Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, 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 damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, 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. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Nonlinear Faraday Waves in a Parametrically Excited Circular Cylindrical Container

In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subjec

Computer Simulation Of Random Sphere Packing In An Arbitrarily Shaped Container

Most simulations of random sphere packing concern a cubic or cylindric container with periodic boundary, containers of other shapes are rarely studied. In this paper, a new relaxation algorithm with pre-expanding procedure for random sphere packing in an arbitrarily shaped container is presented. Boundaries of the container are simulated by overlapping spheres which covers the boundary surface of the container. We find 0.4 similar to 0.6 of the overlap rate is a proper value for boundary spheres. The algorithm begins with a random distribution of small internal spheres. Then the expansion and relaxation procedures are performed alternately to increase the packing density. The pre-expanding procedure stops when the packing density of internal spheres reaches a preset value. Following the pre-expanding procedure, the relaxation and shrinking iterations are carried out alternately to reduce the overlaps of internal spheres. The pre-expanding procedure avoids the overflow problem and gives a uniform distribution of initial spheres. Efficiency of the algorithm is increased with the cubic cell background system and double link data structure. Examples show the packing results agree well with both computational and experimental results. Packing density about 0.63 is obtained by the algorithm for random sphere packing in containers of various shapes.

Surface waves in a vertically excited circular cylindrical container

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.

Instability of the vertically forced surface wave in a circular cylindrical container

The nonlinear amplitude equation, which was derived by Jian Yongjun employing expansion of two-time scales in inviscid fluids in a vertically oscillating circular cylindrical vessel, is modified by introducing a damping term due to the viscous dissipation of this system. Instability of the surface wave is analysed and properties of the solutions of the modified equation are determined together with phase-plane trajectories. A necessary condition of forming a stable surface wave is obtained and unstable regions are illustrated. Research results show that the stable pattern of surface wave will not lose its stability to an infinitesimal disturbance.

Dynamic interaction of an elastic container with fluid

The vibration analysis of an elastic container with partially filled fluid was investigated in this paper. The container is made of a thin cylinder and two circular plates at the ends. The axis of the cylinder is in the horizontal direction. It is difficult to solve this problem because the complex system is not axially symmetric. The equations of motion for this system were derived. An incompressible and ideal fluid model is used in the present work. Solutions of the equations were obtained by the generalized variational method. The solution was expressed in a series of normalized generalized Fourier's functions. This series converged rapidly, and so its approximate solution was obtained with high precision. The agreement of the calculated values with the experimental result is good. It should be mentioned that with our method, the computer time is less than that with the finite-element method.

An inhibitor of c-Jun N-terminal kinases (CEP-11004) counteracts the anti-HIV-1 action of trichosanthin

Trichosanthin (TCS) is a type I ribosome-inactivating protein possessing multiple biological and pharmacological activities. One of its major actions is inhibition of human immunodeficiency virus (HIV) replication. The mechanism is still not clear. It is

Structure-function analysis of the inverted terminal repeats of the Sleeping Beauty transposon

Translocation of Sleeping Beauty (SB) transposon requires specific binding of SB transposase to inverted terminal repeats (ITRs) of about 230 bp at each end of the transposon, which is followed by a cut-and-paste transfer of the transposon into a target DNA sequence. The ITRs contain two imperfect direct repeats (DRs) of about 32 bp. The outer DRs are at the extreme ends of the transposon whereas the inner DRs are located inside the transposon, 165-166 bp from the outer DRs. Here we investigated the roles of the DR elements in transposition. Although there is a core transposase-binding sequence common to all of the DRs, additional adjacent sequences are required for transposition and these sequences vary in the different DRs. As a result, SB transposase binds less tightly to the outer DRs than to the inner DRs. Two DRs are required in each ITR for transposition but they are not interchangeable for efficient transposition. Each DR appears to have a distinctive role in transposition. The spacing and sequence between the DR elements in an ITR affect transposition rates, suggesting a constrained geometry is involved in the interactions of SB transposase molecules in order to achieve precise mobilization. Transposons are flanked by TA dinucleotide base-pairs that are important for excision; elimination of the TA motif on one side of the transposon significantly reduces transposition while loss of TAs on both flanks of the transposon abolishes transposition. These findings have led to the construction of a more advanced transposon that should be useful in gene transfer and insertional mutagenesis in vertebrates. (C) 2002 Elsevier Science Ltd. All rights reserved.

Anisotropic spin transport in two-terminal mesoscopic rings: Rashba and Dresselhaus spin-orbit interactions

We theoretically investigate the spin transport in two-terminal mesoscopic rings in the presence of both the Rashba spin-orbit interaction (RSOI) and the Dresselhaus spin-orbit interaction (DSOI). We find that the interplay between the RSOI and DSOI breaks the original cylindric symmetry of the mesoscopic rings and consequently leads to the anisotropic spin transport, i.e., the conductance is sensitive to the positions of the incoming and outgoing leads. The anisotropic spin transport can survive even in the presence of disorder caused by impurity elastic scattering in a realistic system.

Charge and spin currents in a three-terminal mesoscopic ring

We theoretically investigate the charge and spin currents in a three-terminal mesoscopic ring in the presence of a uniform and nonuniform Rashba spin-orbit interaction (SOI). It is shown that a fully spin-polarized charge current and a pure spin current can be generated by tuning the probe voltages and/or the strength of the Rashba SOI. The charge and spin currents oscillate as the strength of the Rashba SOI increases induced by the spin quantum interference. The ratio of probe voltages oscillates synchronously with the pure spin current as the strength of the Rashba SOI increases in a nonuniform Rashba ring, while it remains constant in a uniform Rashba ring. We demonstrate theoretically that a three-terminal uniform Rashba ring can be used as a spin polarizer and/or spin flipper for different spin injections, and a nonuniform Rashba ring could allow us to detect the pure spin current electrically. (C) 2009 American Institute of Physics. [DOI 10.1063/1.3054322]

Frequency mixing and phase detection functionalities of three-terminal ballistic junctions

Three-terminal ballistic junctions (TBJs) are fabricated from a high-mobility InP/In0.75Ga0.25As heterostructure by electron-beam lithography. The voltage output from the central branch is measured as a function of the voltages applied to the left and right branches of the TBJs. The measurements show that the TBJs possess an intrinsic nonlinearity. Based on this nonlinearity, a novel room-temperature functional frequency mixer and phase detector are realized. The TBJ frequency mixer and phase detector are expected to have advantages over traditional circuits in terms of simple structure, small size and high speed, and can be used as a new type of building block in nanoelectronics.

A New Edge-Coupled Two-Terminal Double Heterojunction Phototransistor (ECTT-DHPT) and Its DC Characteristics

A new ECTT-DHPT with InGaAsP(lambda=1.55 mu m) as base and InGaAsP(lambda=1.3 mu m) as collector as well as waveguide was designed and fabricated, the DC characteristics reveal that the ECTT-DRPT can perform good optoelectronic mix operation and linear amplification operation by optically biased at two appropriate value respectively. Responsivity of more than 52A/W and dark current of 70nA (when V-ce=1V) were obtained.