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1
Kurkin, Semen A., Danil D. Kulminskiy, Vladimir I. Ponomarenko, Mikhail D. Prokhorov, Sergey V. Astakhov, and Alexander E. Hramov. "Central pattern generator based on self-sustained oscillator coupled to a chain of oscillatory circuits." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 3 (March 2022): 033117. http://dx.doi.org/10.1063/5.0077789.
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We have proposed and studied both numerically and experimentally a multistable system based on a self-sustained Van der Pol oscillator coupled to passive oscillatory circuits. The number of passive oscillators determines the number of multistable oscillatory regimes coexisting in the proposed system. It is shown that our system can be used in robotics applications as a simple model for a central pattern generator (CPG). In this case, the amplitude and phase relations between the active and passive oscillators control a gait, which can be adjusted by changing the system control parameters. Variation of the active oscillator’s natural frequency leads to hard switching between the regimes characterized by different phase shifts between the oscillators. In contrast, the external forcing can change the frequency and amplitudes of oscillations, preserving the phase shifts. Therefore, the frequency of the external signal can serve as a control parameter of the model regime and realize a feedback in the proposed CPG depending on the environmental conditions. In particular, it allows one to switch the regime and change the velocity of the robot’s gate and tune the gait to the environment. We have also shown that the studied oscillatory regimes in the proposed system are robust and not affected by external noise or fluctuations of the system parameters. Moreover, using the proposed scheme, we simulated the type of bipedal locomotion, including walking and running.
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Zaitsev, Valery V., and Alexander V. Karlov. "Quasi-harmonic self-oscillations in discrete time: analysis and synthesis of dynamic systems." Physics of Wave Processes and Radio Systems 24, no. 4 (January 16, 2022): 19–24. http://dx.doi.org/10.18469/1810-3189.2021.24.4.19-24.
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For sampling of time in a differential equation of movement of Thomson type oscillator (generator) it is offered to use a combination of the numerical method of finite differences and an asymptotic method of the slowl-changing amplitudes. The difference approximations of temporal derivatives are selected so that, first, to save conservatism and natural frequency of the linear circuit of self-oscillatory system in the discrete time. Secondly, coincidence of the difference shortened equation for the complex amplitude of self-oscillations in the discrete time with Eulers approximation of the shortened equation for amplitude of self-oscillations in analog system prototype is required. It is shown that realization of such approach allows to create discrete mapping of the van der Pol oscillator and a number of mappings of Thomson type oscillators. The adequacy of discrete models to analog prototypes is confirmed with also numerical experiment.
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GEORGIOU, IOANNIS T., and IRA B. SCHWARTZ. "THE SLOW INVARIANT MANIFOLD OF A CONSERVATIVE PENDULUM-OSCILLATOR SYSTEM." International Journal of Bifurcation and Chaos 06, no. 04 (April 1996): 673–92. http://dx.doi.org/10.1142/s0218127496000345.
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We analyze the motions of a conservative pendulum-oscillator system in the context of invariant manifolds of motion. Using the singular perturbation methodology, we show that whenever the natural frequency of the oscillator is sufficiently larger than that of the pendulum, there exists a global invariant manifold passing through all static equilibrium states and tangent to the linear eigenspaces at these equilibrium states. The invariant manifold, called slow, carries a continuum of slow periodic motions, both oscillatory and rotational. Computations to various orders of approximation to the slow invariant manifold allow analysis of motions on the slow manifold, which are verified with numerical experiments. Motion on the slow invariant manifold is identified with a slow nonlinear normal mode.
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Krak, Michael D., and Rajendra Singh. "Asymptotic trends in time-varying oscillatory period for a dual-staged torsional system." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 22 (July 28, 2016): 4126–38. http://dx.doi.org/10.1177/0954406216662087.
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The primary goal of this article is to propose a new analysis tool that estimates the asymptotic trends in the time-varying oscillatory period of a non-linear mechanical system. The scope is limited to the step-response of a torsional oscillator containing a dry friction element and dual-staged spring. Prior work on the stochastic linearization techniques is extended and modified for application in time domain. Subsequently, an instantaneous expected value operator and the concept of instantaneous effective stiffness are proposed. The non-linear system is approximated at some instant during the step-response by a linear time-invariant mechanical system that utilizes the instantaneous effective stiffness concept. The oscillatory period of the non-linear step-response at that instant is then approximated by the natural period of the corresponding linear system. The proposed method is rigorously illustrated via two computational example cases (a near backlash and near pre-load non-linearities), and the necessary digital signal processing parameters for time domain analysis are investigated. Finally, the feasibility and applicability of the proposed method is demonstrated by estimating the softening and hardening trends in the time-varying oscillatory period of the measured response for two laboratory experiments that contain clearance elements and multi-staged torsional springs.
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Matevosyan, Ashot A., and Aram G. Matevosyan. "PARAMETER ESTIMATION FOR OSCILLATORY SYSTEMS." Proceedings of the YSU A: Physical and Mathematical Sciences 55, no. 2 (255) (August 30, 2021): 131–40. http://dx.doi.org/10.46991/pysu:a/2021.55.2.131.
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Simple harmonic motion was investigated of a rotational oscillating system. The effect of dumping and forcing on motion of the system was examined and measurements were taken. Resonance in a oscillating system was investigated and quality factor of the dumping system was measured at different damping forces using three different methods. Resonance curves were constructed at two different damping forces. A probabilistic model was built and system parameters were estimated from the resonance curves using Stan sampling platform. The quality factor of the oscillating system when the additional dumping was turned off was estimated to be $Q = \num{71 \pm 1}$ and natural frequency $\omega_0 = \num{3.105 \pm 0.008}\, \si{\per\second}$.
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Yelisieiev, Volodymyr, Vasyl Lutsenko, Serhii Shevchenko, Anatolii Shevchenko, Oleksandr Tolstopyat, and Leonid Fleer. "Response of oscillatory system “liquid layer-rod” to driving disturbances." E3S Web of Conferences 109 (2019): 00118. http://dx.doi.org/10.1051/e3sconf/201910900118.
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This article deals with main characteristics of the oscillating system “central body – liquid” by means of its well-known representation in the form of a pendulum mathematical model. It makes possible to evaluate spread of specified disturbances at the general physical level and to determine the most dangerous frequencies that lead to increased amplitudes of fluid oscillations. We propose equations for single-frequency pendulums, which influence each other by means of resistance forces and added mass. Several examples with different natural frequencies of the body are considered. The calculation results showed that besides natural frequencies of the components, system has two more natural frequencies. So, system actually responds only to disturbances which frequencies are close to the natural frequency of the liquid layer. In this case, amplitudes of liquid and the body sharply increase. This fact indicates that in real technological processes frequency of dominant disturbance should be as far from the first resonant frequency of the liquid as possible. The further experimental and theoretical studies that take into account the influence of the following modes on the dynamic picture of the process are also of interest.
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Agrawal, Deepak K., Elisa Franco, and Rebecca Schulman. "A self-regulating biomolecular comparator for processing oscillatory signals." Journal of The Royal Society Interface 12, no. 111 (October 2015): 20150586. http://dx.doi.org/10.1098/rsif.2015.0586.
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While many cellular processes are driven by biomolecular oscillators, precise control of a downstream on/off process by a biochemical oscillator signal can be difficult: over an oscillator's period, its output signal varies continuously between its amplitude limits and spends a significant fraction of the time at intermediate values between these limits. Further, the oscillator's output is often noisy, with particularly large variations in the amplitude. In electronic systems, an oscillating signal is generally processed by a downstream device such as a comparator that converts a potentially noisy oscillatory input into a square wave output that is predominantly in one of two well-defined on and off states. The comparator's output then controls downstream processes. We describe a method for constructing a synthetic biochemical device that likewise produces a square-wave-type biomolecular output for a variety of oscillatory inputs. The method relies on a separation of time scales between the slow rate of production of an oscillatory signal molecule and the fast rates of intermolecular binding and conformational changes. We show how to control the characteristics of the output by varying the concentrations of the species and the reaction rates. We then use this control to show how our approach could be applied to process different in vitro and in vivo biomolecular oscillators, including the p53-Mdm2 transcriptional oscillator and two types of in vitro transcriptional oscillators. These results demonstrate how modular biomolecular circuits could, in principle, be combined to build complex dynamical systems. The simplicity of our approach also suggests that natural molecular circuits may process some biomolecular oscillator outputs before they are applied downstream.
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Stein, George Juraj, Peter Tobolka, and Rudolf Chmúrny. "Preliminary Investigations of Machine Frame Vibration Damping Using Eddy Current Principle." Applied Mechanics and Materials 821 (January 2016): 288–94. http://dx.doi.org/10.4028/www.scientific.net/amm.821.288.
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A novel approach to vibration attenuation, based on the eddy current principle, is described. The combined effects of all magnetic forces acting in the oscillatory system attenuate frame vibrations and, concurrently, decrease the damped natural frequency. A mathematical model of the forces balance in the oscillatory system was derived before. Some experimental results from a mock-up machine frame excited by an asynchronous motor are presented.
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Khoroshev, K. G., and S. V. Kykot. "Eigenfrequencies and eigenforms of regular chain oscillatory systems." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 4 (2021): 88–93. http://dx.doi.org/10.17721/1812-5409.2021/4.14.
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The classical approach in the investigation of natural oscillations of discrete mechanical oscillatingsystems is the solution of the secular equation for finding the eigenfrequencies and the system of algebraic equations for determining the amplitude coefficients (eigenforms). However, the analytical solution of the secular equation is possible only for a limited class of discrete systems, especially with a finite degree of freedom. This class includes regular chain oscillating systems in which the same oscillators are connected in series. Regular systems are divided into systems with rigidly fixed ends, with one or both free ends, which significantly affects the search for eigenfrequencies and eigenforms. This paper shows how, having a solution for the secular equation of a regular system with rigidly fixed ends, it is possible to determine the eigenfrequencies and eigenforms of regular systems with one or both free ends.
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Gale, Steven, Mario Prsa, Aaron Schurger, Annietta Gay, Aurore Paillard, Bruno Herbelin, Jean-Philippe Guyot, Christophe Lopez, and Olaf Blanke. "Oscillatory neural responses evoked by natural vestibular stimuli in humans." Journal of Neurophysiology 115, no. 3 (March 1, 2016): 1228–42. http://dx.doi.org/10.1152/jn.00153.2015.
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While there have been numerous studies of the vestibular system in mammals, less is known about the brain mechanisms of vestibular processing in humans. In particular, of the studies that have been carried out in humans over the last 30 years, none has investigated how vestibular stimulation (VS) affects cortical oscillations. Here we recorded high-density electroencephalography (EEG) in healthy human subjects and a group of bilateral vestibular loss patients (BVPs) undergoing transient and constant-velocity passive whole body yaw rotations, focusing our analyses on the modulation of cortical oscillations in response to natural VS. The present approach overcame significant technical challenges associated with combining natural VS with human electrophysiology and reveals that both transient and constant-velocity VS are associated with a prominent suppression of alpha power (8–13 Hz). Alpha band suppression was localized over bilateral temporo-parietal scalp regions, and these alpha modulations were significantly smaller in BVPs. We propose that suppression of oscillations in the alpha band over temporo-parietal scalp regions reflects cortical vestibular processing, potentially comparable with alpha and mu oscillations in the visual and sensorimotor systems, respectively, opening the door to the investigation of human cortical processing under various experimental conditions during natural VS.
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Donovan, F. M., Bruce C. Taylor, and M. C. Su. "One-Dimensional Computer Analysis of Oscillatory Flow in Rigid Tubes." Journal of Biomechanical Engineering 113, no. 4 (November 1, 1991): 476–84. http://dx.doi.org/10.1115/1.2895429.
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The dynamic characteristics of catheter-transducer systems using rigid tubes with compliance lumped in the transducer and oscillatory flow of fluid in rigid tubes were analyzed. A digital computer model based on one dimensional laminar oscillatory flow was developed and verified by exact solution of the Navier-Stokes Equation. Experimental results indicated that the damping ratio and resistance is much higher at higher frequencies of oscillation than predicted by the one dimensional model. An empirical correction factor was developed and incorporated into the computer model to correct the model to the experimental data. Amplitude of oscillation was found to have no effect on damping ratio so it was concluded that the increased damping ratio and resistance at higher frequencies was not due to turbulence but to two dimensional flow effects. Graphs and equations were developed to calculate damping ratio and undamped natural frequency of a catheter-transducer system from system parameters. Graphs and equations were also developed to calculate resistance and inertance for oscillatory flow in rigid tubes from system parameters and frequency of oscillation.
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Lakhova, T. N., F. V. Kazantsev, S. A. Lashin, and Yu G. Matushkin. "The finding and researching algorithm for potentially oscillating enzymatic systems." Vavilov Journal of Genetics and Breeding 25, no. 3 (June 2, 2021): 318–30. http://dx.doi.org/10.18699/vj21.035.
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Many processes in living organisms are subject to periodic oscillations at different hierarchical levels of their organization: from molecular-genetic to population and ecological. Oscillatory processes are responsible for cell cycles in both prokaryotes and eukaryotes, for circadian rhythms, for synchronous coupling of respiration with cardiac contractions, etc. Fluctuations in the numbers of organisms in natural populations can be caused by the populations’ own properties, their age structure, and ecological relationships with other species. Along with experimental approaches, mathematical and computer modeling is widely used to study oscillating biological systems. This paper presents classical mathematical models that describe oscillatory behavior in biological systems. Methods for the search for oscillatory molecular-genetic systems are presented by the example of their special case – oscillatory enzymatic systems. Factors influencing the cyclic dynamics in living systems, typical not only of the molecular-genetic level, but of higher levels of organization as well, are considered. Application of different ways to describe gene networks for modeling oscillatory molecular-genetic systems is considered, where the most important factor for the emergence of cyclic behavior is the presence of feedback. Techniques for finding potentially oscillatory enzymatic systems are presented. Using the method described in the article, we present and analyze, in a step-by-step manner, first the structural models (graphs) of gene networks and then the reconstruction of the mathematical models and computational experiments with them. Structural models are ideally suited for the tasks of an automatic search for potential oscillating contours (linked subgraphs), whose structure can correspond to the mathematical model of the molecular-genetic system that demonstrates oscillatory behavior in dynamics. At the same time, it is the numerical study of mathematical models for the selected contours that makes it possible to confirm the presence of stable limit cycles in them. As an example of application of the technology, a network of 300 metabolic reactions of the bacterium Escherichia coli was analyzed using mathematical and computer modeling tools. In particular, oscillatory behavior was shown for a loop whose reactions are part of the tryptophan biosynthesis pathway.
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Nizhegorodov, A., A. Gavrilin, B. Moyzes, and K. Kuvshinov. "The development of baking technology for bulk materials based on the use of alternative electric furnace." Bulletin of the Karaganda University. "Physics" Series 98, no. 2 (June 30, 2020): 93–100. http://dx.doi.org/10.31489/2020ph2/93-100.
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The article based on the experimental data and it describes the development of a rational design of an oscillatory system for controlled vibrational feeding of bulk materials during their heat treatment in furnaces with a vibratory base plate, which, together with the moving trolley on elastic connections, is the basis to transfer bulk material in the thermal field of an electric heating system with set processing time. To create nonsymmetric oscillations and to obtain unidirectional material motion at the horizontal furnace position, the conical springs are used. They should provide a gently inclined resonant peak, which can significantly reduce the sensitivity of the oscillating system to fluctuations of the natural frequency and excitation frequency, stiffness, friction and other factors under high temperatures and instability of the electrical network. However, the total elastic characteristic of the oscillatory system which is obtained as a result of the experiments consists of conical and cylindrical springs and shows a weakly expressed nonlinearity. Therefore, to achieve a transport effect it will require the installation of the entire furnace unit at an angle to the horizon. According to the available experimental data, a linear model of the oscillatory system was utilized.
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Bhattacharjee, Soumyendu, Aishwarya Banerjee, Amit Rakshit, Swapan Bhattacharyya, Swati Chowdhuri, Biswajit Sarkar, and Biswarup Neogi. "Dynamics of Cardiovascular Muscle Using a Non-Linear Symmetric Oscillator." Symmetry 13, no. 1 (January 18, 2021): 151. http://dx.doi.org/10.3390/sym13010151.
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In this paper, a complete non-linear symmetric oscillator model using the Hamiltonian approach has been developed and used to describe the cardiovascular conduction process’s dynamics, as the signal generated from the cardiovascular muscle is non-deterministic and random. Electrocardiogram (ECG) signal is a significant factor in the cardiovascular system as most of the medical diagnoses can be well understood by observing the ECG signal’s amplitude. A non-linear cardiovascular muscle model has been proposed in this study, where a modified vanderPol symmetric oscillator-based equation is used. Gone are the days whena non-linear system had been designed using the describing function technique. It is better to design a non-linear model using the Hamiltonian dynamical equation for its high accuracy and flexibility. Varying a non-linear spring constant using this type of approach is more comfortable than the traditional describing function technique. Not only that but different initial conditions can also be taken for experimental purposes. It never affects the overall modeling. The Hamiltonian approach provides the energy of an asymmetric oscillatory system of that cardiovascular conduction system. A non-linear symmetric oscillator was initially depicted by the non-linear mass-spring (two degrees of freedom) model. The motion of an uncertain non-linear cardiovascular system has been solved considering second-order approximation, which also demonstrates the possibility of introducing spatial dimensions. Finally, the model’s natural frequency expression has also been simulated and is composed of the previously published result.
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Choi, Jeong Ryeol, Ji Nny Song, and Yeontaek Choi. "Analyzing Density Operator in Thermal State for Complicated Time-Dependent Optical Systems." Advances in Optics 2014 (July 24, 2014): 1–6. http://dx.doi.org/10.1155/2014/141076.
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Density operator of oscillatory optical systems with time-dependent parameters is analyzed. In this case, a system is described by a time-dependent Hamiltonian. Invariant operator theory is introduced in order to describe time-varying behavior of the system. Due to the time dependence of parameters, the frequency of oscillation, so-called a modified frequency of the system, is somewhat different from the natural frequency. In general, density operator of a time-dependent optical system is represented in terms of the modified frequency. We showed how to determine density operator of complicated time-dependent optical systems in thermal state. Usually, density operator description of quantum states is more general than the one described in terms of the state vector.
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Malyshev, V. L., K. V. Moiseyev, and E. F. Moiseeva. "Regimes of fluid flow in mixed convection." Proceedings of the Mavlyutov Institute of Mechanics 8, no. 1 (2011): 124–32. http://dx.doi.org/10.21662/uim2011.1.011.
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In this paper the behavior of the solution of the system of equations of thermal convection in a rectangular region is considered. For natural convection, characteristic numbers are found at which oscillatory regimes arise. Various ratios of the length and height of the cavity are considered. The effect of mixed convection on the nature of the fluid flow is estimated.
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MOJAHEDI, M., M. T. AHMADIAN, and K. FIROOZBAKHSH. "OSCILLATORY BEHAVIOR OF AN ELECTROSTATICALLY ACTUATED MICROCANTILEVER GYROSCOPE." International Journal of Structural Stability and Dynamics 13, no. 06 (July 2, 2013): 1350030. http://dx.doi.org/10.1142/s0219455413500302.
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This paper is concerned with the study of the oscillatory behavior of an electrostatically actuated microcantilever gyroscope with a proof mass attached to its free end. In mathematical modeling, the effects of different nonlinearities such as electrostatic forces, fringing field, inertial terms and geometric nonlinearities are considered. The microgyroscope is subjected to bending oscillations around the static deflection coupled with base rotation. The primary oscillation is generated in drive direction of the microgyroscope by a pair of DC and AC voltages on the tip mass. The secondary oscillation occurring in the sense direction is induced by the Coriolis coupling caused by the input angular rate of the beam along its axis. The input angular rotation can be measured by sensing the oscillation tuned to another DC voltage of the proof mass. First, a system of nonlinear equations governing the flexural–flexural motion of electrostatically actuated microbeam gyroscopes subjected to input rotations is derived by the extended Hamilton principle. The oscillatory behavior of the microgyroscopes subjected to DC voltages in both directions is then analytically investigated. Finally, the effects of the geometric parameters, base rotation and fringing field on the natural frequencies of the system are assessed.
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Girardin, Léo. "Two components is too simple: an example of oscillatory Fisher–KPP system with three components." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 6 (September 24, 2019): 3097–120. http://dx.doi.org/10.1017/prm.2019.46.
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AbstractIn a recent paper by Cantrell et al. [9], two-component KPP systems with competition of Lotka–Volterra type were analyzed and their long-time behaviour largely settled. In particular, the authors established that any constant positive steady state, if unique, is necessarily globally attractive. In the present paper, we give an explicit and biologically very natural example of oscillatory three-component system. Using elementary techniques or pre-established theorems, we show that it has a unique constant positive steady state with two-dimensional unstable manifold, a stable limit cycle, a predator–prey structure near the steady state, periodic wave trains and point-to-periodic rapid travelling waves. Numerically, we also show the existence of pulsating fronts and propagating terraces.
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Kasbawati, Yuliana Jao, and Nur Erawaty. "Dynamic study of the pathogen-immune system interaction with natural delaying effects and protein therapy." AIMS Mathematics 7, no. 5 (2022): 7471–88. http://dx.doi.org/10.3934/math.2022419.
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<abstract> <p>This study aims to propose and analyze a mathematical model of the competitive interaction of the pathogen-immune system. Some effects of the existence of natural delays and the addition of therapeutic proteins are considered in the model. A delay arises from the indirect response of the host body when a pathogen invades. The other comes from the maturation of immune cells to produce immune memory cells since the immune system and antigenic substances responsible for provoking the production of immune memory cells. Analytical investigations suggest several sufficient conditions for the existence of a positive steady-state solution. There is a critical pair of delays at which oscillatory behavior appears around the positive steady-state solution. Numerical simulations were carried out to describe the results of the analysis and show that the proposed model can describe the speed of pathogen eradication due to the addition of therapeutic proteins as antigenic substances.</p> </abstract>
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Suvorov, N. B., T. V. Sergeev, and I. V. Yarmosh. "PHYSIOLOGICAL BASICS OF CARDIORESPIRATORY BIOFEEDBACK CONTROL OF OSCILLATORY POSTURAL LOAD." Medical academic journal 18, no. 2 (June 15, 2018): 78–88. http://dx.doi.org/10.17816/maj18278-88.
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The technology of functional normalization of the cardiovascular system parameters by means of the alternating biofeedback on cardiac rhythm (cardiorespiratory training) with the use of a turning bed (verticalizer) is described, which allows to implement the oscillatory postural effects of ortho- and antiorthostatic nature automatically. Aim of the study. Increasing of application area of cardiorespiratory training due to the variety of options for biofeedback signals. Methods. The oscillation of the turning bed controlled by means of the parameters of heart rate variability sets for the examinee the order of alternation of the inspiration and expiration phases and the phases of the inspiration/expiration beginning. The method is available to patients with low vision, bedridden patients, early ages children; patients who are not able to understand the essence of the procedure. Results of researches. Positive dynamics of the test subjects’ functional state is, in particular, the normalization of activity of components of the autonomic nervous system; the reinstatement of the natural breathing pattern lost due to various reasons; increasing the variability of the heart rate; the cardiovascular system training due to moderate alternating ortho- and antiorthostatic load, estimated by number of physiological parameters.
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Barth, Anna, Leif Karlstrom, Benjamin K. Holtzman, Arthur Paté, and Avinash Nayak. "Sonification and Animation of Multivariate Data to Illuminate Dynamics of Geyser Eruptions." Computer Music Journal 44, no. 1 (2020): 35–50. http://dx.doi.org/10.1162/comj_a_00551.
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Abstract Sonification of time series data in natural science has gained increasing attention as an observational and educational tool. Sound is a direct representation for oscillatory data, but for most phenomena, less direct representational methods are necessary. Coupled with animated visual representations of the same data, the visual and auditory systems can work together to identify complex patterns quickly. We developed a multivariate data sonification and visualization approach to explore and convey patterns in a complex dynamic system, Lone Star Geyser in Yellowstone National Park. This geyser has erupted regularly for at least 100 years, with remarkable consistency in the interval between eruptions (three hours) but with significant variations in smaller scale patterns between each eruptive cycle. From a scientific standpoint, the ability to hear structures evolving over time in multiparameter data permits the rapid identification of relationships that might otherwise be overlooked or require significant processing to find. The human auditory system is adept at physical interpretation of call-and-response or causality in polyphonic sounds. Methods developed here for oscillatory and nonstationary data have great potential as scientific observational and educational tools, for data-driven composition with scientific and artistic intent, and towards the development of machine learning tools for pattern identification in complex data.
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Juyang, Zhang, and Bettina Wolf. "Impact of Type of Sugar Beet Pectin–Sodium Caseinate Interaction on Emulsion Properties at pH 4.5 and pH 7." Foods 10, no. 3 (March 17, 2021): 631. http://dx.doi.org/10.3390/foods10030631.
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Equal parts of sugar beet pectin and sodium caseinate were interacted through electrostatic attraction, enzymatic crosslinking, and the Maillard reaction to prepare three oil-in-water emulsifier systems. Oil-in-water emulsions (10%) were processed via high shear overhead mixing at the natural pH of the emulsifier systems, followed by pH adjustment to pH 4.5 and pH 7. The emulsions were stable against coalescence, except for a slight increase in the mean droplet size for the enzymatic cross-liked emulsion at pH 4.5 over a 14-day storage period. This emulsion also showed the lowest absolute zeta (ζ)-potential value of near 30 mV. The Maillard interaction emulsifier system resulted in larger droplet sizes compared to the other two emulsifier systems. Small deformation oscillatory shear rheology assessment of the emulsion cream phases revealed an impact of the emulsifier system design at pH 4.5.
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MAKOWIEC, DANUTA. "MODELING THE SINOATRIAL NODE BY CELLULAR AUTOMATA WITH IRREGULAR TOPOLOGY." International Journal of Modern Physics C 21, no. 01 (January 2010): 107–27. http://dx.doi.org/10.1142/s0129183110015002.
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The role of irregularity in intercellular connections is studied in the first natural human pacemaker called the sinoatrial node by modeling with the Greenberg–Hastings cellular automata. Facts from modern physiology about the sinoatrial node drive modeling. Heterogeneity between cell connections is reproduced by a rewiring procedure applied to a square lattice. The Greenberg–Hastings rule, representing the intrinsic cellular dynamics, is modified to imitate self-excitation of each pacemaker cell. Moreover, interactions with nearest neighbors are changed to heterogeneous ones by enhancing horizontal connections. Stationary states of the modeled system emerge as self-organized robust oscillatory states. Since the sinoatrial node role relies on a single cell cyclic activity, properties of single cells are studied. It appears that the strength and diversity of cellular oscillations depend directly on properties of intrinsic cellular dynamics. But these oscillations also depend on the underlying topology. Moderate nonuniformity of intercellular connections are found vital for proper function of the sinoatrial node, namely, for producing robust oscillatory states that are able to respond effectively to the autonomic system control.
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Lin, Wei-Hsiang, Edo Kussell, Lai-Sang Young, and Christine Jacobs-Wagner. "Origin of exponential growth in nonlinear reaction networks." Proceedings of the National Academy of Sciences 117, no. 45 (October 22, 2020): 27795–804. http://dx.doi.org/10.1073/pnas.2013061117.
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Exponentially growing systems are prevalent in nature, spanning all scales from biochemical reaction networks in single cells to food webs of ecosystems. How exponential growth emerges in nonlinear systems is mathematically unclear. Here, we describe a general theoretical framework that reveals underlying principles of long-term growth: scalability of flux functions and ergodicity of the rescaled systems. Our theory shows that nonlinear fluxes can generate not only balanced growth but also oscillatory or chaotic growth modalities, explaining nonequilibrium dynamics observed in cell cycles and ecosystems. Our mathematical framework is broadly useful in predicting long-term growth rates from natural and synthetic networks, analyzing the effects of system noise and perturbations, validating empirical and phenomenological laws on growth rate, and studying autocatalysis and network evolution.
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Smith, Matthew J., Jonathan A. Sherratt, and Nicola J. Armstrong. "The effects of obstacle size on periodic travelling waves in oscillatory reaction–diffusion equations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2090 (November 27, 2007): 365–90. http://dx.doi.org/10.1098/rspa.2007.0198.
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Many natural populations undergo multi-year cycles, and field studies have shown that these can be organized into periodic travelling waves (PTWs). Mathematical studies have shown that large-scale landscape obstacles represent a natural mechanism for wave generation. Here, we investigate how the amplitude and wavelength of the selected waves depend on the obstacle size. We firstly consider a large circular obstacle in an infinite domain for a reaction–diffusion system of ‘ λ – ω ’ type. We use perturbation theory to derive a leading order approximation to the wave generated by the obstacle. This shows the dependence of the wave properties on both parameter values and obstacle size. We find that the limiting values of the amplitude and wavelength are approached algebraically with distance from the obstacle edge, rather than exponentially in the case of a flat boundary. We use our results to predict the properties of waves generated by a large circular obstacle for an oscillatory predator–prey system, via a reduction of the predator–prey model to normal form close to Hopf bifurcation. Our predictions compare well with numerical simulations. We also discuss the implications of these results for wave stability and briefly investigate the effects of obstacles with elliptical geometries.
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Lewis, David W., Paul E. Allaire, and Peter W. Thomas. "Active Magnetic Control of Oscillatory Axial Shaft Vibrations in Ship Shaft Transmission Systems Part 1: System Natural Frequencies and Laboratory Scale Model." Tribology Transactions 32, no. 2 (January 1989): 170–78. http://dx.doi.org/10.1080/10402008908981876.
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Jamisola, Rodrigo S., Jr., and Elmer P. Dadios. "Experimental Identification of Manipulator Dynamics Through the Minimization of its Natural Oscillations." Journal of Advanced Computational Intelligence and Intelligent Informatics 14, no. 1 (January 20, 2010): 39–45. http://dx.doi.org/10.20965/jaciii.2010.p0039.
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This work presents amethod of identifying the dynamics parameters of rigid-body manipulators through the minimization of its natural oscillations. It is assumed that each link has an actuated joint that is different from its center of mass, such that its driving torque is influenced by gravitational force. In this earlier results of our study, it is assumed that the inertias can be expressed in terms of the mass and center of mass. This work utilizes the actual force of gravity for the manipulator link to achieve natural oscillation. The oscillatory motion allows the system to be converted into an optimization problem through the minimization of the frequency of oscillation. The correct dynamics parameters are found when the minimum frequency of oscillation is achieved. The proposed method is analyzed and a theorem is presented that supports the claims presented in this work together with implementation results.
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Rose, Mark A., David J. Beattie, and John W. White. "Oscillations of Whole-plant Transpiration in `Moonlight' Rose." Journal of the American Society for Horticultural Science 119, no. 3 (May 1994): 439–45. http://dx.doi.org/10.21273/jashs.119.3.439.
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Two distinct patterns of whole-plant transpiration (WPT) were observed in `Moonlight' rose (Rosa hybrida L.) using an automated system that integrated a greenhouse climate computer, a heat-balance sap-flow gauge, an electronic lysimeter, and an infrared leaf temperature sensor. One pattern consisted of a steady rate of transpiration in a stable greenhouse environment. The second pattern consisted of large oscillations in transpiration unrelated to any monitored microclimate rhythms. These oscillations had a sine-wave pattern with periods of 50 to 90 minutes and ranged from 2 to 69 g·h-1 in natural light and 3 to 40 g·h-1 under high-pressure sodium lamps at night. Leaf-air temperature difference (T1 - Ta) also oscillated and was inversely related to transpiration rate. Oscillatory transpiration has not been reported in roses. Plant scientists need to recognize the complex and dynamic nature of plant responses such as the oscillatory pattern of WPT monitored in Rosa hybrida when selecting monitoring and control strategies.
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LANZA, VALENTINA, LINDA PONTA, MICHELE BONNIN, and FERNANDO CORINTO. "MULTIPLE ATTRACTORS AND BIFURCATIONS IN HARD OSCILLATORS DRIVEN BY CONSTANT INPUTS." International Journal of Bifurcation and Chaos 22, no. 11 (November 2012): 1250267. http://dx.doi.org/10.1142/s0218127412502677.
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Hard oscillators are dynamical systems that show the coexistence of qualitatively different attractors, in the form of limit cycles and equilibrium points. In the presence of external inputs their dynamic behavior is significantly different from those of oscillators, called soft, with a limit cycle as unique attractor. This paper studies the dynamics of a simple hard oscillator under the influence of a constant external input. It is shown that, despite the apparent simplicity, when the input strength and the oscillator's natural frequency are varied the system exhibits many different bifurcation phenomena, including global bifurcations as saddle-node on limit cycle and homoclinic bifurcations. The model under investigation can play a role in neuroscience, as it exhibits two different mechanisms of class I neural excitability and one mechanism for class II. It also highlights a mechanism of transition between the two classes.
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Harleman, David R. F., and William C. Shapiro. "THE DYNAMICS OF A SUBMERGED MOORED SPHERE IN OSCILLATORY WAVES." Coastal Engineering Proceedings 1, no. 7 (January 29, 2011): 41. http://dx.doi.org/10.9753/icce.v7.41.
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The results of an analytical and experimental investigation into the dynamics of a buoyant sphere moored by a single line in shallow water waves are presented. The sphere motion and the mooring line forces are related to the sphere diameter, weight, submergence and the wave frequency, height and water depth. Analytically, the phenomenon is approached as a forced vibration problem. The sphere and its mooring line acts as a spring-mass system driven by the oscillating wave force. The relevant dimensionless parameters are the ratio between the natural frequency of the moored sphere and the wave frequency and the ratio between the dynamic mooring force due to a given wave and the force on the sphere held stationary in the same wave. Experimental values of the frequency and force ratios obtained from tests made at the Massachusetts Institute of Technology Hydrodynamics Laboratory over a range of sphere and wave characteristics are in essential agreement with the analytically determined values. The investigation was supported by the Humble Oil and Refining Company of Houston, Texas.
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Safarov, Ismoil, Мuhsin Теshaev, Sharifboy Axmedov, Doniyor Rayimov, and Farhod Homidov. "Manometric Tubular Springs Oscillatory Processes Modeling with Consideration of its Viscoelastic Properties." E3S Web of Conferences 264 (2021): 01010. http://dx.doi.org/10.1051/e3sconf/202126401010.
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This article is dedicated to the operation and management of systems of machine-building and aviation enterprises, systems of production, transport, storage of oil and gas, issues of control of technological processes are of great importance. Control of technological processes is carried out by monitoring the pressure and other parameters. These measuring instruments must have high reliability and the necessary accuracy. In this connection, there is a sharp increase in interest in determining the dynamic parameters of the elements of measuring devices. The main elements of such devices are monomeric tubular springs (Bourdon tubes). The paper considers the natural and forced steady-state oscillations of a thin curved rod interacting with a liquid. Based on the principle of possible displacements, a resolving system of partial differential equations and the corresponding boundary conditions are obtained. The problem is solved numerically by the Godunov orthogonal run method, and the Muller method and the Eigen frequencies found are compared with the experimental results. As a result, for a given axial perturbation, it was possible to select such an effect, in the orthogonal direction, that the amplitude of the longitudinal vibrations of the rod at the first resonance decreased by 20 times. The described vibration damping effect is due to the interrelation of transverse and longitudinal vibrations and is fundamentally impossible in the case of a straight rod.
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Cintra, Daniel, and Pierre Argoul. "Nonlinear argumental oscillators: A few examples of modulation via spatial position." Journal of Vibration and Control 23, no. 18 (January 22, 2016): 2888–911. http://dx.doi.org/10.1177/1077546315623888.
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Under certain conditions, an oscillator can enter a stable regime when submitted to an external harmonic force whose frequency is far from the natural frequency of the oscillator. This may happen when the external force acts on the oscillator in a way which depends on the oscillator's spatial position. This phenomenon is called “argumental oscillation”. In this paper, six argumental oscillators are described and modeled, and experimental results are given and compared to numerical simulations based on the models. A polar Van der Pol representation, with embedded time indications, is used to allow a precise comparison. The pendulums are modeled as Duffing oscillators. The six models are based on various pendulums excited by spatially localized magnetic-field sources consisting of wire coils. Each pendulum receives the excitation via a steel element, or a permanent magnet, fitted at the tip of the pendulum's rod. The spatial localization induces another nonlinearity besides the Duffing nonlinearity. A control system allowing a real-time Van der Pol representation of the motion is presented. Attractors are brought out from experimental results.
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Plint, M. A., and A. J. Martyr. "Technical Note: Some limitations of the chassis dynamometer in vehicle simulation." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 215, no. 3 (March 1, 2001): 431–37. http://dx.doi.org/10.1243/0954407011525647.
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The chassis dynamometer is the standard tool for legislatively prescribed emission tests. For emission testing and many other vehicle test purposes the dynamic response is an adequate approximation to ‘on road’ conditions. This is not necessarily true if the requirement is to study vehicle driveline dynamics. The present analysis arose from two quite separate requirements to study driveline oscillations and ‘judder’ using chassis dynamometers of the same eVective inertia as the vehicle. During the studies by the authors it became clear that the dynamics of the vehicle-dynamometer combination diVer in important respects from those of a vehicle on the road. As the eVective inertia of the dynamometer falls the natural frequency of the engine-driveline-vehicle system rises while the oscillatory energy imparted to the vehicle falls rapidly. For reasonably accurate simulation of driveline vibration the roll inertia should be some five times that of the vehicle. It is shown that electrical simulation of inertia, as employed in most modern chassis dynamometers, is unsatisfactory where oscillatory phenomena are being studied.
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Eliseev, Andrey, Sergey Eliseev, Nikolay Kuznetsov, and Roman Bolshakov. "Possibilities of Using Frequency Energy Functions in Problems of Dynamics of Machines for Transport and Technological Purposes." MATEC Web of Conferences 346 (2021): 03073. http://dx.doi.org/10.1051/matecconf/202134603073.
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New approaches to the evaluation of the dynamic properties of mechanical vibration systems are proposed, which consider as the design schemes for technical objects operating under dynamic vibration loads. The purpose of the study is to develop ideas for the use of frequency energy functions. In this case, the frequency functions represent the ratio of the potential and kinetic energies in a specific form, based on the use of the relations of the coordinates of the system in the stationary mode. The technologies of system analysis and structural mathematical modeling are used. In this approach, the mechanical oscillatory system is correspond with the block diagram of the automatic control system, which is equivalent in dynamic terms. It is proposed to use the analytical apparatus to take into account the features of interpartial relations, to evaluate the specific modes of dynamic interaction of system elements. A method for determining the natural vibration frequencies of the system based on the use of the frequency energy function is proposed. Methodological bases of approaches to solving problems of system dynamics related to the assessment of the influence of system parameters on their frequency properties are developed. The results of computational modeling are presented.
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Stepanov, Alexey Sergeevich, and Andrei Petrovich Koinosov. "PHYSIOLOGICAL CHANGES IN THE EXTERNAL RESPIRATORY SYSTEM AND OXYGEN-TRANSPORTATION FUNCTIONS OF ATHLETES’S BLOOD IN THE NORTH CONDITIONS. LITERATURE REVIEW." Scientific medical Bulletin of Ugra 28, no. 2 (2021): 25–31. http://dx.doi.org/10.25017/2306-1367-2021-28-2-25-31.
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The regions of the Far North and regions equated to them diff er from central Russia in the severity of their climate. With long-term residence in the North, there is a regular alternation of stress processes necessary to adapt to new seasonal conditions. This review article highlights the view of various researchers on the problem of adaptation of some physiological systems of athletes to the conditions of the North. Physiological changes under the infl uence of natural and climatic factors in the most important systems responsible for providing the body with oxygen are briefl y highlighted. The state of the oxygen transport and respiratory systems is one of the most important values that determine the functional state of the body of athletes, which, in turn, determines the eff ectiveness of their sports activity. The main parameters of the working rhythms of physiological systems are also determined by the regularities of sports training in accordance with the calendar plan. It can be assumed that in the regions of the North, the athlete’s body synchronizes various oscillatory processes: seasonal biorhythms and working rhythms of physiological systems. In this case, the architectonics of biorhythms is determined by the mechanisms of phase synchronization of the functional readiness of the eff ector systems with the rhythms of the functional request [15]. Determination of the patterns of interaction of these oscillatory processes is an urgent task of modern science in the fi eld of sports physiology.
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Wahrburg, Arne, Janne Jurvanen, Matias Niemelä, and Mikael Holmberg. "On reference trajectory generation for overhead crane travel movements." at - Automatisierungstechnik 70, no. 3 (March 1, 2022): 300–311. http://dx.doi.org/10.1515/auto-2021-0147.
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Abstract Input shaping is a well-established approach for suppressing oscillations in systems with flexible modes. When applying input shaping, it is common to assume the system to be at rest initially, i. e., the initial conditions of the oscillatory part of the system have to be at zero. In this paper, we propose a method that allows relaxing the aforementioned assumption for a large class of input signals. The approach relies on the standard input shaper structure but re-parameterizes the shaper such that non-zero initial conditions are cancelled out by the inputs, resulting in zero residual oscillation. Natural physical limitations of the concept are discussed and the application to overhead cranes is presented. The method is validated both in simulation as well as in experiments using a small scale crane. In addition, a simplified trajectory generator is presented that tailors a standard seven-segment jerk-limited motion profile such that zero residual vibrations are achieved without any dedicated input shaping.
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Taratorkin, Igor, Victor Derzhanskii, and Alexander Volkov. "Stabilization of transport tracked vehicle trajectory." MATEC Web of Conferences 224 (2018): 02038. http://dx.doi.org/10.1051/matecconf/201822402038.
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The article presents the research findings of the controlled motion dynamics of tracked vehicles equipped with a steering system with discrete properties. It is established that the potential high-speed performance is limited by motion instability and by dynamic properties i.e. the phase lag of the vehicle response to the harmonic control input and the “engine overshoot” to a unit step function (steering jerk). Technical proposals allowing for the high-speed performance of the vehicle are substantiated, such as yaw moment control, which ensures the positive-difference of the partial differential coefficients of yaw moment and cornering resistance moment with respect to curvature; increase of the dynamic system stiffness for increasing the natural frequency and decreasing energy when exciting oscillatory processes; implementation of Shaper steering brake control algorithms.
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Phung, Viet-Anh, Pavel Kudinov, Dmitry Grishchenko, and Martin Rohde. "Input Calibration and Validation of RELAP5 Against CIRCUS-IV Single Channel Tests on Natural Circulation Two-Phase Flow Instability." Science and Technology of Nuclear Installations 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/130741.
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RELAP5 is a system thermal-hydraulic code that is used to perform safety analysis on nuclear reactors. Since the code is based on steady state, two-phase flow regime maps, there is a concern that RELAP5 may provide significant errors for rapid transient conditions. In this work, the capability of RELAP5 code to predict the oscillatory behavior of a natural circulation driven, two-phase flow at low pressure is investigated. The simulations are compared with a series of experiments that were performed in the CIRCUS-IV facility at the Delft University of Technology. For this purpose, we developed a procedure for calibration of the input and code validation. The procedure employs (i) multiple parameters measured in different regimes, (ii) independent consideration of the subsections of the loop, and (iii) assessment of importance of the uncertain input parameters. We found that predicted system parameters are less sensitive to variations of the uncertain input and boundary conditions in high frequency oscillations regime. It is shown that calculation results overlap experimental values, except for the high frequency oscillations regime where the maximum inlet flow rate was overestimated. This finding agrees with the idea that steady state, two-phase flow regime maps might be one of the possible reasons for the discrepancy in case of rapid transients in two-phase systems.
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van Eysden, C. Anthony. "Oscillatory superfluid Ekman pumping in helium II and neutron stars." Journal of Fluid Mechanics 783 (October 16, 2015): 251–82. http://dx.doi.org/10.1017/jfm.2015.553.
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The linear response of a superfluid, rotating uniformly in a cylindrical container and threaded with a large number of vortex lines, to an impulsive increase in the angular velocity of the container is investigated. At zero temperature and with perfect pinning of vortices to the top and bottom of the container, we demonstrate that the system oscillates persistently with a frequency proportional to the vortex line tension parameter to the quarter power. This low-frequency mode is generated by a secondary flow analogous to classical Ekman pumping that is periodically reversed by the vortex tension in the boundary layers. We compare analytic solutions to the two-fluid equations by Chandler & Baym (J. Low Temp. Phys., vol. 62, 1986, pp. 119–142) with the spin-up experiments by Tsakadze & Tsakadze (J. Low Temp. Phys., vol. 39, 1980, pp. 649–688) in helium II and find that the frequency agrees within a factor of four, although the experiment is not perfectly suited to the application of linear theory. We argue that this oscillatory Ekman pumping mode, and not Tkachenko modes, provides a natural explanation for the observed oscillation. In neutron stars, the oscillation period depends on the pinning interaction between neutron vortices and flux tubes in the outer core. Using a simplified pinning model, we demonstrate that strong pinning can accommodate modes with periods of days to years, which are only weakly damped by mutual friction over longer time scales.
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Pelekasis, Nikolaos A., and John A. Tsamopoulos. "Bjerknes forces between two bubbles. Part 2. Response to an oscillatory pressure field." Journal of Fluid Mechanics 254 (September 1993): 501–27. http://dx.doi.org/10.1017/s002211209300223x.
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The motion of two gas bubbles in response to an oscillatory disturbance in the ambient pressure is studied. It is shown that the relative motion of bubbles of unequal size depends on the frequency of the disturbance. If this frequency is between the two natural frequencies for volume oscillations of the individual bubbles, the two bubbles are seen to move away from each other; otherwise attractive forces prevail. Bubbles of equal size can only attract each other, irrespective of the oscillation frequency. When the Bond number, Bo (based on the average acceleration) lies above a critical region, spherical-cap shapes appear with deformation confined on the side of the bubbles facing away from the direction of acceleration. For Bo below the critical region shape oscillations spanning the entire bubble surface take place, as a result of subharmonic resonance. The presence of the oscillatory acoustic field adds one more frequency to the system and increases the possibilities for resonance. However, only subharmonic resonance is observed because it occurs on a faster timescale, O(1/ε), where ε is the disturbance amplitude. Furthermore, among the different possible periodic variations of the volume of each bubble, the one with the smaller period determines which Legendre mode will be excited through subharmonic resonance. Spherical-cap shapes also occur on a timescale O(1/ε). When the bubbles are driven below resonance and for quite large amplitudes of the acoustic pressure, ε ≈ 0.8, a subharmonic signal at half the natural frequency of volume oscillations is obtained. This signal is primarily associated with the zeroth mode and corresponds to volume expansion followed by rapid collapse of the bubbles, a behaviour well documented in acoustic cavitation experiments.
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Eliseev, V. І., S. А. Shevchenko, A. P. Tolstopyat, L. A. Fleer, and А. Р. Shevchenko. "Dynamics of oscillations of the "liquid bath - lance" system during injection processing of the melt in the ledle." Fundamental and applied problems of ferrous metallurgy, no. 34 (2020): 90–100. http://dx.doi.org/10.52150/2522-9117-2020-34-90-100.
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The aim of the study was to evaluate the influence of key waveform factors on the dynamics of the process during injection molding of cast iron with granular magnesium in ladles, their significance and relationship between them. Based on the theories of wave motion of liquid layers, a mathematical model has been developed that allows to investigate the oscillatory processes in the ladle during the processing of cast iron melt with granular magnesium. The model involved the processing of cast iron by injection of granular magnesium through the tuyeres of devices that are immersed in the melt. The oscillating system "Liquid bath - lance" is considered on the example of the bath of a heavy - duty filling bucket with its own frequency - 0.47 Hz. The influence of the most probable oscillation sources (natural frequency of the lance oscillation and the frequency of the conditional source) on the amplitude-frequency oscillations of the system elements is calculated. It is established that in addition to the natural frequencies of these elements, the system has two more natural oscillations. Given that the mass of the melt is much greater than the mass of the lance, it practically determines the behavior of the system during its excitation. That is, the system responds only to those excitations in which the frequency is close to the natural frequency of the liquid bath. In turn, it is shown that the natural frequency of the bath is largely determined by its diameter at the top. In practice, it is necessary to know the resonant frequencies of the liquid bath, the tuyere device, as well as all other sources of oscillations (gas jet decay, and oscillations of pop-up bubbles). Accordingly, it is necessary to try to dampen the amplitude with this dangerous resonant frequency. To reduce the oscillation amplitude of the bath surface when treating cast iron with granular magnesium, it is recommended to first estimate the natural resonant frequency of the liquid bath, and then select design solutions and processing parameters, avoiding dangerous frequencies close to the natural frequency of the bath. However, it should be noted that the spectrum of oscillation frequencies in the purl zone is quite wide and, of course, contains dangerous low frequencies.
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Lysenko, Iuliia, Yurii Kuts, Anatoliy Protasov, Mykhailo Redka, and Valentin Uchanin. "Enhanced Feature Extraction Algorithms Using Oscillatory-Mode Pulsed Eddy Current Techniques for Aircraft Structure Inspection." Transactions on Aerospace Research 2021, no. 3 (September 1, 2021): 1–16. http://dx.doi.org/10.2478/tar-2021-0013.
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Abstract A review of the existing literature shows that modern pulsed eddy current (PEC) technique for flaw detection in aircraft structure inspection is typically carried out in aperiodic mode. Аt the same time, the unstable characteristic points of the EC signal usually used as informative parameters can restrict the potential of this excitation mode due to significant measurement errors. This article considers an advanced PEC method of NDT based on the oscillatory mode. To obtain the conditions concerned with different modes of EC probe response oscillations, an equivalent scheme of the “testing object – EC probe” system was developed and analyzed. The frequency and attenuation coefficient of natural oscillations are proposed as the informative parameters of the probe signals. The obtained mathematical model of the probe signals allows for the dependence of proposed signal parameters on the characteristics of the testing object to be evaluated. Herein, we first develop algorithmic software for determining and analyzing the discrete amplitude and phase characteristics of PEC NDT signals based on the simulation results. The errors of the natural frequency oscillations and the attenuation coefficient determination as well as the optimal time for its determination are analyzed in order to minimize the possible errors. Next, the proposed informative parameters are experimentally investigated using a set of specimens. The obtained results confirm the possibility of the proposed methodology to enhance the inspection procedures related to the electrical conductivity and geometric parameters measurements as well as the detected defect sizing.
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Bhattacharya, Chandrachur, Ritabrata Saha, Achintya Mukhopadhyay, and Asok Ray. "Identification of Long-Term Behavior of Natural Circulation Loops: A Thresholdless Approach from an Initial Response." Sci 3, no. 1 (February 15, 2021): 14. http://dx.doi.org/10.3390/sci3010014.
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Natural circulation loop (NCL) systems are buoyancy-driven heat exchangers that are used in various industrial applications. The concept of passive heat exchange in NCL systems is attractive, because there is no need for an externally driven equipment (e.g., a pump) to maintain the fluid circulation. However, relying on buoyancy as the sole driving force may lead to several potential difficulties, one of which is generation of (possibly) time-varying nonlinearities in the dynamical system, where a difference in the time scales of heat transfer and fluid flow causes the flow to change from a steady-state regime to either an oscillatory regime or a flow-reversal regime, both of which are undesirable. In this paper, an algorithm is developed using tools of symbolic time-series analysis (e.g., probabilistic finite state automata (PFSA)) for the purpose of identifying selected regimes of operation in NCL systems using only data from the early transient operation, where the underlying principle is built upon the concept of pattern classification from measurements of fluid-flow dynamics. The proposed method is shown to be capable of identifying the current regime of operation from the initial time response under a given set of operational parameters. The efficacy of regime classification is demonstrated by testing on two datasets, generated from numerical simulation of a MATLAB SimuLink model that has previously been validated with experimental data. The results of the proposed PFSA-based classification are compared with those of a hidden Markov model (HMM) that serves as the baseline.
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Gan, Zhenyu, Yevgeniy Yesilevskiy, Petr Zaytsev, and C. David Remy. "All common bipedal gaits emerge from a single passive model." Journal of The Royal Society Interface 15, no. 146 (September 2018): 20180455. http://dx.doi.org/10.1098/rsif.2018.0455.
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In this paper, we systematically investigate passive gaits that emerge from the natural mechanical dynamics of a bipedal system. We use an energetically conservative model of a simple spring-leg biped that exhibits well-defined swing leg dynamics. Through a targeted continuation of periodic motions of this model, we systematically identify different gaits that emerge from simple bouncing in place. We show that these gaits arise along one-dimensional manifolds that bifurcate into different branches with distinctly different motions. The branching is associated with repeated breaks in symmetry of the motion. Among others, the resulting passive dynamic gaits include walking, running, hopping, skipping and galloping. Our work establishes that the most common bipedal gaits can be obtained as different oscillatory motions (or nonlinear modes) of a single mechanical system with a single set of parameter values. For each of these gaits, the timing of swing leg motion and vertical motion is matched. This work thus supports the notion that different gaits are primarily a manifestation of the underlying natural mechanical dynamics of a legged system. Our results might explain the prevalence of certain gaits in nature, and may provide a blueprint for the design and control of energetically economical legged robots.
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Beardo, Albert, Miquel López-Suárez, Luis Alberto Pérez, Lluc Sendra, Maria Isabel Alonso, Claudio Melis, Javier Bafaluy, et al. "Observation of second sound in a rapidly varying temperature field in Ge." Science Advances 7, no. 27 (June 2021): eabg4677. http://dx.doi.org/10.1126/sciadv.abg4677.
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Second sound is known as the thermal transport regime where heat is carried by temperature waves. Its experimental observation was previously restricted to a small number of materials, usually in rather narrow temperature windows. We show that it is possible to overcome these limitations by driving the system with a rapidly varying temperature field. High-frequency second sound is demonstrated in bulk natural Ge between 7 K and room temperature by studying the phase lag of the thermal response under a harmonic high-frequency external thermal excitation and addressing the relaxation time and the propagation velocity of the heat waves. These results provide a route to investigate the potential of wave-like heat transport in almost any material, opening opportunities to control heat through its oscillatory nature.
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Smith, M. J., J. J. Kobine, and F. A. Davidson. "Free and forced motion in an asymmetric liquid-column oscillator." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2092 (January 15, 2008): 905–22. http://dx.doi.org/10.1098/rspa.2007.0375.
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The results of a combined theoretical, numerical and experimental study of liquid oscillations in an asymmetric U-tube are presented. The configuration under investigation is analogous to that of the tuned liquid-column damper used to suppress oscillatory motion in large semi-supported structures. The liquid motion is described by a second-order ordinary differential equation that is nonlinear when the widths of the two vertical columns are unequal. It is shown that this asymmetry can be used as a tuning parameter to determine the natural frequency of free oscillations in the system, in addition to the known tuning effect of the connecting chamber height. The effects of viscous damping and periodic forcing are considered, leading to a description of probable initial and long-term resonance behaviour in a practical asymmetric device.
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Narain, A., J. H. Kurita, M. Kivisalu, A. Siemionko, S. Kulkarni, T. W. Ng, N. Kim, and L. Phan. "Internal Condensing Flows inside a Vertical Pipe: Experimental/Computational Investigations of the Effects of Specified and Unspecified (Free) Conditions at Exit." Journal of Heat Transfer 129, no. 10 (February 10, 2007): 1352–72. http://dx.doi.org/10.1115/1.2755063.
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Reported experimental and computational results confirm that both the flow features and heat-transfer rates inside a condenser depend on the specification of inlet, wall, and exit conditions. The results show that the commonly occurring condensing flows’ special sensitivity to changes in exit conditions (i.e., changes in exit pressure) arises from the ease with which these changes alter the vapor flow field in the interior. When, at a fixed steady mass flow rate, the exit pressure is changed from one steady value to another, the changes required of the interior vapor flow toward achieving a new steady duct flow are such that they do not demand a removal of the new exit pressure imposition back to the original steady value—as is the case for incompressible single phase duct flows with an original and “required” exit pressure. Instead, new steady flows may be achieved through appropriate changes in the vapor/liquid interfacial configurations and associated changes in interfacial mass, heat-transfer rates (both local and overall), and other flow variables. This special feature of these flows has been investigated here for the commonly occurring large heat sink situations, for which the condensing surface temperature (not heat flux) remains approximately the same for any given set of inlet conditions while the exit-condition changes. In this paper’s context of flows of a pure vapor that experience film condensation on the inside walls of a vertical tube, the reported results provide an important quantitative and qualitative understanding and support an exit-condition-based categorization of the flows. Experimental results and selected relevant computational results that are presented here reinforce the fact that there exist multiple steady solutions (with different heat-transfer rates) for multiple steady prescriptions of the exit condition—even though the other boundary conditions do not change. However, for some situations that do not fix any specific value for the exit condition (say, exit pressure) but allow the flow the freedom to choose any exit pressure value within a certain range, experiments confirm the computational results that, given enough time, there typically exists, under normal gravity conditions, a self-selected “natural” steady flow with a natural exit condition. This happens if the vapor flow is seeking (or is attracted to) a specific exit condition and the conditions downstream of the condenser allow the vapor flow a range of exit conditions that includes the specific natural exit condition of choice. However, for some unspecified exit-condition cases involving partial condensation, even if computations predict that a natural exit-condition choice exists, the experimental arrangement employed here does not allow the flow to approach its steady natural exit-condition value. Instead, it only allows oscillatory exit conditions leading to an oscillatory flow. For the reported experiments, these oscillatory pressures are induced and imposed by the instabilities in the system components downstream of the condenser.
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S. Sari, Ma’en, Wael G. Al-Kouz, and Anas M. Atieh. "Transverse Vibration of Functionally Graded Tapered Double Nanobeams Resting on Elastic Foundation." Applied Sciences 10, no. 2 (January 9, 2020): 493. http://dx.doi.org/10.3390/app10020493.
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The natural vibration behavior of axially functionally graded (AFG) double nanobeams is studied based on the Euler–Bernoulli beam and Eringen’s non-local elasticity theory. The double nanobeams are continuously connected by a layer of linear springs. The oscillatory differential equation of motion is established using the Hamilton’s principle and the constitutive relations. The Chebyshev spectral collocation method (CSCM) is used to transform the coupled governing differential equations of motion into algebraic equations. The discretized boundary conditions are used to modify the Chebyshev differentiation matrices, and the system of equations is put in the matrix-vector form. Then, the dimensionless transverse frequencies and the mode shapes are obtained by solving the standard eigenvalue problem. The effects of the coupling springs, Winkler stiffness, the shear stiffness parameter, the breadth and taper ratios, the small-scale parameter, and the boundary conditions on the natural transverse frequencies are carried out. Several numerical examples were conducted, and the authors believe that the results may be interesting in designing and analyzing double and multiple one-dimensional nano structures.
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Vedyernikov, Yuriy, Vasyl Tkachenko, and Volodymyr Shestakov. "The dialectics of cyclicity in the development of law." Naukovyy Visnyk Dnipropetrovs'kogo Derzhavnogo Universytetu Vnutrishnikh Sprav 3, no. 3 (September 30, 2021): 16–22. http://dx.doi.org/10.31733/2078-3566-2021-3-16-22.
Full textAbstract:
The dialectic of cyclicity in the system of dual natural and positive law, as the transition from one opposite to another, involution to evolution, quantitative transformations into qualitative and actually regular cyclicity of crises and stability in the legal system is studied. The dialectic of cyclicity in law occurs as constant oscillating processes of transition from one opposite to another, natural law into positive, involution into evolution, quantity into quality, crisis into stability, and development in a circle gradually turns into a spiral. Defining and substantiating the phases and stages of the cycle allows us to demonstrate the development of a particular cycle and the driving mechanisms of this transformation – the laws of dialectics, in particular, the unity and struggle of opposites in law, the transition from quantity to quality, denial of the old and so on. Oscillatory processes are manifested in opposites of phases and stages of cycles, and small cycles of development of law are embedded in large ones, where each cycle is part of a larger cycle, and that in turn is even larger, and so on. The end of one cycle leads to the transformation of the legal system and its manifestation in a new form and content at a new level of the spiral of development. Ways to overcome the crisis in the legal system should be sought, first of all, in the updated methodological principles of cyclicality in jurisprudence based on the ideas of natural law, based on the principles and laws of dialectics, laws of philosophy of law, and in combination with other branches of modern knowledge.
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Titiloye, E. O., J. A. Gbadeyan, and A. T. Adeosun. "An Oscillatory Radiating Hydromagnetic Internal Heat Generating Fluid Flow Through a Vertcal Porous Channel with Slip and Temperature Jump." International Journal of Applied Mechanics and Engineering 23, no. 2 (May 1, 2018): 503–19. http://dx.doi.org/10.2478/ijame-2018-0029.
Full textAbstract:
Abstract The present study concerns the natural convective heat generating/absorbing, radiative magnetohydrodynamic, oscillatory fluid flow through a vertical porous channel with slip and temperature jump. The effect of Joule dissipation is taken into consideration while it is assumed that the flow is fully developed. The differential transforms method(DTM) is employed to solve the system of non-linear ordinary differential equations that is obtained from the non-linear partial differential equations governing the flow. Semi analytical solutions of the steady and unsteady part of the flow in the slip flow regime through a vertical porous channel are obtained. The effects of various flow parameters on the velocity and temperature profiles as well as Nusselt and skin friction are presented graphically and discussed. An excellent agreement between the results of this article and those available in the literature validated the presented approach.