Cooperative dynamics of coupled motor–cargoes system with stochastic interactions in the crowded environment

In this study, we investigate the cooperative transport behaviors of coupled motor–cargoes system, in which multiple passive cargoes stochastically interact with one active Brownian motor. The environment with stochastic interactions is characterized by the concentration (reflecting the cargo’s number in unit volume) and switching rate (reflecting the interacting stability between motor and cargoes), based on which the stationary multiple-state process can be employed to describe the fluctuating-cargo state in the coupled system. By analyzing the average probability current of decoupled system in the thermodynamic limit, we effectively study the possibility of cooperative transport through stochastic cargoes to behave rich dynamical behaviors, including the directed current, current reversal, stochastic resonance (SR) and stochastic inhibition (SI), inverse SR and SI, even without the effect of external driving force. Based on numerical results, we systematically discuss the transport dependence on various parameters, including the cargo concentration in the crowded environment, cargo capacity of the motor, driving amplitude of external periodic force, and medium temperature. Obviously, the sensitivity of transport process to parameter changes can be used by the environment to regulate its cargo traffic, which also provides latent support for manipulating the transport performance and optimizing the coupled structure in artificial nano-machines.     

Karhunen–Loeve analysis and order reduction of the transient dynamics of linear coupled oscillators with strongly nonlinear end attachments

The Karhunen–Loeve (K–L) decomposition method has become a popular technique to create low-dimensional, reduced-order models of dynamical systems. In this paper this technique is applied to a multi-degree-of-freedom chain of linear coupled oscillators with a strongly nonlinear (nonlinearizable), lightweight end attachment. By performing K–L decomposition we show that the lightweight nonlinear attachment (possessing 0.5% of the total mass of the chain) can affect the global dynamics of the linear chain, exhibiting nonlinear energy-pumping phenomena; that is, irreversible passive targeted energy transfers from the linear chain to the nonlinear end attachment, where this energy is locally confined and dissipated without ‘spreading back’ to the primary system. It is shown that the occurrence of energy pumping can be identified by studying the dominant K–L modes of the dynamics, as well as, the energy distribution among them. Moreover, by comparing the action of the strongly nonlinear attachment to the classical linear vibration absorber, we show robustness of passive nonlinear energy absorption over wide parameter ranges. On the other hand, the case-sensitive nature of K–L-based reduced-order models has always been a constraint for K–L decomposition, since one cannot quantify a priori the error bound of such low-dimensional reduced-order models when different initial conditions are applied to the system. To alleviate this constraint, the paper proposes a multiple correlation coefficient (MCC) as a quantitative measure to effectively assess the applicability of a K–L-based reduced-order model derived for a specific set of initial conditions to a small neighborhood of initial conditions containing that initial state. The derived reduced-order models are validated through reconstruction of the system responses and comparisons to direct numerical integrations.     

A precise integration method for solving coupled vehicle–track dynamics with nonlinear wheel–rail contact

A new method is proposed as a solution for the large-scale coupled vehicle–track dynamic model with nonlinear wheel–rail contact. The vehicle is simplified as a multi-rigid-body model, and the track is treated as a three-layer beam model. In the track model, the rail is assumed to be an Euler-Bernoulli beam supported by discrete sleepers. The vehicle model and the track model are coupled using Hertzian nonlinear contact theory, and the contact forces of the vehicle subsystem and the track subsystem are approximated by the Lagrange interpolation polynomial. The response of the large-scale coupled vehicle–track model is calculated using the precise integration method. A more efficient algorithm based on the periodic property of the track is applied to calculate the exponential matrix and certain matrices related to the solution of the track subsystem. Numerical examples demonstrate the computational accuracy and efficiency of the proposed method.     

Nonlinear fast–slow dynamics of a coupled fractional order hydropower generation system

Internal effects of the dynamic behaviors and nonlinear characteristics of a coupled fractional order hydropower generation system(HGS) are analyzed. A mathematical model of hydro-turbine governing system(HTGS) with rigid water hammer and hydro-turbine generator unit(HTGU) with fractional order damping forces are proposed. Based on Lagrange equations, a coupled fractional order HGS is established. Considering the dynamic transfer coefficient eis variational during the operation, introduced e as a periodic excitation into the HGS. The internal relationship of the dynamic behaviors between HTGS and HTGU is analyzed under different parameter values and fractional order. The results show obvious fast–slow dynamic behaviors in the HGS, causing corresponding vibration of the system, and some remarkable evolution phenomena take place with the changing of the periodic excitation parameter values.     

Synchronization of Complex Network with Drivingly Coupled Scheme

We present a network model with a new coupled scheme which is the generalization of drive-response systems called a drivingly coupled network. The synchronization of the network is investigated by numerical simulations based on Lorenz systems. By calculating the largest transversal Lyapunov exponents of such network, the stable and unstable regions of synchronous state for eigenvalues in such network can be obtained and many kinds of drivingly coupled arrays based on Lorenz systems such as all-to-all, star-shape, ring-shape and chain-shape networks are considered.     

Non-Markovianity of a qubit coupled with an isotropic Lipkin–Meshkov–Glick bath

We study the non-Markovianity of the single qubit system coupled with an isotropic Lipkin–Meshkov–Glick(LMG)model by an effective method proposed by Breuer et al.(Breuer H P and Piilo J 2009 Europhys. Lett. 85 5004). It is discovered that the non-Markovianity is concerned with the quantum phase transitions(QPTs). In the open system, we present that the strong coupling inside the bath and the strong interaction between the system and bath can enhance the degree of non-Markovianity. Moreover, the non-Markovianity is stronger and more sensitive for the bath in the symmetric phase than the symmetry broken phase.     

Synchronization of the Frenet–Serret Linear System with a Chaotic Nonlinear System by Feedback of States

A synchronization procedure of the generalized type in the sense of Rulkov et al. [Phys. Rev. E 51, 980 (1995)] is used to impose a nonlinear Malasoma chaotic motion on the Frenet–Serret system of vectors in the differential geometry of space curves. This could have application in biological molecular motion.     

Rhythm Synchronization of Coupled Neurons with Temporal Coding Scheme

Encoding information by firing patterns is one of the basic neural functions, and synchronization is important collective behaviour of a group of coupled neurons. Taking account of two schemes for encoding information （that is, rate coding and temporal coding）, rhythm synchronization of coupled neurons is studied. There are two types of rhythm synchronization of neurons： spike and burst synchronizations. Firstly, it is shown that the spike synchronization is equivalent to the phase synchronization for coupled neurons. Secondly, the similarity function of the slow variables of neurons, which have relevant to the bursting process, is proposed to judge the burst synchronization. It is also found that the burst synchronization can be achieved more easily than the spike synchronization, whatever the firing patterns of the neurons are. Hence the temporal encoding scheme, which is closely related to both the spike and burst synchronizations, is more comprehensive than the rate coding scheme in essence.     

Complete Synchronization of Coupled Hindmarsh-Rose Neurons with Ring Structure

Complete synchronization of coupled Hindmarsh-Rose (HR) neurons with a ring structure is studied. The criterion for complete synchronization of coupled neurons with the ring structure is obtained through the stability analysis of the linearized synchronization error system. Numerical simulation is given to test the criterion for a system with three coupled HR neurons.     

Ab initio study on the formation of chemically ordered Zr2Al phase by coupled replacive–displacive transformation

We performed plane wave-based first principles calculations using the projector augmented wave (PAW) potential under the generalized gradient approximation (GGA) within the density functional theory to study the formation of ordered omega (B8₂-structured) Zr₂Al phase in β-Zr₃Al alloy. The transformation involves both replacive and displacive processes. We investigated two possible paths for the transformation where steps involving replacive (diffusive) and displacive processes occur in succession with their sequence of occurrence being different in the two paths. From this study, it was possible to show that the initial chemical ordering facilitates the displacive process leading to the transformation. It was also possible to correlate instability with respect to omega-type displacements in Zr₂Al alloy with the number of Zr–Al bonds present in the unit cell. Electronic structure analysis indicated that stronger Zr–Al bonding plays an important role in the formation of chemically ordered omega phase.     

Optical switch effect of metal–dielectric–metal plasmonic waveguide coupled with stub structure

The transmission line theory (TLT) and the finite difference time domain (FDTD) method are applied to investigate the optical transmission characteristics of the metal–dielectric–metal (MDM) plasmonic waveguide coupled with a stub structure. The transmission rate of the FDTD simulation results demonstrates periodically variation from less than 1% to more than 92% as a function of the length of the stub, which fits well with the results of TLT. Furthermore, the transmission also performs a periodically switch distribution with the change of the refractive index of the stub from 1.0 to 2.0 gradually. Both methods are adopted for modulating the superposition phase of the interference between the reflected surface plasmon polaritons (SPPs) wave from the end of the stub and the passing SPPs wave in the waveguide, which can be interpreted as the principle mechanism for the optical switch effect of the MDM waveguide with a stub structure.     

TEM characterization of chemically synthesized copper–gold nanoparticles

Dodecanethiol-capped Cu–Au nanoparticles, synthesized via a successive two-phase (water/toluene) and galvanic-exchange procedure, were characterized using transmission electron microscopy (TEM). The size range of the particles is around 1–7 nm. Electron-induced morphological evolution was observed under high resolution (HR) TEM. Cuboctahedral morphology was found to be thermodynamically stable. Electron-induced aggregation of two particles was also observed. Chemical ordering of cuboctahedral particles was studied by atomic-resolution high angle annular dark field (HAADF) imaging in scanning TEM (STEM) mode and energy dispersive X-ray (EDX) element mapping using a silicon drift detector (SDD). The particles were found to be Cu–Au mixed, and to be stable in air. Surface plasmon resonance (SPR), which is dependent on local structure and morphology, was investigated by electron energy loss spectroscopy (EELS).     

Spin–orbit coupled Bose–Einstein condensates with Rydberg-dressing interaction

Interaction between Rydberg atoms can be used to control the properties of interatomic interaction in ultracold gases by weakly dressing the atoms with a Rydberg state. Here we investigate the effect of the Rydberg-dressing interaction on the ground-state properties of a Bose–Einstein condensate imposed by Raman-induced spin–orbit coupling. We find that,in the case of SU(2)-invariant s-wave interactions, the gas is only in the plane-wave phase and the zero-momentum phase is absent. In particular, we also predict an unexpected magnetic stripe phase composed of two plane-wave components with unequal weight when s-wave interactions are non-symmetric, which originates from the Rydberg-dressing interaction.     

Simulation of superconducting single photon detector coupled with metal–insulator–metal concentric ring grating

Sub-wavelength metal–insulator–metal (MIM) concentric ring grating structure has been introduced to couple with superconducting single photon detector (SSPD) to enhance its response. The effects of the coupling structure parameters on the enhancement factor have been studied systematically. Our numerical simulation results show that the optical density arriving at the detection area of SSPD can be greatly enhanced by the structure of MIM concentric ring grating, corresponding to the improvement of detection response of the detector. A high enhancement factor more than 40 times can be obtained at wavelength of \(1.55~\upmu \hbox {m}\) with proper structure parameters.     

Simulation design of P–I–N-type all-perovskite solar cells with high efficiency

According to the good charge transporting property of perovskite, we design and simulate a p–i–n-type all-perovskite solar cell by using one-dimensional device simulator. The perovskite charge transporting layers and the perovskite absorber constitute the all-perovskite cell. By modulating the cell parameters, such as layer thickness values, doping concentrations and energy bands of n-, i-, and p-type perovskite layers, the all-perovskite solar cell obtains a high power conversion efficiency of 25.84%. The band matched cell shows appreciably improved performance with widen absorption spectrum and lowered recombination rate, so weobtain a high J_(sc) of 32.47 m A/cm~2. The small series resistance of the all-perovskite solar cell also benefits the high J_(sc). The simulation provides a novel thought of designing perovskite solar cells with simple producing process, low production cost and high efficient structure to solve the energy problem.     

Energy feedback and synchronous dynamics of Hindmarsh–Rose neuron model with memristor

We analyze the energy aspects of single and coupled Hindmarsh–Rose(HR) neuron models with a quadratic flux controlled memristor. The energy function for HR neuron with memristor has been derived and the dynamics have been analyzed in the presence of various external stimuli. We found that the bursting mode of the system changes with external forcing. The negative feedback in Hamilton energy function effectively stabilizes the chaotic trajectories and controls the phase space. The Lyapunov exponents have been plotted to verify the stabilization of trajectories. The energy aspects during the synchronous dynamics of electrically coupled neurons have been analyzed. As the coupling strength increases, the average energy fluctuates and stabilizes at the point of synchronization. When the neurons are coupled via chemical synapse,the average energy variations show three important regimes: a fluctuating regime corresponding to the desynchronized, a stable region indicating synchronized and a linearly increasing regime corresponding to the amplitude death states have been observed. The synchronization transitions are verified by plotting the transverse Lyapunov exponents. The proposed method has a large number of applications in controlling coupled chaotic systems and in analyzing the energy change during various metabolic processes.     

Effects of spacing on dynamics of two coupled Bose-Einstein condensates in two finite traps

Interaction between two coupled Bose-Einstein condensates (BECs) is investigated by the variational approach in two finite traps, and the effects of the spacing between the two traps on dynamics of the two BECs are analyzed. The spacing determines the stable condition of stationary states, affects the existence condition of each BEC, and changes the switching and self-trapping effects on the two BECs. The dynamic mechanism is demonstrated by performing a coordinate of classical particle moving in an effective potential field, and confirmed by the evolution of the atom population transferring ratio.     

Invariant analysis with conservation law of time fractional coupled Ablowitz–Kaup–Newell–Segur equations in water waves

ABSTRACT

In this paper, the symmetry analysis and conservation laws of time fractional coupled Ablowitz–Kaup–Newell–Segur (AKNS) equations have been presented. Initially, the Lie symmetry method has been used for similarity reduction of time fractional coupled AKNS equations. Here, the Erdélyi–Kober differential operators have been used for symmetry reduction. Also, the new conservation vectors for time fractional coupled AKNS equations have been derived by using the new conservation theorem with formal Lagrangian.