Dynamical instability and adiabatic evolution of the atom-homonuclear-trimer dark state in a condensate system

This paper investigates the dynamical instability and adiabatic evolution of the atom homonuclear-trimer dark state of a condensate system in a stimulated Raman adiabatic passage aided by Feshbach resonance. It obtains analytically the regions for the appearance of dynamical instability caused by the interparticle interactions. Moreover, the adiabatic property of the dark state is also studied in terms of a newly defined adiabatic fidelity. It shows that the nonlinear collisions have a negative effect on the adiabaticity of the dark state and hence reduce the conversion efficiency.

Dynamical instability of the dark state in the conversion of Bose-Fermi mixtures into stable molecules

In this paper, we investigate the dynamical instability of the dark state in the conversion of Bose-Fermi mixtures into stable molecules through a stimulated Raman adiabatic passage aided by Feshbach resonance. We analytically obtain the regions where the dynamical instability appears and find that such instability in the Bose-Fermi mixture system is caused not only by bosonic interparticle interactions but also by Pauli blocking terms, which is different from the scenario of a pure bosonic system where instability is induced by nonlinear interparticle collisions. Taking a 40K-87Rb mixture as an example, we give the unstable regions numerically.

Nonlinear vibration of Timoshenko FG porous sandwich beams subjected to a harmonic axial load

In this study,the instability and bifurcation diagrams of a functionally graded(FG)porous sandwich beam on an elastic,viscous foundation which is influenced by an axial load,are investigated with an analytical attitude.To do so,the Timoshenko beam theory is utilized to take the shear deformations into account,and the nonlinear Von-Karman approach is adopted to acquire the equations of motion.Then,to turn the partial differential equations(PDEs)into ordinary differential equations(ODEs)in the case of equations of motion,the method of Galerkin is employed,followed by the multiple time scale method to solve the resulting equations.The impact of parameters affecting the response of the beam,including the porosity distribution,porosity coefficient,temperature increments,slenderness,thickness,and damping ratios,are explicitly discussed.It is found that the parameters mentioned above affect the bifurcation points and instability of the sandwich porous beams,some of which,including the effect of temperature and porosity distribution,are less noticeable.

Instability, adiabaticity, and controlling effects of external fields for the dark state in a homonuclear atom tetramer conversion system

In the present paper, we investigate the instability, adiabaticity, and controlling effects of external fields for a dark state in a homonuclear atom-tetramer conversion that is implemented by a generalized stimulated Raman adiabatic passage. We analytically obtain the regions for the appearance of dynamical instability and study the adiabatic evolution by a newly defined adiabatic fidelity. Moreover, the effects of the external field parameters and the spontaneous emissions on the conversion efficiency are also investigated.

Numerical Modelling for Dynamic Instability Process of Submarine Soft Clay Slopes Under Seismic Loading

Marine geological disasters occurred frequently in the deep-water slope area of the northern South China Sea,especially submarine landslides,which caused serious damage to marine facilities.The cyclic elastoplastic model that can describe the cyclic stress-strain response characteristic for soft clay,is embedded into the coupled Eulerian-Lagrangian(CEL)algorithm of ABAQUS by means of subroutine interface technology.On the basis of CEL technique and undrained cyclic elastoplastic model,a method for analyzing the dynamic instability process of marine slopes under the action of earthquake load is developed.The rationality for cyclic elastoplastic constitutive model is validated by comparing its calculated results with those of von Mises model built in Abaqus.The dynamic instability process of slopes under different conditions are analyzed.The results indicate that the deformation accumulation of soft clay have a significant effect on the dynamic instability process of submarine slopes under earthquake loading.The cumulative deformation is taken into our model and this makes the calculated final deformation of the slope under earthquake load larger than the results of conventional numerical method.When different contact conditions are used for analysis,the smaller the friction coefficient is,the larger the deformation of slopes will be.A numerical analysis method that can both reflect the dynamic properties of soft clay and display the dynamic instability process of submarine landslide is proposed,which could visually predict the topographies of the previous and post failure for submarine slope.

NONLINEAR DYNAMIC INSTABILITY OF DOUBLE-WALLED CARBON NANOTUBES UNDER PERIODIC EXCITATION

A multiple-elastic beam model based on Euler-Bernoulli-beam theory is presented to investigate the nonlinear dynamic instability of double-walled nanotubes. Taking the geometric nonlinearity of structure deformation, the effects of van der Waals forces as well as the non- coaxial curvature of each nested tube into account, the nonlinear parametric vibration governing equations are derived. Numerical results indicate that the double-walled nanotube （DWNT） can be considered as a single column when the van der Waals forces are sufficiently strong. The stiffness of medium could substantially reduce the area of the nonlinear dynamic instability region, in particular, the geometric nonlinearity can be out of account when the stiffness is large enough. The area of the principal nonlinear instability region and its shifting distance aroused by the nonlinearity both decrease with the increment of the aspect ratio of the nanotubes.

Some Problems in Nonlinear Dynamic Instability and Bifurcation Theory for Engineering Structures

In civil engineering, the nonlinear dynamic instability of structures occurs at a bifurcation point or a limit point. The instability at a bifurcation point can be analyzed with the theory of nonlinear dynamics, and that at a limit point can be discussed with the theory of elastoplasticity. In this paper, the nonlinear dynamic instability of structures was treated with mathematical and mechanical theories. The research methods for the problems of structural nonlinear dynamic stability were discussed first, and then the criterion of stability or instability of structures, the method to obtain the bifurcation point and the limit point, and the formulae of the directions of the branch solutions at a bifurcation point were elucidated. These methods can be applied to the problems of nonlinear dynamic instability of structures such as reticulated shells, space grid structures, and so on. Key words nonlinear dynamic instability - engineering structures - non-stationary nonlinear system - bifurcation point - instability at a bifurcation point - limit point MSC 2000 74K25 Project supported by the Science Foundation of Shanghai Municipal Commission of Education (Grant No. 02AK04), the Science Foundation of Shanghai Municipal Commission of Science and Technology (Grant No. 02ZA14034)

Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes

In this study, a model for dynamic instability of embedded single-walled car- bon nanotubes （SWCNTs） is presented. SWCNTs are modeled by the sinusoidal shear deformation beam theory （SSDBT）. The modified couple stress theory （MCST） is con- sidered in order to capture the size effects. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear, and damping loads. The motion equations are derived based on Hamilton＇s principle. The differential quadrature method （DQM） in conjunction with the Bolotin method is used in order to calculate the dynamic instability region （DIR） of SWCNTs. The effects of differ- ent parameters, such as nonlocal parameter, visco-Pasternak foundation, mode numbers, and geometrical parameters, are shown on the dynamic instability of SWCNTs. The re- sults depict that increasing the nonlocal parameter shifts the DIR to right. The results presented in this paper would be helpful in design and manufacturing of nano-electromechanical system （NEMS） and micro-electro-mechanical system （MEMS）.

Dynamic Instability of Tunnel in Blocky Rock Mass

The displacements and geometry of the rock blocks and the properties of the rock struc-ture play an important role in the stability of tunnels.Based on the key block model,the dynamic instability analysis of underground tunnel subjected to intensive short-time compressional wave was conducted.The instability of the tunnel caused by the spallation and the inertial effect was distin-guished.And the influence of the roof contour curvature of tunnel was also determined.

ASYMMETRIC DYNAMIC INSTABILITY OF AXISYMMETRIC POLAR DIMPLING OF THIN SHALLOW SPHERICAL SHELLS

If the parameter , which measures the thickness-to-rise of the sliell, is small, the axismnnetrie polar dimpling oj .shallow .spherical .shell due to quadratic pressure distribution i.s dynamic instability, i.e., a small perturbation can change il to an asymmetric polar dimple mode. In two cases, the problem can be reduced to an eigenvalue problem where T can approximately be reduced to a Sturm-Liouvi/le operator if The existence of at least one real eigenvalue of T, which means that the axisyntmetric polar dimpling is dynamically unstable, i.s proved by spectral theorem or Hilbert theorem. Furthermore, an eigenfunction, which represents one of the asymmetric modes of the unstable dimple shell, belonging to an eigenvalue of T, is found.

Collapse period of degrading SDOF systems

Seismic demand estimation for a structure is a critical issue for seismic performance assessment so that the potential damage can be estimated realistically. Many researchers proposed simplified methods to estimate the demand of a structure under strong ground motions. However, most of them did not consider degradation and collapse potential of the structures. Even some of theme considered the degradation effect, stiffness and strength degradation effects were considered separately without collapse potential caused by dynamic instability. In this study, collapse potential of SDOF systems caused by dynamic instability with stiffness and strength degradation has been investigated. Nonlinear time history analyses were performed, using an energy-based, strength and stiffness degraded hysteretic model that considers the collapse potential, with 160 earthquake acceleration time histories. An equation was proposed for the estimation of collapse period of SDOF systems as a function of certain strength reduction factor, ductility level and post-capping stiffness ratio. Finally, effects of parameters of the considered hysteretic model and local site conditions on the collapse period were investigated.

Characterization of deformation stability of in-situ TiB2/6351 composites during hot compression based on Murty criterion

In situ TiB2 reinforced 6351 Al alloy composites were subjected to compression testing at strain rates and temperatures ranging from 0.001 to 10 s -1 and from 300 to 550？欲espectively,using Gleeble-1500D system.And the associated microstructural transformations and instability phenomena were studied by observations of the optical and transmission electron microscope.The power dissipation efficiency and instability parameter were calculated following the dynamic material model and plotted with the temperature and logarithm of strain rate to obtain processing maps for strains of 0.2,0.4,and 0.6.The processing maps present the instability zones at higher strain rates.The result shows that with increasing strain,the instability zones enlarge.The microstructural examination shows that the interface separates even the particle cracks or aligns along the shear direction of the adiabatic shear band in the instability zones.Two domains of higher efficiencies correspond to dynamic recovery and dynamic recrystallization during the hot deformation.Using the processing maps,the optimum processing parameters of stain rates and temperatures can be chosen for effective hot deformation of TiB2/6351 composites.

Dynamics of Two-Photon Lasers with A Atomic Level Configuration

We derive the dimensionless dynamic equations of two-photon lasers with A atomic level configuration by using the quantum Langevin equation method with the considerations of atomic coherence and injected classical fields. Then we analyze the stability and the chaotic dynamics of the two-photon laser by calculating the bifurcation diagram and the maximum Lyapunov exponent （MLE）. Our results show that the Lorenz strange attractors and one-focus strange attractors can exist in this system, and the chaos can be induced or inhibited by the injected classical fields via Hopfbifurcations or crises, while the atomic coherence induces chaos via crises, and inhibit chaos via Hopf bifurcation or crises.

A coarse grain model of microtubules

This paper proposes a 3-dimensional coarse grain model of microtubules and treats the tubulin monomer as a sphere of multiple patches, with parameters chosen to yield experimental values of bending and stretching stiffness. The model has demonstrated the ability to produce the bistability of tubulin sheets, elastic deformation near the tip, and cracking and peeling of protofilaments. This model is expected to take into account the structural and mechanical aspects underlying the physical mechanism of polymerization/depolymerization and dynamic instability of microtubules.

DYNAMIC PULL-IN INSTABILITY OF DOUBLE-SIDED ACTUATED NANO-TORSIONAL SWITCHES

A nonlinear frequency-amplitude relation is developed to investigate the vibrational amplitude effect on the dynamic pull-in instability of double-sided-actuated nano-torsional switches. The governing equation of a nano-electro-mechanical system pre-deformed by an electric field contains the quintic nonlinear term. The influences of basic parameters on the pull-in instability and natural frequency are investigated using a powerful analytical approach called the homotopy perturbation method. It is demonstrated that two terms in series expansion are sufficient to produce an acceptable solution. The numerical results obtained have verified the soundness of the asymptotic procedure. The phase portraits of the double-sided nano-torsionalactuator exhibit periodic, homoclinic and heteroclinic orbits.

Nonlinear size-dependent dynamic instability and local bifurcation of FG nanotubes transporting oscillatory fluids

Oscillation of fluid flow may cause the dynamic instability of nanotubes,which should be valued in the design of hanoelectromechanical systems.Nonlinear dynamic instability of the fluid-conveying nanotube transporting the pulsating harmonic flow is studied.The nanotube is composed of two surface layers made of functionally graded materials and a viscoelastic interlayer.The nonlocal strain gradient model coupled with surface effect is established based on Gurtin-Murdoch's surface elasticity theory and nonlocal strain gradient theory.Also,the size-dependence of the nanofluid is established.by the slip flow model.The stability boundary is obtained by the two-step perturbation-Galerkin truncation-Incremental harmonic balance(IHB)method·and compared with the linear solutions by using Bolotin's method.Further,the Runge-Kutta method is utilized to plot the amplitudefrequency bifurcation curves inside/outside the region.Results reveal the influence of nonlocal stress,strain gradient,surface elasticity and slip flow on the response.Results also suggest that the stability boundary obtained by the IHB method represents two bifurcation points when sweeping from high frequency to low frequency.Differently,when sweeping to high.frequency,there exists a hysteresis boundary where amplitude jump will occur.

Crust-core transition and dynamical instabilities in neutron stars for model with point-coupling interactions

We explore the effects of the density dependence of symmetry energy on the crust-core phase transition and dynamical instabilities in cold and warm neutron stars in the relativistic mean field(RMF)theory with point-coupling interactions using the Vlasov approach.The role of neutrino trapping is also considered.The crust-core transition density and pressure,distillation effect,and cluster size and growth rates are discussed.The present work shows that the slope of symmetry energy at saturation,temperature,and neutrino trapping have non-negligible effects.

Dynamic Stability Improvement of Decentralized Wind Farms by Effective Distribution Static Compensator

Dynamic instability of decentralized wind energy farms is a major issue to deliver continuous green energy to electricity consumers.This instability is caused by variations of voltage and frequency parameters due to intermittencies in wind power.Previously,droop control and inverter-based schemes have been proposed to regulate the voltage by balancing reactive power,while inertial control,digital mapping tech-nique of proportional-integral-differential(PID)controller and efficiency control strategy have been developed to regulate the frequency.In this paper,voltage stability is improved by a new joint strategy of distribution static compensator(DSTATCOM)six-pulse controller based reactive power management among decentralized wind turbines and controlled charging of capacitor bank.The frequency stability is ensured by a joint coordinated utilization of capacitor bank and distributed wind power turbines dispatching through a new DSTATCOM six-pulse controller scheme.In both strategies,power grid is contributed as a backup source with less priority.These new joint strategies for voltage and frequency stabilities will enhance the stable active power delivery to end users.A system test case is developed to verify the proposed joint strategies.The test results of the proposed new schemes are proved to be effective in terms of stability improvement of voltage,frequency and active power generation.

A high-order model of rotating stall in axial compressors with inlet distortion

In this paper,a high-order distortion model is proposed for analyzing the rotating stall inception process induced by inlet distortion in axial compressors.A distortion-generating screen in the compressor inlet is considered.By assuming a quadratic function for the local flow total pressure-drop,the existing Mansoux model is extended to include the effects of static inlet distortion,and a new high-order distortion model is derived.To illustrate the effectiveness of the distortion model,numerical simulations are performed on an eighteenth-order model.It is demonstrated that long length-scale disturbances emerge out of the distorted background flow,and further induce the onset of rotating stall in advance.In addition,the circumferential non-uniform distribution and time evolution of the axial flow are also shown to be consistent with the existing features.It is thus shown that the high-order distortion model is capable of describing the transient behavior of stall inception and will contribute further to stall detection under inlet distortion.

Qualitative analysis for a Wolbachia infection model with diffusion

We consider a reaction-diffusion model which describes the spatial Wolbachia spread dynamics for a mixed population of infected and uninfected mosquitoes. By using linearization method, comparison principle and Leray-Schauder degree theory, we investigate the influence of diffusion on the Wolbachia infection dynamics.After identifying the system parameter regions in which diffusion alters the local stability of constant steadystates, we find sufficient conditions under which the system possesses inhomogeneous steady-states. Surprisingly,our mathematical analysis, with the help of numerical simulations, indicates that diffusion is able to lower the threshold value of the infection frequency over which Wolbachia can invade the whole population.