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.

Effect of Water Activity, Yuza (<i>Citrus junos</i>Sieb. ex Tanaka) Powder and the Mixture of Sodium Lactate and Sodium Acetate on Quality and Safety in Beef Jerky

Despite its low water activity (Aw), food poisoning accidents associated with beef jerky consumption and problems due to mold growth have been reported. The objects of this study were to investigate the effect of yuza powder and the mixture of sodium lactate (SL) and sodium acetate (SA) to prevent the growth of S. aureus and A. flavus, as well as aflatoxin production in beef jerky. Different concentrations of the SL and SA (0, 0.75, and 1%) mixture were added to sliced beef and the Aws were adjusted to 0.70, 0.75, and 0.80. The effect of yuza powder and the SL and SA mixture on S. aureus in beef jerky (Aw 0.80) was also investigated at 10°C and 25°C. A rapid decline is that S. aureus population was observed in beef jerky containing yuza powder and mixtures of SL and SA. Antifungal effects against A. flavus were observed in beef jerky containing the SL and SA mixture at Aw below 0.75. The growth of A. flavus and aflatoxin production were prevented in beef jerky containing the yuza powder and a 1% mixture of SL and SA at 10°C and 0.80 Aw. The addition of yuza powder increased the hardness score of the beef jerky. Under current Aw regulations (0.80), beef jerky may pose a public health risk due to the growth of A. flavus and the presence of aflatoxin.

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 Ni62 Nb38(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.

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 ζ 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 ζ effect （with the assumptionof 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. Numerical analysis is used to derive time series of position, velocity, and acceleration under different sets of parameters, as well as their trajectories in phase space. The time evolution of kinematic variables indicates that a regular wave-like change in acceleration corresponds to steady wave-like variations in position and velocity, while a rapid growth in acceleration （caused by a rapid intensification in the force acting on ,the parcel） corresponds to track shifts and abrupt changes in direction. Stable limiting cases under the f- and f-plane approximations yield periodic wave-like solutions, while unstable limiting cases yield exponential growth in all variables. Perturbing the value of absolute vorticity at the initial position （ζ0） results in significant changes in the stability and dynamic features of the motion. Enhancement of the nonlinear term may cause chaotic behavior to emerge, suggesting a limit to the predictability of inertial motion.