Jerky Dynamics Research Articles

Embolism propagation in Adiantum leaves and in a biomimetic system with constrictions.

Drought poses a significant threat to forest survival worldwide by potentially generating air bubbles that obstruct sap transport within plants' hydraulic systems. However, the detailed mechanism of air entry and propagation at the scale of the veins remains elusive. Building upon a biomimetic model of leaf which we developed, we propose a direct comparison of the air embolism propagation in Adiantum (maidenhair fern) leaves, presented in Brodribb et al. (Brodribb TJ, Bienaimé D, Marmottant P. 2016 Revealing catastrophic failure of leaf networks under stress. Proc. Natl Acad. Sci. USA 113, 4865-4869 (doi:10.1073/pnas.1522569113)) and in our biomimetic leaves. In particular, we evidence that the jerky dynamics of the embolism propagation observed in Adiantum leaves can be recovered through the introduction of micrometric constrictions in the section of our biomimetic veins, mimicking the nanopores present in the bordered pit membranes in real leaves. We show that the intermittency in the propagation can be retrieved by a simple model coupling the variations of pressure induced by the constrictions and the variations of the volume of the compliant microchannels. Our study marks a step with the design of a biomimetic leaf that reproduces particular aspects of embolism propagation in real leaves, using a minimal set of controllable and readily tunable components. This biomimetic leaf constitutes a promising physical analogue and sets the stage for future enhancements to fully embody the unique physical features of embolizing real leaves.

Jerky active matter: a phase field crystal model with translational and orientational memory

Most field theories for active matter neglect effects of memory and inertia. However, recent experiments have found inertial delay to be important for the motion of self-propelled particles. A major challenge in the theoretical description of these effects, which makes the application of standard methods very difficult, is the fact that orientable particles have both translational and orientational degrees of freedom which do not necessarily relax on the same time scale. In this work, we derive the general mathematical form of a field theory for soft matter systems with two different time scales. This allows to obtain a phase field crystal model for active particles with translational and orientational memory. Notably, this theory is of third order in temporal derivatives and can thus be seen as a spatiotemporal jerky dynamics. We obtain the phase diagram of this model, which shows that, unlike in the passive case, the linear stability of the liquid state depends on the damping coefficients. Moreover, we investigate sound waves in active matter. It is found that, in active fluids, there are two different mechanisms for sound propagation. For certain parameter values and sufficiently high frequencies, sound mediated by polarization waves experiences less damping than usual passive sound mediated by pressure waves of the same frequency. By combining the different modes, acoustic frequency filters based on active fluids could be realized.

Correlation between jerky flow and jerky dynamics in a nanoscratch on a metallic glass film

Chaos has been well understood in dynamic system, however, how the chaotic behavior occur in jerky flow in material, is still not clear, and is lack of specific chaotic attractor. Here the jerky evolution of lateral force and the stair-like fluctuation of lateral displacement are observed for Ni62Nb38(at.%) metallic glass film during nanoscratch process. This jerky flow is investigated by using the largest Lyapunov exponent, Kolmogorov entropy and fractal dimension, and chaotic behavior of lateral force-time and normal displacement-lateral displacement sequences is verified. In addition to time series analysis, it is found that jerk equation can be used to describe the jerky flow of the metallic-glass film during nanoscratch. More importantly, unambiguous chaotic attractor is presented by jerky dynamics using “jerk”-singularities, namely the total change rate of lateral force relative to scratch time. These reveal an inner connection between jerky flow and jerky dynamics in nanoscratch of a metallic-glass film.

Barkhausen Noise from Precessional Domain Wall Motion.

The jerky dynamics of domain walls driven by applied magnetic fields in disordered ferromagnets-the Barkhausen effect-is a paradigmatic example of crackling noise. We study Barkhausen noise in disordered Pt/Co/Pt thin films due to precessional motion of domain walls using full micromagnetic simulations, allowing for a detailed description of the domain wall internal structure. In this regime the domain walls contain topological defects known as Bloch lines which repeatedly nucleate, propagate, and annihilate within the domain wall during the Barkhausen jumps. In addition to bursts of domain wall propagation, the in-plane Bloch line dynamics within the domain wall exhibits crackling noise and constitutes the majority of the overall spin rotation activity.

Dynamics of a general jerky equation

Some classic nonlinear dynamical systems, such as Rössler's toroidal model, the Genesio model, and 19 Sprott's models, can be classified into seven distinct basic classes of jerky dynamics, labeled by . This paper is devoted to the dynamics of a general jerky equation which contains as parameters vary. It is shown that the system undergoes fold, Hopf, zero-Hopf, and Bogdanov–Takens bifurcations based on the center manifold theorem and normal form theory. Numerical simulations are also given to make the theoretical results visible and to detect more complicated dynamical behaviors, including degenerate Hopf bifurcation, fold bifurcation of cycle, and limit cycles. Especially, an apple-like attractive portrait is discovered near the zero-Hopf bifurcation point for the first time. Finally, according to the conclusions of the general jerky equation, exact conditions are summarized by two tables on how bifurcations will occur for , respectively.

Dynamics of cracks in disordered materials

Predicting when rupture occurs or cracks progress is a major challenge in numerous elds of industrial, societal and geophysical importance. It remains largely unsolved: Stress enhancement at cracks and defects, indeed, makes the macroscale dynamics extremely sensitive to the microscale material disorder. This results in giant statistical uctuations and non-trivial behaviors upon upscaling dicult to assess via the continuum approaches of engineering. These issues are examined here. We will see: How linear elastic fracture mechanics sidetracks the diculty by reducing the problem to that of the propagation of a single crack in an eective material free of defects, How slow cracks sometimes display jerky dynamics, with sudden violent events incompatible with the previous approach, and how some paradigms of statistical physics can explain it, How abnormally fast cracks sometimes emerge due to the formation of microcracks at very small scales.

Dynamics of Attractively and Repulsively Coupled Elementary Chaotic Systems

We investigate an elementary model for doubly coupled dynamical systems that consists of two identical, mutually interacting minimal chaotic flows in the form of jerky dynamics. The coupling mechanisms allow for the simultaneous presence of attractive and repulsive interactions between the systems. Despite its functional simplicity, the model is capable of exhibiting diverse types of dynamical phenomena induced by the presence of the couplings. We provide an in-depth numerical investigation of the dynamics depending on the coupling strengths and the autonomous dynamical behavior of the subsystems. Partly, the dynamics of the system can be analytically understood using the Poincaré–Lindstedt method. An approximation of periodic orbits is carried out in the vicinity of a phase-flip transition that leads to deeper insights into the organization of the appearing dynamics in the parameter space. In addition, we propose a circuit that enables an electronic implementation of the model. A variation of the coupling mechanism to a coupling in conjugate variables leads to a regime of amplitude death.

On the Possibility of the Jerk Derivative in Electrical Circuits

A subclass of dynamical systems with a time rate of change of acceleration are called Newtonian jerky dynamics. Some mechanical and acoustic systems can be interpreted as jerky dynamics. In this paper we show that the jerk dynamics are naturally obtained for electrical circuits using the fractional calculus approach with order γ. We consider fractional LC and RL electrical circuits with 1⩽γ<2 for different source terms. The LC circuit has a frequency ω dependent on the order of the fractional differential equation γ, since it is defined as ω(γ)=ω0γγ1-γ, where ω0 is the fundamental frequency. For γ=3/2, the system is described by a third-order differential equation with frequency ω~ω03/2, and assuming γ=2 the dynamics are described by a fourth differential equation for jerk dynamics with frequency ω~ω02.

Newtonian jerky dynamics and inertial instability

Newtonian jerky dynamics is applied to inertial instability analysis to study the nonlinear features of atmospheric motion under the action of variable forces. Theoretical analysis of the Newtonian jerky function is used to clarify the criteria for inertial instability, including the influences of the meridional distributions of absolute vorticity (ζg) and planetary vorticity (the β effect). The results indicate that the meridional structure of absolute vorticity plays a fundamental role in the dynamic features of inertial motion. Including only the β effect (with the assumption of constant ζg) does not change the instability criteria or the dynamic features of the flow, but combining the β effect with meridional variations of ζg introduces nonlinearities that significantly influence the instability criteria.

A Driver Modeling Based on the Preview-Follower Theory and the Jerky Dynamics

Based on the preview optimal simple artificial neural network driver model (POSANN), a new driver model, considering jerky dynamics and the tracing error between the real track and the planned path, is established. In this paper, the modeling for the driver-vehicle system is firstly described, and the relationship between weighting coefficients of driver model and system parameters is examined through test data. Secondly, the corresponding road test results are presented in order to verify the vehicle model and obtain the information on drive model and vehicle parameters. Finally, the simulations are carried out via CarSim. Simulation results indicate that the jerky dynamics need to be considered and the proposed new driver model can achieve a better path-following performance compared with the POSANN driver model.

A Simple Jerky Dynamics, Genesio System

The third order explicit autonomous differential equations named as jerk equations represent an interesting subclass of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this paper, we show that an algebraically simple system, the Genesio system can be recast into a jerky dynamics and its jerk equation can be derived from one-dimensional Newtonian equation. We also investigate the global dynamical properties of the corresponding jerk system.

Boundedness of Certain Forms of Jerky Dynamics

In this paper, we find regions in the bifurcation parameter space of certain forms of jerky dynamic systems where they are bounded. The method of analysis is based on a recent result about the boundedness of solutions of a certain type of third-order nonlinear differential equation with bounded delay. In particular, the boundedness of some chaotic attractors displayed by these systems is confirmed analytically.

Intermittency and roughening in the failure of brittle heterogeneous materials

Stress enhancement in the vicinity of brittle cracks makes the macro-scale failure properties extremely sensitive to the micro-scale material disorder. Therefore, (i) fracturing systems often display a jerky dynamics, so-called crackling noise, with seemingly random sudden energy release spanning over a broad range of scales, reminiscent of earthquakes; (ii) fracture surfaces exhibit roughness at scales much larger than that of material microstructure. Here, I provide a critical review of experiments and simulations performed in this context, highlighting the existence of universal scaling features, independent of both the material and the loading conditions, reminiscent of critical phenomena. I finally discuss recent stochastic descriptions of crack growth in brittle disordered media that seem to capture qualitatively—and sometimes quantitatively—these scaling features.

The jerky and knotty dynamics of RNA

RNA is known to exhibit a jerky dynamics, as intramolecular thermal motion, on <0.1 μs time scales, is punctuated by infrequent structural rearrangements on much longer time scales, i.e. from >10 μs up to a few minutes or even hours. These rare stochastic events correspond to the formation or dissociation of entire stems through cooperative base pairing/unpairing transitions. Such a clear separation of time scales in RNA dynamics has made it possible to implement coarse grained RNA simulations, which predict RNA folding and unfolding pathways including kinetically trapped structures on biologically relevant time scales of seconds to minutes. RNA folding simulations also enable to predict the formation of pseudoknots, that is, helices interior to loops, which mechanically restrain the relative orientations of other non-nested helices. But beyond static structural constraints, pseudoknots can also strongly affect the folding and unfolding dynamics of RNA, as the order by which successive helices are formed and dissociated can lead to topologically blocked transition intermediates. The resulting knotty dynamics can enhance the stability of RNA switches, improve the efficacy of co-transcriptional folding pathways and lead to unusual self-assembly properties of RNA.

NEW CONCEPTS IN ELECTROMAGNETIC JERKY DYNAMICS AND THEIR APPLICATIONS IN TRANSIENT PROCESSES OF ELECTRIC CIRCUIT

In this paper, jerk function for a transient process of RL circuit is investigated. Some new concepts such as time rate of change of induced emf, time rate of change of displacement current, and Appell function have been introduced for the flrst time in electromagnetic jerky dynamics. The problems on Appell function of several simple models in electromagnetic jerky dynamics are discussed. In the last conclusions and remarks are also presented.

On nonlinear dynamical systems topologically conjugate to jerky motion via a linear transformation

In a recent paper, it was shown that members of a class of three-dimensional nonlinear dynamical systems are equivalent to jerky dynamics. The transformations used have the restriction that the state variable in the jerky dynamics is the same as one of the state variables of the three-dimensional system. As a consequence, some of the transformations used are necessarily nonlinear. We show that by removing this restriction, some of these systems can be transformed to jerky dynamics via affine transformations. In particular, we give conditions under which the system is topologically conjugate to jerky dynamics via an affine transformation.

Synchronization of simple chaotic flows

Nonlinear scalar third-order differential equation or jerky dynamics … x =J(x, x ̇ , x ̈ ) have recently attracted considerable interest since they constitute an important tool to identify and classify elementary chaotic flows. We investigate whether and under what conditions such systems can be synchronized by various coupling schemes such as the methods of Pecora–Carroll and Cuomo–Oppenheim, BK-coupling and active–passive decomposition. In particular, for the latter two schemes, we present specific, simplified coupling or decomposition approaches that allow for analytical estimates of the rapidity of the synchronization error.

Simple polynomial classes of chaotic jerky dynamics

Third-order explicit autonomous differential equations, commonly called jerky dynamics, constitute a powerful approach to understand the properties of functionally very simple but nonlinear three-dimensional dynamical systems that can exhibit chaotic long-time behavior. In this paper, we investigate the dynamics that can be generated by the two simplest polynomial jerky dynamics that, up to these days, are known to show chaotic behavior in some parameter range. After deriving several analytical properties of these systems, we systematically determine the dependence of the long-time dynamical behavior on the system parameters by numerical evaluation of Lyapunov spectra. Some features of the systems that are related to the dependence on initial conditions are also addressed. The observed dynamical complexity of the two systems is discussed in connection with the existence of homoclinic orbits.

No-chaos criteria for certain jerky dynamics

Autonomous third-order scalar differential equations or jerky dynamics given by x ⃛ +Aẍ+Bẋ=g(x) are known to constitute an elementary class of dynamical systems that can exhibit chaotic behavior if the nonlinearity g( x), the entering control parameters and the initial conditions are appropriately chosen. We investigate conditions on g( x) and the control parameters that are necessary for the appearance of chaotic behavior in these equations by deriving several analytical criteria that exclude chaotic long-time solutions.

Transformations of nonlinear dynamical systems to jerky motion and its application to minimal chaotic flows

Third-order explicit autonomous differential equations in one scalar variable or, mechanically interpreted, jerky dynamics constitute an interesting subclass of dynamical systems that can exhibit many major features of regular and irregular or chaotic dynamical behavior. In this paper, we investigate the circumstances under which three dimensional autonomous dynamical systems possess at least one equivalent jerky dynamics. In particular, we determine a wide class of three-dimensional vector fields with polynomial and non-polynomial nonlinearities that possess this property. Taking advantage of this general result, we focus on the jerky dynamics of Sprott's minimal chaotic dynamical systems and R\ossler's toroidal chaos model. Based on the interrelation between the jerky dynamics of these models, we classify them according to their increasing polynomial complexity. Finally, we also provide a simple criterion that excludes chaotic dynamics for some classes of jerky dynamics and, therefore, also for some classes of three-dimensional dynamical systems.