Nonlinear network dynamics on earthquake fault systems

Earthquake faults occur in interacting networks having emergent space-time modes of behavior not displayed by isolated faults. Using simulations of the major faults in southern California, we find that the physics depends on the elastic interactions among the faults defined by network topology, as well as on the nonlinear physics of stress dissipation arising from friction on the faults. Our results have broad applications to other leaky threshold systems such as integrate-and-fire neural networks.     

Nonlinear dynamics of breathers in the spiral structures of magnets

The structure and properties of pulsating solitons (breathers) in the spiral structures of magnets are analyzed within the sine-Gordon model. The breather core pulsations are shown to be accompanied by local shifts and oscillations of the spiral structure with the formation of “precursors” and “tails” in the moving soliton. The possibilities for the observation and excitation of breathers in the spiral structures of magnets and multiferroics are discussed.     

Nonlinear dynamics of two harmonically excited elastic structures with impact interaction

In this paper, non-smooth dynamics of two elastic beams excited by harmonic force with impact interaction is studied through analyses, simulations, and experiments. A two degree-of-freedom vibro-impact model is improved by applying the Galerkin approach and Newton's impact law for the two cantilever beams with impact interaction. Numerical analysis is taken to investigate the vibro-impact motions of cantilever beams excited by harmonic force. The l-adding periodic motions and k=1/1, k=2/2, k=3/4, and k=4/4 type of stable periodic motions of the impacted cantilever beam are presented. Poincaré map is established and the Floquet multipliers of the periodic motions are obtained through semi-analytical method to determine the stability of the motions near the bifurcation point. Through associated experiments, typical bifurcations and chaos of the non-smooth system are examined, which are in good agreement with numerical results.     

Nonlinear and stochastic dynamics in the heart

In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.     

Nonlinear effects in resonant tunneling; bistabilities and self-sustained oscillating currents

We study nonlinear phenomena in double barrier heterostructures. Systems in 3D under the effect of an external magnetic field along the current and 1D systems are analyzed. Nonlinearities are reflected in theI–Vcharacteristic curve as bistabilities, instabilities and time-dependent oscillations of the currents. The nature of the nonlinear behavior depends upon the parameters that define the system.     

Nonlinear dynamics of longitudinal structures in the electron cloud of a coaxial electron string ion source

The results of 2.5D particle-in-cell simulation of a coaxial electron trap with an internal anode are reported. It is found that, when the circulating current reaches the value of the ultimate vacuum current, first a virtual cathode arises in the trap and then the beam compresses (distributed virtual cathode). The transient preceding the compressed state exhibits complicated nonlinear dynamics, when compressed regions alternate with regions that are in a two-flow state (phase-space bubbles or phase-space holes). Physically, phase-space holes are similar to the well-known Bernstein-Greene-Kruskal plasma structures. Three types of phasespace holes with different dynamics (oscillating holes, flying holes, and chaotic holes) are revealed. Consideration of phase-space holes as quasi-particles makes it possible to find several channels of their interaction in pair collisions. The feasibility of the coaxial trap as a source of highly charged ions is analyzed. Although the compressed beam mode provides a larger amount of accumulated electrons compared with the conventional two-flow mode, the mean kinetic energy in the presence of a virtual cathode turns out to be much lower. A way of elevating the mean kinetic energy is suggested that consists in increasing the limit vacuum current in the axial configuration with an internal electrode.     

Nonlinear and nonequilibrium dynamics in geomaterials

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.     

Spray flame dynamics with oscillating flow and droplet grouping

The co-flow laminar spray diffusion flame in an oscillating flow field is investigated. Mild slip is permitted between the droplets and their host surroundings and droplet grouping resulting from the host flow oscillations is accounted for. The spray is modelled using the sectional approach and a perturbation analysis using a small sectional Stokes number is utilised for solving the liquid phase governing equations. The effect of droplet grouping is described through a specially constructed model for the vaporisation Damkohler number. The large chemical Damkohler number assumption is adopted and a formal analytical solution is developed for Schwab-Zeldovitch parameters through which the dynamics of the spray flame front shapes and thermal fields are deduced. Computed results based on the solutions demonstrate how the phenomenon of droplet grouping can lead to the existence of multiple flame sheets as a result of the dynamic change in the type of the main homogeneous flame from under- to over-ventilated as the flow field oscillates. Concomitant fluctuating thermal fields are also shown to be present indicating a potential impact on undesirable pollutants production.     

Mechanism and nonlinear dynamics of an oscillating chemical reaction

A mechanism and a model of a ferroin-catalyzed oscillating chemical system are descrined. This reaction presents an excellent example of a far-from-equilibrium system that forms spatial and temporal dissipative structures. The model shows that while the well-stirred system has a unique and stable stationary state, the same reagent spread in a thin layer may form complex spatiotemporal paterns. Stationary periodic patterns of both small and large amplitude, standing waves, and inhomogeneous chaotic oscillations are found in the model.     

Nonlinear structures in electroencephalogram signals

We apply a nonlinear prediction algorithm to investigate the presence of nonlinear structure in electroencephalogram (EEG) recordings. The EEG signal could be modeled as a realization of a nonlinear model plus a residual noise (uncorrelated Gaussian noise). Using linear and nonlinear models we analyze the statistical nature of these residual noises in the case of epileptic patients and normal subjects. We found that the residual noise presents Gaussian distribution for epileptic patients if a nonlinear model is used whereas in the case of normal subjects the residual noise will exhibit a Gaussian distribution only if a linear model (autoregressive) is used. These results provide another evidence of the nonlinear character of the epileptic seizure recordings, while the normal EEG seems to be better described as linearly correlated noise.     

Complex dynamics of a particle in an oscillating potential field

In this paper, Mg-doped ZnO nanoparticles were synthesized by the facile sol–gel method. The crystalline structure, characteristic absorption bands and morphology of the obtained Mg-doped ZnO nanoparticles were studied by XRD, FTIR and TEM. The thermal degradation behaviour of the samples was investigated by differential scanning calorimetry (DSC) and thermogravimetry (TG). The effect of Mg concentrations and annealing temperatures on the antibacterial properties of the obtained nanoparticles was investigated in detail. The results indicated that doping Mg ions into ZnO lattice could enhance its antibacterial activity. Antibacterial assay demonstrated that Mg-doped ZnO with 7% Mg content annealed at 400 ^°C had the strongest antibacterial activity against Listeria monocytogenes (98.7%). This study indicated that the inhibition rate of ZnO nanoparticles increased with the formation of granular structure and the decrease of ZnO size due to the doping of Mg ions into the ZnO lattice.