Effects of mass transfer on the unsteady free convection flow past an accelerated vertical porous plate with variable suction

An exact analysis of the effects of mass transfer on the flow of a viscous incompressible fluid past an uniformly accelerated vertical porous and non-porous plate has been presented on taking into account the free convection currents. The results are discussed with the effects of the Grashof number Gr, the modified Grashof number Sc, the Schmidt number Sc, and the suction parametera for Pr (the Prandtl number)=0.71 representating air at 20°C.Nomenclature a suction parameter - C species concentration - C species concentration at the free stream - g acceleration due gravity - Gc modified Grashof number (vg^*(C –C )/U ₀ ³ ) - Pr Prandtl number (C _p/K) - T temperature of the fluid near the plate - T dimensionless temperature near the plate ((T-T )/(T -T )) - U(t) dimensionless velocity of the plate (U/U ₀) - v normal velocity component - v ₀ suction/injection velocity - x, y coordinate along and normal to the plate - v kinematic viscosity (/gr) - C _p specific heat at constant pressure - C _w species concentration at the plate - C non-dimensional species concentration ((C-C )/(C _w -C )) - Gr Grashof number (g(T _w -T )/U ₀ ³ ) - D chemical molecular diffusivity - K thermal conductivity - Sc Schmidt number (/D) - T _w temperature of the plate - T free stream temperature - t time variable - t dimensionless time (tU ₀ ² /) - U ₀ reference velocity - u velocity of the fluid near the plate - u non-dimensional velocity (u/U ₀) - v dimensionless velocity (v/U ₀) - v ₀ non-dimensionalv ₀ (v ₀ /U₀)=–at^–1/2 - y dimensionless ordinate (yU ₀/) - density of the fluid - coefficient of viscosity     

Internal temperature of isothermal neutron star core matter

Two new equations of state obtained for matter constituting isothermal neutron star core by using isentropic nature of matter for the equalities =₂ and =₃ (where 's are usual adiabatic exponents) have been utilised to discuss the internal temperature of core. The temperature of matter has been obtained asT=T _a(P+E)/. Variation ofT/T _a(t) with energy density has been discussed for these new equations of state and some standard equations of state for nuclear matter.     

Cyclotron waves in the solar wind

Cyclotron waves in the solar wind near 1 AU with frequencies well below the electron cyclotron frequency and wavelengths much larger than the electron cyclotron radius but less than the proton cyclotron radius are considered. The cyclotron radii are defined from parallel thermal velocity of electron component and proton component with respect to the interplanetary magnetic field. No LH cyclotron waves are found to propagate for _p < 0, where _p 1 –T _p/T _p is the temperature anisotropy of the proton component with respect to the interplanetary magnetic field. The damping or growth of RH cyclotron waves is found to depend on the frequency range and the temperature anisotropy of the proton component. The RH cyclotron waves are damped in the frequency range _r | _p | _p for _p < 0, where _p is the proton cyclotron frequency. RH cyclotron instabilities occur in the frequency range | _p | _p > _r > | _p | _p /(1– _r ) for _p < 0. The marginal state is at _r =| _p | _p .Abstract presented at theInternational Symposium on Solar-Terrestrial, São Paulo, Brazil, 17–22 June, 1974     

Nonsemisimple 1∶1 resonance at an equilibrium

Consider a Hamiltonian system of two degrees of freedom at an equilibrium. Suppose that the linearized vectorfield has eigenvaluesi,i,–i,–i ( , >0) and is not semisimple. In this paper we discuss the real normalization of the Hamiltonian function of such a system. We normalize the Hamiltonian up to 4th order and show how to compute its coefficients. For the planar restricted three body problem atL ₄ the coefficient that plays an important role in the investigation of the qualitative behaviour of periodic solutions near the equilibrium is explicitly calculated.     

Theory of the Trojan asteroids,IV

In a previous publication (1977) the author has constructed a family () of long-periodic orbits in the Trojan case of the restricted problems of three bodies. Here he constructs the domain of the analytical solution of the problem of the motion, excluding the vicinity of thecritical divisor which vanishes at the exact commensurability of the natural frequencies ₁ and ₂. In terms of thecritical masses m_j(₂), or the associatedcritical energies _j ² (m), is the intersection of the intervals ofshallow resonance, of the form. Inasmuch as the intervals |₂– _j ² |<_j ofdeep resonance aredisjoint, it follows that (1) the disjointed family () embraces the tadpole branch, 0²1, lying in: and (2) despite the clustering of _j ² (m) atj=, the family () includes, for ²=1, an asymptoticseparatrix that terminates the branch in the vicinity of the Lagrangian pointL ₃.In a similar manner, the family () can be extended to the horseshoe branch 1<_{2 2} ² .     

Effects of metal abundances on the evolutionary period changes of classical Cepheids

Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity , , respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values , for modeling such fluctuations. Perturbed values _i = _i + _i ,v _i = _i + v _i were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (= v =0,² =v ² = 10^–8) grow many times in marginally-stable state.     

Compton scattering of relativistic electrons in compact X-ray sources

The problem of single Compton scattering is considered and the resulting spectrum, angular distribution and polarization of scattered photons in a general case are obtained. The inverse Compton scattering (ICS) for arbitrary energies of electronsE and photons ₀ is investigated in detail. In the case of isotropically-distributed initial photons and relativistic electrons, a strong rise of the scattered spectrum near the upper edge takes place, starting from the values of the characteristic parameterb4E ₀10 (in units of mc²=1). The energy-loss rate of relativistic electrons due to ICS is calculated. It is shown that the relativistic electrons of the energiesE100 MeV, when scattering on the X-rays with ₀~10KeV, transmit the dominant part of their energy to the photons which fall after scattering into the energy range of the electrons (100 MeV).The radiation spectrum of ICS, as well as the energy-losses of relativistic electrons distributed by power-lawE ^–, are calculated. The radiation spectrum reveals the power-law behaviour with the different indices in two limits: the dependence ^–(1)/2 at ₀1 gradually changes to ^–(+1) ln (₀) law for ₀1.     

Hubble sequence,angular momenta and time-scales of the early evolution of galaxies

The empirical evidence for a connection between type and relative angular momentum of galaxies is reviewed and some constraints for the theoretical explanation are discussed.

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Search for the matter clumps in scalesZ ~ 1

The diagramV - log(1 +z _e ) as function of (, ) is considered for the quasars. HereV is the apparent visual magnitude,z _e is the emission line redshift, and are the equatorial coordinates. Two opposite extreme spots NE and SE are observed on the sky, where the inclination of the straight line fitting the dependenceV - log(1 +z _e ) is maximum and minimum. The coordinates of the centres of these extreme spots are ( _NE, _NE) = (282°, +42°) and ( _SE, _SE) = (70°, -38°) with errors 5°. A hypothesis of the Superattractor (SA) is proposed to explain such an effect. Two independent tests of this hypothesis are realized. First, the dependence or the frequency a of the absorbers in QSO spectra on (, ) is investigated. A region of the larger a is found. The coordinates of its centre are (, ) = (82°, - 10°) with error 5°. Second, the cases ofz _a >z _e are plotted in the Mercatorial projection (, ). The most of the casesz -z _e > 0.02 are concentrated within the circle with radiusR = 34° and centre (, ) = (50°, - 15°). The both anomalous regions overlap the Southern extreme spot around SE. The SA direction is (, ) = (67°, -21°) with errors about 12°. The redshift of SA isz _SA = 1.7 ± 0.3 that corresponds to the distancer _SA = (3100 ± 300)h ^–1 Mpc for the Hubble constantH ₀ = 75h kms^–1 Mpc^–1. The SA mass isM _SA ~ 10¹⁸-10²⁰ M . The orientation of the normal to the quasiperiodical large-scale sheet structure on the sky occurs near SA.     

Hidden mass in the solar neighborhood

It is suggested that the minimum mass of a star at the time of its formation is approximately 0.01M . Making use of this fact and the stellar mass functionF(M) M ^–, it is found that the hidden mass (or the missing mass) in the solar neighborhood may be explained by the presence of a large number of invisible stars of very low mass (0.01M M<0.07M ).     

Взаимодействие Быстрых частиц с магнито-гидродинамической турБулентностью

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Multi-cloud model (MCM) method and its applications to the study on asymmetric spectral profiles

A method of multi-cloud model (MCM) is proposed in this paper in order to research asymmetric profiles of spectral line formed by solar discrete active objects aligned along the line-of-sight difection. Based on the MCM method, under the conditions of certain assumptions and approximations, the line-of-sight velocityV and three other physical parameter approximation values, (i.e. Doppler width _D , source functionS and optical depth at line center ₀) within different clouds may be derived simultaneously by fitting both profiles theoretical and observational. An application example of the method withm=3 shows that MCM method is suitable to measure the velocity fields of multi-object at the same time from their non-Gaussian profiles of complex. TheV and _D derived from the method are reliable,S and ₀ are approximation. An influence of the variations of initial values in the parameter on the solution is given as well.     

Cosmological parameters and redshift periodicity

This work is the continuation of the search for such a cosmological model using which the observed redshift distribution of galaxies in the sample of Broadhurstet al. (1990) turns out to be maximally periodic in the calculated spatial distance. In a previous work, Paálet al. (1992) have demonstrated that among theflat models with non-negative cosmological constant (e.e., vacuum density) the one with a vacuum: dust ratio 2:1 provides the optimum. Now we extend that study to the case of arbitrary space curvature and find equally good periodicity in a surprisingly wide range of models. By use of the dimensionless parameters ₀= ₀/ _crit and ₀=/3H ₀ ² acceptable periodicity is obtained forall points of the parameter plane within the strip between the parallel lines 0.83₀–0.30< ₀(₀)<0.83₀+0.85(₀<1.8), whilst the best periodicities appear along the line ₀=0.83₀+0.39 fitting to the previous optimum at ₀=1/3, ₀=2/3. Any nonpositive value of ₀ gives bad periodicity unless the space curvature is strongly negative and ₀<0.4. Fairly good periodicity is observed only in the range of the deceleration parameter –1.2q ₀<0.2, corresponding to a small or even negative total gravitational attraction and an expansion time-scale longer than usually expected.     

Masses of macroscopic quark configurations in metric and dynamic theories of gravitation

Within the bounds of the general relativity and in gravidynamics, spherically-symmetric configurations are considered with the limit equation of state (P = ( - 4B)/3) and with the density increasing to the center. It is shown that unlike GR, where the existence of strange stars only is permissible (u-, d-, s-quarks), in the consistent dynamic theory of gravitation the existence ofstable configuration withr ^–2 (quark star) is possible with a bag out of quark-gluon plasma which includes all possible quark flavors (u, d, s, c, b, t, .. .). The total mass of such a compact object with the bag of the radius of 10 km (whose surface consists of the strange self-bound matter) must be 6 - 7M .     

Unsteady free-convective flow and mass transfer in a rotating porous medium with Hall current,I

The Hall effect on the unsteady hydromagnetic free-convection resulting from the combined effects of thermal and mass diffusion of an electrical-conducting liquid through a porous medium past an infinite vertical porous plate in a rotating system have been analysed. The expressions for the mean velocity, mean skin friction, and mean rate of heat transfer on the plate are derived. The effects of magnetic parameterM, Hall parameterm, Ekman numberE, and permeability parameterK ^* on the flow field are discussed with the help of graphs and tables.Nomenclature C _p specific heat at constant pressure - C the species concentration inside the boundary layer - C _w the species concentration at porous plate - C the species concentration of the fluid at infinite - C dimensionless species concentration - D chemical molecular diffusivity - E Ekman number - Ec Eckert number - g acceleration due to gravity - Gr Grashof number - Gm modified Grashof number - H ₀ applied magnetic field - (J _x, J_y, J_z) components of current density - M magnetic parameter - m Hall parameter - P Prandtl number - q _m mean rate of heat transfer - Sc Schmidt number - t time - t dimensionless time - T temperature of fluid - T _w temperature of the plate - T temperature of fluid at infinite - T dimensionless temperature - (u, v, w) components of the velocityq - w ₀ suction velocity - (x, y, z) Cartesian coordinates - z dimensionless coordinate normal to the plate Greek symbols coefficient of volume expansion - * coefficient of thermal expansion with concentration - frequency - dimensionless frequency - k thermal conductivity - K ^* permeability parameter - dinematic viscosity - density of the fluid in the boundary layer - coefficient of viscosity - _e magnetic permeability - angular velocity - electrical conductivity of the fluid - _m mean skin friction - _mn mean skin friction in the direction ofx - _mv mean skin friction in the direction ofy     

An Apparent Gap in Stellar Mass Distributions at ≈ 0.7 M⊙ and a Possible Explanation

Mass functions for samples of white dwarf stars and for a largeheterogeneous sample of nearby stars appear to have unexplained deficitsin the 0.70 M to 0.75 M range. The existence, ornon-existence, of this anomaly constitutes a definitive test of afractal cosmological model that inherently predicts a gap in stellarmass functions at 0.73 M .     

A new type of a photoelectric magnetograph

The electro-optic deflector as an analyzer of circular polarization in the photoelectric magnetograph is described. The electro-optic deflector consists of an electro-optic crystal and a polarizing beamsplitter. The plane bifurcation of this beamsplitter coincides with the spectrograph dispersion direction. The beamsplitter bifurcates a spectral line in two components. The distance between them is ₀. The photometer slit is situated between these components. Both components of Zeeman splitting fall on the photometer slit but the distance between them varies from ₀ + 2 _H to ₀ – 2 _H (where _H is the Zeeman splitting) with the electric voltage frequency applied to the electro-optic crystal. The intensity variations at the photometer slit are proportional to 4 _H .     

Strong coronal shocks and ‘thermal’ solar X-ray bursts

I find that a one-dimensional strong coronal shock (M _s 3) will grow outward until the Mach number (M _s ) ceases to increase with height (dM _s /dh = 0). The shock is driven by the pressure gradient and it is damped by gravity and by energy losses (radiative and conductive). The driving and damping terms reach equilibrium for M _s - 4.Standard shock jump conditions for M _s - 4 lead to post-shock temperatures in the corona in the range 10⁷ to 1.8 × 10⁷K and emission measures from 3.8 × 10⁴⁷ to 3.8 × 10⁴⁸ cm^-3. For isolated simple events, I predict an exponential decay of the emission measure with decay times in the range 1 6.5 min.In a detailed study of over 4000 X-ray bursts, Drake (1970) compares 1 to 6 keV X-ray data with 7.7 to 12.5 keV X-ray data (the thermal component) and finds ranges for the temperatures of 1.2 × 10⁷ to 1.8 × 10⁷K, for the emission measures of 5.1 × 10⁴⁷ to 3.8 x 10⁴⁸ cm^-3 and for the decay times 0.5 20 min. He also finds that the emission measure varies ... both from event to event and within the event, by more than a factor of two.The agreement between the predictions and the observations makes it appear that a strong shock in the corona will produce a post-shock state that yields the observed characteristics of the soft component of X-ray bursts (the thermal X-rays).I give several examples where sprays and fast eruptive prominences 1} \right)$$ " align="middle" border="0"> , that are not associated with solar flares, are associated with thermal X-ray bursts. There were two slow eruptive prominences (M 1) in the sample, and neither of them yielded a detectable X-ray burst.Now at the Dept. of Physics and Astronomy (NASA), Univ. of New Mexico; Albuquerque, N.M. 87106.     

Угловые Флуктуации Реликтового излучения, порождаемые космологической турбу лентностью

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