Molecular Dynamics Simulation on Behaviors of Water Nanodroplets Impinging on Moving Surfaces

Droplets impinging on solid surfaces is a common phenomenon. However, the motion of surfaces remarkably influences the dynamical behaviors of droplets, and related research is scarce. Dynamical behaviors of water nanodroplets impinging on translation and vibrating solid copper surfaces were investigated via molecular dynamics (MD) simulation. The dynamical characteristics of water nanodroplets with various Weber numbers were studied at four translation velocities, four vibration amplitudes, and five vibration periods of the surface. The results show that when water nanodroplets impinge on translation surfaces, water molecules not only move along the surfaces but also rotate around the centroid of the water nanodroplet at the relative sliding stage. Water nanodroplets spread twice in the direction perpendicular to the relative sliding under a higher surface translation velocity. Additionally, a formula for water nanodroplets velocity in the translation direction was developed. Water nanodroplets with a larger Weber number experience a heavier friction force. For cases wherein water nanodroplets impinge on vibration surfaces, the increase in amplitudes impedes the spread of water nanodroplets, while the vibration periods promote it. Moreover, the short-period vibration makes water nanodroplets bounce off the surface.

Transitional Periodic Patterns and Triple Attractors in a Predator-Prey System with Fear and Refuge

We report the existence of periodic structures in the transitional and chaotic regimes in bi-parameter spaces of a predator-prey system. A model is constructed taking into consideration of two important effects: namely, the prey refuge and fear of predation risk. The fixed points, their existence and stability behaviors are analyzed. The Neimark-Sacker bifurcation in the neighborhood of the interior fixed point is shown selecting refuge strength as a bifurcation parameter. The complex dynamical behaviors are explored in the biparameter space with the help of the largest Lyapunov exponent and isoperiodic diagrams. The period-bubbling transitional patterns, and triple heterogeneous attractors resulting in qualitative unpredictability are identified in the present system. The Wada basin sets for the triple coexisting attractors are found. The study reveals that the oscillations of the populations in certain control parameter regions are highly dependent upon the initial densities of the populations.

Fission and Fusion Solutions in the (2+1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation

Fission and fusion are important phenomena, which have been observed experimentally in many physical areas. In this paper, we study the above two phenomena in the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation. By introducing some new constraint conditions to its N-solitons, the fifission and fusion are obtained. Numerical figures show that the two types of solutions look like the capital letter Y in spacial structures. Then, by taking a long wave limit approach and complex conjugation restrictions, some hybrid resonance solutions are generated, such as the interaction solutions between the L-order lumps and Q-fifission (fusion) solitons, as well as hybrid solutions mixed by the T-order breathers and Q-fifission (fusion) solitons. Dynamical behaviors of these solutions are analyzed theoretically and numerically. The results obtained can be helpful for understanding the fusion and fifission phenomena in many physical models, such as the organic membrane, macromolecule material and even-clump DNA, plasmas physics and so on.

Transverse Instability of Dust Acoustic Solitary Waves in Magnetized Dusty Plasma composed of Vortex-like Distribution Ions

The dynamical behaviors of dusty plasma can be described by a (3+1)-dimensional modified Zakharov-Kuznetsov equation (mZKE) when the distribution of ions is vortex-like. The critical stable conditions for the line solitons are obtained by the linear stability analysis, which are also confirmed by the nonlinear dynamic evolution. An interesting phenomenon is found from the numerical results, maybe the first time, that the unstable line solitons of the mZKE will evolve into one or more completely localized soliton(s) after a long time evolution. Subsequently, we numerically studied the collision process of two line solitons. The results show that two stable line solitons can restore to their original states. However, if one of the two solitons or both of them are unstable, one or more completely localized solitons will appear during the collision. The results indicate that there are both elastic and inelastic collisions between line solitons.

Effects of Asymmetric Coupling Strength on Nonlinear Dynamics of Two Mutually Long-Delay-Coupled Semiconductor Lasers

This study investigates the effects of asymmetric coupling strength on nonlinear dynamics of two mutually long-delay-coupled semiconductor lasers through both experimental and numerical efforts. Dynamical maps and spectral features of dynamical states are analyzed as a function of the coupling strength and detuning frequency for a fixed coupling delay time. Symmetry in the coupling strength of the two lasers, in general, symmetrizes their dynamical behaviors and the corresponding spectral features. Slight to moderate asymmetry in the coupling strength moderately changes their dynamical behaviors from the ones when the coupling strength is symmetric, but does not break the symmetry of their dynamical behaviors and the corresponding spectral features. High asymmetry in the coupling strength not only strongly changes their dynamical behaviors from the ones when the coupling strength is symmetric, but also breaks the symmetry of their dynamical behaviors and the corresponding spectral features. Evolution of the dynamical behaviors from symmetry to asymmetry between the two lasers is identified. Experimental observations and numerical predictions agree not only qualitatively to a high extent but also quantitatively to a moderate extent.

Dynamical behavior of alternate base expansions

We generalize the greedy and lazy $\beta $ -transformations for a real base $\beta $ to the setting of alternate bases ${\boldsymbol {\beta }}=(\beta _0,\ldots ,\beta _{p-1})$ , which were recently introduced by the first and second authors as a particular case of Cantor bases. As in the real base case, these new transformations, denoted $T_{{\boldsymbol {\beta }}}$ and $L_{{\boldsymbol {\beta }}}$ respectively, can be iterated in order to generate the digits of the greedy and lazy ${\boldsymbol {\beta }}$ -expansions of real numbers. The aim of this paper is to describe the measure-theoretical dynamical behaviors of $T_{{\boldsymbol {\beta }}}$ and $L_{{\boldsymbol {\beta }}}$ . We first prove the existence of a unique absolutely continuous (with respect to an extended Lebesgue measure, called the p-Lebesgue measure) $T_{{\boldsymbol {\beta }}}$ -invariant measure. We then show that this unique measure is in fact equivalent to the p-Lebesgue measure and that the corresponding dynamical system is ergodic and has entropy $({1}/{p})\log (\beta _{p-1}\cdots \beta _0)$ . We give an explicit expression of the density function of this invariant measure and compute the frequencies of letters in the greedy ${\boldsymbol {\beta }}$ -expansions. The dynamical properties of $L_{{\boldsymbol {\beta }}}$ are obtained by showing that the lazy dynamical system is isomorphic to the greedy one. We also provide an isomorphism with a suitable extension of the $\beta $ -shift. Finally, we show that the ${\boldsymbol {\beta }}$ -expansions can be seen as $(\beta _{p-1}\cdots \beta _0)$ -representations over general digit sets and we compare both frameworks.

The impact of sources and sinks on the dynamics of homogeneous and heterogeneous boolean networks

Random Boolean networks, originally introduced as simplified models for the genetic regulatory networks, are abstract models widely applied for the study of the dynamical behaviors of self-organizing complex systems. In these networks, connectivity and the bias of the Boolean functions are the most important factors that can determine the behavioral regime of the systems. On the other hand, it has been found that topology and some structural elements of the networks such as the reciprocity, self-loops and source nodes, can have relevant effects on the dynamical properties of critical Boolean networks. In this paper, we study the impact of source and sink nodes on the dynamics of homogeneous and heterogeneous Boolean networks. Our research shows that an increase of the source nodes causes an exponentially growing of the different behaviors that the system can exhibit regardless of the network topology, while the amount of order seems to undergo modifications depending on the topology of the system. Indeed, with the increase of the source nodes the orderliness of the heterogeneous networks also increases, whereas it diminishes in the homogeneous ones. On the other hand, although the sink nodes seem not to have effects on the dynamic of the homogeneous networks, for the heterogeneous ones we have found that an increase of the sinks gives rise to an increasing of the order, although the different potential behaviors of the system remains approximately the same.

The transition from conservative to dissipative flows in class-B laser model with fold-Hopf bifurcation and coexisting attractors

Dynamical behaviors of a class-B laser system with dissipative strength are analyzed for a model in which the polarization is adiabatically eliminated. The results show that the injected signal has an important effect on the dynamical behaviors of the system. When the injected signal is zero, the dissipative term of the class-B laser system is balanced with external interference, and the quasi-periodic flows with conservative phase volume appear. And when the injected signal is not zero, the stable state in the system is broken, and the attractors (period, quasi-period, and chaos) with contractive phase volume are generated. The numerical simulation finds that the system has not only one attractor, but also coexisting phenomena (period and period, period and quasi-period) in special cases. When the injected signal passes the critical value, the class-B laser system has a fold-Hopf bifurcation and exists torus ”blow-up” phenomenon, which will be proved by theoretical analysis and numerical simulation.

Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model

In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynamics of our proposed model.