Stressed State of a Magnetically Soft Ferromagnetic Material with a Parabolic Crack Acted on by a Uniform Magnetic Field

The stressed-deformed state of an unbounded isotropic body consisting of a magnetically soft ferromagnetic material and containing a parabolic crack is examined. It is assumed that the body is acted on by an external magnetic field perpendicular to the plane of the crack. The major characteristics of the stressed-deformed state and the induced magnetic field are determined and their features near the parabolic crack are studied. Formulas are given for determining the stress intensity factors for the mechanical force and magnetic fields at the crack vertex.     

The deformation of a liquid drop by an electric field

Summary The shape and stability of an incompressible dielectric drop which is stressed by a uniform external electric field are re-examined by considering small perturbations from a prolate spheroid. Compared with the shapes predicted by other approximations it is found that, for a given field strength, the drops should be a little longer and consequently a little flatter at the equator in order to satisfy the equilibrium conditions. It is also shown that beyond a certain drop deformation the L. P. E. (Legendre polynomial expansion) method fails because the equilibrium conditions at the surface of the drop are not satisfied.     

Flow of a Maxwell fluid between two side walls induced by a constantly accelerating plate

The unsteady flow of a Maxwell fluid induced by a constantly accelerating plate between two side walls perpendicular to the plate is studied. Exact solutions for the velocity field are established by means of the Fourier sine transforms. The adequate tangential stresses are also determined. The similar solutions for a Newtonian fluid are obtained as limiting cases of our solutions. In the absence of the side walls, the similar solutions for the unsteady flow over an infinite flat plate are recovered. Finally, for comparison, the velocity field in the middle of the channel and the shear stresses at the bottom wall and on the side walls are plotted for different values of the material constants.      

MHD boundary-layer flow of a micropolar fluid past a wedge with constant wall heat flux

The steady laminar magnetohydrodynamic (MHD) boundary-layer flow past a wedge with constant surface heat flux immersed in an incompressible micropolar fluid in the presence of a variable magnetic field is investigated in this paper. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables, and then they are solved numerically by means of an implicit finite-difference scheme known as the Keller-box method. Numerical results show that micropolar fluids display drag reduction and consequently reduce the heat transfer rate at the surface, compared to the Newtonian fluids. The opposite trends are observed for the effects of the magnetic field on the fluid flow and heat transfer characteristics.     

On magnetoelastic problems of a plane with an arbitrarily shaped hole under stress and displacement boundary conditions

An analytical method for the static plane problem of magnetoelasticityis developed for an infinite plane containing a hole of arbitraryshape under stress and displacement boundary conditions in aprimary uniform magnetic field. The magnetic field influencesthe elastic field by introducing a body force called the Lorentzponderomotive force in the equilibrium equations. The body forcecan be further described in a form relating with the electromagneticstress tensor. The complex variable method in conjunction withthe rational mapping function technique is used in the analysisfor both magnetic field and mechanical field. Governing equationsand boundary conditions are expressed in terms of complex functions.Complex magnetic potential and stress functions are obtainedusing Cauchy integrals for the paramagnetic and soft ferromagneticmaterials, respectively. The distributions of magnetic fieldand the stress components are shown for certain directions ofprimary magnetic fields in an infinite plane with a square hole,as an example. It is found that the stress distributions forthe two types of materials are identical despite the differenceof magnetic fields. The extreme cases of a free and a fixedhole reduced to a crack and a rigid fibre, respectively, arealso investigated. The stress intensity factors at the tipsof crack and rigid fibre are computed, and their variation forcertain directions of primary magnetic field is shown.     

Diffraction of a sinusoidal impulse by a rigid strip

The diffraction of a sinusoidal impulse by an absolutely rigid strip is considered. Approximate formulas are obtained for the field measured at large distances from the strip in the direction of the incident impulse (the case of location). The results are expressed in terms of Fresnel integrals. The possibility of determining the width of the strip and the angle between it and the direction of the incident impulse or the basis of the envelope of the location field is discussed. Graphs of the envelopes for certain specific cases are presented.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 62, pp. 39–47, 1976.The author is grateful to D. P. Kouzov for his attention to the work.     

Radiation of short waves by a pair of plates backed by a semi-infinite set of ribbed stiffeners

The following acoustic diffraction problem is considered. The upper half-space is filled by an acoustic medium. Two semi-infinite thin plates are situated on the boundary of the upper half-space. One of the plates is backed by a semi-infinite periodical set of ribbed stiffeners. The source of an acoustic field is positioned on the other plate. The problem is reduced to an infinite system of linear algebraic equations. Such a system can be solved in a shortwave approximation. An expression for the acoustic field at a large distance from the junction of the plates is obtained. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210, 1994, pp. 38–46. Translated by A. V. Badanin.     

Biomagnetic viscoelastic fluid flow over a stretching sheet

Of concern in this paper is an investigation of biomagnetic flow of a non-Newtonian viscoelastic fluid over a stretching sheet under the influence of an applied magnetic field generated owing to the presence of a magnetic dipole. The viscoelasticity of the fluid is characterised by Walter’s B fluid model. The applied magnetic field has been considered to be sufficiently strong to saturate the ferrofluid. The magnetization of the fluid is considered to vary linearly with temperature as well as the magnetic field intensity. The theoretical treatment of the physical problem consists of reducing it to solving a system of non-linear coupled differential equations that involve six parameters, which are solved by developing a finite difference technique. The velocity profile, the skin-friction, the wall pressure and the rate of heat transfer at the sheet are computed for a specific situation. The study shows that the fluid velocity increases as the rate of heat transfer decreases, while the local skin-friction and the wall pressure increase as the magnetic field strength is increased. It is also revealed that fluid viscoelasticity has an enhancing effect on the local skin-friction. The study will have an important bearing on magnetic drug targeting and separation of red cells as well as on the control of blood flow during surgery.     

Aerodynamic Sound Due to a Source Near a Half-Plane

The effect of applying a Kutta-Joukowski condition at the edgeof a semi-infinite plane which is generating noise in a turbulentfluid at low Mach numbers is examined. It is found that in somecircumstances the noise is increased and the intensity of thedistant sound field may depend upon the third power of a typicalfluid velocity. When the sound field is convected the orders of magnitude ofthe acoustic far field are the same whether or not the Kutta-Joukowskicondition is applied, provided that the point of observationis not near the wake. Near the wake there is an acoustic "surface"wave which is much stronger than the distant field elsewhere.     

Memorable Experiences of a Science Field Trip

Potential immediate outcomes of a science field trip are the retention of knowledge associated with the program and an improved attitude toward the site visited during the trip. The length of associated memories regarding this experience are less clear. In an attempt to begin learning more about memorable experiences associated with a science field trip, a 1‐month and an 18‐month evaluation was conducted of elementary school students who had participated in an environmental science program at a community park in a midwestern city. Results of the evaluation found that students' memories were nonspecific and disassociated from information given by the field teacher. On the other hand, results from both tests yielded positive responses toward wanting to learn more about the subject matter and an interest in returning to the field trip site. This would indicate that, while not retaining specific objective‐oriented content, students did gain a positive reaction to returning that continued over the long‐term. Research related to memorable experiences is outlined, using a theory of long‐term memory developed by Tulving (1972) as a basic paradigm of correlation for the subsequent investigation.     

Problem of magnetoelasticity for a solid with the spherical cavity

The solution of a static problem of magnetoelastisity for a soft ferromagnetic elastic solid with the spherical cavity is obtained on the base of the linear theory of Brown, Pao and Yeh. It is assumed that the solid has a multi-domain structure, so the hysteresis loss and remanent magnetization are neglected. The solid is affected by a magnetic field which is uniform at infinity and determined by the magnetic induction vector. The cavity causes some distortion of the field distribution near the interface. So the field induces magnetic moments and produces stresses and deformations in the body. The problem is solved for an unperturbed strain state. An approach is discussed to find the perturbed values on the base of the solution obtained. The Fourier variable separation method is used. The stresses are presented via harmonic functions. As a result magnetoelastic stresses are obtained in the closed form. Their distribution in the body is studied and some results of numerical calculations are shown. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Love-type waves in a finitely deformed magnetoelastic layered half-space

In this paper, the propagation of Love-type waves in a homogeneously and finitely deformed layered half-space of an incompressible non-conducting magnetoelastic material in the presence of an initial uniform magnetic field is analyzed. The equations and boundary conditions governing linearized incremental motions superimposed on an underlying deformation and magnetic field for a magnetoelastic material are summarized and then specialized to a form appropriate for the study of Love-type waves in a layered half-space. The wave propagation problem is then analyzed for different directions of the initial magnetic field for two different magnetoelastic energy functions, which are generalizations of the standard neo-Hookean and Mooney?CRivlin elasticity models. The resulting wave speed characteristics in general depend significantly on the initial magnetic field as well as on the initial finite deformation, and the results are illustrated graphically for different combinations of these parameters. In the absence of a layer, shear horizontal surface waves do not exist in a purely elastic material, but the presence of a magnetic field normal to the sagittal plane makes such waves possible, these being analogous to Bleustein?CGulyaev waves in piezoelectric materials. Such waves are discussed briefly at the end of the paper.     

Transfer of a Passive Vector Admixture by a Two-Dimensional Turbulent Flow

We consider a model of a passive vector field transfer by a random two-dimensional transverse velocity field that is uncorrelated in time and has Gaussian spatial statistics given by a powerlike correlator. We use the renormalization group and the operator product expansion techniques to show that the asymptotic approximation of the structure functions of a vector field in the inertial range is determined by the energy dissipation fluctuations. The dependence of the asymptotic approximation on the external scale of turbulence is essential and has a powerlike form (the case of an anomalous scaling). The corresponding exponents are calculated in the one-loop approximation for structure functions of an arbitrary order.     

Radiation from a Point Charge Moving through a Circular Aperture in a Screen

This paper deals with the problem of diffraction radiation froman electric point charge that moves, at a constant speed, througha circular aperture in a plane screen. The screen is assumedto be electrically perfectly conducting. The problem is reducedto the solution of an integral equation for an unknown fieldfunction in the aperture. Low-frequency solutions as well ashigh-frequency solutions are obtained. Results pertaining tothe far-field behaviour of the radiated field are given. Finally,numerical results pertaining to the radiation loss of the chargeare presented.     

Stress analysis in a sheet with multiple cracks

The stress field due to the presence of a Volterra dislocation in an isotropic elastic sheet is obtained. The stress components exhibit the familiar Cauchy type singularity at dislocation location. The solution is utilized to construct integral equations for elastic sheets weakened by multiple embedded or edge cracks. The cracks are perpendicular to the sheet boundary and applied traction is such that crack closing may not occur. The integral equations are solved numerically and stress intensity factors (SIFs) are determined on a crack edges.     

Spherical shock wave generated by a moving piston in mixture of a non-ideal gas and small solid particles under a gravitational field

Self-similar solutions are obtained for one-dimensional isothermal and adiabatic unsteady flows behind a strong spherical shock wave propagating in a dusty gas. The shock is assumed to be driven out by a moving piston and the dusty gas to be a mixture of a non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-conditions are maintained and variable energy input is continuously supplied by the piston. The medium is under the influence of the gravitational field due to a heavy nucleus at the origin (Roche model). The effects of an increase in the mass concentration of solid particles, the ratio of the density of the solid particles to the initial density of the gas, the gravitational parameter and the parameter of non-idealness of the gas in the mixture, are investigated. It is shown that due to presence of gravitational field the compressibility of the medium at any point in the flow-field behind the shock decreases and all other flow-variables and the shock strength increase. A comparison has also been made between the isothermal and adiabatic flows. It is investigated that the singularity in the density and compressibility distributions near the piston in the case of adiabatic flow are removed when the flow is isothermal.     

On the flow of an electrically conducting,incompressible fluid near an accelerated plate in the presence of a parallel plate,under transverse magnetic field

This paper deals with hydromagnetic flow of an electrically conducting, incompressible viscous fluid near an accelerated flat, non-conducting plate, in the presence of another parallel plate, when there is a transversely applied magnetic field. Induced magnetic field is neglected in comparison with the applied magnetic field. Laplace transform techniques are used. The equations are integrated by applying residue principle, and expressions for velocity profiles and skin-friction at both plates are derived for different values of Hartmann number M. It is observed that, with the increase of the value of the Hartmann number M, the velocity profiles are flattened, the shear stress at the stationary plate decreases, as the value of the time T and Hartmann number M increases, but the shear stress at the accelerated plate increases directly in proportion with the increase in time and Hartmann number.     

Super-computer simulation of a multichambered muffler

The problem of attenuating muzzle blast noise produced by firing a gun weapon is studied. A multichambered muffler is attached to a M242 25mm cannon. For this weapons configuration, the transitional ballistics problem is solved numerically using the CRAY XMP computer. The second-order accurate total variation diminishing (TVD) shock capturing scheme of Harten is used to solve the Euler equations of compressible flow. The simulation yields a detailed picture of the flow field, as displayed by pressure and Mach contours. Pressure time histories at selected field locations are recorded for future comparison with experiment. Energy efflux time history, from which predictions of noise attenuation can be made, is also recorded. Noise reduction levels so obtained are seen to compare well with experimental data. From this evidence it appears that the simulation method can become an effective aid in muffler design.     

Magnetic field in a turbulent conducting fluid

The problem of magnetic field in conducting turbulent, incompressible fluid is considered. The velocity of the fluid is taken to be independent of the magnetic field and is described by a Gaussian field, ‘white noise’ in time with smooth space correlation. The main result is that no fast dynamo (by which is meant almost sure exponential growth of magnetic field) can exist for an incompressible fluid when the magnetic viscosity is positive. For d = 2, sharper results are obtained; the magnetic field dies out when the magnetic viscosity is strictly positive. Furthermore, when d = 2, existence and characterization of invariant measure are given for d = 2 when the magnetic viscosity is zero. The results are compared to those discussed by Baxendale and Rosovskii in [2]     

Steady Magnetogasdynamic Flow Past a Source

This paper presents an asymptotic solution for the disturbanceat large distance from a source placed in a flow of conductingcompressible fluid in the presence of an applied magnetic field.The solution is obtained by a Fourier transform method usingtechniques developed for magnetohydrodynamic waves by Lighthill(1960). The results are discussed in detail for the cases ofthe undisturbed flow aligned with and perpendicular to the field,although they apply for any angle between the two, and showa Mach cone type of disturbance together with Alfvénwaves.