Periodic Regimes Research Articles

A Material Law Based on Neural Networks and Homogenization for the Accurate Finite Element Simulation of Laminated Ferromagnetic Cores in the Periodic Regime

Electromagnetic fields and eddy currents in thin electrical steel laminations are governed by the laws of magnetodynamics with hysteresis. If the lamination is large with respect to its thickness, field and current distributions are accurately resolved by solving a 1-D finite element magnetodynamic problem with hysteresis across half the lamination thickness. This 1-D model is able to deliver mesoscopic information to be used, after appropriate homogenization, in the macroscopic modeling of an electrical machine or transformer. As each evaluation of such a homogenized model implies a finite element simulation at the mesoscale, a monolithic coupling might be very time-consuming. This article proposes an alternative approach, assuming a periodic excitation of the system, where the parameters of a parametric homogenized material law are determined in each finite element with a neural network. The local material law can then be used as a conventional constitutive relationship in a 2-D or 3-D modeling, with a massive speed-up with respect to the monolithic coupling.

Vortex-induced vibrations of two rigidly coupled circular cylinders in tandem arrangement

In this paper, we study the transverse vortex-induced vibrations (VIV) of two rigidly connected circular cylinders of equal size, arranged in a tandem configuration, by means of two-dimensional numerical computations. Results are examined for Re=250 and a fixed center-to-center separation of 2D. The dynamic response of the two-cylinder system is investigated in detail over a domain of reduced velocities ranging from Ur=2 to 8. The diverse types of branches are identified, on the basis of their distinct characteristics in the amplitude and frequency responses. Among them, the lower branch is of particular interest as it is quasi-periodic in nature, instead of the periodic regime that is well documented for the isolated cylinder case. By scrutinizing the vorticity dynamics, it reveals that this quasi-periodicity arises from the switching between two flow states, which are essentially distinguished by whether an active gap flow is present. The dynamically rich response leads to a rich variety of phase dynamics, involving phase locking, trapping, slipping and drifting; in particular, phase drifting is indicative of a forthcoming phase jump of 180° between the lift force and the displacement. It is also found that in the initial branch, the excitation of the system is driven by the pressure lift force on the rear cylinder; by contrast, in the lower branch, it is the pressure lift force on the front cylinder that acts as a source of excitation.

Periodic regimes of motion of capsule system on rough plane

Periodic regimes of motion of capsule system on rough plane

МОДЕЛИРОВАНИЕ НЕСТАЦИОНАРНОГО ТЕПЛОВОГО РЕЖИМА ПОМЕЩЕНИЯ С ДЕРЕВЯННЫМИ ОГРАЖДАЮЩИМИ КОНСТРУКЦИЯМИ

A non-stationary approach to the calculation of periodic thermal regimes of low-rise buildings with enclosing structures made of wooden beams equipped with double-glazed windows is considered. The application of the proposed method allows to determine the non-stationary thermal load of the air conditioning system for this type of house, as well as the required compensating capacities during the day. The conditions of applicability of plane-layered thermophysical calculation schemes in the presence of spatially inhomogeneous heating are analyzed. A refinement of the procedure for averaging convective heat transfer coefficients for vertical walls by periodic temperature fluctuations is carried out. An algorithm for calculating the periodic thermal regime based on the representation of time dependencies in the form of a Fourier series is proposed. The role of solar radiation flow through double-glazed windows in the heat exchange and energy efficiency of a wooden house is shown. The proposed mathematical model of room heat exchange takes into account the effects of the delay in the propagation of the temperature field in the walls when the ambient temperature changes and the dynamic change in heat flux from light flows outside and inside the room. It is determined that protection from direct sunlight entering the room through the window opening allows reducing peak air conditioning costs in the summer by a third for peak air conditioning modes.

Quantum reflection of dark solitons scattered by reflectionless potential barrier and position-dependent dispersion.

We investigate theoretically and numerically quantum reflection of dark solitons propagating through an external reflectionless potential barrier or in the presence of a position-dependent dispersion. We confirm that quantum reflection occurs in both cases with a sharp transition between complete reflection and complete transmission at a critical initial soliton speed. The critical speed is calculated numerically and analytically in terms of the soliton and potential parameters. Analytical expressions for the critical speed were derived using the exact trapped mode, time-independent, and time-dependent variational calculations. It is then shown that resonant scattering occurs at a critical speed, where the energy of the incoming soliton is resonant with that of a trapped mode. Reasonable agreement between analytical and numerical values for the critical speed is obtained as long as a periodic multisoliton ejection regime is avoided.

Historic and Contemporary Land Use Shape Plant-Pollinator Networks and Community Composition

Globally, grasslands represent a critical but shrinking habitat for native plants and pollinators, with declines driven by alterations to landscape-scale habitat cover and local-scale disturbance regimes, among other factors. Specifically, as cities expand in size, an increasing proportion of regional pasture and grassland habitat is being replaced by urban development, and fewer periodic grazing and burning regimes are being supported locally, despite evidence that such regimes promote plant species richness and facilitate their interaction with native pollinators. The quantification of these plant-pollinator networks—through indices such as network connectance, specialization, nestedness, and robustness—can provide a unique opportunity to characterize key structural properties of species interactions and their response to human management and seasonal phenology. While urbanization and local disturbance regimes likely influence plant and pollinator communities and their interactions, past research in this area has primarily been conducted at limited spatial and temporal scales and has not typically quantified the impacts of both local and landscape forces on network properties. In this study, we investigate the effects of contemporary (past 10 years) and historic (prior 90 years) disturbance regimes on plant-pollinator community composition and network structure across more than 200 km of grassland in Central Texas. Our analyses indicate that for plant and pollinator communities, both contemporary and historic land management practices have led to significantly dissimilar community composition. Plant and pollinator richness and network nestedness are negatively correlated with phenological period, while pollinator richness is positively correlated with landscape-scale (2 km) urbanized land cover and is higher in historically grazed land, likely due to greater food and nesting resource availability. In contrast, we show that network connectance is positively correlated with phenological period and negatively correlated with landscape-scale urban cover. Finally, we show that pollinator robustness, a measure of resilience to plant species loss, is positively correlated with landscape-scale urbanization, likely due to greater redundancy provided by common weedy plant species. Overall, our results demonstrate that historic grazing regimes, current urbanization levels, and distinct phenological periods can simultaneously drive plant-pollinator community composition and network dynamics in shrinking but critical grassland ecosystems.

Tuning inter-modal energy exchanges of a nonlinear electromechanical beam by a nonlinear circuit

A model of a nonlinear beam with a piezoelectric patch linked to a nonlinear circuit is considered. The physical and mechanical parameters of the system are such that it presents a 1:3 internal resonance. The aim is to study, for different time scales, the effect of the nonlinearity of the electrical circuit on energy exchanges between the resonant modes. In fact, we would like to master energy channelling between two internally resonant modes of a composite beam via a nonlinear circuit. The investigations are carried out on the projected system equations on its internally resonant modes. The system behaviours at different scales of time are studied by coupled methods of complexification and multiple scale. Analytical developments permit to reveal different system dynamics characterized by periodic and/or non-periodic regimes. Finally, the paper is accompanied by comparisons between systems equipped with a resonant circuit (linear) and a nonlinear one.

Wind driven plantigrade machine capable of moving against the flow

The wind powered walking mechanism is proposed that is able to perform a self-sustained up-wind motion. The device consists of the Chebyshev plantigrade machine and a wind turbine installed on it. A mathematical model of the mechanism is constructed on the basis of the quasi-steady description of the aerodynamic load. In frames of the model, sufficient conditions of existence of a periodic up-wind motion regime are derived based on the Andronov-Pontryagin approach. Parametrical analysis of the model is performed. Values of parameters ensuring high speed of motion and self-start of the machine are found. General features of behavior of the system are revealed and discussed. The laboratory prototype is constructed. The possibility of the up-wind walking is shown not only theoretically, but experimentally as well.

A Cluster Based Algorithm Coupled With Shooting Method for Estimation of Parametric Clusters Yielding Optimal Stable Periodic Solutions in Nonlinear Vibrating Systems

Abstract This work presents a novel cluster based optimization procedure for estimating parameter values that yield stable, periodic responses with desired amplitude in nonlinear vibrating systems. The parameter values obtained by conventional nonlinear optimization schemes, with minimization of amplitude as the objective, may not furnish periodic and stable responses. Moreover, global optimization strategies may converge to isolated optima that are sensitive to parametric perturbations. In practical engineering systems, unstable or isolated optimal orbits are not practically realizable. To overcome these limitations, the proposed method tries to converge to a cluster in the r-dimensional parameter space in which the design specifications including the specified optimality, periodicity, stability and robustness are satisfied. Thus, it eliminates the need for computationally expensive bifurcation studies to locate stable, periodic parameter regimes before optimization. The present method is based on a hybrid scheme which involves the algebraic form of the governing equations in screening phase and its differential form in the selection phase. In the screening phase, force and energy balance conditions are used to rephrase the nonlinear governing equations in terms of the design parameter vector. These rephrased equations are reduced to algebraic form using a harmonic balance procedure which also specifies the desired amplitude and frequency of the response. An error norm based on this algebraic form is defined and is used to contract the search bounds in the parameter space leading to convergence to a cluster. The selection phase of the algorithm uses shooting method coupled with evaluation of Floquet multipliers to retain only those vectors in the arrived cluster yielding stable periodic solutions. The method is validated with Den Hartog's vibration absorbers and is then applied to vibration absorbers with material nonlinearity and vibration isolators with geometric nonlinearity. In both the cases, the converged cluster is shown to yield stable, periodic responses satisfying the amplitude condition. Parametric perturbation studies are conducted on the cluster to illustrate its robustness. The use of algebraic form of governing equations in the screening phase drastically reduces the computational time needed to converge to the cluster. The fact that the present method converges to a cluster in the parameter space rather than to a single parameter value offers the designer more freedom to choose the design vector from inside the cluster. It also ensures that the design is robust to small changes in parameter values.

Periodical discharge regime transitions under long-term repetitive nanosecond pulses

Intuitively, the nanosecond repetitively pulsed (NRP) corona and spark regimes are sustained successively after onsets due to the high background electron density and/or the surplus heat. In this paper, the NRP discharge unexpectedly swings among different regimes (corona → glow → spark → corona → …) in one pulse train, which is characterized by the periodical spark quench and reestablishment. We have investigated discharge regime instabilities by applying long-term repetitive high-voltage nanosecond pulses of ∼15 ns duration to needle–needle and needle–plane gaps in atmospheric-pressure N2 and N2–O2 mixtures. Pulse-sequence resolved electrical and optical diagnostics have been implemented to capture transition processes. The initial corona gradually grows into glow and then spark ‘pulse-by-pulse’, however, the spark regime was interrupted after a certain number of voltage pulses until the next reestablishment. Narrow pulse width impedes the discharge instability growth within one pulse, and a certain number of voltage pulses are required for the discharge regime transition. The addition of O2 dramatically boosts the duration length of spark regime. A lower output impedance of the power supply induces a higher deposited energy into a spark, however, not necessarily leads to a longer spark regime duration, although both the energy storage and the average electric field strength are approximate. Polarity effects, conventionally diminished in pulse-periodic discharges, are still evident during the discharge regime transition. The periodical discharge regime transition is qualitatively explained based on the plasma–source coupling and the evolution trajectory along the power transfer curve. Feedback mechanisms and residual-conductivity related screening effect in NRP spark discharges are analyzed based on a simplified 0D simulation. The periodical feature is probably caused by the insufficient average deposited energy per unit distance per one pulse cycle. In-depth understandings of ‘non-binary’ regimes (neither corona nor spark) and memory effect mechanisms of NRP discharges could be reached.

Hunt for chimeras in fully coupled networks of nonlinear oscillators

The purpose of this work is to study the dynamic properties of solutions to special systems of ordinary differential equations, called fully connected networks of nonlinear oscillators. Methods. A new approach to obtain periodic regimes of the chimeric type in these systems is proposed, the essence of which is as follows. First, in the case of a symmetric network, a simpler problem is solved of the existence and stability of quasi-chimeric solutions — periodic regimes of two-cluster synchronization. For each of these modes, the set of oscillators falls into two disjoint classes. Within these classes, full synchronization of oscillations is observed, and every two oscillators from different classes oscillate asynchronously. Results. On the basis of the proposed methods, it is separately established that in the transition from a symmetric system to a general network, the periodic regimes of two-cluster synchronization can be transformed into chimeras. Conclusion. The main statements of the work concerning the emergence of chimeras were obtained analytically on the basis of an asymptotic study of a model example. For this example, the notion of a canonical chimera is introduced and the statement about the existence and stability of solutions of chimeric type in the case of asymmetry of the network is proved. All the results presented are extended to a continuous analogue of the corresponding system. The obtained results are illustrated numerically.

Effects of Volume Changes on the Thermal Performance of PCM Layers Subjected to Oscillations of the Ambient Temperature: Transient and Steady Periodic Regimes.

The Stefan problem regarding the formation of several liquid–solid interfaces produced by the oscillations of the ambient temperature around the melting point of a phase change material has been addressed by several authors. Numerical and semi-analytical methods have been used to find the thermal response of a phase change material under these type of boundary conditions. However, volume changes produced by the moving fronts and their effects on the thermal performance of phase change materials have not been addressed. In this work, volume changes are incorporated through an additional equation of motion for the thickness of the system. The thickness of the phase change material becomes a dynamic variable of motion by imposing total mass conservation. The modified equation of motion for each interface is obtained by coupling mass conservation with a local energy–mass balance at each front. The dynamics of liquid–solid interface configurations is analyzed in the transient and steady periodic regimes. Finite element and heat balance integral methods are used to verify the consistency of the solutions to the proposed model. The heat balance integral method is modified and adapted to find approximate solutions when two fronts collide, and the temperature profiles are not smooth. Volumetric corrections to the sensible and latent heat released (absorbed) are introduced during front formation, annihilation, and in the presence of two fronts. Finally, the thermal energy released by the interior surface is estimated through the proposed model and compared with the solutions obtained through models proposed by other authors.

Nonlinear Forced Vibrations of Plates with Oscillating Inclusions

These studies focus on the forced vibrations of rectangular plates incorporating oscillating inclusions uniformly distributed in the carrier elastic medium. Plate’s equations of motion consist of the Lamé equation for a carrier material and the equation for oscillators representing the inclusions. The oscillators are acted upon by the nonlinear friction force, described by Coulomb’s modified law, and a cubically nonlinear elastic force. The simply supported forced plate is considered. Using the Galerkin approximation, the problem of plate vibrations is reduced to the study of a system of ODEs. According to numerical and qualitative analyses, the application of harmonic forcing causes the appearance of periodic, quasiperiodic, and chaotic regimes in the system. In particular, the analytical expression is derived for the periodic regimes of the forcing frequency. The scenarios of vibration’s development is identified at the variation of forcing amplitude. The quasiperiodic and chaotic modes are studied by means of Poincaré section technique, and Fourier and Lyapunov spectra analyses. The statistical properties of the sequences of temporal intervals between maxima of system’s solutions are considered in more detail. The sequence extracted from the chaotic trajectory is shown to possess long-term correlations and approximately obeys the Weibull distribution.

Aperiodic bursting dynamics of active rotors.

We report experiments on an active camphor rotor. A camphor rotor is prepared by infusing camphor on a regular rectangular paper strip. It performs self-propelled motion at the air-water interface due to Marangoni driven forces. After some transient (periodic) dynamics, the rotor enters into the aperiodic bursting regime, which is characterized as an irregularly repeated rest (halt) and run (motion) of the rotor. Subsequently, this aperiodic (irregular) rotor is entrained to a periodic (regular) regime with the help of a suitable external periodic forcing. Furthermore, we conducted experiments on two such coupled aperiodic camphor rotors. In this set of experiments, synchronized bursting was observed. During this bursting motion, one rotor follows the movement of the other rotor. A numerical point particle model, incorporating excitable underlying equations, successfully replicated experimentally observed aperiodic bursting.

Mixing Improvement in a T-Shaped Micro-Junction through Small Rectangular Cavities.

The T-shaped micro-junction is among the most used geometry in microfluidic applications, and many design modifications of the channel walls have been proposed to enhance mixing. In this work, we investigate through numerical simulations the introduction of one pair of small rectangular cavities in the lateral walls of the mixing channel just downstream of the confluence region. The aim is to preserve the simple geometry that has contributed to spread the practical use of the T-shaped micro-junction while suggesting a modification that should, in principle, work jointly with the vortical structures present in the mixing channel, further enhancing their efficiency in mixing without significant additional pressure drops. The performance is analyzed in the different flow regimes occurring by increasing the Reynolds number. The cavities are effective in the two highly-mixed flow regimes, viz., the steady engulfment and the periodic asymmetric regimes. This presence does not interfere with the formation of the vortical structures that promote mixing by convection in these two regimes, but it further enhances the mixing of the inlet streams in the near-wall region of the mixing channel without any additional cost, leading to better performance than the classical configuration.

Updating the Duty to Update

For decades, courts have struggled to determine whether and when public companies are obligated to update prior disclosures that, although true when made, become misleading as a result of a subsequent event. Prior to 2020, a lack of urgency coupled with an increasingly periodic disclosure regime furthered obscured the role and relevance of this dubious obligation, otherwise known as the duty to update. However, with the paradigmatic subsequent event of COVID-19 still permeating through every aspect of life nearly two years after its onset, the duty to update—and all of its uncertainties—has come into the fore once again. 
 This Note suggests three recommendations to the duty to update in light of its renewed relevance. First, the framework for identifying a statement subject to the duty should be streamlined. Second, courts should adopt a consistent materiality test when evaluating potential violations of the duty. Finally, and most importantly, the SEC should utilize its rulemaking power to clarify its calls for more continuous disclosures in the wake of the pandemic. Only then will the duty to update claim its appropriate role in the grand scheme of securities regulation.

Quantifying periodic, multi-periodic, hidden and unstable regimes of a magnetic pendulum via semi-analytical, numerical and experimental methods

The dynamics of a magnetic pendulum mounted on a shaft with an elastic element is considered. The impulsive excitation of the pendulum is performed through the interaction of a strong neodymium magnet and an electric coil. The mathematical model of the pendulum is represented by the non-autonomous ordinary nonlinear differential equation. The model is verified in a wide range of motion regimes by the laboratory experiment. Periodic motions are considered in more detail by the semi-analytic approximate method utilizing the averaging ideas. The amplitude and phase shift of system solutions possess highly nonlinear features which we propose to approximate by the saw-tooth functions. This new approach allows one to improve the results of the application of the conventional averaging method and is promising for the application and analysis of nonlinear systems with a strong nonlinearity.

Piecewise Affine Dynamical Models of Petri Nets – Application to Emergency Call Centers*

We study timed Petri nets, with preselection and priority routing. We represent the behavior of these systems by piecewise affine dynamical systems. We use tools from the theory of nonexpansive mappings to analyze these systems. We establish an equivalence theorem between priority-free fluid timed Petri nets and semi-Markov decision processes, from which we derive the convergence to a periodic regime and the polynomial-time computability of the throughput. More generally, we develop an approach inspired by tropical geometry, characterizing the congestion phases as the cells of a polyhedral complex. We illustrate these results by a current application to the performance evaluation of emergency call centers in the Paris area. We show that priorities can lead to a paradoxical behavior: in certain regimes, the throughput of the most prioritary task may not be an increasing function of the resources.

Effects of flow unsteadiness and chemical kinetics on the reaction yield in a T-microreactor

Experimental flow visualizations and velocity measurements are used jointly with numerical simulations to investigate the mixing and monitor the reaction progress in the periodic flow regimes occurring in a T-shaped microreactor. We considered the effects of different kinetic constants, with very different characteristic chemical time scales resulting in a wide range of Damköhler numbers.A remarkable agreement between experiments and simulations is found both in terms of flow pattern and reaction progress. Two different flow regimes are present for increasing Reynolds number. The first is the periodic asymmetric regime, characterized by the shedding of vorticity-blobs along the mixing channel leading to a further increase of the mixing performance compared to the steady engulfment regime. The second regime is the periodic asymmetric one, which is mainly a poorly mixed segregated regime with periodic oscillation at the interface between the two reactants. The mixing degree significantly increases in the unsteady asymmetric regime, whereas it predictably drops down in the unsteady symmetric regime. In the periodic asymmetric regime the reaction yield follows the same function of the Damköhler number, describing the residence to chemical time-scale ratio, and of a non-dimensional kinetic constant, taking into account also fluid properties, previously proposed for the steady vortex and engulfment regimes. In the periodic symmetric regime, the reaction yield is found to depend only on the Damköhler number, with the same dependence previously highlighted for the steady segregated regime.

Energy Cyclo-Directionality, Average Equipartition and Exergy Efficiency of Multidomain Power Networks

A recent formalization of thermodynamics under a dynamical systems approach introduces an axiom restricting the direction of power transmission between two subsystems, reflecting heat transfer from hot to cold bodies. This axiom enables precise results paralleling the statements of classical thermodynamics, including its second law, which places a limit on the amount of work that may be transferred to across system boundaries beyond that imposed by energy conservation. Systems exhibiting non-diffusive power transfer, including those with Hamiltonian dynamics are ruled out. Given that power networks with Hamiltonian dynamics fail the directionality axiom, are they still subject to limitations on their ability to perform work on the surroundings? This paper shows that such systems can satisfy a version of the above axiom involving averages over periodic regimes, revealing limitations on external power transfer and allowing a definition of second-law efficiency and a cyclic interpretation of energy equipartition. Focus is on a class of linear port-Hamiltonian systems, with frequency-domain methods used to describe the pertinent average quantities. The ability to establish an order relationship between the weighted average kinetic and potential energies has a central role. We show that this can be cast as a generalized eigenvalue problem.