Free convective flow through porous medium with variable permeability in slip flow regime with couple stress in the presence of heat source

The unsteady free convective MHDflow of a polar fluid through a porous medium with variable permeability in the presence of heat source bounded by an infinite horizontal porous plate in slip flow regime is analyzed. The transformed nondimensional equations are solved by a perturbation method. The obtained results are presented graphically to illustrate the influence of different physical parameters on the velocity profile, angular velocity profile, temperature profile, and concentration profile. Further the effect of variable permeability parameter on the velocity profile is investigated. Some special cases with their physical significance are discussed and compared with the existing published work.     

Energy Characteristics of Wave Fields Radiated from Elementary Oscillators in a Nondispersive Medium Moving with Subluminal Velocity

We study the energy characteristics of fields radiated from electric, magnetic, and toroidal dipoles in a nondispersive medium moving with velocity lower than the speed of light in this medium. The angular dependences of Abraham's energy-flux density of electromagnetic field are analyzed. In particular, it is shown that if the medium velocity is high enough, then the radial component of the vector of energy-flux density is negative in a certain angular range. Expressions for the electromagnetic energy flux through a sphere of large radius are obtained. It is shown that if the velocity of a moving medium is high enough, then the energy flux is negative and its absolute value can exceed the energy losses of sources.     

A multidimensional pendulum in a nonconservative force field under the presence of linear damping

A nonconservative force field in the dynamics of a multidimensional solid is constructed according to the results from the dynamics of real solids occurring in the force field of the action of the medium. In this case, it becomes possible to generalize the equations of motion of a multidimensional solid in a similarly constructed field of forces and to obtain a complete list of, generally speaking, transcendental first integrals expressed through a finite combination of elementary functions. In the study, the integrability in elementary functions is shown for the simultaneous equations of motion of a dynamically symmetric fixed multidimensional solid under the action of a nonconservative pair of forces in the presence of the linear damping moment (the additional dependence of the force field on the tensor of angular velocity of the solid).     

Experimental verification of the technique for calculating light scattering in turbid media and determination of the single-scattering albedo based on the spectroscopy of elastically reflected electrons

The equations of light transfer in a turbid medium and transfer equations for electrons undergoing only elastic collisions in a solid body are shown to be equivalent. The angular distributions of elastically reflected electrons were calculated using the DISORT and MDOM optical codes. The calculation data are compared with the results of experimental measurements for the angular distributions of elastically reflected electrons and with calculations according to the Monte-Carlo method. Optical codes are shown to be highly efficient in calculating the angular distributions of electrons elastically reflected from multilayer media.     

Nearly smooth granular gases

Hydrodynamic equations for nearly smooth granular gases are derived from the pertinent Boltzmann equation. The angular velocity distribution field needs to be included in the set of hydrodynamic fields. The angular velocity distribution is strongly non-Maxwellian for the homogeneous cooling state and any homogeneous steady state. In the case of steady wall-bounded shear flows the average spin (created at the boundaries) has a finite penetration length into the bulk.     

Robertson-Walker Fluid Sources Endowed with Rotation Characterised by Quadratic Terms in Angular Velocity Parameter

Einstein's equations for a Robertson-Walker fluid source endowed with rotation are presented up to and including quadratic terms in angular velocity parameter. A family of analytic solutions are obtained for the case in which the source angular velocity is purely time-dependent. A subclass of solutions is presented which merge smoothly to homogeneous rotating and non-rotating central sources. The particular solution for dust endowed with rotation is presented. In all cases explicit expressions, depending sinusoidally on polar angle, are given for the density and internal supporting pressure of the rotating source. In addition to the non-zero axial velocity of the fluid particles it is shown that there is also a radial component of velocity which vanishes only at the poles. The velocity four-vector has a zero component between poles.     

Single cell analysis using a glass microchamber for studying movement fluctuations of Navicula pavillardii and Seminavis robusta diatom cells

We propose a new technique for quantitative trajectory analysis of gliding phenomenon of Navicula pavillardii (NP) and Seminavis robusta (SR) diatom cells by single cell observation using a glass microchamber in this short technical note. Two-dimensional trajectory analysis of cell movements was used to determine the angular velocity, velocity, and migration distances of the diatom movement. Based on the trajectory analysis, we found that asymmetrically shaped SR had a larger angular velocity with large fluctuations compared to symmetrically shaped NP, although the velocity of SR was less than that of NP. It suggests that lateral frictional force in a culture medium is an important factor for diatom movements. Our results revealed that the single cell observation using a glass microchamber is effective on quantitative analysis of angular velocity of diatom gliding.     

Collisional granular flow as a micropolar fluid

We show that a micropolar fluid model successfully describes collisional granular flows on a slope. A micropolar fluid is the fluid with internal structures in which coupling between the spin of each particle and the macroscopic velocity field is taken into account. It is a hydrodynamical framework suitable for granular systems which consists of particles with macroscopic size. We demonstrate that the model equations can quantitatively reproduce the velocity and the angular velocity profiles obtained from the numerical simulation of the collisional granular flow on a slope using a simple estimate for the parameters in the theory.     

Fragment angular momenta in low and medium energy fission of242Pu

Independent isomeric yield ratios of¹²⁸Sb were determined radiochemically in the thermal neutron induced fission of²⁴¹Pu and 34 MeV alpha particle induced fission of²³⁸U, both involving the same compound nucleus (²⁴²Pu). Fragment angular momenta estimated from the measured isomer ratios using the statistical model analysis showed significantly larger fragment angular momenta in the medium energy fissioning system compared to the low energy fissioning system. This has been attributed to the effect of higher excitation energy and angular momentum in the entrance channel leading to increased fragment temperature, moments of inertia and angular velocity. An attempt was made to calculate the fragment angular momentum in the medium energy fission using the Fermi gas model for the fissioning nucleus, taking into account the multichance fission, saddle shapes of the fissioning nuclei and the angular velocity components of the fissioning nuclei both along and orthogonal to the fission axis. The calculated angular momenta agree well with the experimental results.     

Interference effects in backscattering of light by a layer of a discrete random medium

Multiple backscattering of light by a layer of a discrete random medium is considered. A brief derivation of equations for describing the coherent and incoherent components of scattered light is presented. These equations are solved numerically in the approximation of doubled scattering of light by a semi-infinite medium of spherical scatterers having a size comparable with the wavelength in order to study the effect of the properties of particles on the angular dependence of interference effects. Calculations show that the half-width of the interference peak decreases upon an increase in lateral scattering by particles and that the degree of polarization has a complex angular dependence on the properties of the particles. For an optically thin layer of the medium, the relations defining the interference peak half-width and the scattering angle upon extreme linear polarization as functions of the effective refractive index are given.     

Angular structure of laser radiation in a Markov binary mixture

Laser-radiation transfer in a Markov binary mixture is compared to transfer in an equivalent homogeneous medium. Within the framework of a small-angle approximation a system of equations that describe the angular moments of the second order (angular dispersion) for a laser beam and the equation for laser-beam intensity is obtained. The results of the calculations show a significant effect of the stochastic nature of the medium on the intensity and the angular structure of the laser beam. Deceased Institute of Applied Optics, National Academy of Sciences of Belarus, 11, Belynitskii-Birulya St., Mogilev, 272793. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 1, pp. 36–42, January–February, 1999.     

Perturbation technique for unsteady MHD mixed convection periodic flow, heat and mass transfer in micropolar fluid with chemical reaction in the presence of thermal radiation

An analytical study is presented for the problem of unsteady hydromagnetic heat and mass transfer for a micropolar fluid bounded by semi-infinite vertical permeable plate in the presence of first-order chemical reaction, thermal radiation and heat absorption. A uniform magnetic field acts perpendicularly to the porous surface which absorbs the micropolar fluid with a time-dependent suction velocity. The basic partial differential equations are reduced to a system of nonlinear ordinary differential equations which are solved analytically using perturbation technique. Numerical calculations for the analytical expressions are carried out and the results are shown graphically. The effects of the various dimensionless parameters related to the problem on the velocity, angular velocity, temperature and concentration fields are discussed in detail.     

Acousto-optic interaction in crystals with large acoustic anisotropy

The Bragg diffraction of light from a sinusoidal phase grating induced in an anisotropic medium by an acoustic wave has been studied theoretically for the case of a large acoustic energy walk-off. Based on the modified coupled-wave equations, the frequency and angular characteristics of an anisotropic diffraction in a paratellurite crystal have been calculated. It is shown that the acoustic beam walk-off significantly changes the angular and frequency ranges of acousto-optic interactions.     

Sagnac effect in ring interferometers on “slow” waves

We consider the Sagnac effect in ring interferometers on magnetostatic and surface acoustic waves. It is shown that the Sagnac effect for waves of arbitrary type (including both magnetostatic and surface acoustic waves) propagating in an arbitrary medium cannot be calculated using Galilean transformations but is explained within the framework of the special relativity and is related to the difference between the phase velocities rather than group velocities of counter-propagating waves in the rotating reference frame. We also show that the phase difference of counterpropagating waves due to the Sagnac effect depends on neither the phase velocity of the wave in a medium at rest nor the dispersion of the medium; it depends only on the wave frequency and the angular velocity of interferometer rotation. The minimum angular velocity that can be measured in the ring interferometers using magnetostatic and surface acoustic waves is estimated. N. I. Labachevsky State University, Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 4, pp. 373–382, April 1999.     

Mechanics of a particle near the center of a rotating ring

The equations of motion of a test particle moving near the center of a massive rotating ring are derived up to the post-post-Newtonian order of approximation, by using the metric tensor for many body system which is Minkowskian at spatial infinity. Logarithmic divergences due to self-interaction of the ring appear in the equations of motion. These divergences can be removed by the procedure which is similar to the renormalization method in particle physics. In the equations of motion there appears a force directing to the rotation axis and depending on the angular velocity of the ring. This force vanishes when the magnitude of the gravitational constant times the mass of the ring divided by the radius of the ring is about one tenth of the square of the velocity of light. Under this condition it is shown that the relative magnitude of the Coriolis force to the centrifugal force in the equations of motion agrees with the expected one from the equations of motion in a rotating reference frame.     

Theory of rotational Brownian motion

The correlation function for the angular velocity of a Brownian particle suspended in a liquid is analyzed with an account of the viscous aftereffect. The main term in the asymptotic exression for this function is equal to the eddy correlation function for the translational velocity of a liquid found from the Navier-Stokes equations.Translated from Izvestiya VUZ. Fizika, No. 10, pp. 13–17, October, 1969.In conclusion the author thanks Professor I. Z. Fisher for guidance and for constant interest in his study.     

Equations for finite-difference, time-domain simulation of sound propagation in moving inhomogeneous media and numerical implementation

Finite-difference, time-domain (FDTD) calculations are typically performed with partial differential equations that are first order in time. Equation sets appropriate for FDTD calculations in a moving inhomogeneous medium (with an emphasis on the atmosphere) are derived and discussed in this paper. Two candidate equation sets, both derived from linearized equations of fluid dynamics, are proposed. The first, which contains three coupled equations for the sound pressure, vector acoustic velocity, and acoustic density, is obtained without any approximations. The second, which contains two coupled equations for the sound pressure and vector acoustic velocity, is derived by ignoring terms proportional to the divergence of the medium velocity and the gradient of the ambient pressure. It is shown that the second set has the same or a wider range of applicability than equations for the sound pressure that have been previously used for analytical and numerical studies of sound propagation in a moving atmosphere. Practical FDTD implementation of the second set of equations is discussed. Results show good agreement with theoretical predictions of the sound pressure due to a point monochromatic source in a uniform, high Mach number flow and with Fast Field Program calculations of sound propagation in a stratified moving atmosphere.     

Induced rotation in the Papapetrou equations

We obtain an integral form of the Papapetrou equations, which describes the motion of an extended body in an external gravitational field. Using the Fock method, we calculate an explicit form for the components of the spin tensor and derive relativistic equations of rotational motion in the Schwarzschild space V₄. We show that the spin of the body becomes proportional not only to the angular velocity but also to the angular momentum. Thus, induced rotation also follows from the Papapetrou equations.Astrophysics Institute, Kazan Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 117–124, October, 1992.     

Propagation of light inside shear flows: a remote sensing method to retrieve velocity fields

Inside a moving dielectric medium a wave perceives the matter as an effective gravitational field. The medium and its velocity field alter the way in which an electromagnetism field propagates. We propose an optical method for remote sensing of the velocity fields inside shear flows by angular scanning.     

Features of Radiation Fields of Some Sources in a Subluminal Flow of a Nondispersive Medium

We study radiation fields of various dipole sources as well as of a source of bisphere type moving in a nondispersive medium with velocity less than the speed of light in this medium. In particular, it is shown that in certain cases, there is a displacement of the angular pattern of a source in the direction opposite to the medium flow. Expressions for energy losses of the considered sources are obtained. It is pointed out that the radiation power of both a bisphere and a toroidal dipole increases with increasing velocity of motion of the medium more rapidly compared with the ordinary dipoles.