Dynamical transition in a nonlinear two-level system driven by a special hyperbolic-secant external field

Nonlinear Dynamics - We propose an exact solution to a linear two-level system with the existence of a special hyperbolic secant external field and elucidate its transition dynamics. We then extend...     

Energy dependence on modes of electric activities of neuron driven by multi-channel signals

Nonlinear Dynamics - Neuron can receive electric signals or forcing currents from more than one channel, and these forcing currents could show some diversity. Based on the Hindmarsh–Rose...     

Interface motion by interface diffusion driven by bulk energy: justification of a diffusive interface model

We construct an asymptotic solution of a system consisting of the partial differential equations of linear elasticity theory coupled with a degenerate parabolic equation, and show that when a regularity parameter tends to zero, this solution converges to a solution of a sharp interface model, which describes the phase interface in an elastically deformable solid moving by interface diffusion. Therefore, the coupled system can be used as diffusive interface model. Differently from diffusive interface models based on the Cahn–Hilliard equation, the interface diffusion is solely driven by the bulk energy, hence the Laplacian of the curvature is not part of the driving force. Also, no rescaling of the parabolic equation is necessary. Since the asymptotic solution does not solve the system exactly, the proof is formal.     

Dynamical behaviors of a trimolecular response model with impulsive input

In the paper, we consider a trimolecular response model with impulsive input. Sufficient conditions for globally stable positive equilibrium point of the trimolecular response model with constant input are obtained. By impulsive differential theory, we obtain conditions for permanence of the trimolecular response model with impulsive input. By numerical analysis, we demonstrate complex phenomena such as limit cycles, periodic solutions, and chaos.     

水下非接触爆炸作用下舱段模型的动态响应

对舱段缩比模型遭受水下爆炸冲击载荷时的动态响应进行了测量与分析。模型是参照水面舰船的典型舱段而设计的,用于评估普通船用钢材料模型的冲击响应。试验工况为远场非接触爆炸,介绍了药包/模型的几何特性,以及用装在舱室内、甲板处和龙骨上的加速度计来测量舱段模型的冲击运动。     

Thermomechanical response of a viscoelastic rod driven by a sinusoidal displacement

The forced vibrations of a rod of thermoviscoelastic material are studied. The rod is considered to be laterally insulated but not constrained, such that a one-dimensional analysis may be employed. Temperature dependence of the material properties and the resulting thermomechanical coupling effects are included. The vibrations are forced by the imposition of a sinusiodal displacement of known amplitude and frequency at one end of the rod. This problem corresponds to a dissipative material bonded to the surface of a relatively rigid, vibrating structure.Initial transient behavior is not considered. A steady-state response is found by means of a finite difference formulation. Material properties of a Lockheed solid propellant are used.The presence of critical frequencies, characterized by high stresses and temperatures, is found for small amplitudes of vibration. Nonlinearities and instabilities lead to a lack of one-to-one correspondence between stress and displacement boundary conditions. No relationship is found between the critical frequencies of the driven rod and the natural frequencies of a rod with an equivalent temperature profile.     

Probabilistic response and analysis for a vibro-impact system driven by real noise

Nonlinear Dynamics - In this paper, a new stochastic averaging method is proposed to derive the stationary probabilistic response of vibro-impact system subject to real noise excitation, and the...     

Self-stability of a simple walking model driven by a rhythmic signal

In this paper, we analyzed the dynamic properties of a simple walking model of a biped robot driven by a rhythmic signal from an oscillator. The oscillator receives no sensory feedback and the rhythmic signal is an open loop. The simple model consists of a hip and two legs that are connected at the hip. The leg motion is generated by a rhythmic signal. In particular, we analytically examined the stability of a periodic walking motion. We obtained approximate periodic solutions and the Jacobian matrix of a Poincaré map by the power-series expansion using a small parameter. Although the analysis was inconclusive when we used only the first order expansion, by employing the second order expansion it clarified the stability, revealing that the periodic walking motion is asymptotically stable and the simple model possesses self-stability as an inherent dynamic characteristic in walking. We also clarified the stability region with respect to model parameters such as mass ratio and walking speed.     

Bifurcation and chaos of a simple walking model driven by a rhythmic signal

The walk of animals is achieved by the interaction between the dynamics of their mechanical system and the central pattern generator (CPG). In this paper, we analyze dynamic properties of a simple walking model of a biped robot driven by a rhythmic signal from an oscillator. In particular, we examine the long-term global behavior and the bifurcation of the motion that leads to chaotic motion, depending on the model parameter values. The simple model consists of a hip and two legs connected at the hip through a rotational joint. The joint is driven by a rhythmic signal from an oscillator, which is an open loop. In order to analyze the bifurcation, we first obtained approximate solutions of the walking motion and then constructed discrete dynamics using the Poincaré map. As a result, we found that consecutive period-doubling bifurcations occur as the model parameter values change, and that the walking motion leads to chaotic motion over the critical value of the model parameters. Moreover, we approximately obtained the period-doubling solutions and the critical value by employing a Newton-Raphson method. Our analytical results were verified by the numerical simulations.     

Flow driven by a stamped metal cooling fan – Numerical model and validation

This paper presents a numerical fluid flow model for the stamped metal cooling fans popularly employed in electric motors. An experimental system is constructed to measure the performance of the cooling fan. The agreements between model prediction and experimental data are reasonably good. Parametric studies with the numerical model indicate that the viscous heating in the fluid and the variation of the air density have negligible effects on the fan performance. The blade edge thickness affects the flow driving capability of the fan. With various pressure differentials, three flow regimes are recognized. The first is the axial component dominated flow. In the second regime, the flow has a forward axial flow and a backward leakage flow. The third one is the leakage flow dominated regime, when the pressure differential across the fan is large.     

Increase of the density,temperature and velocity of plasma jets driven by a ring of high energy laser beams

Supersonic plasma outflows driven by multi-beam, high-energy lasers, such as Omega and NIF, have been and will be used as platforms for a variety of laboratory astrophysics experiments. Here we propose a new way of launching high density and high velocity, plasma jets using multiple intense laser beams in a hollow ring formation. We show that such jets provide a more flexible and versatile platform for future laboratory astrophysics experiments. Using high resolution hydrodynamic simulations, we demonstrate that the collimated jets can achieve much higher density, temperature and velocity when multiple laser beams are focused to form a hollow ring pattern at the target, instead of focused onto a single spot. We carried out simulations with different ring radii and studied their effects on the jet properties. Implications for laboratory collisionless shock experiments are discussed.     

Dynamical model and control of a small-world network with memory

This paper proposes a dynamical model of influence volume of small-world-network with memory to investigate the effects of multiple delays on network dynamics. We calculate the influence volume covered by the spreading quantity, discuss the effect of finite size on the network dynamics, and then give the saturate time. The dynamical control is also investigated by introducing the delayed state feedback to simulate the adaptivity of network. With properly chosen delay and gain in feedback path, the controlled model may have stable equilibrium, periodic solution, quasi-periodic solution, or a complex chaotic attractor from a sequence of period-doubling bifurcations. It shows delayed feedback control may find important applications in the management and dynamical control of complex networks.     

The matrix model,a driven state variables approach to non-equilibrium thermodynamics

One of the new approaches in non-equilibrium thermodynamics is the so-called matrix model of Jongschaap. In this paper some features of this model are discussed. We indicate the differences with the more common approach based upon internal variables and the more sophisticated Hamiltonian and GENERIC formulations. Applications to rheological models as well as transport phenomena and finally the connection with the general control system theory are discussed.     

A shape memory alloy model by a second order phase transition

Motivated by the experimental results of the paper [1] and unlike the general theories of shape memory alloys (SMAs), in this paper we suggest for such materials a phase field model by a second order phase transition. So that, with this new system we obtain a simulation of phase dynamics very convenient to describe the natural behavior of these materials. The differential system is governed by the motion equation, the heat equation and the Ginzburg–Landau (GL) equation and by a constitutive law between the phase field, the temperature, the strain and the stress. The use of this new model is characterized by new potentials of the GL equation and by a new dependence on the temperature in the constitutive equation. Using this new model, we obtain simulations in better agreement with experimental data and respect to previous work [2].     

Large conversion of energy in dielectric elastomers by electromechanical phase transition

When air is pumped in, a tubular balloon initially inflates slightly and homogeneously. A short section of the balloon then forms a bulge, which coexists with the unbulged section of the balloon. As more air is pumped in, the bulged section elongates at the expense of the unbulged section, until the entire balloon is bulged. The phenomenon is analogous to the liquid-to-vapor phase transition. Here we study the bulging transition in a dielectric elastomer tube as air is pumped into the balloon and a voltage is applied through the thickness of the membrane. We formulate the condition for coexistent budged and unbulged sections, and identify allowable states set by electrical breakdown and mechanical rupture. We find that the bulging transition dramatically amplifies electromechanical energy conversion. Energy converted in an electromechanical cycle consisting of unbulged and bulged states is thousands of times that in an electrome-chanical cycle consisting of only unbulged states.     

Dynamical behavior of a competition model of Telcom and Cable Television industry

Under the trend of the integration of the Internet, Telcom, and Cable Television (CATV) in China, the penetration and integration in the service of CATV industry and telecom industry will be conducted. With its service changing from the original single video transmission to the diverse communication service, the CATV industry will transform its development plan, thus the adjustment of its developmental strategies. From the influence of the involvement of the three telecommunication operators in Internet Protocol Television (IPTV) on CATV industry and the mutual competitive relationship among them, an analysis of the operating enterprises of the two industries was made by using differential equations. The results show that, under some conditions, one operator in the telecom industry will monopolize the market. And under other conditions, market share of the three operators in IPTV will change periodically.     

Viscoplastic response of electrode particles in Li-ion batteries driven by insertion of lithium

Constitutive equations are derived for the viscoplastic behavior of a host medium driven by diffusion of guest atoms. With reference to the trapping concept, two states of a guest atom are distinguished: mobile and immobilized (due to alloying with the host matrix). This allows propagation of a sharp interphase to be described between regions rich and poor in guest atoms. The model is applied to study the mechanical response of a spherical electrode particle in a Li-ion battery. Ability of the constitutive equations to capture basic phenomena observed in anode particles under lithiation is demonstrated by numerical simulation.     

Synchrony and lag synchrony on a neuron model coupling with time delay

A neuron model of the Morris and Lecar form is investigated, which is composed of two individuals and is considered to be functioned by the gap junction coupling. When the level of the reversal potential in the calcium ion channel is small, neurons adjust their activities to the common asymptotic states. However, if we increase the level of the reversal voltage in the calcium ion channel, the exact synchrony firing of neurons is produced. Patterns of synchrony activity and the stability are observed to vary with the choice of time delay, which also enhances the multi-variety of the spike bursting firing rhythm. The lag synchrony of time trajectories of the voltage is illustrated near the boundary of the synchrony regime.