Vibration of a beam due to a random stream of moving forces with random velocity

The problem of dynamic response of a beam to the passage of a train of concentrated forces with random amplitudes and velocities is considered. Force arrivals at the beam are assumed to constitute the point stochastic process of events. Thus, the excitation process is an idealization of vehicular traffic loads on a bridge. An analytical technique is developed to determine the response of the beam. Explicit expressions for the expected value and the variance of the beam deflection are provided. As an example, the response of a beam to a stationary stream of forces is determined for some practical situations, and discussed.     

Spatial instabilities in reaction random walks with direction-independent kinetics

We study spatial instabilities in reacting and diffusing systems, where diffusion is modeled by a persistent random walk instead of the usual Brownian motion. Perturbations in these reaction walk systems propagate with finite speed, whereas in reaction-diffusion systems localized disturbances affect every part instantly, albeit with heavy damping. We present evolution equations for reaction random walks whose kinetics do not depend on the particles' direction of motion. The homogeneous steady state of such systems can undergo two types of transport-driven instabilities. One type of bifurcation gives rise to stationary spatial patterns and corresponds to the Turing instability in reaction-diffusion systems. The other type occurs in the ballistic regime and leads to oscillatory spatial patterns; it has no analog in reaction-diffusion systems. The conditions for these bifurcations are derived and applied to two model systems. We also analyze the stability properties of one-variable systems and find that small wavelength perturbations decay in an oscillatory manner.     

Vibrations of double-string complex system under moving forces. Closed solutions

In this paper the dynamic response of a double-string system traversed by a constant or a harmonically oscillating moving force is considered. The force is moving with a constant velocity on the top string. The strings are identical, parallel, one upon the other and continuously coupled by a linear Winkler elastic element. The classical solution of the response of a double-string system subjected to a force moving with a constant velocity has a form of an infinite series. The main goal of this paper is to show that in the considered case a part of the solution can be presented in a closed, analytical form instead of an infinite series. The presented method of finding the solution in a closed, analytical form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations.     

Frequency domain response of a parametrically excited riser under random wave forces

Floating Production, Drilling, Storage and Offloading units represent a new technology with a promising future in the offshore oil industry. An important role is played by risers, which are installed between the subsea wellhead and the Tension Leg Deck located in the middle of the moon-pool in the hull. The inevitable heave motion of the floating hull causes a time-varying axial tension in the riser. This time dependent tension may have an undesirable influence on the lateral deflection response of the riser, with random wave forces in the frequency domain. To investigate this effect, a riser is modeled as a Bernoulli–Euler beam. The axial tension is expressed as a static part, along with a harmonic dynamic part. By linearizing the wave drag force, the riser's lateral deflection is obtained through a partial differential equation containing a time-dependent coefficient. Applying the Galerkin method, the equation is reduced to an ordinary differential equation that can be solved using the pseudo-excitation method in the frequency domain. Moreover, the Floquet–Liapunov theorem is used to estimate the stability of the vibration system in the space of parametric excitation. Finally, stability charts are obtained for some numerical examples, the correctness of the proposed method is verified by comparing with Monte-Carlo simulation and the influence of the parametric excitation on the frequency domain responses of the riser is discussed.     

Fractal chemical kinetics: Reacting random walkers

Computer simulations on binary reactions of random walkers (A + A A) on fractal spaces bear out a recent conjecture: ( ^–1 – ₀ ^–1) t ^f , where is the instantaneous walker density and ₀ the initial one, andf=d _s /2, whered _s is the spectral dimension. For the Sierpinski gaskets:d=2, 2f=1.38 (d _s =1.365);d=3, 2f=1.56 (d _s =1.547); biased initial random distributions are compared to unbiased ones. For site percolation:d= 2,p=0.60, 2f= 1.35 (d _s =1.35); d=3,p=0.32, 2f=1.37 (d _s =1.4); fractal-to-Euclidean crossovers are also observed. For energetically disordered lattices, the effective 2f (from reacting walkers) andd _s (from single walkers) are in good agreement, in both two and three dimensions.Supported by NSF Grant No. DMR 8303919.     

量子微腔中运动原子的辐射压力

利用全量子理论研究了量子微腔中运动原子的辐射压力. 从量子微腔与运动原子相互作用模型出发, 利用代数动力学方法对系统的哈密顿量进行规范变换, 推导出系统的时间演化算符和原子内态约化密度算符的表达式, 在此基础上给出辐射压力的解析解, 并讨论了驻波场和行波场中运动二能级原子和三能级原子的辐射压力, 数值结果与实验符合. 关键词： 量子微腔 运动原子 代数动力学 辐射压力     

Intensity fluctuations in a moving random medium

We consider the intensity fluctuations arising when a point source of radiation moves in a randomly inhomogeneous scattering medium. The medium itself can also move with a velocity whose component normal to the direction of propagation can have an arbitrary distribution. We derive an expression for the space–time autocorrelation function of the intensity fluctuations transverse to the direction of propagation. The result is analysed for some particular cases and it is shown how the resulting information can be useful in examining the behaviour of random media in situations of practical interest.     

Vibration control of beams on elastic foundation under a moving vehicle and random lateral excitations

The formulation of three-dimensional dynamic behavior of a Beam On Elastic Foundation (BOEF) under moving loads and a moving mass is considered. The weight of the vehicle is modeled as a moving point load, however the effect of the lateral excitation is considered by modeling: (case 1) a lateral moving load with random intensity for wind excitation and (case 2) a moving mass just in lateral direction of the beam for earthquake excitation. A Dirac-delta function is used to describe the position of the moving load and the moving mass along the beam. The beam foundations are considered as elastic Winkler-type in two perpendicular transverse directions. This model is proposed to investigate the bending response of the rails under the effect of traveling vehicle weight while a random excitation such as earthquake or wind takes place. The results showed the importance of considering the effect of earthquake/wind actions as in bending stress of the beam on elastic foundations. The effect of different regions (different support stiffness) and different velocities of the vehicle on the response of the beam are investigated in mentioned directions. At the end, a linear optimal control algorithm with displacement–velocity feedback is proposed as a solution to suppress the response of BOEFs. By the method of modal analyses and taking into account enough number of vibration modes, state-space equation is obtained, then sufficient number of actuators was chosen for each direction. Stochastic analyses were performed in lateral direction in order to illustrate a comprehensive view for the response of the beam under the random moving load in both controlled and uncontrolled systems. Furthermore, the efficiency of control algorithm on critical velocities is verified by parametric analyses in the vertical direction with the constant moving load for different regions.     

Multi-agent coordination in directed moving neighbourhood random networks

This paper considers the consensus problem of dynamical multiple agents that communicate via a directed moving neighbourhood random network.Each agent performs random walk on a weighted directed network.Agents interact with each other through random unidirectional information flow when they coincide in the underlying network at a given instant.For such a framework,we present sufficient conditions for almost sure asymptotic consensus.Numerical examples are taken to show the effectiveness of the obtained results.     

Radiation of charge moving in one-dimensional fine-scale random medium

Institute of Radio Physics and Electronics, Academy of Sciences of the Ukrainian SSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, pp. 853–856, July, 1991.     

Negative nonconservative forces: optical "tractor beams" for arbitrary objects

Based on the conservation of linear momentum on scattering from arbitrary objects, we demonstrate the generation of nonconservative optical forces that act in a direction opposite to the propagation of the incident beam. The concept can be applied to tailor the force fields produced on nonabsorbing bodies regardless of their sizes and shapes.     

Electromagnetic friction forces on the scanning probe asperity moving near surface

Using the Lifshitz electromagnetic theory a general expression is derived for the lateral force on a single spherical atom and a paraboloidal nanoasperity moving near the surface. For the first time it is shown that the sign of the force can be both negative and positive, depending on the dielectric properties of the tribopartners.     

Radiative forces acting on point sources moving in a stratified fluid

Both components of the total radiative force acting on uniformly moving mass sources in a stratified incompressible fluid are calculated. These forces are related to the emission of internal gravity waves. One component of the radiative force is directed opposite to the direction of motion. This is the well-known wave drag force. Different useful representations of this component are derived for several typical point sources (monopole, dipole, and others). The other component, directed perpendicular to the direction of the motion, is calculated for the first time. The results obtained are extended to the case of rotating media, where internal inertial-gravity waves exist. Zh. éksp. Teor. Fiz. 112, 507–523 (August 1997)     

Solvent diffusion kinetics in the dilute random alloy

In this paper we address the problem of enhancement of the solvent diffusivity by the addition of very small amounts of solute. The random alloy model is employed at the dilute limit. No Monte Carlo calculations have been available for evaluating the available theoretical treatments. In the present study we report on very-high-precision results of the solvent correlation factors as obtained from Monte Carlo calculations with averaging over 6 210 7 atoms and very long runs (2000 jumps per atom). The results are expressed in terms of the usual solvent enhancement factors b 1 and b 2 . There is good agreement with the theory of Holdsworth and Elliott and excellent agreement with the theory of Moleko et al . but not with other available theories.     

Diffusion with random traps: Transient one-dimensional kinetics in a linear potential

The problem of one-dimensional diffusion with random traps is solved without and with a constant field of force. Using an eigenvalue expansion for long times and the method of images for short times we give an exact, straightforward solution for the time dependence of the mean survival probability and the mean probability density for returning to the origin. Using the backward equation approach, we determine the mean survival time and the mean residence time density at the origin. We comment on the relation between these solutions and those for one-dimensional diffusion with random reflectors.