Impact of nanoparticles and radiative heat flux in von Kármán swirling flow of Maxwell fluid

In this paper, the classical von Kármán swirling flow problem due to a rotating disk is modeled and studied for the rate type Maxwell nanofluid together with heat and mass transfer mechanisms. The model under consideration predicts the relaxation time characteristics. The novel aspects of thermophoresis and Brownian motion features due to nanoparticles are investigated by employing an innovative Buongiorno’s model. The analysis further explores the impact of linear Rosseland radiation on heat transfer characteristics. The concept of boundary layer approximations is utilized to formulate the basic governing equations of Maxwell fluid. The dimensionless form of a system of ordinary differential equations is obtained through similarity approach adopted by von Kármán. The system of equations is integrated numerically in domain [0,∞) by using bvp midrich scheme in Maple software. The obtained results intimate that higher rotation raises the radial and angular velocity components. The nano-particles concentration enhances with Brownian motion parameter. Further, the heat transfer rate at the disk surface diminishes with thermophoresis parameter. The achieved numerical computations of velocity profiles, friction coefficient and Nusselt number are matched in limiting cases with previously published literature and an outstanding agreement is observed.     

Fluctuation-dissipation relations and statistical temperatures in a turbulent von Kármán flow

We experimentally characterize the fluctuations of the nonhomogeneous nonisotropic turbulence in an axisymmetric von Kármán flow. We show that these fluctuations satisfy relations, issued from the Euler equation, which are analogous to classical fluctuation-dissipation relations in statistical mechanics. We use these relations to estimate statistical temperatures of turbulence.     

Numerical study of homogeneous dynamo based on experimental von Kármán type flows

A numerical study of the magnetic induction equation has been performed on von Kármán type flows. These flows are generated by two co-axial counter-rotating propellers in cylindrical containers. Such devices are currently used in the von Kármán sodium (VKS) experiment designed to study dynamo action in an unconstrained flow. The mean velocity fields have been measured for different configurations and are introduced in a periodic cylindrical kinematic dynamo code. Depending on the driving configuration, on the poloidal to toroidal flow ratio and on the conductivity of boundaries, some flows are observed to sustain growing magnetic fields for magnetic Reynolds numbers accessible to a sodium experiment. The response of the flow to an external magnetic field has also been studied: The results are in excellent agreement with experimental results in the single propeller case but can differ in the two propellers case.     

On the Kelvin–Helmholtz and von Kármán vortices in the near-wake of semicircular cylinders with flaps

The signatures of the Kelvin–Helmoltz (K–H) and von Kármán (VK) vortices shed from a semicircular cylinder with flaps of length L/d = 0, 1/3, 1, 2, and 3 were investigated using hotwire anemometry. Here, L and d denote the flap length and diameter of the semi-circular cylinder, respectively. Experiments were performed at Reynolds numbers spanning one order of magnitude, Re ∈ [8.4 × 10³,?6.7 × 10⁴]. The results highlight the impact of the flow modulation through rigid flaps on the wake characteristics and dominant vortex shedding. The increase of flap length resulted in reduced mean shear in the near-wake, which influenced the onset and coherence of the K-H instability. Indeed, these motions are less likely to be present in the wake of the L/d = 3 case. The flaps also impacted the frequency of the VK shedding; the associated Strouhal number increased from 0.2 to 0.3 for flaps L/d ? 1. Only the cases without with the shortest flaps (L/d = 1/3) followed St = 0.2. There is a distinctive dependence of the f_{K ? H}/f_VK on Reynolds number and flap length. This ratio followed the well-known power-law relationship of circular cylinders in the case without flaps. However, the Reynolds number exponent decreased with increased flap length.     

Slow dynamics in a turbulent von Kármán swirling flow

An experimental study of a turbulent von Kármán flow in a cylinder is presented. The mean flow is stationary up to a Reynolds number Re=10(4) where a bifurcation takes place. The new regime breaks some symmetries of the problem and becomes time dependent because of equatorial vortices moving with a precession movement. In the exact counterrotating case, a bistable regime appears and spontaneous reversals of the azimuthal velocity are registered. A three-well potential model with additive noise reproduces this dynamic. A regime of periodic response is observed when a very weak forcing is applied.     

Self-interaction in the von Kármán cosmic string street configuration

We study the problem of electromagnetic self-interaction of line sources in the presence of an array of parallel cosmic strings akin to the von Kármán vortex street configuration. Keeping in mind possible applications in condensed matter physics we consider also a mixed array where both deficit angle and excess angle cosmic strings appear. We obtain explicit expressions for both the electric and magnetic self-energies for the cases studied and demonstrate that these results reproduce the known self-energies in the single-string limit.     

New interaction solutions and nonlocal symmetry of an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form

The nonlocal symmetry is derived for an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form from the truncated Painlevéexpansion method. The nonlocal symmetries are localized to the Lie point symmetry by introducing new auxiliary dependent variables. The finite symmetry transformation and the Lie point symmetry for the prolonged system are solved directly. Many new interaction solutions among soliton and other types of interaction solutions for the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form can be obtained from the consistent condition of the consistent tanh expansion method by selecting the proper arbitrary constants.     

Lagrangian form of Schrödinger equation

Lagrangian formulation of quantum mechanical Schrödinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible quantum system results in a well defined second order equation on a real vector space. The Klein–Gordon equation for a real field is shown to be the Lagrangian form of the corresponding Schrödinger equation.     

Kinematic dynamo simulations of von Kármán flows: application to the VKS experiment

The VKS experiment has evidenced dynamo action in a highly turbulent liquid sodium von Kármán flow [R. Monchaux et al., Phys. Rev. Lett. 98, 044502 (2007)]. However, the existence and the onset of a dynamo happen to depend on the experimental configuration. Performing kinematic dynamo simulations on real flows, we study the influence of the configuration on dynamo action, namely the sense of rotation and the presence of an annulus in the shear layer plane. The 3 components of the mean velocity fields are measured in a water prototype for different VKS configurations through Stereoscopic Particle Imaging Velocimetry. Experimental data are then processed in order to use them in a periodic cylindrical kinematic code. Even if the kinematic predicted mode appears to be different from the experimental saturated one, the results concerning the existence of a dynamo and the thresholds are in qualitative agreement, showing the importance of the flow characteristics.     

Ludwig Prandtl’s envisage: elimination of von Kármán vortex street with boundary-layer suction

Journal of Visualization - The present study is a revisit to Ludwig Prandtl’s elimination of von Kármán vortex street behind a circular cylinder by using steady suction in the...     

The forms of three-order Lagrangian equation in relative motion

In this paper, the general expressions of three-order Lagrangian equations in a motional coordinate system are obtained. In coordinate systems with some specific forms of motion, the expressions corresponding to these equations are also presented.     

Mechanism Responsible for the Complete Suppression of Kármán Vortex in Flows Past a Wavy Square-Section Cylinder

The Kármán vortex shedding is totally suppressed in flows past a wavy square-section cylinder at a Reynolds number of 100 and the wave steepness of 0.025. Such a phenomenon is illuminated by the numerical simulations. In the present study, the mechanism responsible for it is mainly attributed to the vertical vorticity. The geometric disturbance on the rear surface leads to the appearance of spanwise flow near the base. The specific vertical vorticity is generated on the rear surface and convecting into the near wake. The wake flow is recirculated with the appearance of the pair of recirculating cells. The interaction between the upper and lower shear layers is weakened by such cells, so that the vortex rolls could not be formed and the near wake flow becomes stable.     

Another representation of the β form of the inhomogeneous Picard-Fuchs equation

In this letter we give another representation of the β form in the inhomogeneous Picard-Fuchs equation for open topological string for some one-parameter Calabi-Yau hypersurfaces in weighted projective spaces. Furthermore, the corresponding domain wall tensions calculated by using these β forms are consistent with the results that appear in literature. The β form is essential for the calculation of the D-brane domain wall tension, and a convenient choice of β forms should simplify the calculation. The freedom of the choice of β forms shows some symmetries in Calabi-Yau space.     

Painlev property of the modified C-KdV equation and its exact solutions

In this paper,the Painlev’e properties of the modified C-KdV equation are verified by using the W-K algorithm.Then some exact soliton solutions are obtained by applying the standard truncated expansion method and the nonstandard truncated expansion method with the help of Maple software,respectively.     

Probabilistic and controlled teleportation of tripartite state in a general form and its quantum networks

We discuss a scheme for probabilistic and controlled teleportation of an unknown arbitrary three-particle state by constructing a peculiar non-maximally entangled state as a controlled quantum channel，which is teleported between two sides with the help of the auxiliary particle and the cooperation of the third side (Charlie) as a supervisor. In comparison with some existing schemes, on the receiver's side it is easy to have the sender's state through operating two uniform unitary transformations in turn. In addition, we also give an efficient quantum network for implementing the new scheme by means of some primitive operations.     

Analytic approximations of Von Krmn plate under arbitrary uniform pressure—equations in integral form

Analytic approximations of the Von Krmn's plate equations in integral form for a circular plate under external uniform pressure to arbitrary magnitude are successfully obtained by means of the homotopy analysis method(HAM), an analytic approximation technique for highly nonlinear problems. Two HAM-based approaches are proposed for either a given external uniform pressure Q or a given central deflection, respectively. Both of them are valid for uniform pressure to arbitrary magnitude by choosing proper values of the so-called convergence-control parameters c_1 and c_2 in the frame of the HAM. Besides, it is found that the HAMbased iteration approaches generally converge much faster than the interpolation iterative method. Furthermore, we prove that the interpolation iterative method is a special case of the first-order HAM iteration approach for a given external uniform pressure Q when c_1 =.θ and c_2 =-1, where θ denotes the interpolation iterative parameter. Therefore, according to the convergence theorem of Zheng and Zhou about the interpolation iterative method, the HAM-based approaches are valid for uniform pressure to arbitrary magnitude at least in the special case c_1 =.θ and c_2 =-1. In addition, we prove that the HAM approach for the Von Krmn's plate equations in differential form is just a special case of the HAM for the Von Krmn's plate equations in integral form mentioned in this paper. All of these illustrate the validity and great potential of the HAM for highly nonlinear problems,and its superiority over perturbation techniques.     

On spectral relaxation method approach for steady von Kármán flow of a Reiner-Rivlin fluid with Joule heating, viscous dissipation and suction/injection

In this study we use the spectral relaxation method (SRM) for the solution of the steady von Kármán flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipation. The spectral relaxation method is a new Chebyshev spectral collocation based iteration method that is developed from the Gauss-Seidel idea of decoupling systems of equations. In this work, we investigate the applicability of the method in solving strongly nonlinear boundary value problems of von Kármán flow type. The SRM results are validated against previous results present in the literature and with those obtained using the bvp4c, a MATLAB inbuilt routine for solving boundary value problems. The study highlights the accuracy and efficiency of the proposed SRM method in solving highly nonlinear boundary layer type equations.     

Inclusive production of charged hadrons and {\rm K}^0_{\rm S} mesons in photon–photon collisions

The production of charged hadrons and mesons in the collisions of quasi-real photons has been measured using the OPAL detector at LEP. The data were taken at centre-of-mass energies of 161 and 172 GeV. The differential cross-sections as a function of the transverse momentum and the pseudorapidity of the charged hadrons and mesons have been compared to the leading order Monte Carlo simulations of PHOJET and PYTHIA and to perturbative next-to-leading order (NLO) QCD calculations. The distributions have been measured in the range GeV of the hadronic invariant mass W. By comparing the transverse momentum distribution of charged hadrons measured in interactions with -proton and meson-proton data we find evidence for hard photon interactions in addition to the purely hadronic photon interactions. Received: 4 June 1998 / Published online: 6 November 1998     

Gauge and Bäcklund transformations for the generalized sine-Gordon equation and its η-dependent modified equation

We study the generalized sine-Gordon hierarchy and its associated-dependent modified sine-Gordon hierarchy. Two Bäcklund transformations for these two families are constructed. One of them is a generalization of the Bäcklund transformations of Wadatiet al. and the other one is new. Gauge transformations of a relevant AKNS system are employed to reduce the integration of these equations via the Bäcklund transformations to quadratures. Three generations of explicit solutions of the sine-Gordon equation are presented.