Approximate expressions for Gyrosynchrotron radiation in Transverse Propagation

Two sets of accurate approximate expressions for the gyrosynchrotron radiation in the transverse propagation case are presented for the first time. They contain emissivity _–/BNand absorptivity _– B/Nfor e-mode, effective temperature T _effand frequency of peak brightness _p. The expressions are designed for the range 2 to 7 of electron energy spectral index and for the ranges from 2 to 10 and 10 to 100 of harmonic numbers s(=/_B). Their statistical error is, respectively, ±18% and ±29% for _–/BNand _– B/Nfor 10/_B100, ±128% and and ±170% for 2/_B10.     

Cherenkov emissions of Langmuir plasmons and light neutrinosby the flux of neutrinos

We consider the system of neutrino-antineutrino – plasma taking into account theirweak Fermi interaction, when the density of neutrinos andthe plasma particles are rather high and their collective interactionplays a vital role. New fluid instabilities driven by strong neutrino flux in aplasma are observed. It is shown that a bunch of neutrinos, drifting witha constant velocity across a homogeneous plasma, can also induce emission oflower energy neutrinos due to scattering, i.e. the decay of a heavy neutrino_H into a heavy and a light neutrino _L(_HHL) in a plasma. Furthermore we find thatthe neutrino production in stars does not lead in general to energy lossesfrom the neutron stars.     

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     

Constraints of the neutrino magnetic moment from white dwarf cooling

The neutrino magnetic moment provides an additional energy emission in stars. It will accelerate the white dwarf cooling process and reduce the life time of the white dwarf, but it causes a conflict with the observation. We use observational constraints to derive an upper limit for the neutrino magnetic moment: 4.0×10^–12 _B      

Free-convection effects on MHD flow past a porous plate with step function change in suction velocity

Free convection effects on MHD flow past a semi infinite porous flat plate is studied when the time dependent suction velocity changes in step function form. The solution of the problem is obtained in closed form for the fluid with unit Prandtl number. It is observed that for both cooling and heating of the plate the suction velocity enhances the velocity field. The heat transfer is higher with increase in suction velocity.Notations B intensity of magnetic field - G Grashof number - H magnetic field parameter,H=(M+1/4) ^1/2–1/2 - M magnetic field parameter - N _u Nusselt number - P Prandtl number of the fluid - r suction parameter - T temperature of the fluid - T _w temperature of the plate - T temperature of the fluid at infinity - t time - t non-dimensional time - u velocity of the fluid parallel to the plate - u non-dimensional velocity - U velocity of the free stream - suction velocity - ₁ suction velocity att0 - ₂ suction velocity att>0 - x,y coordinate axes parallel and normal to the plate, respectively - y non-dimensional distance normal to the plate - coefficient of volume expansion - thermal diffusivity - kinematic viscosity - electric conductivity of the fluid - density of the fluid - non-dimensional temperature of the fluid - shear stress at the plate - non dimensional shear stress - erf error function - erfc complementary error function     

The motion of a satellite in an axi-symmetric gravitational field

The equations for the variation of the osculating elements of a satellite moving in an axi-symmetric gravitational field are integrated to yield the complete first-order perturbations for the elements of the orbit. The expressions obtained include the effects produced by the second to eighth spherical harmonics. The orbital elements are presented in the most general form of summations by means of Hansen coefficients. Due to their general forms it is a simple matter to estimate the perturbations of any higher harmonic by simply increasing the index of summation. Finally, this paper gives the respective general expressions for the secular perturbations of the orbital elements. The formulae presented should be useful for the reductions of Earth-satellite observations and geopotential studies based on them.List of Symbols semi-major axis - C _jk ⁿ (, ) cosine functions of and - e eccentricity of the orbit - f acceleration vector of perturbing force - f sin²t - i inclination of the orbit - J _n coefficients in the potential expansion - M mean anomaly - n mean motion - p semi-latus rectum of the orbit - R, S, andW components of the perturbing acceleration - r radius-vector of satellite - r magnitude ofr - S _jk ⁿ (, ) sine functions of and - T time of perigee passage - u argument of latitude - U gravitational potential - true anomaly - V perturbing potential - G(M₊+m) (gravitational constant times the sum of the masses of Earth and satellite) - _n,k coefficients ofR component of disturbing acceleration (funtions off) - _n,k coefficients ofS andW components of disturbing acceleration (functions off) - mean anomaly at timet=0 - X ₀ ^n,m zero-order Hansen coefficients - argument of perigee - right ascension of the ascending node     

Central holes in disks of spiral galaxies

On the basis of the solutions obtained in the previous paper, the changes in the scenario of the standard model of the Big Bang are found. The chaos degree (constrainst on fluctuation spectra) is obtained, which could be still preserved by the initially completely chaotic Universe at the time of light elements nucleosynthesist _es. The time boundaries of hadron and lepton eras and the time the electron neutrinos and neutrons become frozen in reactions of weak interaction may be shifted up to 1.4 times. The corresponding temperatures may shift off from the standard ones 0.88 times if the mean-square level of fluctuations is close to unity. If the density of the energy of fluctuations concentrated in the short-wave region of the spectrum is less than 1.5 ^– , the nucleosynthesis leads to a helium abundance coinciding with the observe one. If at the timet _es the maximum of the spectral density of the energy is in the long-wave region, that is _max ct _es the level of the chaos during the period of nucleosynthesis is restricted to 1.76 (where |C _K |² d³ K,C _K is Fourier component of the amplitude of metric fluctuations). In particular, the protogalactic vortical disturbances with a wide spectrum 4 × 10^{3 -1}( = K/K, = /_crit) are compatible with the observed helium abundance.     

The universal solution of Einstein's equations of general relativity

Einstein's equations of general relativity are solved in terms of gravitational potential derivatives, withT equal to mass and/or field energy such thatT 0 outside a body. The line element equation then describes the variance of test particle internal geometrical structure and time-rate due to work done in a field, not the space-time curvature. Specific properties of gravitational fields and bodies come from this new solution: (a) The gravitational field consists of electromagnetic spin 2 gravitons which produce the gravitational force through the magnetic vector. (b) The gravitational mass is the Newtonian mass, not the relativistic mass, of a moving body. (c) An action principle exists in gravitation theory. (d) Attractive gravity exists between matter and antimatter. (e) Unification with quantum physics appears possible.     

Implications of a strongly peaked polar magnetic field

Using the flux-transport equation in the absence of sources, we study the relation between a highly peaked polar magnetic field and the poleward meridional flow that concentrates it. If the maximum flow speed _m greatly exceeds the effective diffusion speed /R, then the field has a quasi-equilibrium configuration in which the poleward convection of flux via meridional flow approximately balances the equatorward spreading via supergranular diffusion. In this case, the flow speed () and the magnetic field B() are related by the steady-state approximation () (/R)B()/B() over a wide range of colatitudes from the poles to midlatitudes. In particular, a general flow profile of the form sin ^p cos ^q which peaks near the equator (q p) will correspond to a cos ⁿ magnetic field at high latitudes only if p = 1 and _m = n /R. Recent measurements of n 8 and 600 km² s^–1 would then give _m 7 m s^–1.     

The three principal secular resonances ν5, ν6, and ν16 in the asteroidal belt

We review theoretical and numerical results obtained for secular resonant motion in the asteroidal belt. William's theory (1969) yields the locations of the principal secular resonances ₅, ₆, and ₁₆ in the asteroidal belt. Theories by Nakai and Kinoshita (1985) and by Yoshikawa (1987) allow us to model the basic features of orbital evolution at the secular resonances ₁₆ and ₆, respectively. No theory is available for the secular resonance v₅. Numerical experiments by Froeschlé and Scholl yield quantitative and new qualitative results for orbital evolutions at the three principal secular resonances ₅, ₆, and ₁₆. These experiments indicate possible chaotic motion due to overlapping resonances. A secular resonance may overlap with another secular resonance or with a mean motion resonance. The role of the secular resonances as possible sources of meteorites is discussed.     

Spectrophotometric study of the comet P/Swift-Tuttle (1992t)

Spectrophotometric observations of the periodic comet P/Swift-Tuttle (1992t) were taken through 104 cm telescope of Uttar Pradesh State Observatory Nainital, using EG & G spectrograph coupled with optical multichannel analyser and reticon array detector in the optical region of the spectrum, during four nights of December 1992. The molecular emission bands of CN ( = 0) at 3888 Å, CH + C₃ at 4050 Å and C₂ ( = +1,0, –1) at 4690 A, 5160 Å and 5530 Å respectively, were identified. Column densities and production rates have been determined.     

Secular resonances in the primitive solar nebula

We present here a very simple model that could explain the relatively high eccentricities and inclinations observed in the minor planet belt. This model is based upon the sweeping of the secular resonances ₆ and ₁₆ through the belt due to the gravitational effect of the dissipation of a primitive solar nebula. The sweeping of the ₁₆ secular resonance (responsible for the high inclinations) is very sensitive to the density profile of the nebula. For the model to work we need a density profile proportional to ^–k with between 1.0 and 1.5.     

An Improved Optical Model for the Non-LTE Problem for the CO2 Molecule in the Atmosphere of Mars: Nighttime Populations of Vibrational States and the Rate of Radiative Cooling of the Atmosphere

The estimates of the population of excited vibrational states of the CO₂ molecule and of the rate of radiative cooling of the atmosphere in the 15-m CO₂ band are given for the nighttime mesosphere and thermosphere of Mars. For the first time, these estimates are made (1) with allowance for the overlap of lines in the 15-m band; (2) for a wide set of vibrational states of seven isotopes of the CO₂ molecule, which was used earlier in the solution of a similar terrestrial problem; and (3) using the rate constant for quenching of the CO₂(01¹0) state in collisions with oxygen atoms, which has been recently measured for low temperatures by Khvorostovskaya et al. (2002). The main results are as follows. 1. The approximation of isolated lines provides a satisfactory accuracy of determining the radiative cooling rate and overestimates vibrational temperatures of the states of the ₂ mode by no more than 3 K for the ¹²C¹⁶O₂ molecule and by no more than 2 K for low-abundant isotopes of the CO₂ molecule. 2. A reasonably high accuracy of estimating the cooling rate can be achieved by taking into account only fundamental vibrational transitions in ¹²C¹⁶O₂, ¹³C¹⁶O₂, ¹⁶O¹²C¹⁸O, and ¹⁶O¹²C¹⁷O molecules and the hot transitions 2_{2 2} and 3₂ 2₂ in the ¹²C¹⁶O₂ molecule. 3. The vertical profile of the total rate of radiative cooling displays two peaks. The maximum near a height of 130 km is very sensitive to temperature and to the ratio of the mixture for oxygen in the atmosphere.     

Absolute wavelengths of Fraunhofer lines: Convective motions in the solar photosphere and the gravitational red shift

Absolute wavelengths for Fraunhofer lines are compared with laboratory measurements for several atomic and molecular spectra. The wavelength differences are shown to be consistent with the proposal that the deeper layers of the photosphere are in convective motion: _e -3 km/sec for log ₀> -1.0. Convective motions in the outer layers (log₀< - 1.0) are shown to be very small. Wavelength shifts of Fraunhofer lines formed in these outer layers are in good quantitative agreement with the predictions of the General Theory of Relativity.     

Effects of Hall current on hydromagnetic free-convective flow through a porous medium

An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c _p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H ₀ applied magnetic field - H magnetic field intensity - (j _x , j _y , j _z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n _e electron number density - P Prandtl number - q velocity vector - (T, T _w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U ₀ uniform velocity - v ₀ suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - _e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - _e charge density - electrical conductivity - _e electron collision time     

Fourier analysis of the light curves of eclipsing variables-XXV: Error analysis in the frequency-domain

The aim of the present paper has been two-fold. In the first part (Sections 1–2), closed algebraic formulae will be set up furnishing the momentsA of the light curves of arbitrary index , and, due to arbitrary type of eclipses, in terms of the coefficientsa of Fourier cosine series obtained by least-squares fit to the given data; and the uncertainty of the momentsA deduced from that of thea 's.In the second part (Sections 3–4) we shall establish the explicit forms of the lincar functions r _1,2, (cosi) and L ₁ for the variation of the respective elements expressible likewise in terms of the Fourier coefficientsa . The probable errors of these elements can then be identified with those of the respective linear functions, and are obtainable from the same matrix of coefficients which furnished the most probable values of the elements.     

On Geovenelli's approximate form of j(τ)

The accuracy of the approximate replacement of the frequency meanj() of the total intensityJ () byJ _c+a{J ₀()–J _c} by Geovenelli, whereJ _c is the total intensity at the continuum,J ₀() is that at the line center anda is independent of depth, is studied. Numerical calculations for strong solar lines show very high values of the residual intensities. A slight change in the approximation is then suggested to get a result quite consistent with observational and existing calculated data.     

The kink instability in infinite cylindrical flux tubes: Eigenvalues for power-law twist profiles

We develop simple accurate methods of calculating ideal MHD instability eigenvalues for infinitely-long cylindrical tubes, with twist functionT(r)=B /rB _z . A complete theoretical treatment is presented for force-free magnetic equilibria with arbitraryT(r), and detailed semi-analytic results for the kink instability are given for the particular case of a power-law twistT(r)=r , where the index is non-negative. Our results show that the most rapidly growing and energetic instabilities occur in the Gold-Hoyle =0 field, with the instability progressively weakening with increasing . However, the maximum force eigenvalue is always small, so that even in the Gold-Hoyle case (where =O(10^–2) in dimensionless units) only a small proportion of the available magnetic energy can be released in the linear phase. Our results also confirm that the linear pinch (=) is remarkably weak (=O(10^–3)) yet relatively resistant to line-tying! It is shown that the weakness of the force eigenvalue implies that the influence of uniform gas pressure on stability is negligible. Implications for the energy-release mechanism in solar flares are discussed.     

Free convection and mass transfer effects on the hydro-magnetic oscillatory flow past an infinite vertical porous plate

Two-dimensional unsteady free convection and mass transfer, flow of an incompressible viscous dissipative and electrically conducting fluid, past an infinite, vertical porous plate, is considered, when the flow, is subjected in the action of uniform transverse magnetic field. The magnetic Reynolds number is taken to be small enough so that the induced magnetic field is negligible. The solution of the problem is obtained in the form of power series of Eckert numberE, which is very small for incompressible fluids. Analytical expressions for the velocity field and temperature field are given, as well as for the skin friction and the rate of heat transfer for the case of the mean steady flow and for the unsteady one. The influence of the magnetic parameter,M, modified Grashof numberG _c , Schmidt numberS _c and frequency , on the flow field, is discussed with the help of graphs, when the plate is being cooled, by the free convection currents (G _r ,E>0), or heated (G _r ,E<0). A comparative study with hydrodynamic case (M=0) and the hydromagnetic one (M0) is also made whenever necessary.List of symbols B₀ applied magnetic field - |B| amplitude of the skin friction - C concentration inside the boundary layer - C concentration in the free stream - C _w concentration at the porous plate - C _p specific heat at constant pressure - D diffusion coefficient - E Eckert number - g _x acceleration due to gravity - G _c modified Grashof number - G _r Grashof number - M magnetic parameter - N _u Nusselt number - P Prandtl number - |Q| amplitude of the rate of heat transfer - S _c Schmidt number - T temperature of the fluid - T _w temperature of the plate - T temperature of the fluid in the free stream - T _r ,T _i fluctuating parts of the temperature profile - u, v velocity components in thex, y directions - u dimensionless velocity in thex direction - u ₀ mean steady velocity - u ₁ unsteady part of the velocity - u _r ,u _i fluctuating parts of the velocity profile - U dimensionless free stream volocity - U ₀ mean free stream velocity - v ₀ suction velocity - x, y co-rodinate system Greek Symbols phase angle of the skin-friction - coefficient of volume expansion - _* coefficient of expansion with concentration - phase angle of the rate of heat transfer - dimensionless co-ordinate normal to the plate - dimensionless temperature - ₀ mean steady temperature - ₁ unsteady part of temperature - k thermal conductivity - v kinematic viscocity - density of fluid in the boundary layer - density of fluid in the free stream - electrical conductivity of the fluid - skin friction - ₀ mean skin friction - frequency - dimensionless frequency     

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 .