完全非弹性蹦球的动力学行为

对振动台面上的完全非弹性球的蹦跳行为进行了初步分析.受约化振动加速度的控制，球的运动可以表现出一系列倍周期分岔过程.对几种典型的倍周期运动及分岔情况进行了讨论. 关键词： 蹦球 倍周期分岔 混沌 颗粒物质     

摩擦力对非弹性蹦球倍周期运动的影响

分析了摩擦力对竖直振动台面上完全非弹性蹦球动力学行为的影响.当控制参数Γ由1逐渐增大时,作用在蹦球上的恒定摩擦力不会改变倍周期分岔的序列,但会使倍周期分岔点的数值变大.与无摩擦力时的情况相比,在飞行时间的分岔图中也存在倍周期分岔密集区,只是被横向拉伸纵向压缩,且具有不同的分形特性.与受振颗粒体系中的倍周期分岔过程做了比较,发现当摩擦力取值为颗粒总重量的20%—30%时两者符合很好.     

基于MATLAB中SIMULINK的准周期弹跳运动的仿真模拟

使用MATLAB/SIMULINK仿真软件建立了刚性小球在谐振桌面上做准周期性弹跳运动的动力学模型,对小球在不同倍频下的准周期运动进行了仿真模拟,并得到了小球运动的相图。结果表明：控制参数的选取对小球的动力学行为有着很大的影响。     

Dynamics of a stochastically driven Brownian particle in one dimension

We present a study on the dynamics of a system consisting of a pair of hardcore particles diffusing with different rates. We solved the drift-diffusion equation for this model in the case when one particle, labeled F, drifts and diffuses slowly toward the second particle, labeled M. The displacements of particle M exhibits a crossover from diffusion to drift at a characteristic time which depends on the rate constants. We show that the positional fluctuation of M exhibits an intermediate crossover regime of subdiffusion separating initial and asymptotic diffusive behavior; this is in agreement with the complete set of Master Equations that describe the stochastic evolution of the model. The intermediate crossover regime can be considerably large depending on the hopping probabilities of the two particles. This is in contrast to the known crossover from diffusive to subdiffusive behavior of a tagged particle that is in the interior of a large single-file system on an unbound real line. We discuss our model with respect to the biological phenomena of membrane protrusions, where polymerizing actin filaments (F) push the cell membrane (M).     

弹跳运动中混沌现象的电子模拟

给出了一个电子实验电路，用以模拟刚性小球在振动台面上的弹跳运动，可给出在逐渐增大台面的振动幅度或振动频率时，小球表现出的从规则运动到无规运动的各种动力学行为。     

On the quantum Fermi accelerator and its relevance to ‘quantum chaos’

We discuss a quantum version of the Fermi acceleration model, which consists of a particle bouncing between a fixed and oscillating wall. The actual movement of the particle crucially depends on the boundary conditions of the Schrödinger equation. Under Dirichlet boundary conditions, the quantum system displays a regular behaviour, but its classical limit exhibits some unphysical attributes. Only for certain initial conditions does it correspond to the stable motion of a ball bouncing once for an integer number of wall oscillations. In the classical model that situation gives rise to regular islands imbedded in the chaotic sea.     

弹跳运动的Simulink仿真模拟

本文建立了小球在谐振桌面上做弹跳运动的动力学模型,并用Simulink仿真软件模拟了小球在不同参数下从规则运动到无规则运动的各种动力学行为,仿真的结果表明,控制参数对系统的动力学行为有重要的影响.     

Causal horizons in a bouncing universe

As our understanding of the past in a bouncing universe is limited, it becomes difficult to propose a cosmological model which can give some understanding of the causal structure of the bouncing universe. In this article we address the issue related to the particle horizon problem in the bouncing universe models. It is shown that in many models the particle horizon does not exist, and consequently the horizon problem is trivially solved. In some cases a bouncing universe can have a particle horizon and we specify the conditions for its existence. In the absence of a particle horizon the Hubble surface specifies the causal structure of a bouncing universe. We specify the complex relationship between the Hubble surface and the particle horizon when the particle horizon exists. The article also address the issue related to the event horizon in a bouncing universe. A toy example of a bouncing universe is first presented where we specify the conditions which dictate the presence of a particle horizon. Next we specify the causal structures of three widely used bouncing models. The first case is related to quintom matter bounce model, the second one is loop quantum cosmology based bounce model and lastly f(R) gravity induced bounce model. We present a brief discussion on the horizon problem in bouncing cosmologies. We point out that the causal structure of the various bounce models fit our general theoretical predictions.     

Reproduction and application of human bouncing and jumping forces from visual marker data

State-of-the-art facilities for measuring bouncing and jumping ground reaction forces (GRFs) comprise typically equipment for direct force measurement, i.e. single or multiple floor-mounted force plates. Artificial laboratory conditions and constraints imposed by the direct measurement systems, such as the small measuring area of a force plate, can have a strong influence on human ability to bounce and jump, naturally yielding unrepresentative force data. However, when dealing with issues like vibration serviceability assessment of real full-scale structures, such as floors, footbridges, staircases and grandstands, there is a growing need to estimate realistic GRFs under a wide range of natural conditions. This paper presents a novel method in the civil engineering context utilising ‘free-field’ measurement of human bouncing and jumping forces recorded continuously in time using motion capture technology transferred and adapted from biomechanical research. Results show that this kind of data can be used successfully in studies of human-structure dynamic interaction, specifically negative cue effect of a perceptibly vibrating structure on GRFs, energy flow and power in the human-structure system, and also synchronisation between individuals when bouncing/jumping in groups on more or less perceptibly moving structures.     

Langevin equation for a free particle driven by power law type of noises

We study a generalized Langevin equation for a free particle driven by N internal noises. The mean square displacement and velocity autocorrelation function are derived in case of a mixture of Dirac delta, power law and Mittag-Leffler noises. Additionally, a frictional memory kernel of distributed order is considered. The long time limit and short time limit are analyzed, and the dominant contributions of noises on particle dynamics is discussed. Various different diffusive behaviors (subdiffusion, superdiffusion, normal diffusion, ultraslow diffusion) are obtained. The considered problem may be used in the theory of anomalous diffusion in complex environment.     

A Method for Identifying Diffusive Trajectories with Stochastic Models

Single particle tracking is a tool that is being increasingly used to study diffusive or dispersive processes in many branches of natural science. Often the ability to collect these trajectories experimentally or produce them numerically outpaces the ability to understand them theoretically. On the other hand many stochastic models have been developed and continue to be developed capable of capturing complex diffusive behavior such as heavy tails, long-range correlations, nonstationarity, and combinations of these things. We describe a computational method for connecting particle trajectory data with stochastic models of diffusion. Several tests are performed to demonstrate the efficacy of the method, and the method is applied to polymer diffusion, RNA diffusion in E. coli, and RAFOS dispersion in the Gulf of Mexico.     

Path-length-resolved diffusive particle dynamics in spectral-domain optical coherence tomography

We describe a new method to measure the decorrelation rate of the optical coherence tomography (OCT) magnitude simultaneously in space and time. We measure the decorrelation rate of the OCT magnitude in a Fourier-domain OCT system for a large range of translational diffusion coefficients by varying the sphere diameter. The described method uses the sensitivity advantage of Fourier-domain OCT over time-domain OCT to increase the particle diffusion imaging speed by a factor of 200. By coherent gating, we reduce the contribution of multiple scattering to the detected signal, allowing a quantitative study of diffusive particle dynamics in high concentration samples. We demonstrate that this technique is well suited to image diffusive particle dynamics in samples with a complex geometry as we measure the morphology and diffusive particle dynamics simultaneously with both high spatial and high temporal resolution.     

器壁滑动摩擦力对受振颗粒体系中冲击力倍周期分岔过程的影响

颗粒物质由离散的固体颗粒组成, 受到周期性振动时可以表现出复杂的动力学行为. 这些行为往往受众多因素的影响, 如空气阻力和器壁摩擦力等. 针对受振颗粒体系中冲击力的倍周期分岔现象, 通过抽真空或将容器底镂空消除空气阻力, 单独研究器壁滑动摩擦力的影响. 结果表明在仅有器壁摩擦力作用的情况下, 倍周期分岔过程仅受约化振动加速度的控制, 与颗粒的尺寸、颗粒层数及振动频率无关. 将器壁摩擦力处理成一个大小恒定、方向与颗粒和器壁相对速度反向的阻力, 并包含到完全非弹性蹦球模型中, 能够对所观察到的现象给出很好的解释. 通过对倍周期分岔点测量平均值的拟合, 得到器壁滑动摩擦力的大小约为颗粒总重量的10%. 关键词： 颗粒物质 器壁摩擦力 倍周期分岔 冲击力     

The evolution equation for the radius of a premixed flame ball in fractional diffusive media

The evolution equation for the radius of an isolated premixed flame ball is derived in the framework of a new method that strongly simplifies previous ones and highlights that they are based on Gaussian modelling of diffusion. The main idea is to split the flame ball in two components: the inner kernel, which is driven by a Poisson-type equation with a general polynomial forcing term, and the outer part, which is driven by a generalized diffusion process valid for fractional diffusive media. The evolution equation for the radius of the flame ball is finally determined as the evolution equation for the interface that matches the solution of the inner spherical kernel and the solution of the outer diffusive part and it emerges to be a nonlinear fractional differential equation. The effects of fractional diffusion on stability of solution are also picked out.     

Saddle points and rare collisions under scaling approach in a Fermi accelerator with two nonlinear terms

Rare collisions of a classical particle bouncing between two walls are studied. The dynamics is described by a two-dimensional, nonlinear and area-preserving mapping in the variables velocity and time at the instant that the particle collides with the moving wall. The phase space is of mixed type preventing diffusion of the particle to high energy. Successive and therefore rare collisions are shown to have a histogram of frequency which is scaling invariant with respect to the control parameters. The saddle fixed points are studied and shown to be scaling invariant with respect to the control parameters too.     

Acceleration noise generated by a random repeated impact process

Acceleration noise levels generated by a random repeated impact process have been predicted and compared with experimental measurements. The process consisted of a ball bouncing on a randomly vibrating surface, and is an idealized representation of random impact phenomena which can occur in machinery and transportation systems where a rolling element is in intermittent contact with the rolling surface. Predictions of the magnitudes of impacts and the times between them have been used in conjunction with established acoustic theory to estimate acceleration noise levels generated by the impacting ball. Measured sound pressure levels were in excellent agreement with the predicted levels.     

Computational transport methodology based on decomposition of a problem domain into transport and diffusive subdomains

A large class of radiative transfer and particle transport problems contain highly diffusive regions. It is possible to reduce computational costs by solving a diffusion problem in diffusive subdomains instead of the transport equation. This enables one to decrease the dimensionality of the transport problem. In this paper we present a methodology for decomposition of a spatial domain of a transport problem into transport and diffusion subregions. We develop methods for solving one-group problems in 1D slab geometry. To identify and locate diffusive regions, we develop metrics for measuring transport effects that are based on the quasidiffusion (Eddington) factor. We present the results of test problems that demonstrate the accuracy of the proposed methodology.     

Quantum ohmic dissipation: Particle on a one-dimensional periodic lattice

We investigate the dynamics of a particle on a periodic lattice, coupled to phonons with ohmic dissipation. At T = 0 a symmetry breaking appears, which corresponds to a transition between a localized and a delocalized regime. For T > 0 we recover a diffusive motion for which the diffusion coefficient is computed.     

Design optimization of a damped hybrid vibration absorber

In this article, the H_∞ optimization design of a hybrid vibration absorber (HVA), including both passive and active elements, for the minimization of the resonant vibration amplitude of a single degree-of-freedom (sdof) vibrating structure is derived by using the fixed-points theory. The optimum tuning parameters are the feedback gain, the tuning frequency, damping and mass ratios of the absorber. The effects of these parameters on the vibration reduction of the primary structure are revealed based on the analytical model. Design parameters of both passive and active elements of the HVA are optimized for the minimization of the resonant vibration amplitude of the primary system. One of the inherent limitations of the traditional passive vibration absorber is that its vibration absorption is low if the mass ratio between the absorber mass and the mass of the primary structure is low. The proposed HVA overcomes this limitation and provides very good vibration reduction performance even at a low mass ratio. The proposed optimized HVA is compared to a recently published HVA designed for similar propose and it shows that the present design requires less energy for the active element of the HVA than the compared design.     

A joint relaxation technique for the receptance solution of structural vibration problems

A well-established technique for the analysis of a complex vibrating system is to cut it into a convenient number of simpler subsystems. An alternative approach, suggested by recent studies of displacement excitation, is to convert the system into a set of independent subsystems by clamping it at a sufficient number of co-ordinates. Exact solutions for free and forced vibration are then obtained by considering the relaxation of the clamps. Data in the Vibration Analysis Tables [1] are used for the numerical solution of framed structures by this method. This displacement approach is in some cases simpler than the standard methods and leads to smaller frequency determinants.