Rotating thin-shell wormhole from glued Kerr spacetimes

We construct a model of a rotating wormhole made by cutting and pasting two Kerr spacetimes. As a result, we obtain a rotating thin-shell wormhole with exotic matter at the throat. Two candidates for the exotic matter are considered: (i) a perfect fluid; (ii) an anisotropic fluid. We show that a perfect fluid is unable to support a rotating thin-shall wormhole. On the contrary, the anisotropic fluid with the negative energy density can be a source for such a geometry.     

On the rotating beam: Some theoretical and numerical results

A bifurcation analysis for a thin beam rotating about an axis is carried out by the Golubitsky-Schaeffer theory of singularities. The rotation velocity is the bifurcation parameter, while the constants describing the position of the beam are considered as small perturbation parameters. A finite difference approximation of the problem is also introduced, and an error analysis is given.     

Application of the Over-Set Grid Technique to a Model Singular Perturbation Problem

The numerical solution of a singularly perturbed problem, in the form of a two-dimensional convection-diffusion equation, is studied by using the technique of over-set grids. For this purpose the Overture software library is used. The selection of component grids is made on basis of asymptotic analysis. The behavior of the solution is studied for a range of small diffusion parameters. Also the possibilities of rotating the grid with the convection direction is considered. The basic discretisation method is central differencing, and in order to fit global properties of the solution, the composite grid used is made parameter dependent. In view of possible ɛ-uniform convergence, in the resulting composite grid the number of grid points is kept constant for the different values of the small parameter. Only the grid spacing is adapted, depending on the parameters. We see that, even with such careful adaptation of the grid, in the discrete maximum norm no ɛ-uniform convergence is achieved. Received October 10, 1999     

A liquid film motor

It is well known that electro-hydrodynamical effects in freely suspended liquid films can force liquids to flow. Here, we report a purely electrically driven rotation in water and some other liquid suspended films with full control on the velocity and the chirality of the rotating vortices. The device, which is called “film motor”, consists of a quasi two-dimensional electrolysis cell in an external in-plane electric field, crossing the mean electrolysis current density. If either the external field or the electrolysis voltage exceeds some threshold (while the other does not vanish), the liquid film begins to rotate. The device works perfectly with both DC and AC fields.     

Notes on wormhole existence in scalar-tensor and <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

Some recent papers have claimed the existence of static, spherically symmetric wormhole solutions to gravitational field equations in the absence of ghost (or phantom) degrees of freedom. We show that in some such cases the solutions in question are actually not of wormhole nature while in cases where a wormhole is obtained, the effective gravitational constant G _eff is negative in some region of space, i.e., the graviton becomes a ghost. In particular, it is confirmed that there are no vacuum wormhole solutions of the Brans-Dicke theory with zero potential and the coupling constant ω > −3/2, except for the case ω = 0; in the latter case, G _eff < 0 in the region beyond the throat. The same is true for wormhole solutions of F(R) gravity: special wormhole solutions are only possible if F(R) contains an extremum at which G _eff changes its sign.     

Stability in impulsive systems with markov perturbations in averaging scheme. 3. Weak convergence of solutions of impulsive systems

For a stochastic dynamic system with a small parameter, the uniform boundedness of the p-th moment of the solution (p > 1), the weak convergence of the solution of the system to the solution of Ito stochastic differential equation, and the weak convergence of normalized deviations are proved. The stability of linear systems with a small parameter and Markov perturbations is analyzed.     

Control of rotating pulses in a loop reactor

We consider the stabilization of a rotating pulse in a system of connected chemical reactors that are organized in a loop with periodic switching of the feed between units. Such a solution has been shown to exist in a narrow domain of switching velocities (unit length/switching time). We use the switch velocity as control parameter and design it to follow the pulse: the switch velocity is formed at every step on-line using the discrepancy between the temperature at the front of a pulse and the set point. We present a systematic methodology to control design using a mathematical model of the network of reactors. We present analytical results for a limiting many-unit system and apply this know how to design a system with finite number of units.     

Rotating flow of viscoelastic fluid with nonlinear thermal radiation: a numerical study

This work is concerned with the numerical solution for rotating viscoelastic flow developed by an exponentially stretching impermeable surface. Temperature at the sheet is also assumed to vary exponentially. Energy equation involves the novel nonlinear radiation heat flux term. Suitable transformations are utilized to nondimensionalize the relevant boundary layer equations. Numerical solutions are developed by means of standard shooting approach. The results demonstrate that both rotation and viscoelasticity serve to reduce the hydrodynamic boundary layer thickness. Temperature function has a special S-shaped profile when the difference between wall and ambient temperatures is sufficiently large. Heat transfer coefficient at the surface diminishes when rotation parameter is increased. Current numerical computations are consistent with those of the existing studies in the literature.

     

旋转粘弹性夹层梁非线性自由振动特性研究

对旋转粘弹性夹层梁的非线性自由振动特性进行了分析.基于Kelvin-Voigt粘弹性本构关系和大挠度理论,建立了旋转粘弹性夹层梁的非线性自由振动方程,并使用Galerkin法将偏微分形式振动方程化为常微分振动方程.采用多重尺度法对非线性常微分振动方程进行求解,通过小参数同次幂系数相等获得微分方程组,并通过求解方程组及消除久期项来获得旋转粘弹性夹层梁非线性自由振动的一次近似解.用数值方法讨论了粘弹性夹层厚度、转速和轮毂半径对梁固有频率的影响.结果表明:固有频率随转速增大而增大,随夹层厚度增大而减小,随轮毂半径的增大而增大.     

A parallel algorithm for the parametric synthesis of a system for the angular stabilization of a rotating elastic beam under the action of longitudinal acceleration

A parallel algorithm for the parametric synthesis of a family of controlled linearized combined dynamic systems in which the configuration of the stability regions in the feedback parameter space depends on some slowly varying design parameters is proposed. The parametric synthesis of a system for the angular stabilization of an elastic beam rotating about a longitudinal axis under the action of a longitudinal acceleration is implemented. This kind of synthesis can substantially reduce the errors of the stabilization system and the typical regulation time in the entire range of the slow increase in the rotation velocity of the beam.     

A study of controllable motion of a mobile vibration system moving with breakaway from the surface

We consider a model of a two-mass mechanical system consisting of an external body (box) and an internal body (unbalance), which moves on a rough rigid surface with a breakaway from it. We derive differential equations describing the system motion in the phase of flight and determine the conditions of location on the reference surface. The control parameter is proposed to be the angular velocity of unbalance rotation. To find the dependence of hopping height and length on the control frequency of unbalance rotation, we analyze the equations. An algorithm of numerical integration of the system of differential equations of motion was developed. The numerical solution confirms the theoretical conclusions on the dependence of hopping height and length on rotation frequency. At the same time, the form of trajectory of body mass center was found to depend on the value of the control parameter. Also, we reveal the dependence of the direction of robot motion on hopping height and length, and unbalance (on the ratio of system mass).     

Micro-PIV measurements of flows induced by rotating microparticles near a boundary

We report on the hydrodynamics induced by single-digit micron-sized superparamagnetic particles rotating at low Reynolds number and analyze the resultant flow fields using microparticle image velocimetry (µPIV). Magnetic microparticles floating a few nanometers above a glass substrate, in an otherwise quiescent fluid, were actuated wirelessly using a rotating magnetic field controlled using two pairs of orthogonally positioned electromagnetic coils. A high-speed camera was used to sufficiently capture the motion of nanometer-sized seeding particles at 500 frames per second as well as track the rotation of microparticles. Data from µPIV are compared with the analytical solution for Stokes flow generated by a sphere in an infinite fluid and numerical simulations using finite element analysis. Two-dimensional velocity data obtained from stacks of planar flow fields at incremental depths for individual microparticles show non-symmetrical profiles that are an indication of increased viscous effects due to the boundary confining wall. Additionally, the flow fields generated by two particles, at various separation distances, are also analyzed. It is observed that as two synchronously rotating beads, of approximately equal diameter, are placed closed together, complex flows offset, superimpose, and merge into single, larger microvortices. We find that the flow fields generated by two physically bound microparticles, rotating as one unit, are well approximated by the flow generated by a single microparticle with twice the diameter.     

Dynamics of a rotating flexible and symmetric spacecraft using impedance matrix in terms of the flexible appendages cantilever modes

The subject of this work is the dynamics of a rotating spacecraft. The spacecraft is modeled as a main rigid body connected to two flexible solar panels. The orbital motion of the whole spacecraft with a constant angular velocity is considered, interacting with small rigid motions of the main body, and small elastic deformations and infinitesimal vibrations of the solar panels. A continuum approach based on the Rayleigh–Ritz discretization is used to describe the distributed flexibility in the spacecraft. Rayleigh–Ritz discretization functions used are the clamped modes of the solar panels. This method enables us to construct the impedance matrix of the whole system relating to the displacement of the main body and the external torque. A spectral expansion of this impedance matrix, in terms of these clamped modes is obtained in the frequency domain. The numerical results presented show that for small values of orbital angular velocity, the vibration motion frequencies of the flexible parts (solar panels) are not perturbed substantially. Moreover, when great values of orbital angular velocity are simulated, these frequencies change considerably. The present investigation based on the Rayleigh–Ritz discretization shows the effect of the interaction between the orbital motion of the whole spacecraft and the vibration motions of the flexible parts.     

Rotating nonstationary cosmological models and astrophysical observations

A Bianchi type II cosmological model has been built with expansion and rotation. The sources of gravity in the model are a perfect fluid, pure radiation and a scalar field, where the perfect fluid describes rotating a phantom matter. This solution can be used for modeling both the first and the second inflationary stages of the Universe evolution with rotation. We discuss the possible manifestation of cosmological rotation in astrophysical observations.     

Integrating rotation from angular velocity

The integration of the rotation from a given angular velocity is often required in practice. The present paper explores how the choice of the parametrization of rotation, when employed in conjuction with different numerical time-integration schemes, effects the accuracy and the computational efficiency. Three rotation parametrizations - the rotational vector, the Argyris tangential vector and the rotational quaternion - are combined with three different numerical time-integration schemes, including classical explicit Runge-Kutta method and the novel midpoint rule proposed here. The key result of the study is the assessment of the integration errors of various parametrization-integration method combinations. In order to assess the errors, we choose a time-dependent function corresponding to a rotational vector, and derive the related exact time-dependent angular velocity. This is then employed in the numerical solution as the data. The resulting numerically integrated approximate rotations are compared with the analytical solution. A novel global solution error norm for discrete solutions given by a set of values at chosen time-points is employed. Several characteristic angular velocity functions, resulting in small, finite and fast oscillating rotations are studied.     

An optimum design of robotic food handling by using Burger model

This paper discusses an optimum design approach on robotic food handling by considering the characteristics of viscoelasticity of object. We pick up a traditional Japanese food, “Norimaki” as a typical example with the viscoelastic characteristics. We first show that the dynamic characteristics of Norimaki can be expressed by utilizing the Burger model. After testing the parameter sensitivity, we show an example of the optimum design for determining the combination of the hand stiffness and the operating velocity. We further show that the resultant plastic deformation can be formulated with the exact solution.     

Cylindrically and axially symmetric wormholes. Throats in vacuum?

This brief review discusses the existence conditions of wormhole throats and wormholes as global configurations in general relativity under the assumptions of cylindrical and axial symmetries. It is pointed out, in particular, that wormhole throats can exist in static, cylindrically symmetric space-times under slightly different conditions as compared with spherical symmetry. In cylindrically symmetric spacetime with rotation, throats can exist in the presence of ordinary matter or even in vacuum; however, there are substantial difficulties in obtaining asymptotically flat wormhole configurations without exotic matter: such examples are yet to be found. Some features of interest are discussed in static, axially symmetric configurations, including wormholes with singular rings and wrongly seeming regular wormhole throats in the Zipoy-Voorhees vacuum space-time.     

Critical rotational speed,critical velocity of fluid flow and free vibration analysis of a spinning SWCNT conveying viscous fluid

In this article, the influences of rotational speed and velocity of viscous fluid flow on free vibration behavior of spinning single-walled carbon nanotubes (SWCNTs) are investigated using the modified couple stress theory (MCST). Taking attention to the first-order shear deformation theory, the modeled rotating SWCNT and its equations of motion are derived using Hamilton’s principle. The formulations include Coriolis, centrifugal and initial hoop tension effects due to rotation of the SWCNT. This system is conveying viscous fluid, and the related force is calculated by modified Navier–Stokes relation considering slip boundary condition and Knudsen number. The accuracy of the presented model is validated with some cases in the literatures. Novelty of this study is considering the effects of spinning, conveying viscous flow and MCST in addition to considering the various boundary conditions of the SWCNT. Generalized differential quadrature method is used to approximately discretize the model and to approximate the equations of motion. Then, influence of material length scale parameter, velocity of viscous fluid flow, angular velocity, length, length-to-radius ratio, radius-to-thickness ratio and boundary conditions on critical speed, critical velocity and natural frequency of the rotating SWCNT conveying viscous fluid flow are investigated.     

Analysis of systems of singular ordinary differential equations

Systems of ordinary differential equations with a small parameter at the derivative and specific features of the construction of their periodic solution are considered. Sufficient conditions of existence and uniqueness of the periodic solution are presented. An iterative procedure of construction of the steady-state solution of a system of differential equations with a small parameter at the derivative is proposed. This procedure is reduced to the solution of a system of nonlinear algebraic equations and does not involve the integration of the system of differential equations. Problems of numerical calculation of the solution are considered based on the procedure proposed. Some sources of its divergence are found, and the sufficient conditions of its convergence are obtained. The results of numerical experiments are presented and compared with theoretical ones. Translated from Kibemetika i Sistemnyi Analiz, No. 5, pp. 103–110, September–October, 1999.     

基于永磁约束腔的线偏振光旋转特性研究

在法拉第磁光效应基础上,设计了一种永磁约束磁腔,通过将法拉第磁光元件置于约束磁腔中,研究了线偏振光穿过结构参数可变的约束磁腔后其旋转角的变化情况.实验发现,随着磁腔半径的增大和磁体块数的减小,线偏振光的旋转角呈逐渐降低趋势,随着磁体间距的增大,旋转角呈先增大后减小的趋势,同时磁体块数越多,旋转角减小的越缓慢.在6块磁体磁腔半径为4.3 mm磁体间距为16 mm时,旋转角最大达到85.1°;在2块磁体磁腔半径为9.5 mm,磁体间距为14 mm时,旋转角最小为9.8°.