Application of Stability Theory in Study of Local Dynamics of Nonlinear Systems

Investigating local dynamics of equilibrium points of nonlinear systems plays an important role in studying the behavior of dynamical systems. There are many different definitions for stable and unstable solutions in the literature. The main goal to develop stability definitions is exploring the responses or output of a system to perturbation as time approaches infinity. Due to the wide range of application of local dynamical system theory in physics, biology, economics and social science, it still attracts many researchers to play with its definitions to find out the answers for their questions. In this paper, we start with a brief review over continuous time dynamical systems modeling and then we bring useful examples to the playground. We study the local dynamics of some interesting systems and we show the local stable behavior of the system around its critical points. Moreover, we look at local dynamical behavior of famous dynamical systems, Hénon-Heiles system, Duffing oscillator and Van der Pol equation and analyze them. Finally, we discuss about the chaotic behavior of Hamiltonian systems using two different and new examples.

Dynamical localization in a non-Hermitian Floquet synthetic system

We investigate the non-Hermitian effects on quantum diffusion in a kicked rotor model where the complex kicking potential is quasi-periodically modulated in the time domain.The synthetic space with arbitrary dimension can be created by incorporating incommensurate frequencies in the quasi-periodical modulation.In the Hermitian case,strong kicking induces the chaotic diffusion in the four-dimension momentum space characterized by linear growth of mean energy.We find that the quantum coherence in deep non-Hermitian regime can effectively suppress the chaotic diffusion and hence result in the emergence of dynamical localization.Moreover,the extent of dynamical localization is dramatically enhanced by increasing the non-Hermitian parameter.Interestingly,the quasi-energies become complex when the non-Hermitian parameter exceeds a certain threshold value.The quantum state will finally evolve to a quasi-eigenstate for which the imaginary part of its quasi-energy is large most.The exponential localization length decreases with the increase of the non-Hermitian parameter,unveiling the underlying mechanism of the enhancement of the dynamical localization by nonHermiticity.

Positioning a fluorescent probe at the core of a glassy star polymer for detection of local dynamics

Accessing local dynamics within a single macromolecule is the key to understand the physical origin of the viscoelasticity and especially the glass transition. In order to extract specific information on the dynamics of the branch point of a star polymer around its glass transition temperature, four-arm star poly （n-butyl methacrylate） with a fluorescent core was synthesized using perylene diimide as initiator and polymerization conducted via atom transfer radical polymerization. The process is found to be effective in positioning the fluorophore at the branch point with the fluorophore intact, which allows the successful application of single molecule fluorescence defocus imaging in examining the local site- sensitive dynamics. The power spectra of rotation trajectories, the population of rotating fluorophores as well as the distribution of angular displacement were used to revel the difference in local dynamics between branch point and the arm＇s end. It is discovered that the local dynamics at the core of the star polymer is much less activated than that at the arm＇s end. The results demonstrate the strong effect dues to the topological constrain at the branch point and the more free space at the arm＇s end.

A Local Region Molecular Dynamics Simulation Method for Nanoscale Sliding Contacts

Computational e ciency and accuracy always conflict with each other in molecular dynamics(MD) simulations. How to enhance the computational e ciency and keep accuracy at the same time is concerned by each corresponding researcher. However, most of the current studies focus on MD algorithms, and if the scale of MD model could be reduced, the algorithms would be more meaningful. A local region molecular dynamics(LRMD) simulation method which can meet these two factors concurrently in nanoscale sliding contacts is developed in this paper. Full MD simulation is used to simulate indentation process before sliding. A criterion called contribution of displacement is presented, which is used to determine the e ective local region in the MD model after indentation. By using the local region, nanoscale sliding contact between a rigid cylindrical tip and an elastic substrate is investigated. Two two?dimensional MD models are presented, and the friction forces from LRMD simulations agree well with that from full MD simulations, which testifies the e ectiveness of the LRMD simulation method for two?dimensional cases. A three?dimensional MD model for sliding contacts is developed then to show the validity of the LRMD simulation method further. Finally, a discussion is carried out by the principles of tribology. In the discussion, two two?dimensional full MD models are used to simulate the nanoscale sliding contact problems. The results indicate that original smaller model will induce higher equivalent scratching depth, and then results in higher friction forces, which will help to explain the mechanism how the LRMD simulation method works. This method can be used to reduce the scale of MD model in large scale simulations, and it will enhance the computational e ciency without losing accuracy during the simula?tion of nanoscale sliding contacts.

The Two Faces of Urbanity： Exploring Global and Local Values---Two Urban Studios in Taksim Square and along the Shores of the Golden Horn in Istanbul

Since the 18th century, the irritating but also fascinating scenes of urbanity--a complex phenomenon with cultural, social, political, economic, temporal, spatial, functional, and formal dimensions--have been described in literary works. Many seemingly opposite facts, such as individuality/society, freedom/loneliness/socialization, anonymity/strangeness/identity/belonging, diversity/chaos/segregation, indifferent city-dweller/initiative citizenship, have been revealed through literary works, travel and utopian writing, urban theories, scientific studies, manifestos, and newspaper articles. On the one hand, there are those who advocate a life outside the city because they consider the problems produced by the city and the phenomenon of density which they perceive merely in quantitative terms, as unsolvable problems. On the other hand, there are those who see the production of loose urban fabric as a solution or those who accept the （seemingly） opposite facts of urbanity as positive values and therefore support city life. All of these ideas are still as actual today as they were in the past. We are often unable to use our citizen rights to the city, to encounter different classes （social/etlmic/religious）, to experience heterogeneity as an aspect inherent in city life and in the route of our daily life--following the orders of the capitalist system mainly organized around work--and we are often drawn into the same districts on the same paths. Our perception of our urban environments may get monotonous and shallow, but the irritating yet fascinating features of the first big cities still exist and may be grasped and brought into consciousness. Throughout their architectural education, especially in urban design studios, students can be encouraged to investigate the rhythm of their daily life, the conditions of their urban environments, and discovering the city as an intellectual and sensual programme, so that the phenomenon of urbanity can be grasped not just on formal, but on various other dimensions as well. This study focuses on the process and outcomes of two urban studios located in Taksim Square and along the shores of the Golden Horn in Istanhul. Taking the multidimensional content of urbanity into account, acquired theoretically through literary works and studies on urban planning and its history, the main aim of these studios has been the phenomenological understanding of the dynamic content of urbanity by the students. Through creative analysis of permanent/temporary spaces engendered by the diversity of user profiles and actions discovered on phenomenological excursions, students examine the qualitative values of density and global and local dynamics. We believe that designing spaces as ＂prototypes＂ helps highlight the multidimensional content of urbanity. The present study aims not only to highlight the multidimensional content of urbanity, but also to encourage its discussion in architectural design education and to emphasize the positive contribution of theoretical readings and phenomenological studies to urban design studios. The present study also aims to emphasize the beneficial correlation of global and local dynamics as the two faces of urbanity; important more than ever for the big cities of the 21 st century if we advocate for a vivid and resilient city life and citizens.

Progressive Modelling of the Gravity-induced Landslide Using the Local Dynamic Strength Reduction Method

The failure of slope is a progressive process, and the whole sliding surface is caused by the gradual softening of soil strength of the potential sliding surface. From this viewpoint, a local dynamic strength reduction method is proposed to capture the progressive failure of slope. This method can calculate the warning deformation of landslide in this study. Only strength parameters of the yielded zone of landslide will be reduced by using the method. Through continuous local reduction of the strength parameters of the yielded zone, the potential sliding surface developed gradually and evolved to breakthrough finally. The result shows that the proposed method can simulate the progressive failure of slope truly. The yielded zone and deformation of landslide obtained by the method are smaller than those of overall strength reduction method. The warning deformation of landslide can be obtained by using the local dynamic strength reduction method which is based on the softening characteristics of the sliding surface.

A survey: which features are required for dynamic visual simultaneous localization and mapping?

In recent years,simultaneous localization and mapping in dynamic environments(dynamic SLAM)has attracted significant attention from both academia and industry.Some pioneering work on this technique has expanded the potential of robotic applications.Compared to standard SLAM under the static world assumption,dynamic SLAM divides features into static and dynamic categories and leverages each type of feature properly.Therefore,dynamic SLAM can provide more robust localization for intelligent robots that operate in complex dynamic environments.Additionally,to meet the demands of some high-level tasks,dynamic SLAM can be integrated with multiple object tracking.This article presents a survey on dynamic SLAM from the perspective of feature choices.A discussion of the advantages and disadvantages of different visual features is provided in this article.

Local dynamic balance theory and technology of flow field in multilayer gob area

Flow field in multilayer gob area, which formed in small hiden-depth, multi-coal layer groups, close distance, hard coal layer, and hard roof, possesses characteristics such as complex, changeable and unstable. Dynamic balance theory of local flow field in multilayer gob area was built based on the realistic requirement that the serious threat on current mining coal layer by large-scale spontaneous combustion fire on close spontaneous combustion coal layer group of Datong Coal mining area at the ＇di-hard＇ conditions was caused by small coal pit mining. The kernel was in dynamic balance between flow field pressures of working face and local flow field in multilayer gob area was kept by transformation. Corresponding technology and set of devices were developed.

Effect of temporal disorder on wave packet dynamics in one-dimensional kicked lattices

Inspired by the recent experimental progress in noisy kicked rotor systems,we investigate the effect of temporal disorder or quasi-periodicity in one-dimensional kicked lattices with pulsed on-site potential.We found that,unlike the spatial disorder or quasi-periodicity which usually leads to localization,the effect of the temporal one is more complex and depends on the spatial configuration.If the kicked on-site potential is periodic in real space,then the wave packet will stay diffusive in the presence of temporal disorder or quasi-periodicity.On the other hand,if the kicked on-site potential is spatially quasi-periodic,then the temporal disorder or quasi-periodicity may lead to a shift of the transition point of the dynamical localization and destroy the dynamical localization in a certain parameter range.The results we obtained can be readily tested by experiments and may help us better understand the dynamical localization.

Effect of external noise on the dynamical localization of two coupling electrons in quantum dot array

The effect of external noise, which is characterized by an Ornstein-Uhlenbeck process, on the dynamical localization of two coupling electrons in a quantum dot array under the action of an ac electric field is studied. A numerical solution of the stochastic equations is obtained by averaging over stochastic trajectories. The results show that the external noise may destroy the dynamical localization, but the anti-noise capacity of the system is stronger when the two electrons are localized at the ends of the quantum dot array.

A LOCAL DYNAMIC CLUSTER SELF-ORGANIZATION ALGORITHM IN WIRELESS SENSOR NETWORKS FOR RAINFALL MONITORING

Wireless Sensor Networks for Rainfall Monitoring (RM-WSNs) is a sensor network for the large-scale regional and moving rainfall monitoring,which could be controlled deployment. Delivery delay and cross-cluster calculation leads to information inaccuracy by the existing dynamic collabo-rative self-organization algorithm in WSNs. In this letter,a Local Dynamic Cluster Self-organization algorithm (LDCS) is proposed for the large-scale regional and moving target monitoring in RM-WSNs. The algorithm utilizes the resource-rich node in WSNs as the cluster head,which processes target information obtained by sensor nodes in cluster. The cluster head shifts with the target moving in chance and re-groups a new cluster. The target information acquisition is limited in the dynamic cluster,which can reduce information across-clusters transfer delay and improve the real-time of information acquisition. The simulation results show that,LDCS can not only relieve the problem of "too frequent leader switches" in IDSQ,also make full use of the history monitoring information of target and con-tinuous monitoring of sensor nodes that failed in DCS.

Dynamics of a pair of electron and hole in semiconductor superlattice under an intense electric field

This paper investigates the behaviour of a pair of electron and hole in semiconductor superlattice under an external electric field with the consideration of Coulomb interaction. By numerically calculating the corresponding probability in the nearest neighbour tight binding approximation, we find that the single electron （or the hole） can not be dynamically localized due to the Coulomb interaction, while the dynamic localization of exciton （the pair of the electron and hole） still exists. Moreover we find that with the increase of the intensity of electric field, the exciton can be dynamically localized more completely.

Two-electron localization in a quantum dot molecule driven by a cosine squared field

We investigate the dynamics of two interacting electrons confined in a quantum dot molecule under the influence of cosine squared electric fields. The conditions for two-electron localization in the same quantum dot are analytically derived within the frame of the Floquet formalism. The analytical results are compared to numerical results obtained from the solution of the time-dependent Schtdinger equation.

Dynamic localization of two electrons in AC-driven triple quantum dots and quantum dot shuttles

We analyze the dynamic localization of two interacting electrons induced by alternating current electric fields in triple quantum dots and triple quantum dot shuttles. The calculation of the long-time averaged occupation probability shows that both the intra-and inter-dot Coulomb interaction can increase the localization of electrons even when the AC field is not very large. The mechanical oscillation of the quantum dot shuttles may keep the localization of electrons at a high level within a range if its frequency is quite a bit smaller than the AC field. However, the localization may be depressed if the frequency of the mechanical oscillation is the integer times of the frequency of the AC field. We also derive the analytical condition of two-electron localization both for triple quantum dots and quantum dot shuttles within the Floquet formalism.

Dynamical localization effect in a coupled quantum dot array driven by an AC magnetic field

We have studied the transport properties of a ring-coupled quantum dot array driven by an AC magnetic field, which is connected to two leads, and we give the response of the transport current to the dynamical localization. We found that when the ratio of the magnetic flux to the total quantum dots number is a root of the zeroth order Bessel function, dynamical localization and collapse of quasi-energy occurs and importantly~ the transport current displays a dip which is the signal of dynamical localization. The dynamical localization effect is strengthened as a result of the increase of the quantum dot number, and it is weakened on account of the increase of the dots-lead hopping rate.

Transport Properties of Two Coupled Quantum Dots Under Optical Pumping

Using the Keldysh-Green function,we present a theoretical study on the electron transport properties of two coupled quantum dots under optical pumping. Plateaus in the I-V curve and resonant peaks in the transmission coefficient occur and can be explained by the local electron density of states in the quantum dots. The effects of the optical pumping frequency and intensity on the transport properties of the system are also discussed. The electron dynamical localization phenomenon occurs when the optical pumping frequency is equal to the discrete hole energy level. This result can be used to realize optical control switches.

ELASTIC DYNAMIC ANALYSIS OF MODERATELY THICK PLATE USING MESHLESS LRPIM

A meshless local radial point interpolation method （LRPIM） for solving elastic dy-namic problems of moderately thick plates is presented in this paper. The discretized system equation of the plate is obtained using a locally weighted residual method. It uses a radial basis function （RBF） coupled with a polynomial basis function as a trial function,and uses the quartic spline function as a test function of the weighted residual method. The shape function has the properties of the Kronecker delta function,and no additional treatment is done to impose essen-tial boundary conditions. The Newmark method for solving the dynamic problem is adopted in computation. Effects of sizes of the quadrature sub-domain and influence domain on the dynamic properties are investigated. The numerical results show that the presented method can give quite accurate results for the elastic dynamic problem of the moderately thick plate.

Development and Prospect of Study on Soil Nonlinear Dynamic Characteristics under Strong-Motion

Ground motions are significantly influenced by dynamic characteristics of overburden soil layers near ground surface,as thick and soft soil layers would obviously amplify the ground motion strength. The conventional research method on soil nonlinear dynamic characteristics under strong motions is based on experiments in laboratories for the deficiency of observation data,but it is difficult to reliably simulate the complex factors of soils in actual earthquake durations,including loading paths,boundary conditions,and drainage conditions. The incremental data of the vertical downhole observation array,which is comprised of at least one observation point on ground surface and one observation point in a downhole rock base, makes it possible to study soil nonlinear dynamics according to in situ observation data,and provides new basic data and development opportunities to soil nonlinear dynamics studies.

Quantum control of two interacting electrons in a coupled quantum dot

Quantum-state engineering, i.e. active manipulation over the coherent dynamics of suitable quantum-mechanical systems, has become a fascinating prospect of modern physics. Here we discuss the dynamics of two interacting electrons in a coupled quantum dot driven by an external electric field. The results show that the two quantum dots can be used to prepare a maximally entangled Bell state by changing the strength and duration of an oscillatory electric field. Different from the suggestion made by Loss et al （1998 Phys. Rev. A 57 120）, the present entanglement involves the spatial degree of freedom for the two electrons. We also find that the coherent tunnelling suppression discussed by Grossmann et al （1991 Phys. Rev. Lett. 67 516） persists in the two-particle case： i.e. two electrons initially localized in one dot can remain dynamically localized, although the strong Coulomb repulsion prevents them from behaving so. Surprisingly, the interaction enhances the degree of localization to a large extent compared with that in the non-interacting case. This phenomenon is referred to as the Coulomb-enhanced dynamical localization.

Coherence destruction of tunneling in a quantum-dot molecule with bias

This paper studies the constraint conditions for coherence destruction in tunneling by using perturbation theory and numerical simulation for an AC-field with bias and Coulomb interaction between electrons in a quantum dot molecule. Such conditions can be described by using the roots of a Bessel function Jn（x）, where n is determined by both the bias and the Coulomb interactions, and x is the ratio of the amplitude to the frequency of the AC-field. Under such conditions, a coherent suppression of tunneling occurs between localized electronic states, which results from the dynamical localization phenomenon. All the conditions are verified with numerical simulations.