Effect of Hall currents on interaction of pulsatile and peristaltic transport induced flows of a particle-fluid suspension

The interaction of purely periodic mean flow with a peristaltic induced flow is investigated within the framework of a two-dimensional analogue. The mathematical model considers a viscous incompressible fluid under the effect of transverse magnetic field, taking into account the effect of Hall currents for a magneto-fluid with suspended particles between infinite parallel walls on which a sinusoidal traveling wave is imposed. A perturbation solution to the complete set of Navier-Stokes equations is found for the case in which the frequency of the traveling wave and that of the imposed pressure gradient are equal. The ratio of the traveling wave amplitude to channel width is assumed to be small. For this case a first order steady flow is found to exist, as contrasted to a second order effect in the absence of the imposed periodic pressure gradient. The effect of Hall parameter, Hartmann number and the various parameters included in the problem are discussed numerically.     

Numerical Investigation of Cavitation Interacting with Pressure Wave

A computational fluid dynamics solver based on homogeneous cavitation model is employed to compute the two-phase cavitating flow. The model treats the two-phase regime as the homogeneous mixture of liquid and vapour which are locally assumed to be under both kinetic and thermodynamic equilibrium. As our focus is on pressure wave formation, propagation and its impact on cavitation bubble, the compressibility effects of liquid water have to be accounted for and hence the flow is considered to be compressible. The cavitating flow disturbed by the introduced pressure wave is simulated to investigate the unsteady features of cavitation due to the external perturbations. It is observed that the cavity becomes unstable, locally experiencing deformation or collapse, which depends on the shock wave intensity and freestream flow speed.     

Laminar magnetohydrodynamic duct flow in the presence of a magnetic dipole

We study magnetohydrodynamic flow of a liquid metal in a straight duct. The magnetic field is produced by an exterior magnetic dipole. This basic configuration is of fundamental interest for Lorentz force velocimetry (LFV), where the Lorentz force opposing the relative motion of conducting medium and magnetic field is measured to determine the flow velocity. The Lorentz force acts in equal strength but opposite direction on the flow as well as on the dipole. We are interested in the dependence of the velocity on the flow rate and on strength of the magnetic field as well as on geometric parameters such as distance and position of the dipole relative to the duct. To this end, we perform numerical simulations with an accurate finite-difference method in the limit of small magnetic Reynolds number, whereby the induced magnetic field is assumed to be small compared with the external applied field. The hydrodynamic Reynolds number is also assumed to be small so that the flow remains laminar. The simulations allow us to quantify the magnetic obstacle effect as a potential complication for local flow measurement with LFV. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The transmission of a flexural-gravitational wave through a rigid end-stop in a floating plate

An elastic plate is located on the surface of a liquid, in continuous contact with it and rigidly clamped in a support along a certain straight line. The orthogonal incidence of a small amplitude flexural-gravitational wave on the support is considered. Exact expressions are obtained for the wave field in the fluid and the flexural field in the plate. The transmission coefficient of the incident flexural-gravitational wave through the support and its reflection coefficient from it are determined. The forces which arise in the support are found. The investigation is carried out for liquids of finite and infinite depth. The effect of the depth of the liquid on the wave processes is indicated. The liquid is assumed to be inviscid and its friction on the bottom and the lower surface of the plate in the neighbourhood of the support is therefore ignored.     

Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler–Bernoulli beam theory

In the present work, the effect of longitudinal magnetic field on wave dispersion characteristics of equivalent continuum structure (ECS) of single-walled carbon nanotubes (SWCNT) embedded in elastic medium is studied. The ECS is modelled as an Euler–Bernoulli beam. The chemical bonds between a SWCNT and the elastic medium are assumed to be formed. The elastic matrix is described by Pasternak foundation model, which accounts for both normal pressure and the transverse shear deformation. The governing equations of motion for the ECS of SWCNT under a longitudinal magnetic field are derived by considering the Lorentz magnetic force obtained from Maxwell’s relations within the frame work of nonlocal elasticity theory. The wave propagation analysis is performed using spectral analysis. The results obtained show that the velocity of flexural waves in SWCNTs increases with the increase of longitudinal magnetic field exerted on it in the frequency range; 0–20 THz. The present analysis also shows that the flexural wave dispersion in the ECS of SWCNT obtained by local and nonlocal elasticity theories differ. It is found that the nonlocality reduces the wave velocity irrespective of the presence of the magnetic field and does not influences it in the higher frequency region. Further it is found that the presence of elastic matrix introduces the frequency band gap in flexural wave mode. The band gap in the flexural wave is found to independent of strength of the longitudinal magnetic field.     

Collision of a solar wind shock wave with the Earth’s bow shock. Wave flow pattern

The wave pattern of the flow developed when a solar wind shock wave propagates along the surface of the Earth’s bow shock is studied. The investigation is carried out in the three-dimensional non-plane-polarized formulation within the framework of the ideal magnetohydrodynamic model in which the medium is assumed to be inviscid and non-heat-conducting and to have the infinite conductivity. The global three-dimensional pattern of the interaction which is a function of the latitude and longitude of elements on the surface of the bow shock is constructed as a mosaic of solutions to the problem of breakdown of a discontinuity developed between the states behind the impinging and bow shocks on the moving curve of intersection of their fronts. The investigation is carried out for typical solar wind parameters and interplanetary magnetic field strength in the Earth’s orbit and for several Mach numbers of the interplanetary shock wave, which makes it possible to trace the evolution of the flow developed as a function of the intensity of the shock perturbation of the solar wind. The solution obtained is necessary for interpreting measurements carried out by spacecraft located in the neighborhood of the Lagrange point and the Earth’s magnetosphere.     

Cost analysis of the M/M/R machine repair problem with balking,reneging, and server breakdowns

We consider the machine repair problem in which failed machines balk (do not enter) with a constant probability (1 – b) and renege (leave the queue after entering) according to a negative exponential distribution. A group of identical automatic machines are maintained by R servers which themselves are subject to breakdowns. Failure and service times of the machines, and breakdown and repair times of the servers, are assumed to follow a negative exponential distribution. Each server is subject to breakdown even if no failed machines are in the system. This paper presents a matrix geometric method for deriving the steady-state probabilities, using which various system performance measures that can be obtained. A cost model is developed to determine the optimum number of servers. The minimum expected cost, the optimal number of servers, and various system performance measures are provided based on assumed numerical values given to the system parameters. Also the sensitivity analysis is investigated.     

Steady and Unsteady Jet Wiping Processes

The jet wiping process is widely used in continuous coating applications to remove the excess amount of liquid entrained by a sheet moving out of a liquid bath. Typical fields of applications are hot dip galvanization of metal strips and coating of photographic films. The process is based on the impact of a gas jet onto the liquid film carried by the solid substrate. In the present study the process is investigated for the case of strictly two‐dimensional flow. It is assumed that inertia effects on the film flow can be neglected, whereas the effects of the pressure gradient and the shear stress distribution of the impinging jet and the surface tension of the liquid film are taken into account. As a result it is possible to derive a single kinematic wave equation which governs the distribution of the film thickness. Numerical results for representative steady and unsteady processes including the formation of shock discontinuities are presented.     

The stability of nematic liquid crystals under crossed electric and magnetic fields

The alignment of the director in nematic liquid crystals is known to be influenced by electric and/or magnetic fields. The stability of known traveling wave solutions is examined for a best fit cubic equation which approximates the nonlinear sinusoidal terms in the dynamic equation for the director when it is subjected to crossed electric and magnetic fields.     

Converging strong shock waves in magnetogasdynamics under isothermal condition

The similarity solutions to the problem of cylindrically symmetric strong shock waves in an ideal gas with a constant azimuthal magnetic field are presented. The flow behind the shock wave is assumed to spatially isothermal rather than adiabatic. We use the method of Lie group invariance to determine the possible class of self-similar solutions. Infinitesimal generators of Lie group transformations are determined by using the invariance surface conditions to the system and on the basis of arbitrary constants occurring in the expressions for the generators, four different possible cases of the solutions are reckoned and we observed that only two out of all possibilities hold self-similar solutions, one of which follows the power law and another follows the exponential law. To obtain the similarity exponents numerical calculations have been performed and comparison is made with the existing results in the literature. The flow patterns behind the shock are analyzed graphically.

     

Diffraction of the Electromagnetic Wave on a Small Obstacle of Elliptic Form in a Layer

The problem on the diffraction of the electromagnetic plane wave on a small obstacle included in a layer is investigated. The obstacle is assumed to be an elliptic cylinder whose diameter and focal distance are small in comparison with the length of the incident wave. It is proved that the small obstacle radiates as a point source, and its amplitude is proportional to the area of the cross-section and the jumps of the dielectric and magnetic constants on the interfaces. Bibliography: 5 titles.     

Measuring magnetic liquid crests by radioscopy

We present a quantitative method, capable of measuring the three‐dimensional shape of a fluid surface. Utilizing the attenuation of x‐rays in magnetic liquids we are able to map amplitude and relief of large wave crests, a regime which is not accessible by the common optical methods. The technique is applied for measuring the static surface deformations of the Rosensweig instability. It will also be useful for measuring the surface profile of the Faraday instability in magnetic liquids, in standard fluids, in liquid metals, or even in granular material.     

Nonlinear temporal dynamics in magnetic fluids between undulatory parallel walls

The effects of undulatory parallel walls and a normal magnetic field on the stability of weakly nonlinear waves at a horizontal interface of two magnetic inviscid fluids are investigated. We assumed that the walls have a weak sinusoidal undulation. The frequency of the main waves is similar to a problem having smooth boundaries. The breaker surface tension and the breaker magnetic field are obtained. The stability analysis concerns the interaction of two propagation wave numbers satisfying the resonance condition imposed by the periodicity of the sinusoidal walls. The first-resonance case occurs whenever the wall wave number is nearly equal to twice the propagation wave number while the second-resonance case occurs whenever the two kinds of wave numbers are nearly equal. When the wave number of the undulation is far from the propagation wave number, the sinusoidal walls have the same effect of the smooth walls on the stability criterion. The stability conditions and the transition curves in the two resonance cases are treated away from the critical state. The existence conditions and stability of Stokes waves near the critical state are discussed. Numerous illustrations and graphs amplify the work.     

Scattering theory for the Schrödinger equation in some external time-dependent magnetic fields

We study the theory of scattering for a Schrödinger equation in an external time-dependent magnetic field in the Coulomb gauge, in space dimension 3. The magnetic vector potential is assumed to satisfy decay properties in time that are typical of solutions of the free wave equation, and even in some cases to be actually a solution of that equation. That problem appears as an intermediate step in the theory of scattering for the Maxwell-Schrödinger (MS) system. We prove in particular the existence of wave operators and their asymptotic completeness in spaces of relatively low regularity. We also prove their existence or at least asymptotic results going in that direction in spaces of higher regularity. The latter results are relevant for the MS system. As a preliminary step, we study the Cauchy problem for the original equation by energy methods, using as far as possible time derivatives instead of space derivatives.     

Scattering of Plane Electromagnetic Waves on a Small Inhomogeneity in a Slightly Curved Layer

The diffraction problem for the electromagnetic plane wave scattered on a small inhomogeneity in a slightly curved layer is investigated. The inhomogeneity is assumed to be a cylinder. The area of the cross-section and the the diameter of the cylinder are small in comparison with the length of the incident wave. It is proved that the small inhomogeneity radiates as a point source the power of which is proportional to the area of the cross-section and to the jumps of the dielectric and magnetic constants on the interfaces. The bend of the layer manifests itself in the exponential factors of reflected and refracted waves and in the radiation pattern of scattered waves. Bibliography: 10 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 297, 2003, pp. 93–115.     

Optimal Design of Periodic Diffractive Structures

The problem of designing a periodic interface between two different materials, which gives rise to a specified far-field diffraction pattern for a given incoming plane wave, is considered. The time harmonic waves are assumed to be TM (transverse magnetic) polarized. The diffraction problem is modeled by a generalized Helmholtz equation with transparent boundary conditions. In this paper the design problem is relaxed to include highly oscillatory profiles. Existence of an optimal design is established. The principal method is based on the theory of homogenization for the model equation. Accepted 31 May 2000. Online publication 26 February 2001.     

Diffraction of Plane Electromagnetic Waves on a Small Obstacle Inside a Layer

The problem on the diffraction of the electromagnetic plane wave on a small obstacle in a layer is investigated. The obstacle is assumed to be a circular cylinder and its radius is small in comparison with the length of the incident wave. It is proved that the small obstacle radiates as a linear source. Its intensity is proportional to the area of a cross-section and the jumps of the dielectric and magnetic constants on the interfaces. Bibliography: 4 titles.     

A mechanical model of swimming using two-link extremities

The motion of a multilink mechanical system in a liquid, which models the swimming of some animals (the frog) using a pair of extremities, is investigated. It is assumed that the liquid acts on the moving bodies through forces that are proportional to the squares of their velocities. Periodic motions of the system are constructed. The mean velocity of motion of the system is estimated and its dependence on parameters of the motion is shown.     

Wave parameter identification problem for ocean test structure data,part 1, continuous formulation

This paper deals with the solution of the wave parameter identification problem for ocean test structure data. A continuous formulation is assumed. An ocean test structure is considered, and wave elevation and velocities are assumed to be measured with a number of sensors. Within the frame of linear wave theory, a Fourier series model is chosen for the wave elevation and velocities. Then, the following problem is posed: Find the amplitudes of the various wave components of specified frequency and direction, so that the assumed model of wave elevation and velocities provides the best fit to the measured data. Here, the term best fit is employed in the least-square sense over a given time interval.At each time instant, the wave representation involves three indexes (frequency, direction, instrument); hence, three-dimensional arrays are required. This formal difficulty can be avoided by switching to an alternative representation involving only two indexes (frequency-direction, instrument); hence, standard vector-matrix notation can be used. Within this frame, optimality conditions are derived for the amplitudes of the assumed wave model.Numerical results are presented. The effect of various system parameters (number of frequencies, number of directions, sampling time, number of sensors, and location of sensors) is investigated in connection with global or strong accuracy, local or weak accuracy, integral accuracy, and condition number of the system matrix.From the numerical experiments, it appears that the identification problem has a unique solution if the number of directions is smaller than or equal to the number of sensors; it has an infinite number of solutions otherwise. In the case where a unique solution exists, the condition number of the system matrix increases as the size of the system increases, and this has a detrimental effect on the accuracy. However, the accuracy can be improved by proper selection of the sampling time and by proper choice of the number and location of the sensors.This work was supported by Exxon Production Research Company, Houston, Texas. This paper is based partly on Ref. 1–4.