Abstract:
The nonlinear free surface amplitude equation, which has been derived from the inviscid fluid by solving the potential equation of water waves with a singular perturbation theory in a vertically oscillating rigid circular cylinder, is investigated successively in the fourth-order Runge－Kutta approach with an equivalent time-step. Computational results include the evolution of the amplitude with time, the characteristics of phase plane determined by the real and imaginary parts of the amplitude, the single-mode selection rules of the surface waves in different forced frequencies, contours of free surface displacement and corresponding three-dimensional evolution of surface waves, etc. In addition, the comparison of the surface wave modes is made between theoretical calculations and experimental measurements, and the results are reasonable although there are some differences in the forced frequency.

Abstract:
Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier－Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.

Abstract:
Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate pattern-forming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term, an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tension was introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important. However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.

Abstract:
It is numerically demonstrated by means of a magnetohydrodynamics (MHD) code that precession can trigger the dynamo effect in a cylindrical container. This result adds credit to the hypothesis that precession can be strong enough to be one of the sources of the dynamo action in some astrophysical bodies.

Abstract:
We report the experimental findings of formation and motion of heap in granular materials in an inclined and vertically vibrated container. We show experimentally how the transport velocity of heap up container is related to the driving acceleration as well as the driving frequency of exciter. An analogous experiment was performed with a heap-shaped Plexiglas block. We propose that cohesion force resulted from pressure gradient in ambient gas plays a crucial role in enhancing and maintaining a heap, and ratchet effect causes the movement of the heap. An equation which governs the transport velocity of the heap is presented.

Abstract:
Appropriate conformal mapping transformation in combination with the linear potential theory is employed to develop mathematical model for two-dimensional sloshing in horizontal circular cylindrical containers with overall eccentric hole. The tube-type tank is filled with inviscid incompressible fluid up to its half depth and subjected to lateral accelerations. A ramp-step excitation encountered in a road turning maneuver as well as real seismic event is used to simulate the lateral acceleration excitation. The resulting linear sets of ordinary differential equations are truncated and then solved numerically by employing Laplace transform technique followed by Durbin’s numerical inversion pattern. The effects of excitation input time, eccentricity, and radii ratio on the hydrodynamic responses and suppression of the induced destabilizing lateral forces are examined. Limiting cases are considered and good agreements with available analytic and numerical solutions as well as the simulations performed by using a commercial FEM software package are obtained. 1. Introduction Slosh refers to the splash of liquid which has a free surface inside a container that it may also undergo an undesirable motion. Practical examples consist of propellant slosh in spacecraft storage tanks, rockets, cargo slosh in battleship, road vehicles transporting liquids, and nuclear reactors. In order to model this phenomenon extensive mathematical relationships have been derived to explain liquid slosh such as [1]. Slosh is an imperative effect not only in safety of aircrafts, spacecrafts [2] but also in performance of instruments such as Earth-orbiting satellites [3, 4] and attitude control system (ACS), especially for spinning satellites [5]. Recently, a wide amount of studies on liquid sloshing in horizontal cylindrical tanks with application in road and marine vehicles is done such as [6–10]. Budiansky [11] estimated the natural frequencies, mode shapes, and hydrodynamic forces in a circular cylindrical horizontal tank with partially full liquid and under transverse load excitation for the first time. McCarty and Stephens [12] calculated natural frequencies for transverse sloshing in flat cylindrical vessels with various sizes, fullness, and orientations, verifying the results presented in [11]. Moiseev and Petrov [13] measured natural frequencies with Ritz variation method for different tank geometries containing partially full liquid. They also studied the results of the horizontal circular cylindrical container in their results. McIver [14] exerted special coordinate systems

Abstract:
We report experimental observations obtained by particule image velocimetry (PIV) of the behavior of a flow driven by rotation and precession of a cylindrical container. Various hydrodynamical regimes are identified according to the value of the control parameter which is the ratio of the precession frequency to the rotation frequency. In particular when this parameter is increased from small values, we have observed an induced differential rotation followed by the apparition of permanent cyclonic vortices.

Abstract:
An experimental system was developed and used to study the nanofluid flow and heat transfer in circular conduits. Experiments were performed for a variety of nanofluid flow features in the system. Results obtained from the study show that the heat transfer rate for flow of the base fluid is less than that of the nanofluid used in the study. It was also found that the observed relationship between molecular diffusivity of momentum and the molecular diffusivity of thermal energy at the macroscale may not necessarily be the same at the nanoscale. A heat transfer correlation for turbulent forced convection flow in circular pipes was developed from the results in terms of Nusselt number, Reynolds number and Prandtl number. The correlation developed was compared to related correlations in the literature. Important factors that affect nanofluid flow and heat transfer in circular conduits were also determined. This type of study is essential for heat exchanger applications.

Abstract:
In this paper, the nonlinear sloshing of liquid in a circle cylindrical tank under pitching excitation is studied analytically for the first time. Owing to the complexity of problem, it is very difficult to solve the nonlinear sloshing of liquid in a container subjected to forced pitching and (or) yawing oscillation by existing methods. Therefore, a method used to analyze this problem is presented. Firstly the nonlinear initial-boundary problem of PDE system for liquid sloshing in a container under pitching and (or) yawing excitation is established. With regard to the previous problem, variational principle and Lagrange function in the form of the volume integration of liquid pressure are obtained. Based on the variation equation and new Lagrange function proposed, nonlinear dynamic system for sloshing of liquid in a circle cylindrical container under pitching and (or) yawing excitation is derived. Subsequently, the nonlinear dynamic system gives the free surface kinematics and dynamic boundary condition. At the same time, the present method greatly reduces the work of formula derivation. Finally, the nonlinear dynamic system is solved by the multiple scale method. The dynamic characteristic of nonlinear liquid sloshing is analyzed in detail. Some kinds of motion which may appear in the liquid sloshing are discussed. Response curves and stable-unstable regions of liquid motion are determined. As to two-dimensional sloshing in a rigid, rectangular, open tank, the comparison between theoretical result by the present method and experiments shows good agreement. So, the present method is proved feasible. By means of the present method, the coupled dynamics of liquid in a tank and structure may also be investigated analytically.

Abstract:
We present a quantization procedure for the electromagnetic field in a circular cylindrical cavity with perfectly conducting walls, which is based on the decomposition of the field. A new decomposition procedure is proposed; all vector mode functions satisfying the boundary conditions are obtained with the help of this decomposition. After expanding the quantized field in terms of the vector mode functions, it is possible to derive the Hamiltonian for this quantized system.