description of strongly modulated regimes. The role of LPTs in the theory of resonance non-stationary processes turns out to be similar to that of NNMs in stationary case.As an example we present results of analytical and numerical study of planar dynamics of a string with uniformly distributed discrete masses without a preliminary stretching. Each mass is also affected by grounding support with cubic characteristic (which is equivalent to transversal unstretched string). We consider the most important case of low-energy transversal dynamics. This example is especially instructive because the considered system cannot be linearized. Adequate analytical description of resonance non-stationary processes which correspond to intensive energy exchange between different parts of the system (clusters) in low frequency domain was obtained in terms of LPTs. We have revealed also in these terms the conditions of energy localization on the initially excited cluster. Analytical results are in agreement with the results of numerical simulations. It is shown that the considered system can be used as an efficient energy sink.

Non-stationary resonance dynamics of weakly coupled pendula

In this letter we fill the gap in understanding the non-stationary Hamiltonian dynamics of the weakly coupled pendula model having significant applications in numerous fields of physics. While common knowledge of this model is predominantly based on the stationary theory and quasi-linear approach to non-stationary dynamics, we consider a strongly nonlinear system without any polynomial approximation of the anharmonic potential. In the adopted asymptotics only closeness to any inter-pendulum resonance frequency is assumed. Being able to explore the whole diapason of initial conditions, two key nonlinear features are revealed by means of the Limiting Phase Trajectories concept: the conditions of intense energy exchange between the pendula and transition to energy localization. The roots and the domain of chaotic behavior are clarified as they are associated with the latter, purely non-stationary, topological transition.

Non-stationary resonance dynamics of a nonlinear sonic vacuum with grounding supports

In a recent work [L.I. Manevitch, A.F.Vakakis, Nonlinear oscillatory acoustic vacuum, SIAM Journal of Applied Mathematics 74(6) (2014), 1742–1762] it was shown that a periodic chain of linearly coupled particles performing low-energy in-plane transverse oscillations behaves as a strongly nonlinear sonic vacuum (with corresponding speed of sound equal to zero). In this work we consider the grounded version of this system by coupling each particle to the ground through lateral springs in order to study the effect of the grounding stiffness on the strongly nonlinear dynamics. In that context we consider the simplest possible such system consisting of two coupled particles and present analytical and numerical studies of the non-stationary planar dynamics. The most significant limiting case corresponding to predominant low energy transversal excitations is considered by taking into account leading order geometric nonlinearities. Then we show that the grounded system behaves as a nonlinear sonic vacuum due to the purely cubic stiffness nonlinearities in the governing equations of motion and the complete absence of any linear stiffness terms. Under certain assumptions the nonlinear normal modes (i.e., the time-periodic nonlinear oscillations) in the configuration space of this system coincide with those of the corresponding linear one, so they obey the same orthogonality relations. Moreover, we analytically find that there are two transitions in the dynamics of this system, with the parameter governing these transitions being the relation between the lateral (grounding) and the interchain stiffnesses. The first transition concerns a bifurcation of one of the nonlinear normal modes (NNMs), whereas the second provides conditions for intense energy transfers and mixing between the NNMs. The drastic effects of these bifurcations on the non-stationary resonant dynamics are discussed. Specifically, the second transition relates to strongly non-stationary dynamics, and signifies the transition from intense energy exchanges between different particles of the system to energy localization on one of the particles. Both of these regimes, as well as transitions between them are adequately described in the frameworks of the new concept of Limiting Phase Trajectories (LPTs) corresponding to maximum possible energy exchanges between the oscillators. Hence, a further example is provided by a particle chain where geometric nonlinearities lead to the realization of a sonic vacuum.

Transient and chaotic low-energy transfers in a system with bistable nonlinearity.

The low-energy dynamics of a two-dof system composed of a grounded linear oscillator coupled to a lightweight mass by means of a spring with both cubic nonlinear and negative linear components is investigated. The mechanisms leading to intense energy exchanges between the linear oscillator, excited by a low-energy impulse, and the nonlinear attachment are addressed. For lightly damped systems, it is shown that two main mechanisms arise: Aperiodic alternating in-well and cross-well oscillations of the nonlinear attachment, and secondary nonlinear beats occurring once the dynamics evolves solely in-well. The description of the former dissipative phenomenon is provided in a two-dimensional projection of the phase space, where transitions between in-well and cross-well oscillations are associated with sequences of crossings across a pseudo-separatrix. Whereas the second mechanism is described in terms of secondary limiting phase trajectories of the nonlinear attachment under certain resonance conditions. The analytical treatment of the two aformentioned low-energy transfer mechanisms relies on the reduction of the nonlinear dynamics and consequent analysis of the reduced dynamics by asymptotic techniques. Direct numerical simulations fully validate our analytical predictions.

Energy exchange and localization in the planar motion of a weightless beam carrying two discrete masses

We present analytical and numerical studies of nonstationary resonance processes in a system with four degrees of freedom. The system under consideration can be considered as one of the simplest geometrically nonlinear discrete models of an elastic beam supported by nonlinear elastic grounding support. Two symmetrically distributed discrete masses reflect the inertial properties of the beam, two angular springs simulate its bending stiffness. The longitudinal springs, as is usual in systems of oscillators, reflect the tensile stiffness and two transversal springs simulate the reaction of grounding support. Dealing with low-energy dynamics, we singled out the equations of transversal motion corresponding to the approximation of two coupled oscillators with nonlocal nonlinearity in elastic forces. We have analyzed this model using the concept of limiting phase trajectories (LPT). LPT’s concept was recently developed to study the nonstationary resonance dynamics. An analytical description of intensive interparticle energy exchange was obtained in terms of nonsmooth functions, which is consistent with numerical results. We have identified two dynamic transitions the first of which corresponds to the instability of out-of-phase normal mode and the second one is a transition from the intense energy exchange to the energy localization on the initially excited oscillator. Special attention was paid to the influence of bending stiffness on the conditions that ensure the implementation of each of the dynamic transitions.

A concept of limiting phase trajectories and description of highly non-stationary resonance processes

We discuss a recently developed concept of limiting phase trajectories (LPTs) allowing a unified description of resonance, highly non-stationary processes for a wide range of classical and quantum dynamical systems with constant and varying parameters. This concept provides a far going extension and adequate mathematical description of the well-known linear beating phenomenon to a diverse variety of nonlinear systems ranging from classical multi-particle models up to nonlinear quantum tunneling. Contrary to stationary and non-stationary, but non-resonance oscillations, described in the framework of nonlinear normal modes (NNMs) concept, the non-stationary processes under consideration are characterized by strong modulation and intense energy exchange between different parts of the system. They include, e.g. targeted energy transfer, non-stationary vibrations of carbon nanotubes, quantum tunneling, auto-resonance and non-conventional synchronization. Besides the non-linear beating, the LPT concept allows to find the conditions of transition from intense energy exchange to strongly localized (e.g. breather-like) excitations. A special mathematical technique based on the non-smooth temporal transformations leads to the clear and simple description of strongly modulated regimes. The role of LPTs in the theory of resonance non-stationary processes turns out to be similar to that of NNMs in stationary case.

Multiphase dynamic flash simulations using entropy maximization and application to compressible flow with phase change

A isochoric‐isoenergetic flash solver using a direct entropy maximization principle for phase splitting and Gibbs free energy minimization for phase stability is developed. The solver searches for the global stable state in a rigorous and thermodynamically consistent way. The solver is demonstrated to be robust and efficient to handle multiphase flash, even in the vicinity of phase boundaries. Dynamic flash computations and gas dynamics simulations of shock waves are considered for pure ethylene and for binary ethylene‐nitrogen mixtures. The simulations show significantly different shock wave characteristics when phase separation is considered due to intensive energy exchange, compared to the frozen flow limiting single‐phase solution. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3013–3024, 2014

Vibration analog of a superradiant quantum transition

A vibrational analog of the superradiant quantum transition (SQT) in a classical system of weakly bound oscillators of van der Pole-Duffing (self-generators), in which the coupling element is a linear oscillator, is described. Such an analog is a strongly modulated oscillatory process of almost complete periodic energy exchange between the generators. This type of mode is alternative to nonlinear normal modes (NNM) and close in its character to limiting phase trajectories (LPTs), which have been introduced recently as applied to conservative systems, but in contrast to them, as the attractor. It is shown that the necessary condition of the transition to intense energy exchange in the classical system is the instability of one of the NNMs similarly to that when the condition of the superradiant transition is the instability of the ground state in a quantum model.

Superradiant transition and its classical analogue

The two-level quantum model proposed by Preparata, according to which the interaction of a material system with a electromagnetic field can cause the loss of stability of the lower level, is examined. As a result of this instability, the role of the ground state is played by a periodic process generating superradiance (in contrast to laser radiation induced by overpopulation of the upper level). A classical analogue of a super-radiant quantum transition, a system of van der Pol-Duffing oscillators (generators) weakly coupled via a linear oscillator, is for the first time described. Such an analogue is a strongly modulated oscillatory process of almost complete periodic energy exchange between the generators. It is shown that a necessary condition for the transition to intense energy exchange in the classical system is the instability of one of the nonlinear normal modes, similar to how the condition for a superradiant transition to occur is the instability of the ground state of a two-level quantum system coupled with a resonant electromagnetic field.

On intense energy exchange and localization in periodic FPU dimer chains

Dynamics of periodically heterogeneous, nonlinear lattices is a subject of intense research in great variety of aspects of theoretical and applied physics. In fact almost all the studies pursued to date in the field of lattice dynamics have been mostly concerned with the analysis of stationary and near stationary regimes. However, not much has been done with respect to highly non-stationary processes existing in periodically heterogeneous nonlinear lattices such as FPU dimers etc. The system under consideration in the present paper is the FPU dimer chain given to periodic boundary conditions and composed of two identical cells of particles. Each cell of the chain comprises exactly one heavy particle succeeded by a group of N light particles of identical masses (i.e. 1:N dimer chain). In the current work we present an extensive analytical study of the mechanism of the formation of highly non-stationary regimes excited in FPU dimer chains subject to periodic boundary conditions. In particular we show that the initial excitation provided to a single group of light particles (belonging to a single cell), may lead to the two opposing regimes, namely energy localization on the same (initially excited) group of light particles as well as the recurrent (near complete) energy exchanges between the two groups of light particles of both cells. It is important to emphasize that for both the regimes heavy particles remain near completely stationary. An analytical study of the dynamics of the system under consideration reveals the threshold value of the parameter of nonlinearity (stiffness nonlinearity) above which the initial energy supplied to a specific group of light particles of the chain gets permanently localized on it. The developed analytical procedure correctly predicts the threshold value for the transition from the regime of strong energy exchange between the two groups of light particles to the permanent energy localization on a single group. It should be emphasized that to date the analytical procedure developed in the paper is the only possible tool for addressing the highly non-stationary regimes which by no means can be replaced with the well-known modal analysis. Results of analytical predictions are in a spectacular correspondence with those of numerical simulations.